Full and reduced model solutions of steady axi-symmetric ice sheet flow over small and large bed topography slopes

Two numerical methods for solving the full steady ice-sheet equations in axi-symmetric flow are described. The free-boundary problem is treated by transforming the problem to a fixed domain using either an orthogonal co-ordinate transformation or a variant of a transformation proposed by Landau, and difficulties with the former, more sophisticated, method are demonstrated. The simpler Reduced Model is also presented, and accurate solutions for flows over bed topography with moderate to large slopes are generated by an inverse method for comparison with the numerical solutions of the full equations. The reduced model is not valid for such bed slopes, and the comparisons demonstrate the extent and nature of the errors arising from the use of the simpler model.