Response of surface topography to basal variability along glacial flowlines

Predicting the amplitude and distribution of surface undulations on ice sheets and glaciers is useful because of their influence on surface mass and energy balance, atmospheric boundary-layer processes, and supraglacial meltwater routing. We develop an approximate method of calculating the surface elevation response due to spatial perturbations in basal topography and slipperiness, on two-dimensional flow sections whose thickness, surface slope and basal slip ratio vary along flow. Our main result is an integral expressing nonuniform transfer of basal variability to the surface. It uses published Fourier transfer functions derived through perturbing plane-slab Stokes flow, but circumvents the need to sub-window the spatial domain to estimate the response. We test the method on ice flow synthesised by a finite-element model of Stokes flow with constant viscosity and known basal topography and slipperiness perturbations; in this case, it predicts the observed size and shape of the surface undulations well, capturing more than 90% of their variance. Application of the method to the central flowline of Columbia Glacier, Alaska and a flowline on the Greenland Ice Sheet ending on Nordenskiöld Glacier, using knowledge of the approximate bed topography and ignoring the unknown slipperiness forcing, yields less faithful prediction of their surface undulations (40–50% of their variance) but demonstrates the method’s potential to reproduce their qualitative features. We discuss the factors limiting the method’s performance on real flowlines.