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Numerical Modelling of Ice Sheets, Streams, and Shelves

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Glaciers and Ice Sheets in the Climate System

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Abstract

The chapter describes numerical methods for ice sheet and ice shelf models, focussing on the use of explicit finite-difference schemes to solve the shallow ice approximation for ice sheets and the shallow shelf approximation for ice shelves. The aspects covered include numerical stability and convergence. Examples of computer code in Matlab are given to aid the exposition.

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Notes

  1. 1.

    Evaluating the exact solution at a grid point would give a different value from the one we compute by the numerical scheme! Of course we plan that these numbers will be close, but that needs checking or proof.

  2. 2.

    The delta function \(\delta (x)\) is a generalised function having the property that it is zero everywhere, except at zero, where it is infinite in such a way that the integral \(\int _{-\infty }^\infty \delta (x)\,dx=1\).

  3. 3.

    Specifically, we can compute \(V_0=\displaystyle {\frac{2\pi n}{n+1}B\left( \frac{2n}{n+1},\frac{3n+1}{2n+1}\right) R_0^2H_0}\), where B(z, w) is the beta function. For \(n=3\), this gives \(V_0=1.974R_0^2H_0\).

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, USA

    Ed Bueler

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  1. Ed Bueler
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Correspondence to Ed Bueler .

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Editors and Affiliations

  1. MACSI, University of Limerick, Limerick, Ireland

    Andrew Fowler

  2. Department of Geography, University of Sheffield, Sheffield, UK

    Felix Ng

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Bueler, E. (2021). Numerical Modelling of Ice Sheets, Streams, and Shelves. In: Fowler, A., Ng, F. (eds) Glaciers and Ice Sheets in the Climate System. Springer Textbooks in Earth Sciences, Geography and Environment. Springer, Cham. https://doi.org/10.1007/978-3-030-42584-5_8

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