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 andocean 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.