A Moving Mesh Approach to a Shallow Ice Glacier Model incorporating Data Assimilation

We present a conservation-based moving point method and some data assimilation experiments using the method, applied to a simplified shallow ice model with a moving boundary that incorporates ice diffusion and net ice-equivalent accumulation/ablation. We assess the behaviour of the diffusive velocity in the vicinity of the moving boundary and determine criteria upon the local profile under which the glacier front will advance or remain stationary. A conservation-based description of the flow is then introduced which determines a deformation velocity that is used to define the movement of the glacier in the presence of both ice diffusion and accumulation. A finite difference approximation based on the conservation description is applied and tested using a simple test scenario to reproduce different types of glacier flow. Comparisons are drawn with some existing non-moving mesh solutions and exact solutions to one of the European Ice Sheet Modelling INiTiative (EISMINT) test problems. Techniques for data assimilation within the moving framework are then presented and used to incorporate sparsely measured observations of the ice sheet profile into the computational model, resulting in better forecasts of the ice flow.