Effects of including the adjoint sea ice rheology on estimating Arctic Ocean–sea ice state

Abstract. The adjoint assimilation method has been applied to coupled ocean and sea ice models for sensitivity studies and Arctic state estimations. However, the accuracy of the adjoint model is degraded by simplifications of the adjoint of the sea ice model, especially the adjoint sea ice rheologies. As part of ongoing developments in coupled ocean and sea ice estimation systems, we incorporate and approximate the adjoint of viscous-plastic sea ice dynamics (adjoint-VP) and compare it with the adjoint of free-drift sea ice dynamics (adjoint-FD) through assimilation experiments. Using the adjoint-VP results in a further cost reduction of 7.9 % in comparison to adjoint-FD, with noticeable improvements in the ocean temperature over the open water and the intermediate layers of the Arctic Ocean. Adjoint-VP adjusts the model input more efficiently than adjoint-FD does by involving different sea ice retreat processes. For instance, adjoint-FD melts the sea ice up to 1.0 m in the marginal seas from May to June by overadjusting air temperature (>8 ∘C); adjoint-VP reproduces the sea ice retreat with smaller adjustments to the atmospheric state within their prior uncertainty range. These developments of the adjoint model here lay the foundation for further improving Arctic Ocean and sea ice estimations by comprehensively adjusting the initial conditions, atmospheric forcings, and parameters of the model.