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

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Abstract
The length of time TM 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: TM 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 τM = 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, Tm are insensitive to details of the terminus dynamics, in contrast to conclusions derived from some simplified kinematic wave models. A more robust estimate of Tm independent of terminus dynamics is given by TM= 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 Tm for mountain glaciers can be substantially less than the 1O2–103 years commonly considered to be theoretically expected.

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