Time–Scale for Adjustment of Glaciers to Changes in Mass Balance

Abstract The length of time T M over which a glacier responds to a prior change in climate is investigated with reference to the linearized theory of kinematic waves and to results from numerical models. We show the following: T M may in general be estimated by a volume time-scale describing the time required for a step change in mass balance to supply the volume difference between the initial and final steady states. The factor f in the classical estimate of τ M = ƒl/u , where I is glacier length and u is terminus velocity, has a simple geometrical interpretation. Ft is the ratio of thickness change averaged over the full length I to the change at the terminus. Although both u and f relate to dynamic processes local to the terminus zone, the ratio f/u and, therefore, T m are insensitive to details of the terminus dynamics, in contrast to conclusions derived from some simplified kinematic wave models. A more robust estimate of T m independent of terminus dynamics is given by T M = h/(–b) where h is a thickness scale for the glacier and –b is the mass-balance rate (negative) at the terminus. We suggest that T m for mountain glaciers can be substantially less than the 1O 2 –10 3 years commonly considered to be theoretically expected.