Contribution to the Movement and the form of Ice Sheets in the Arctic and Antarctic

Abstract

Starting from Glen’s flow law for ice and from a series of assumptions based in part on observations in Greenland and in the Jungfraujoch, the velocity distribution (horizontal velocity component) and surface configuration is derived for a strip-shaped ice sheet in a stationary state. For the choice n = 3 − 4 of the exponent in the power-law flow relation, there is extensive agreement between the theoretically calculated surface profile and the east-west profile measured through “Station Centrale” by Expéditions Polaires Françaises. The corresponding theoretical solution for a circular ice sheet is also given. As a first application of this theory, an attempt is made to calculate the average rate of accumulation in Antarctica from its surface profile (assumed circular in plan) and from the flow-law parameters derived from the Greenland Ice Sheet. It is also shown that a change in accumulation has only a small influence on the total ice thickness of an ice sheet. A method of calculating approximately the age of ice in an ice sheet, based on the foregoing theory, is illustrated by applying it to the Greenland Ice Sheet. After comparing the present theory with that of Nye, a general expression for the surface profile of an ice sheet with constant accumulation is set up and discussed by means of comparison with two profiles through Antarctica.