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

Abstract

The buoyancy boundary condition applied to floating portions of ice sheets and glaciers in Stokes models requires special consideration when the glacier rapidly departs from hydrostatic equilibrium. This boundary condition can manifest in velocity fields that are unphysically (and strongly) dependent on time step size, thereby contaminating diagnostic stress fields. This can be especially problematic for models of calving glaciers, where rapid changes in geometry cause configurations that suddenly depart from hydrostatic equilibrium and lead to inaccurate estimates of the stress field. Here we show that the unphysical 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 consistent velocity solutions for all time step sizes.