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.

Response of the large-scale subglacial drainage system of Northeast Greenland to surface elevation changes

“…We calculate the outflux of subglacial water at the fjord outlets using the simple, central difference flux calculation by Budd and Warner (1996), modified to follow the hydropotential instead of surface elevation. This scheme has been shown to be the most suitable for calculating fluxes across profiles since it is consistent for different orientations and resolutions, which is not always a given for routing schemes (Le Brocq et al, 2006).…”

A balanced water layer concept for subglacial hydrology in large-scale ice sheet models

“…We perform two more benchmark experiments, where we apply the Budd and Warner (1996) balance flux scheme with the same flux-sliding coupling as in BWF. For the calculation of the balance flux we use the hydraulic potential (Eq.…”

“…According to Budd and Warner (1996) the vector flux φ i,j at the center of a grid cell with side length l = x = y is given by…”

“…Another well-established method to trace the paths of subglacial melt water is the balance flux concept Budd and Warner, 1996;Tarboton, 1997;Le Brocq et al, 2006. The concept is easy to implement, fast and well applicable to continental-scale modeling (e.g., .…”

13 Flow and balance of the polar ice sheets

“…A useful synoptic estimate of the flow field can be obtained by calculating so-called balance fluxes or balance velocities ([96Bud]; [97Jou]; [00Huy]; [00Bam]). The balance flux is the depth averaged ice flux required at any point to maintain the ice sheet in a state of balance, given a specified distribution of net surface flux.…”