September 2012

Inverse methods are used to estimate model parameters from observations, here basal shear stress from the surface velocity of an ice sheet. One starts with an initial estimate of the model parameters and then updates them to improve the match to observations in an iterative process. Large-scale spatial features are adjusted first. A stopping criterion prevents the overfitting of data. In this paper, iterative inverse methods are applied to the shallow-shelf approximation forward model. A new incomplete Gauss–Newton method is introduced and compared to the steepest descent and nonlinear conjugate gradient methods. Two different stopping criteria, the discrepancy principle and a recent-improvement threshold, are compared. The IGN method shows faster convergence than the others. Though PISM is not mentioned by this paper, and the experiments were done in python, code supporting these inversion methods is already present in the PISM dev branch.