A simple stress-based cliff-calving law

Abstract. Over large coastal regions in Greenland and Antarctica the ice sheet calves directly into the ocean. In contrast to ice-shelf calving, an increase in cliff calving directly contributes to sea-level rise and a monotonously increasing calving rate with ice thickeness can constitute a self-amplifying ice loss mechanism that may significantly alter sea-level projections both of Greenland and Antarctica. Here we seek to derive a minimalistic stress-based parameterization for cliff calving. To this end we compute the stress field for a glacier with a simplified two-dimensional geometry from the two-dimensional Stokes equation. First we assume a constant yield stress to derive the failure region at the glacier front from the stress field within the ice sheet. Secondly, we assume a constant response time of ice failure due to exceedance of the yield stress. With this strongly constraining but very simple set of assumption we propose a cliff-calving law where the calving rate follows a power-law dependence on the freeboard of the ice with exponents between 2 and 3 depending on the relative water depth at the calving front. The critical freeboard below which the ice front is stable decreases with increasing relative water depth of the calving front. For a dry water front it is, for example, 75m. The purpose of this study is not to provide a comprehensive calving law, but to derive a particularly simple equation with a transparent and minimalistic set of assumptions.