A simple inverse method for deducing the large-scale distribution of basal sliding coefficients below the Antarctic Ice Sheet

Variations in basal roughness and the distribution of deformable sediments versus hard bedrock are important boundary conditions for large-scale ice-sheet models, but are hard to observe and remain largely uncertain below the modern Greenland and Antarctic ice sheets. Previous modeling studies have used relatively sophisticated control method inversions (adjoint, Lagrange Multipliers) to deduce patterns of basal stress or roughness, given observed ice thicknesses and observed or balance velocities. Here we describe a much simpler method that does not require observed velocities: running the model forward in time for modern conditions, and periodically increasing or decreasing the basal sliding coefficient at each grid point depending on whether the local ice elevation is too high or too low compared to observed. Continent-wide results are described for Antarctica, where the method considerably reduces model errors in ice elevation. The method is extended in a series of steps to also optimize the internal-deformation coefficient in Glen's Law, and to account for areas of frozen bed.