The response of a glacier to changes in the rate of nourishment and wastage

Abstract A glacier changes its length in response to variations in the rate of nourishment and wastage. This process is discussed by means of a linearized perturbation theory. The cross-section and slope of the glacier valley are allowed to be arbitrary and non-uniform , and the discharge of ice through any cross-section is assumed to be a function of the local thickness and surface slope of the ice. It is shown how the response, at any point of the glacier surface, to a given Fourier component of the rate of supply and loss can be computed numerically. The amplitude and phase of the response for all frequencies are adequately covered by series approximations valid for high and low frequencies, respectively. The low-frequency approximation is the important one in practical cases, for it leads to a simple method, not involving Fourier analysis, for translating a known history of glacier variation into a history of nourishment and wastage rates. The frequency response of South Cascade Glacier, Washington, U. S. A., is computed as a practical illustration of the method. It is suggested that the response curves of most glaciers are of the same general shape.