Linear analysis of ice-shelf topography response to basal melting and freezing

Abstract

Floating ice shelves in Antarctica and Greenland limit land-ice contributions to sea level rise by resisting the flow of grounded ice. Melting at the surface and base of ice shelves can lead to destabilisation by promoting thinning and fracturing. Basal melting often results in channelised features that manifest as surface topography due to buoyancy. The assumption of hydrostatic flotation commonly underlies estimates of basal melting rates. However, numerical simulations and ice-penetrating radar data have shown that narrow topographic features do not necessarily satisfy the local flotation condition. Here, we introduce a linearised model for ice-shelf topographic response to basal melting perturbations to quantify deviations from hydrostatic flotation and the stability of topography. While hydrostatic flotation is the dominant behaviour at wavelengths greater than the ice thickness, ice elevation anomalies diminish relative to the perfect flotation condition at smaller wavelengths. The linearised analysis shows that steady solutions are stable. However, we do not consider physical effects such as fracturing, which could lead to instability. We find a Green’s function for one-dimensional steady-state solutions in the absence of background advection. We validate the linearised analysis by comparing numerical solutions to a nonlinear ice-flow model with steady-state solutions obtained via the Green’s function.