A variationally derived, depth-integrated approximation to a higher-order glaciological flow model

Abstract

An approximation to the first-order momentum balance with consistent boundary conditions is derived using variational methods. Longitudinal and lateral stresses are treated as depthindependent, but vertical velocity gradients are accounted for both in the nonlinear viscosity and in the treatment of basal stress, allowing for flow over a frozen bed. A numerical scheme is presented that is significantly less computationally expensive than that of a fully three-dimensional (3-D) solver. The numerical solver is subjected to the ISMIP-HOM experiments and experiments involving nonlinear sliding laws, and results are compared with those of 3-D models. The agreement with first-order surface velocities is favorable down to length scales of 10 km for flow over a flat bed with periodic basal traction, and ∼40 km for flow over periodic basal topography.