A simple 1 1/2-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= Bt m/b, where
tb 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)
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