Parameter sensitivity analysis of dynamic ice sheet models.

The velocity and the height at the surface of a dynamic ice sheet are observed. The ice sheets are modeled by the full Stokes, SIA and SSA equations. The sensitivity of the observed quantities at the ice surface to parameters in the models, e.g. the base topography and friction coefficients, is analyzed by first deriving the time dependent adjoint equations. Using the adjoint solutions, the effect of a perturbation in a parameter is obtained. The adjoint equations are solved analytically and numerically and the sensitivity is determined in several examples in two dimensions.