The transient response of glaciers to climate variations is investigated with a novel low-order model of an idealized glacier resting on uniformly inclined bedrock. The model consists of two volumes representing the accumulation and ablation areas, which are joined by a flux gate controlling mass flow according to the shallow-ice approximation. Under the assumption of a constant vertical mass-balance gradient, a volume–length scaling relation is derived which depends explicitly on mass-balance gradient and bedrock slope. Analytic expressions for the volume and area timescales are given, which are inversely proportional to the mass-balance gradient and a geometric factor which is the ratio between the vertical extent of the ablation area and the ice thickness at the equilibrium line. From the low-order model, a dynamical system in length and volume is obtained. Results from this system are in good agreement with solutions obtained from a transient finite-element model solving the full force-balance and mass-conservation equations. Under periodic forcing there are significant deviations of the length response, which show that the usual relaxation-type parameterization of length change is not well suited for short-term reactions. Switching on and off periodic climate forcing, the model glaciers show surprisingly large initial and final transient responses that have not been investigated before. These results are of significance for the interpretation of length and thickness changes observed on glaciers.
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