Time scales for adjustment in the length of a glacier to changing climate may be described in terms of a relatively short time scale, TS and a longer memory time, Tm. The memory Tm represents the time scale needed for asymptotic approach of the glacier to a steady state following a climate change event. Tm is determined by simple continuity considerations concerning the total volume change that must occur to reach steady state and the balance rate that drives the change. We show that Tm is relatively independent of the size of the climate change or to details of how ice flow is related to the geometry of the glacier. The time scale TS represents the time between a climate event and the occurrence of substantial changes in the glacier length. We show that, in contrast to Tm, Ts is highly dependent on the size of the climate change and on details of ice dynamics. This dependence is investigated by several ice-flow models including a simple one in which ice transport is determined by local thickness and slope, as in the analysis of kinematic waves, and a finite element representation that fully includes longitudinal stress gradients. The ice-flow models are subjected to mass-balance perturbations of varying size — from small, for which linearization approximations are valid, to large, for which linearization breaks down.

The following behavior may be identified. Increasing the size of a mass-balance rate change causes a more rapid initial response of a glacier terminus, which tends to shorten Ts. Longitudinal stress gradients damp local variations in velocity and thereby slow the propagation and diffusion of kinematic waves and retard the response of the terminus, which tends to lengthen Ts. Longitudinal stress gradients transmit forces to the terminus region and influence the terminus motion without the necessity of redistributing mass from the glacier length into the terminus zone, which tends to shorten Ts. These various results indicate that accurate modeling of the short term responses of glaciers to climate change requires fairly sophisticated ice-flow models, However, for purposes of tracking glacier lengths (or areas) over time scales considerably great than Ts, fairly simple ice-flow models may suffice.