IngentaConnect Exact solutions and verification of numerical models for isotherm...

Authors: Bueler, Ed; Lingle, Craig S.; Kallen-Brown, Jed A.; Covey, David N.; Bowman, Latrice N.

Source: Journal of Glaciology, Volume 51, Number 173, March 2005 , pp. 291-306(16)

Publisher: International Glaciological Society

Abstract:

Comparison of numerically computed solutions to exact (analytical) time-dependent solutions, when possible, is superior to intercomparison as a technique for verification of numerical models. At least two sources of such exact solutions exist for the isothermal shallow ice-sheet equation: similarity solutions and solutions with 'compensatory accumulation'. In this paper, we derive new similarity solutions with non-zero accumulation. We also derive exact solutions with (i) sinusoidal-in-time accumulation and (ii) basal sliding. A specific test suite based on these solutions is proposed and used to verify a standard explicit finite-difference method. This numerical scheme is shown to reliably track the position of a moving margin while being characterized by relatively large thickness errors near the margin. The difficulty of approximating the margin essentially explains the rate of global convergence of the numerical method. A transformed version of the ice-sheet equation eliminates the singularity of the margin shape and greatly accelerates the convergence. We also use an exact solution to verify an often-used numerical approximation for basal sliding and we discuss improvements of existing benchmarks.

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Exact solutions and verification of numerical models for isothermal ice sheets