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

Abstract

Abstract The length of time TMover 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: TMmay 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 factorfin the classical estimate of τM=ƒl/u, whereIis glacier length anduis terminus velocity, has a simple geometrical interpretation. Ft is the ratio of thickness change averaged over the full lengthIto the change at the terminus. Although bothuandfrelate to dynamic processes local to the terminus zone, the ratiof/uand, therefore, Tmare insensitive to details of the terminus dynamics, in contrast to conclusions derived from some simplified kinematic wave models. A more robust estimate of Tmindependent of terminus dynamics is given by TM=h/(–b)wherehis a thickness scale for the glacier and–bis the mass-balance rate (negative) at the terminus. We suggest that Tmfor mountain glaciers can be substantially less than the 1O2–103years commonly considered to be theoretically expected.