Iterative improvement of the shallow-ice approximation

We present a new algorithm for a fast iterative improvement of the shallow-ice approximation (SIA) for the modeling of glacier flow. Based on the traditional SIA scaling assumptions, the solution of the Stokes problem is found by an operator-splitting iterative technique. The SIA solution obtained in the first step is successively improved to obtain a higher-order approximation. Each iterative step has computational demands comparable to solving the SIA, which makes the algorithm substantially faster than other higher-order or full-Stokes solvers. The performance of the algorithm is tested on a model example taken from the ISMIP-HOM intercomparison project.