Steady-State Temperatures at the Bottom of Ice Sheets and Computation of the Bottom Ice Flow Law from the Surface Profile

Abstract

A solution for the steady flow of a cold ice sheet is recalled, which takes account of the heat released by deformation. As this strain heating increases the strain velocity, the bottom temperature may be unstable. A set of five equations with five unknowns is written, which allows the surface profile and the bottom temperature to be computed step by step by an iterative process. This has been done by computer for three very different models of ice sheets. and in each case with three distinct values of the constantBin Glen’s ice flow law. It was found in every case that steady-state temperature profiles could not be computed beyond a moderate distance from the ice divide. The correct value ofBfor bottom ice may be deduced from the actual surface profile. At the bottom of Greenland ice sheet,B≈ 2.18 bar⁻³year⁻¹. This is about thirteen times bigger than for the bulk of the alpine glaciers.