Effects of including the adjoint sea ice rheology on estimating Arctic ocean-sea ice state

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