A conceptual coupled ocean-atmosphere model was used to study coupled ensemble data assimilation schemes with a focus on the role of ocean-atmosphere interaction in the assimilation. The optimal scheme was the fully coupled data assimilation scheme that employs the coupled covariance matrix and assimilates observations in both the atmosphere and ocean. The assimilation of synoptic atmospheric variability that captures the temporal fluctuation of the weather noise was found to be critical for the estimation of not only the atmospheric, but also oceanic states. The synoptic atmosphere observation was especially important in the mid-latitude system, where oceanic variability is driven by weather noise. The assimilation of synoptic atmospheric variability in the coupled model improved the atmospheric variability in the analysis and the subsequent forecasts, reducing error in the surface forcing and, in turn, in the ocean state. Atmospheric observation was able to further improve the oceanic state estimation directly through the coupled covariance between the atmosphere and ocean states. Relative to the mid-latitude system, the tropical system was influenced more by ocean atmosphere interaction and, thus, the assimilation of oceanic observation becomes more important for the estimation of the ocean and atmosphere.
