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

[1] Understanding the dynamics of marine ice sheets is integral to studying the evolution of the Antarctic ice sheet in both the short and long terms. An important component of the dynamics, grounding line migration, has proved difficult to represent in numerical models, and most successful attempts have made use of techniques that are only readily applicable to flow line models. However, to capture the stress transmission involved in another important component, the buttressing of a marine ice sheet by its ice shelf, the transverse direction must also be resolved. We introduce a model that solves the time-dependent shelfy stream equations and makes use of mesh adaption techniques to overcome the difficulties typically associated with the numerics of grounding line migration. We compare the model output with a recent benchmark for flow line models and show that our model yields an accurate solution while using far less resources than would be required without mesh adaption. We also show that the mesh adapting techniques extend to two horizontal dimensions. Experiments are carried out to determine how both ice shelf buttressing and ice rises affect the marine instability predicted for an ice sheet on a foredeepened bed. We find that buttressing is not always sufficient to stabilize such a sheet but collapse of the grounded portion is still greatly delayed. We also find that the effect of an ice rise is similar to that of narrowing the ice shelf.

Rapid dynamic changes at the margins of the Greenland Ice Sheet, synchronous with ocean warming, have raised concern that tidewater glaciers can respond sensitively to ocean forcing. Understanding of the processes encompassing ocean forcing nevertheless remains embryonic. The authors use buoyant plume theory to study the dynamics of proglacial discharge plumes arising from the emergence of subglacial discharge into a fjord at the grounding line of a tidewater glacier, deriving scalings for the induced submarine melting. Focusing on the parameter space relevant for high discharge tidewater glaciers, the authors suggest that in an unstratified fjord the often-quoted relationship between total submarine melt volume and subglacial discharge raised to the 1 /3 power is appropriate regardless of plume geometry, provided discharge lies below a critical value. In these cases it is then possible to formulate a simple equation estimating total submarine melt volume as a function of discharge, fjord temperature, and calving front height. However, once linear stratification is introduced-as may be more relevant for fjords in Greenland-the total melt rate discharge exponent may be as large as 3 /4 ( 2 /3) for a point (line) source plume and display more complexity. The scalings provide a guide for more advanced numerical models, inform understanding of the processes encompassing ocean forcing, and facilitate assessment of the variability in submarine melting both in recent decades and under projected atmospheric and oceanic warming.