Force budget: I. Theory and numerical methods

Abstract

A practical method is developed for calculating stresses and velocities at depth using field measurements of the geometry and surface velocity of glaciers. To do this, it is convenient to partition full stresses into lithostatic and resistive components. The horizontal gradient in vertically integrated lithostatic stress is the driving stress and it describes the horizontal action of gravity. The horizontal resistive stress gradients describe the reactions. Resistive stresses are simply related to deviatoric stresses and hence to strain-rates through a constitutive relation.

A numerical scheme can be used to calculate stresses and velocities from surface velocities and slope, and from ice thickness. There is no mathematical requirement that the variations in these quantities be small.