  Iceberg calving accounts for around half of the ice lost annually from
Antarctica, but realistic representation of fracture and calving in large-scale
ice sheet models remains a major unsolved problem in glaciology. We present a
new phase-field viscoelastic model for fracture that simulates the slow
deformation of ice and the distribution and evolution of cracks. Cracks
nucleate and propagate in response to the evolving stress field, and are
influenced by water pressure below sea level. The model incorporates
nonlinear-viscous rheology, linear-elastic rheology, and a phase-field
variational formulation, which allows simulation of complex fracture phenomena.
We show that this approach is capable of simulating the physical process of
calving. Numerical experiments supported by a simplified model suggest that
calving rate will scale with the fourth power of ice thickness for a floating
ice front that has no variation across flow. The equations make no assumptions
about the style of calving, so they would also simulate numerous more realistic
settings in Antarctica for which material parameters and three-dimensional
effects can be expected to influence the calving rate.
