ADISM v.1.0: an adjoint of a thermomechanical ice-sheet model obtained using an algorithmic differentiation tool

Abstract. A number of problems in contemporary glaciology could benefit from the application of adjoint models. On a simple level, adjoint models can be used to calculate ice-sheet sensitivities with respect to spatially varying parameters such as the basal sliding coefficient. At a more sophisticated level, adjoint models may be used as components of variational data assimilation schemes, allowing problems of model initialization and data-constrained evolution to be tackled.

Fundamentally, adjoint models calculate the sensitivity of a cost function to a suite of control parameters. Such model sensitivities can alternatively be obtained by running the model many times, perturbing each control parameter separately in turn, and calculating the resulting sensitivity in each case. For large numbers of control parameters, however, such as the case where a control parameter corresponds to each point in the model domain, the computational cost becomes prohibitive. The use of adjoint models allows sensitivities to be obtained more efficiently – adjoint model sensitivities are obtained in a single run – and more accurately, since the differentiation of the model is done with machine precision.

We present a finite-difference shallow ice approximation (SIA), thermomechanical ice-sheet model (the forward model), and its adjoint, as generated by using the OpenAD algorithmic differentiation tool. We verify the ice-sheet model using standard SIA benchmark tests and check the consistency between derivatives computed by OpenAD and certain numerically approximated derivatives. Typical adjoint calculations are demonstrated by application to the Greenland ice sheet.