A Monte Carlo error analysis for basal sliding velocity calculations

Since glacier beds are mostly inaccessible, numerical inversion of the surface velocity field provides a valuable method for calculating the basal shear stress and sliding velocity. However, previous theoretical studies (limited either to planar slabs or linear ice rheology) have suggested small errors in surface velocity measurements lead to large uncertainties in calculated basal sliding. Here a numerical ice flow model and Monte Carlo simulation are used to calculate the sliding velocity and basal shear stress and their associated uncertainties from field measurements of surface velocity along a two-dimensional long section of Glacier de Tsanfleuron, Switzerland. The model does not require the restrictive assumption of a sliding law since both sliding and basal shear stress are calculated independently and can include a spatially variable rate factor in the flow law for ice. Results indicate that sliding contributes between 45 and 84% of the surface velocity and that calculated sliding velocities are strongly dependent on ice rheology. Amplification of surface velocity errors is generally smaller than theoretical estimates and is a power law function of the horizontal grid spacing in the ice flow model.