Some basic experiments with a vertically-integrated ice sheet model

A simple 1½-dimensional continental ice sheet model is presented. The model is based on Nye’s (1959) proposal to express the vertical mean horizontal ice-velocity as u = Bτ^m _b, where τ_b is the basal shear stress and B and m are constants. Essentially, the spread of ice is governed by a nonlinear diffusion equation for the ice thickness. The diffusivity increases with both ice thickness and surface slope. In one direction (y) a typical scale is prescribed that governs the lateral ice-mass discharge, whereas in the other direction (x) the ice-sheet evolution is computed explicitly on a grid with a spacing of 70 km.

A series of experiments has been carried out with various boundary conditions and parameterizations of the annual mass balance. It appears that the boundedness of continents and bedrock elevations creates a strongly nonlinear response of ice sheets to climatic variations. The behaviour of Northern Hemisphere ice sheets as computed with the numerical model is compared to that predicted by a perfect-plasticity model. It is found that those models give qualitatively the same results.

Including bedrock sinking in a simple way reveals that this causes Northern Hemisphere ice sheets to disappear spontaneously within 15,000 years, after about 50,000 years of growth (initiated by a cold period).