Implementation of large-scale ice shelf dynamics in the ice sheet model SICOPOLIS

The importance of ice shelves for the evolution of ice sheets has recently been discussed, and methods are currently being developed in order to couple ice shelf dynamics with ice sheet dynamics. SICOPOLIS (http://sicopolis.greveweb.net/) is an ice sheet model which has been successively applied to large ice sheets. However, special treatment of ice shelf dynamics is not yet included. The aim of this study is to couple a model of ice shelf dynamics with the ice sheet model SICOPOLIS. The dynamic/thermodynamic equations of the shallow shelf approximation are usually given in Cartesian coordinates. However, in order to account for projection distortions or geographical coordinates in a flexible way, a formulation in general orthogonal curvilinear coordinates is required. This is achieved by a general coordinate transformation using Riemann metrics. The shallow shelf approximation is then derived from the full-Stokes problem by using the hydrostatic and plug flow approximations in the general coordinate system. The set of equations is constructed in contravariant and mixed form. A numerical solution technique for the shallow shelf approximation is developed. The performance of the coupled system is tested for the case of an ice shelf ramp for which an analytical solution exists. The model is then applied to realistic geometries of existing ice shelves in Antarctica.