Adjoint sensitivity theory for a pack ice momentum model

Abstract

The adjoint sensitivity method is applied to a pack ice motion model based on the solution of the two-dimensional momentum equations for a floating ice cover. The equations were solved using the Galerkin method of weighted residuals. Adjoint sensitivity theory is used to efficiently calculate the rate of change of a model performance measure with respect to any model parameter. The sensitivities are shown to be functions of the solution of the ice-motion model, called the primary problem, and the solution of an adjoint problem obtained from the primary problem through suitable transformation. Adjoint sensitivity theory is applied to both the continuum and discretized forms of the primary problem to generate corresponding adjoint and sensitivity equations. Single solutions of the primary equation and the adjoint form are sufficient to calculate total sensitivity with respect to any model parameter as well as showing the spatial variation of sensitivity contributions for a distributed parameter. Adjoint sensitivity theory may be more computationally efficient than sampling-based techniques. The application of the finite element forms of the primary problem and adjoint sensitivity calculations are demonstrated. Key words : ice mechanics, ice parameters, sensitivity theory, finite elements, adjoint method.