The effect of hydrology and crevasse wall contact on calving

Abstract

Abstract. Calving is one of the main controls on the dynamics of marine ice sheets. We solve a quasi-static linear elastic fracture dynamics problem, forced by a viscous pre-stress describing the stress state in the ice prior to the introduction of a crack, to determine conditions under which an ice shelf can calve for a variety of different surface hydrologies. Extending previous work, we develop a boundary-element-based method for solving the problem, which enables us to ensure that the faces of crevasses are not spuriously allowed to penetrate into each other in the model. We find that a fixed water table below the ice surface can lead to two distinct styles of calving, one of which involves the abrupt unstable growth of a crack across a finite thickness of unbroken ice that is potentially history-dependent, while the other involves the continuous growth of the crack until the full ice thickness has been penetrated, which occurs at a critical combination of extensional stress, water level and ice thickness. We give a relatively simple analytical calving law for the latter case. For a fixed water volume injected into a surface crack, we find that complete crack propagation almost invariably happens at realistic extensional stresses if the initial crack length exceeds a shallow threshold, but we also argue that this process is more likely to correspond to the formation of a localized, moulin-like slot that permits drainage, rather than a calving event. We also revisit the formation of basal cracks and find that, in the model, they invariably propagate across the full ice shelf at stresses that are readily generated near an ice shelf front. This indicates that a more sophisticated coupling of the present model (which has been used in a very similar form by several previous authors) needs modification to incorporate the effect of torques generated by buoyantly modulated shelf flexure in the far field.