Realistic, yet simple bottom boundary conditions for glaciers and ice sheets

Over a nondeformable and impermeable bed, the sliding law has to be a relationship between the bottom shear stress τ b , the sliding velocity u , and the effective pressure N = p i — p w , where p i is the ice load and p w is the pressure in the interconnected water cavities. Three horizontal scales are recognized: 0.1 m, 10 m, and 10 km. Classical theories consider the smallest scale; they are of dubious value because temperate ice is neither dry nor totally impermeable. The intermediate scale yields sliding laws to be used in glacier modeling; melting‐refreezing processes may then be ignored. For modeling large, cold ice sheets, the sliding law at the largest scale is needed; it is suggested that sliding occurs only when a bottom temperate layer exists. How to tackle non‐Newtonian rheology is discussed. At the intermediate scale a microrelief model consisting of two superimposed “bumpy profiles” is favored. If the smaller one had bumps of equal height, τ b would be double valued, but this model is unrealistic (the ice avalanche at the Allalingletscher in 1965 may be explained otherwise). Therefore a model with the smaller bumps of unequal height is adopted. It yields an asymptotic sliding law at large sliding velocities τ b = ƒ N + cuN 1−n , with ƒ and c as adjustable parameters. A third one has to be introduced at low velocities. Although the correct interpolation function between both extreme cases remains unknown, some qualitative results about kinematic waves are obtained.