Brief communication: Time step dependence (and fixes) in Stokessimulations of calving ice shelves

Abstract. The buoyancy boundary condition applied to floating portions of ice sheets and glaciers in Stokes models is numerically ill-posed when the glacier rapidly departs from hydrostatic equilibrium. This manifests in velocity solutions that diverge with decreasing time step size, contaminating diagnostic strain rate and stress fields. This can be especially problematic for models of calving glaciers, where rapid changes in geometry lead to configurations that depart from hydrostatic equilibrium and accurate measures of the stress field are needed. Here we show that the singular behavior can be cured with minimal computational cost by reintroducing a regularization that corresponds to the acceleration term in the stress balance. This regularization provides numerically stable velocity solutions for all time step sizes.