Two-Dimensional, Time-dependent Modelling of an Arbitrarily Shaped Ice Mass with the Finite-Element Technique

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Abstract
The two-dimensional, time-dependent flow of an arbitrarily shaped ice mass can be successfully modeled with the finite-element technique on a small computer. Methods developed for automatically generating the mesh data greatly simplify the data preparation and optimize the numerical simulations. Using quadratic basis functions permits the flow to be approximated quite adequately by only two element rows (five nodes vertically). Mixed-order basis functions, however, must be used so that numerical oscillations do not set in, and the ends of the ice mass, where the thickness tends to zero, must be treated carefully. Time simulations to a steady-state condition are necessary to test such numerical models adequately. South Cascade Glacier, Washington, is currently close to equilibrium. A bedrock sill dominates the bed topography in the lower half of the glacier, rising to a height of about 20% of the ice thickness. This sill produces a maximum increase in the overall thickness of about 6–7% compared to what the thickness would have been if the sill were not present. Finally, this glacier does not appear to be sliding much, if at all, despite its maritime alpine environment. This could help explain the difficulties encountered when trying to measure sliding and basal water pressures on the same glacier (Hodge, 1979), or it could imply that drag exerted by the valley walls has a significantly greater effect than conventional shape-factor concepts imply.

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