Nonlinear longitudinal stress coupling in glacier and ice sheet flow

Abstract The Greenland and Antarctic ice sheets exhibit high variability in flow speed, over multiple orders of magnitude. This flow integrates forcings from complex, multi-scale and spatially heterogeneous pressure gradient and friction fields into smooth and continuous flow fields, over a finite scale known as the longitudinal coupling length (LCL). The strongly nonlinear, shear-thinning rheology of ice complicates the stress transmission, but previous work has relied on either linear (Newtonian) models or linearized, small-perturbation models, to determine the coupling length. Here, we derive new exact solutions to the nonlinear shallow shelf/shelfy-stream approximation (SSA), which explain how nonlinear feedbacks between the stress state and the nonlinear rheology of ice determine the coupling length. For complex and multi-scale flow fields, these exact solutions provide a foundation for Green's function approximations that can reconstruct the effects of a non-local stress balance, given input data for the driving stress and friction fields. This allows us to rapidly reconstruct the ice velocity field, asses changes in basal drag and interpret the effect of rheology on shear margins.