Greenland ice-sheet volume sensitivity to basal, surface and initial conditions derived from an adjoint model

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Abstract
We extend the application of control methods to a comprehensive three-dimensional thermomechanical ice-sheet model, SICOPOLIS (SImulation COde for POLythermal Ice Sheets). Lagrange multipliers, i.e. sensitivities, are computed with an exact, efficient adjoint model that has been generated from SICOPOLIS by rigorous application of automatic differentiation. The case study uses the adjoint model to determine the sensitivity of the total Greenland ice volume to various control variables over a 100 year period. The control space has of the order 1.2 × 106 elements, consisting of spatial fields of basal flow parameters, surface and basal forcings and initial conditions. Reliability of the adjoint model was tested through finite-difference perturbation calculations for various control variables and perturbation regions, ascertaining quantitative inferences of the adjoint model. As well as confirming qualitative aspects of ice-sheet sensitivities (e.g. expected regional variations), we detect regions where model sensitivities are seemingly unexpected or counter-intuitive, albeit ‘real’ in the sense of actual model behavior. An example is inferred regions where sensitivities of ice-sheet volume to basal sliding coefficient are positive, i.e. where a local increase in basal sliding parameter increases the ice-sheet volume. Similarly, positive (generally negative) ice temperature sensitivities in certain parts of the ice sheet are found, the detection of which seems highly unlikely if only conventional perturbation experiments had been used. The object of this paper is largely a proof of concept. Available adjoint-code generation tools now open up a variety of novel model applications, notably with regard to sensitivity and uncertainty analyses and ice-sheet state estimation or data assimilation.