Abstract
This article comments on some basic glaciological algorithms for solving the shallow-ice-approximation-based ice-sheet equation and the motion of tracers within ice. The emphasis is practical, with discussion of the merits and demerits of popular algorithms.
Finite difference, pseudo-spectral and characteristic methods are compared for the tracer equation. Second-order upstreaming is found to give the most robust results.
Robust stability criteria applicable to explicit and semi-implicit marching schemes for the ice-sheet equation are derived. The accuracies of three spatial discretization methods are compared; one method is clearly more accurate than the others, but requires twice as much computation time per time-step. A stable semi-implicit method for the ice-sheet equation is suggested by the stability analyses in this paper.
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References
Budd, W. F. and Jenssen, D. 1975. Numerical modelling of glacier systems. In: Symposium Neiges et Glaces, IAHS-AIHS Publication No. 104, 257–291.
Calov, R., Savvin, A. A., Greve, R., Hansen, I. and Hutter, K. 1998. Simulation of the Antarctic ice sheet with a three-dimensional polythermal ice-sheet model, in support of the EPICA project. Ann. Glaciol., 27, 201–206.
Fornberg, B. 1996. A practical guide to pseudospectral methods. Cambridge University Press.
Glen, J. W. 1955. The creep of polycrystalline ice. Proc. R. Soc. Lond., Ser. A, 228, 519–538.
Hindmarsh, R. C. A. 1990. Timescales and degrees of freedom operating in the evolution of continental ice-sheets. Trans. Roy. Soc. Ed. Earth Sci., 81, 371–384.
Hindmarsh, R. C. A. 1993. Qualitative dynamics of marine ice-sheets. In: Ice in the Climate System, NATO ASI Series 112, ed. W. R. Peltier, Reidel, Dordrecht, 67–99.
Hindmarsh, R. C. A. 1996. Stochastic perturbation of divide position. Ann. Glaciol., 23, 94–104.
Hindmarsh, R. C. A. 1999. On the numerical computation of temperature in an ice sheet. J. Glaciol., 45, 568–574.
Hindmarsh, R. C. A. and Hutter, K. 1988. Numerical fixed domain mapping solution of free-surface flows coupled with an evolving interior field. Int. J. Numer. Anal. Meth. Geomech., 12, 437–459.
Hindmarsh, R. C. A. and Payne, A. J. 1996. Time-step limits for stable solutions of the ice-sheet equation. Ann. Glaciol., 23, 74–85.
Hindmarsh, R. C. A., Morland, L. W., Boulton, G. S. and Hutter, K. 1987. The unsteady plane flow of ice-sheets, a parabolic problem with two moving boundaries. J. Geophys. Astrophys. Fluid Dyn., 39, 183–225.
Hindmarsh, R. C. A., Boulton, G. S. and Hutter, K. 1989. Modes of operation of thermo-mechanically coupled ice sheets. Ann. Glaciol., 12, 57–69.
Hutter, K. 1983. Theoretical Glaciology. Reidel, Dordrecht.
Huybrechts, P. 1992. The Antarctic ice sheet and environmental change: a three-dimensional modelling study. Berichte zur Polarforschung, 99 (Alfred Wegener Institute for Polar and Marine Research, Bremerhaven).
Huybrechts, P., Payne, A. J. and the EISMINT Intercomparison Group. 1996. The EISMINT benchmarks for testing ice-sheet models. Ann. Glaciol., 23, 1–12.
Jenssen, D. 1977. A three-dimensional polar ice-sheet model. J. Glaciol., 18, 373–389.
Ladyzhenskaya, O. 1997. The Bounday Value Problems of Mathematical Physics. Springer, New York etc.
Le Meur, E. and Hindmarsh, R. C. A. 2001. Coupled marine ice-sheet/earth dynamics using a dynamically consistent ice-sheet model and a self-gravitating viscous earth model. J. Glacioi. (submitted).
MahaiFy, M. A. W. 1976. A three-dimensional numerical model of ice sheets: Test on the Barnes ice cap, Northwest Territories. J. Geophys. Res., 81, 1059–1066.
Nye, J. F. 1959. The motion of ice sheets and glaciers. J. Glaciol., 3, 493–507.
Oerlemans, H. and van der Veen, C. J. 1984. Ice Sheets and Climate. Reidel, Dordrecht.
Peaceman, D. W. and Rachford, H. H. 1955. The numerical solution of parabolic and elliptic differential equations. J. Soc. Indust. Applied Maths., 3, 28–41.
van der Veen, C. J. 1999. Fundamentals of Glacier Dynamics. Balkema, Rotterdam/Brookfield.
Weertman, J. 1957. On the sliding of glaciers. J. Glaciol., 3, 33–38.
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Hindmarsh, R.C.A. (2001). Notes on Basic Glaciological Computational Methods and Algorithms. In: Straughan, B., Greve, R., Ehrentraut, H., Wang, Y. (eds) Continuum Mechanics and Applications in Geophysics and the Environment. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-04439-1_13
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DOI: https://doi.org/10.1007/978-3-662-04439-1_13
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