A Simple Method for Determining the Response Time of Glaciers

Abstract

The response time of temperate glaciers is estimated by the following continuity argument: The difference in the steady state ice volume of a glacier, before and after a mass balance perturbation must be accumulated (or ablated) before the glacier can reach a new steady state. This leads to a time scale which is termed the “volume time scale” of the glacier. It is argued that the response time of the glacier can be expected to be equal to the volume time scale. The volume time scale can be derived by a simple argument and is under fairly general conditions expressed by the formula T_v = H/(−b_t) where H is a thickness scale of the glacier and b_t is a scale of the ablation along the terminus of the glacier. This estimate of the response time of glaciers is of the order of decades for small maritime glaciers, which is in reasonable agreement with experience. This is much shorter than the theoretical long response time of the order of several hundred or a thousand years which has been derived in the past from kinematic wave theory.