Numerical simulation of glacier terminus evolution using the dual action principle for momentum balance

Abstract

The momentum conservation equation for glacier flow can be described through minimization of an action functional. Several software packages for glacier flow modeling use this action principle in the design of numerical solution procedures. We derive here an equivalent dual action principle for the shallow stream approximation and implement this model using the finite element method. The key feature of the dual action is that the flow law and friction law are both inverted, which changes the character of the non-linearities. This altered character makes it possible to implement numerical solvers for the dual form that work even when the ice thickness or strain rate are exactly equal to zero. Solvers for the primal form typically fail on such input data and require regularization of the problem. This robustness makes it possible to implement iceberg calving in a simple way: the modeler sets the ice thickness to zero in the desired area. We provide several demonstrations and a reference implementation.

Keywords

• calving
• glacier flow
• glacier modeling