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

Enhanced Reduced Model

. The standard Reduced Model is strictly valid only for bed slopes not exceeding the very small surface slope of the ice sheet, whereas the Enhanced Reduced Model is a leading order approximation for larger moderate bed slopes, with a correction error depending on both the bed slope and the length scale or amplitude of the topography variation. The solution comparisons demonstrate the consistency between the finite-element solutions of the full equations and the Enhanced Reduced Model solutions for moderate bed slopes, with differences within the predicted correction errors, which confirms the validity and accuracy of both the Enhanced Reduced Model solution and the finite element algorithm for the full free-surface problem, and further, demonstrate the merits of the much simpler Enhanced Reduced Model as a leading order approximation.