Force Budget: Numerical Methods and Application to Two-Dimensional Flow Along the Byrd Station Strain Network, West Antarctica (Abstract)

Abstract

Using the partitioning of full stresses into resistive and lithostatic parts, force balance for plane flow is expressed in terms of strain-rates and a vertical coordinate scaled to the ice thickness. The balance equation and constitutive relation can then be used to calculate stresses through a vertical section of a glacier. Because the flow law is highly non-linear, these calculations are done numerically. Starting at the surface, the force-balance equation is solved by using measured surface velocities to calculate vertical shearing, and this yields velocities at a depth just below the surface. These velocities are used to compute vertical shearing at that depth, from which velocities at the next deeper layer follow. In this way, going progressively downward, velocities and stresses are calculated throughout a section of a glacier.

The theory for calculating resistive stresses and velocities in a glacier is applied to the Byrd Station Strain Network. Large longitudinal variations in basal drag and in sliding velocity occur and this result is little affected by errors in the input data or by uncertainties in the constitutive relation for ice. The basal drag is usually equal to the driving stress to within 10–20%, and both vary by a factor of about 2 along the strain network. Sites of high drag and little sliding are not always correlated with basal highs, indicating that some process (for example, complex bed drainage) is controlling the friction at the bed of the West Antarctic ice sheet.