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 massbalance. Finally, we present preliminary results for bed elevations in three space dimensions. (Some figures may appear in colour only in the online journal)