Estimating Forecast Error Covariances for Strongly Coupled Atmosphere-Ocean 4D-Var Data Assimilation

Strongly coupled data assimilation emulates the real-world pairing of the atmosphere and ocean by solving the assimilation problem in terms of a single combined atmosphere-ocean state. A significant challenge in strongly coupled variational atmosphere-ocean data assimilation is a priori specification of the cross covariances between the errors in the atmosphere and ocean model forecasts. These covariances must capture the correct physical structure of interactions across the air-sea interface as well as the different scales of evolution in the atmosphere and ocean; if prescribed correctly, they will allow observations in one medium to improve the analysis in the other. Here, the nature and structure of atmosphere-ocean forecast error cross correlations are investigated using an idealized strongly coupled single-column atmosphere-ocean 4D-Var assimilation system. Results are presented from a set of identical twin-type experiments that use an ensemble of coupled 4D-Var assimilations to derive estimates of the atmosphere-ocean error cross correlations. The results show significant variation in the strength and structure of cross correlations in the atmosphere-ocean boundary layer between summer and winter and between day and night. These differences provide a valuable insight into the nature of coupled atmosphere-ocean correlations for different seasons and points in the diurnal cycle.