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Time-scales and degrees of freedom operating in the evolution of continental ice-sheets

Published online by Cambridge University Press:  03 November 2011

Richard C. A. Hindmarsh
Richard C. A. Hindmarsh
Affiliation:
Department of Geology and Geophysics, Grant Institute, University of Edinburgh, West Mains Road, Edinburgh EH9 3JW, U.K.
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Abstract

Comprehensible explanations of the operation of earth climate systems should consist of descriptions of the operation of a few degrees of freedoms. Qualitative interpretations of results from large-scale numerical models generally follow this principle, but do not render formal definitions of the precise nature of such degrees of freedom.

At its simplest, ice-sheet kinematics requires knowledge of the evolving height and span. Rheology and surface mass-balance impose different requirements upon the co-evolution of these variables, meaning a two-degree of freedom model is over-prescribed. By means of a perturbation expansion about the analytic similarity solution for viscous spreading, eigenfunctions corresponding to degrees of freedom in the ice-sheet profile are obtained, and are used to decompose mass-balance distributions. Only a few eigenfunctions are needed to replicate numerical models, implying that ice-sheets in plane flow may operate with fewer than ten degrees of freedom.

Unstable evolution of ice-sheets can occur, when the operation of a very large number of degrees of freedom can be manifested. Previous work is reviewed and new results for the unstable transformation of valley glaciers into ice-sheets are presented. Phasing of initiation may be an unpredictable phenomenon.

Keywords

glaciologypalaeoclimate.
Type
Research Article
Information
Earth and Environmental Science Transactions of The Royal Society of Edinburgh , Volume 81 , Issue 4: The Late Cezozoic Ice Age , 1990 , pp. 371 - 384
Copyright
Copyright © Royal Society of Edinburgh 1990

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