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The Effect of Longitudinal Strain on the Shear Stress of an Ice Sheet: In Defence of Using Stretched Coordinates

Abstract Thickness changes of ice sheets are, except perhaps at the snout region, small as compared to unity. This suggests using a coordinate stretching so as to make the surface changes in the new coordinates of order one. The explicit occurrence of the smallness parameter in the governing equations then allows us to search for perturbation solutions in various problems. Here, it is shown that the classical formula for the basal shear stress follows easily from such a perturbation procedure. Furthermore it can be improved to account for longitudinal strain effects. As compared to previous work in this area, these formulae are explicit and allow us to take vertical variations of material properties into account in a straightforward manner.