Glacier flow modelling: a comparison of the Shallow Ice Approximation and the full-Stokes solution

Abstract

Several different approaches of various complexities have been used in glacier and ice sheet modelling studies. Amongst them, owing to its simplicity, the Shallow Ice Approximation appears to be the most widely adopted method. This approach, essentially used for ice sheets, owes its success to the shallow aspect of the modelled ice mass embodied in an aspect ratio ζ. When considering smaller ice bodies like alpine-type glaciers, the question arises as to whether the SIA is still valid, given that the method is all the more accurate as ζ is small. In order to test the domain of applicability of the method, results of a SIA finite difference model are compared to those of a finite element model in which the flow equations are fully considered. From a set of two-dimensional flow tests, it is shown that the accuracy of the method is much more deteriorated with increasing bedrock slopes than it is with increasing accumulation rates, even if higher accumulations lead to thicker glaciers with a larger ζ. This leads to the conclusion that when slopes become pronounced, it is a bedrock-related aspect ratio that becomes of relevance such that the bedrock slope should be the most important parameter to consider for assessing the validity of the SIA Method. A 3-dimensional simulation shows that longitudinal shear stresses explain a large part of the misfit between SIA and full-Stokes approaches. To cite this article: E. Le Meur et al., C. R. Physique 5 (2004).