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[1] Extensive bed topography at the scale of the ice thickness occurs frequently in the form of drumlins. By analogy with hard-bed sliding, ice flow over this type of topography leads to the generation of drag on the ice, particularly when ice flow is rapid. A crucial difference with classical Nye-Kamb sliding is that the upper, free surface of the ice has a significant effect on the sliding process through the formation of a standing wave. Using a theoretical model, we demonstrate that the presence of this wave introduces a non-linearity into the sliding motion which can lead to multiple sliding velocities for the same large-scale ice stream geometry, and that switches between these velocities can cause surging behavior.