Direct Reconstruction of Three-dimensional Glacier Bedrock and Surface Elevation from Free Surface Velocity

Abstract

This study presents a new algorithm to reconstruct both the ice-surface elevation and the altitude of the bedrock of a glacier from the knowledge of the ice-surface velocity which could potentially be obtained from satellite data. It requires the prior knowledge of the surface mass balance and basal conditions. The algorithm is realized in two steps: the first one involves the solution of a partial differential equation obtained from a rearrangement of the shallow-ice approximation and the second one involves the mere downslope integration of a non-linear function of the ice velocity and ice thickness. It is therefore an efficient algorithm which is in principle easy to implement. The algorithm is tested on synthetic data and is shown to be very successful with an ideal dataset and robust even when significant noise is added to the input data. Importantly, the inversion algorithm does not appear to amplify the input error in the data

Keywords

• Glacier
• Inverse problem
• Bedrock reconstruction
• Shallow-Ice-Approximation