Numerical methods are used to examine the interaction between the spatial distribution of the basal shear traction and the corresponding basal velocity for an inclined slab geometry. In our improved treatment, we reject the common assumption that basal velocity is a simple function of local variables in favour of a non-local treatment that includes normal deviatoric stress and takes basal velocity to be an integrated response to spatially varying influences. Computationally, one must either iterate the basal velocity with a friction parameterization that relates basal shear traction to basal velocity or, alternatively, prescribe the basal shear traction that results from bed decoupling and substrate déformation.
The average of basal shear traction over the entire bed of the ice mass is invariant under changes in sliding distribution and thus constitutes a useful reference; any local relative reduction of traction leads to basal movement, either sliding over the bed or moving with a deforming subglacial layer. The local stress réduction is accompanied by a concentration of traction up-and down-glacier of the moving base. Growth, decay and possible migration of basal stress concentrations may be closely related to short-lived sliding events and to surges.