An extended perfect-plasticity method for estimating ice thickness along the flow line of mountain glaciers

Direct measurement of the thickness of mountain glaciers is difficult over large areas, yet knowledge of the thickness is essential for calculating their volumes and future evolution. We develop a new method for estimating the ice thickness along glacier flow lines, using the perfect-plasticity rheological assumption that relates the thickness and surface slope to a yield stress. Previous studies have used this assumption with the shallow-ice approximation to estimate the ice thickness, but the standard approach neglects the effect of side drag on glacier stress balance. Our method addresses this shortcoming and extends the standard method by accounting for the side drag via the glacier width. Besides the assumed yield stress, the inputs for our method are the outline and surface topography of the glacier; surface velocity and mass balance data are unnecessary. We validated the extended method on five glaciers in northwest China where thickness data are available from radio echo soundings, finding that it can reproduce measured thicknesses with a mean absolute error of 11.8% (like the standard method). Moreover, for long glacier tongues confined to flow between parallel valley sides, this method is found to give more accurate thickness estimates than does the standard method, with a mean absolute error of as low as 5.3%. Sensitivity analysis shows that the estimated ice thickness depends strongly on yield stress and surface slope and less strongly on glacier width. Because this method is physically more realistic than the standard method and its inputs are easily derivable from remote-sensing observations, it has the potential to be used for processing large glacier data sets.