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Estimating the ice thickness of mountain glaciers with an inverse approach using surface topography and mass-balance

We present a numerical method to estimate the ice thickness distribution within a two-dimensional, non-sliding mountain glacier, given a transient surface geometry and a mass-balance distribution, which are relatively easy to obtain for a large number of glaciers. The inverse approach is based on the shallow ice approximation (SIA) of ice flow and requires neither filtering of the surface topography with a lower slope limit nor approximation of constant basal shear stress. We first address this problem for a steady-state surface geometry. Next, we use an apparent surface mass-balance description that makes the transient evolution quasi-stationary. Then, we employ a more elaborated fixed-point method in which the bedrock solution is iteratively obtained by adding the difference between the computed and known surface geometries at the end of the considered time interval. In a sensitivity study, we show that the procedure is much more susceptible to small perturbations in surface geometry than mass-balance. Finally, we present preliminary results for bed elevations in three space dimensions.