Exact solutions and verification of numerical models for isothermal ice sheets
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.
Document Type: Research Article
Publication date: March 1, 2005
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- The Journal of Glaciology is published six times per year. It accepts submissions from any discipline related to the study of snow and ice. All articles are peer reviewed. The Journal is included in the ISI Science Citation Index.
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