Applicability of the Shallow Ice Approximation inferred from model inter-comparison using various glacier geometries

Abstract. This paper presents an inter-comparison of three different models applied to various glacier geometries. The three models are built on different approximations of the Stokes equations, from the well known Shallow Ice Approximation (SIA) to the full-Stokes (FS) solution with an intermediate higher-order (HO) model which incorporates longitudinal stresses. The studied glaciers are synthetic geometries, but two of them are constructed so as to mimic a valley glacier and a volcano glacier. For each class of glacier, the bedrock slope and/or the aspect ratio are varied. First, the models are compared in a diagnostic way for a fixed and given geometry. Here the SIA surface velocity can overestimate the FS velocity by a factor of 5 to a factor of 10. Then, the free surface is allowed to evolve and the time-dependent evolution of the glacier is studied. As a result, the difference between the models decreases, but can still be as large as a factor of 1.5 to 2. This decrease can be explained by a negative feedback for the SIA which overestimates velocities.