Mathematical Modelling of Iceberg Calving.

Iceberg calving contributes more than half of mass loss in both Greenland and Antarctica.Despite its importance, the dynamic of calving glaciers are only partially understood. Weanalyse a model of calving based on linear elastic fracture mechanics, extending prior workdue to van der Veen (1998). Crack propagation is assumed to occur along a predefined,vertical failure plane until the stress intensity factors at the tips of two mutually alignedvertical crevasses reaches the "fracture toughness" of ice. One of the crevasses extendsupwards from the base, and the other downwards from the surface, with the latter potentiallyconfining water that extends upwards to a prescribed water table. Such solutions are stable iffurther lengthening of the cracks results in an increase in the stress intensity factors.Calving occurs when the stable solution disappears under an infinitesimal changes ingeometrical (thickness, distance from ice edge) or hydrological (water table height)parameter. By contrast with van der Veen, we model both crevasses simultaneously and computestress intensity factors directly using a displacement discontinuity method rather than relyingon tabulated or interpolated elasticity kernels. We find that, for a prescribed water tableheight, calving occurs at a critical ice thickness (or vice versa), generalizing the more ad hocmodel of Nick et al. (2010). This is a joint work with Christian Schoof. [ABSTRACT FROM AUTHOR]