Stress and velocity fields in glaciers: Part I. Finite-difference schemes for higher-order glacier models

The set of force equations and stress-strain-rate relations for ice masses can be solved with the method of lines and shooting the stress-free conditions at the free surface. Single- and multiple-shooting schemes with fixed point or Newton iterations for solving the stress equations including the deviatoric stress gradients are described and their performances are discussed. The single-shooting Newton iteration proved to be the fastest scheme for typical valley glaciers, although its horizontal grid limitation is restrictive. Grid resolution can be improved substantially with a multiple-shooting scheme but computation time and storage requirements increase substantially. The Newton iteration allo ius the handling of mixed basal boundary conditions, partly basal velocity and partly basal shear traction being prescribed. A stick-slip free gravity flow illustrates the performance of the scheme.