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

• Published in: Transactions of the Royal Society of Edinburgh: Earth Sciences
• Main Author: Hindmarsh, Richard C. A.
• Format: Article in Journal/Newspaper
• Language: English
• Published: Cambridge University Press (CUP) 1990
• Subjects: Paleontology; Earth and Planetary Sciences (miscellaneous); Ice Sheet
• Online Access: http://dx.doi.org/10.1017/s0263593300020861; https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0263593300020861

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.