Effects of Inclusion of Adjoint Sea Ice Rheology on Backward Sensitivity Evolution Examined Using an Adjoint Ocean–Sea Ice Model

As part of the ongoing development of an ocean data assimilation system for operational ocean monitoring and seasonal prediction, an adjoint sea ice model was developed that incorporates sea ice rheology, which was omitted from previously developed adjoint models to avoid model instability. The newly developed adjoint model was merged with the existing system to construct a global ocean–sea ice adjoint model. A series of sensitivity experiments, in which idealized initial values were given for the adjoint sea ice area fraction and thickness, were conducted, with particular attention to the differences between the cases with free-drift approximation in the adjoint sea ice model as in previous studies and with full sea ice dynamics including rheology. The internal stress effects represented in the adjoint rheology induced remarkable differences in the evolution of the initialized and generated adjoint variables, such as for the sea ice velocity by O(102) in magnitude, which highlighted the importance of the adjoint rheology in the central Arctic Ocean. In addition, sensitivities with respect to the nonprognostic variables associated with the sea ice dynamics were obtained only through the adjoint rheology. These results suggested a potential for providing an improved global atmosphere–ocean–sea ice state estimation through a four-dimensional variational approach with the adjoint sea ice model as developed in this study.