An improved numerical scheme to compute horizontal gradients at the ice-sheet margin: Its effect on the simulated ice thickness and temperature

Abstract

In three-dimensional numerical ice-sheet models that use finite-difference schemes, the position of ice margins is poorly represented with a regular quadratic grid. As a result, in a centered difference scheme, the surface gradient term and the flux divergence term computed for the gridpoints next to the ice margin may be inaccurate. In this paper, an improved scheme is presented that computes the horizontal gradients at the ice-sheet margin using an asymmetric (upstream) second-order difference scheme in order to avoid using information from the zero-thickness gridpoints. The model is applied to an idealized synthetic geometry to obtain a steady-state ice-sheet topography. The improved model shows a realistically smooth thickness distribution near the margin. Thermomechanical coupling is found to enhance the error near the margin. The error in simulated thicknesses with the centered-difference method was significantly reduced with the new upstream scheme.