A computer scheme for rapid calculations of balance-flux distributions

Abstract

A simple computer scheme developed by Budd and Smith (1985) and modified by D. Jenssen has been further developed to provide a rapid computation of steady-state balance fluxes over arbitrary ice masses, given the surface elevations and net accumulation distribution. The scheme provides a powerful diagnostic tool to examine the flux and state of balance over whole ice masses or limited regions to interpret field observations for dynamics or the state of balance. In many cases the uncertainty in the state of balance may be much less than the uncertainty in the deformation and sliding properties of the ice and so the flux and velocities derived from balance could provide a useful guide for the dynamics where direct observations are sparse. The scheme assumes that, on a horizontal scale of many ice thicknesses, the ice-flow direction is approximately down the steepest surface slope. The continuity equation is used to compute steady-state implied downslope fluxes at each grid point from integrations of the net accumulation over the area from the summits to the edges. The algorithm ensures the exact integral balance of the surface net flux over the area with flow through boundaries. Applications are demonstrated for the whole of Antarctica and for regional areas. Comparisons are made between fluxes computed from observed ice thicknesses and velocities and those computed from balance. The observed ice thicknesses can also be used to compute surface velocities from assumed column-to-surface velocity ratios. The combined fluxes from observations and balance can be used to compute rates of change of elevation with time.