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 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 the outer loop coupling, it has been unclear just how closely does the CERA system with implicit coupled covariances approximates a strongly coupled DA with ensemble based coupled covariances.

A series of single-observation experiments in a perfect twin framework have been conducted to evaluate the effectiveness and the efficiency of the 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 explicitly specifies cross-correlations from an ensemble of coupled forecasts. We find that both the implicit outer loop and the explicit ensemble-based methods produce equally skillful estimates of the coupled state in the middle of a 24 hour assimilation window. Our estimates of the rate of the outer loop convergence suggest that atmospheric and ocean states synchronise within the first 6 to 10 hours of the assimilation window. We conclude, that the outer loop coupling is effective when the window is long enough that original imbalances in the atmospheric and ocean increments can synchronise 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 hours or less).