On the characterization of glacier response by a single time-scale

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Abstract
Glacier response to climate can be characterized by a single time-scale when the glacier changes sufficiently slowly. Then the derivative of volume with respect to area defines a thickness scale similar to that of Jóhannesson and others, and the time-scale follows from it. Our version of the time-scale is different from theirs because it explicitly includes the effect of surface elevation on mass-balance rate, which can cause a major increase in the time-scale or even lead to unstable response. The time constant has a dual role, controlling both the rate and magnitude of response to a given climate change. Data from South Cascade Glacier, Washington, U.S.A., illustrate the ideas, some of the difficulty in obtaining accurate values for the thickness and time-scales, and the susceptibility of all response models to potentially large errors.