Transfer of Basal Sliding Variations to the Surface of a Linearly Viscous Glacier

Abstract

The transfer of basal velocity anomalies to the surface of a glacier is investigated using a model of a planar parallel-sided slab (thickness H) of linear viscous rheology. Surface velocity parallel (u_s) and normal (v_s) to the surface is calculated for various spatial distributions of basal velocity anomalies with components parallel (u_b) and normal (v_b) to the surface. Four scales of differing behavior can be identified depending on the spatial length L of the basal anomalies. At very short scales (L ≤ 1H) there is essentially no response at the surface. At short scales (1H ≤ L ≤ 5H), a basal anomaly u_b induces a response in both u_s and v_s. The spatial pattern of u_s is such that velocity peaks in u_s can be shifted from peaks in u_b, and may differ in number. The amplitude of u_s is up to about 0.3|u_b|. The amplitude of the cross-component effect v_s may be greater than the amplitude of u_s. A basal anomaly v_b induces a response in both v_s and us. The pattern of v_s is the same as the pattern of v_b, and the amplitude of v_s is up to about 0.7 |v_b|. The amplitude of the cross-component effect u_s is less than the amplitude of v_s. At intermediate scales (5H ≤ L ≤ 10H), results differ from the short scale in two respects; velocity peaks in u_s correspond with peaks in u_b; and surface amplitudes are increased, except for cross-component effects for which surface amplitudes are of the same order as at the short scale. These cross-component effects at the short and intermediate scales show in particular that substantial anomalous surface-normal motions can be induced by deformation, even though the basal velocity anomaly is parallel to the surface. At long scales (10H ≤ L), the velocity anomaly at the surface is essentially the same as the anomaly at the bed. For all scales, the longitudinal strain-rate averaged over depth is larger in magnitude than the longitudinal strain-rate at the surface and, at the short scale, it may differ in sign, so that v_s cannot be easily estimated from surface strain-rate. Although the simplifications of the model do not allow its rigorous quantitative application to field measurements, the results indicate the need for caution in interpreting surface-velocity variations in terms of basal velocity anomalies. It is important to establish the spatial pattern of surface motions for any chance of a confident interpretation in terms of basal motions.