Modeling Iceberg Calving From Ice Shelves Using a Stress Based Calving Law: The Stabilizing Effect of Vertical Compression

Iceberg calving from ice shelves and ice tongues provides an efficient mechanism to transfer larges amounts of ice to the ocean in a near-instantaneous fashion. This not only drastically changes the mass balance of the ice shelf, but the geometry of the ice-sheet-shelf system. The potential for a positive feedback between the ice shelf and the flow of inland ice ('buttressing') combined with the sensitive of ice shelves to forcing from both the atmosphere and the ocean suggests that iceberg calving is an important process. However, iceberg calving remains a poorly understood process. As a first step, we attempt to construct a calving law for ice shelves, based on a combination of scaling and physical arguments, which yields appropriate steady states. This leads us to postulate that calving rate is primarily a function of the ratio of tensile stress to vertical compressive stress, i.e., the calving rate is a function of the ratio of the largest to smallest principle stress. Implementing this calving law in a numerical model, we show that this law predicts that (i) embayed ice shelves are stable; (ii) ice shelves do not protrude (much) beyond their embayment. More importantly, this calving law provides a criterion for ice shelf instability: if a small calving event causes the tensile stress to increase faster than the compressive stress, the ice shelf will retreat and vice versa. Using this stability criterion we map out the 'phase-space' of parameters (basal melting/freezing, lateral shear, divergence of embayment walls) that allow a steady-state ice shelf to exist as opposed to those combinations of parameters that do not permit a steady-state ice shelf. Comparing our predictions of the parameter regime where ice shelves are stable with the observed parameter regime of healthy ice shelves can provide an independent estimate showing where our (and other) calving laws fails.