Implicit and explicit cross‐correlations in coupled data assimilation

The European Centre for Medium‐Range Weather Forecasts has recently developed an implicit coupling approach in the coupled atmosphere–ocean assimilation (CERA) system, where atmospheric 4D‐Var and ocean 3D‐Var are synchronized using multiple outer iterations in the incremental variational formulation. Since this original work on outer‐loop coupling, it has been unclear just how closely the CERA system with implicit coupled covariances approximates a strongly coupled data assimilation with ensemble‐based coupled covariances. A series of single‐observation experiments in a perfect twin framework has been conducted to evaluate the effectiveness and efficiency of outer‐loop coupling and the amplitude of the implicit cross‐correlations between atmospheric and ocean temperature. They are compared against a coupled assimilation system that specifies cross‐correlations explicitly from an ensemble of coupled forecasts. We find that both the implicit outer‐loop and explicit ensemble‐based methods produce equally skilful estimates of the coupled state in the middle of a 24 hr assimilation window. Our estimates of the rate of outer‐loop convergence suggest that atmospheric and ocean states synchronize within the first 6–10 hr of the assimilation window. We conclude that outer‐loop coupling is effective when the window is long enough that original imbalances in the atmospheric and ocean increments can synchronize within the length of the assimilation window. On the other hand, we suggest that explicit coupling is preferable for data assimilation systems with short assimilation windows (e.g. 6 hr or less).