A Monte Carlo error analysis for basal sliding velocity calculations

[ 1] 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.