On the relationship between surface and basal properties on glaciers, ice sheets, and ice streams

The influence of basal disturbances on the steady state surface topography and on surface velocities of glaciers and ice sheets is investigated numerically. This is done for finite amplitude basal perturbations in both bed topography and basal slipperiness using a nonlinear ice rheology and a nonlinear sliding law. The effects of varying the exponent n in Glen's flow law on transfer characteristics are mainly quantitative and do not affect qualitative aspects of the transfer amplitudes and phase shifts, such as the number of maxima and inflection points when plotted as functions of wavelength. In particular, the well-known maximum in bed-to-surface transfer amplitude for a Newtonian medium at sufficiently high slip ratios (ratio between mean sliding velocity and mean ice deformational velocity) also forms for n > 1. Transfer amplitudes generally become smaller with increasing n for wavelengths less than about 3 times the mean ice thickness (h). For larger wavelengths the situation is reversed and transfer amplitudes increase with n. For active ice streams, characterized by high basal slipperiness, low surface slopes (0.5) and fairly constant for all wavelengths longer than about 3-5h. With increasing n and decreasing surface slope the lower limit of wavelengths over which horizontal stress gradients can be ignored increases markedly. Perturbation solutions for Newtonian medium are found to give an accurate description of the transfer characteristics for bedrock amplitudes up to 50% ice thickness and for fractional amplitudes of slipperiness perturbations up to 0.5