Analytical and numerical bedrock reconstruction in glacier flows from free surface elevation data
This paper presents a simple analytical and numerical approach to reconstruct the bedrock in glacier flows from given free surface data. The approach relies on the Shallow Ice Approximation in one space dimension to describe the glacier flow dynamics. Remarkably, we show that this complex, non-linear partial differential equation can be integrated once to yield and explicit relationship between the ice free surface elevation and the ice depth and therefore the bedrock. The applicability of the proposed approach is broadened by proposing a transient numerical scheme capable of reconstructing the ice depth and underlying bedrock topography.