Review article: Towards strongly coupled ensemble data assimilation with additional improvements from machine learning

We assessed different coupled data assimilation strategies with a hierarchy of coupled models, ranging from a simple coupled Lorenz model to the state-of-the-art coupled general circulation model CFSv2 (Climate Forecast System version 2). With the coupled Lorenz model, we assessed the analysis accuracy by strongly coupled ensemble Kalman filter (EnKF) and 4D-Variational (4D-Var) methods with varying assimilation window lengths. The analysis accuracy of the strongly coupled EnKF with a short assimilation window is comparable to that of 4D-Var with a long assimilation window. For 4D-Var, the strongly coupled approach with the coupled model produces more accurate ocean analysis than the Estimating the Circulation and Climate of the Ocean (ECCO)-like approach using the uncoupled ocean model. Experiments with the coupled quasi-geostrophic model conclude that the strongly coupled approach outperforms the weakly coupled and uncoupled approaches for both the full-rank EnKF and 4D-Var, with the strongly coupled EnKF and 4D-Var showing a similar level of accuracy higher than other coupled data assimilation approaches such as outer-loop coupling. A strongly coupled EnKF software framework is developed and applied to the intermediate-complexity coupled model SPEEDY-NEMO and the state-of-the-art operational coupled model CFSv2. Experiments assimilating synthetic or real atmospheric observations into the ocean through strongly coupled EnKF show that the strongly coupled approach improves the analysis of the atmosphere and upper ocean but degrades observation fits in the deep ocean, probably due to the unreliable error correlation estimated by a small ensemble. The correlation-cutoff method is developed to reduce the unreliable error correlations between physically irrelevant model states and observations. Experiments with the coupled Lorenz model demonstrate that strongly coupled EnKF informed by the correlation-cutoff method produces more accurate coupled analyses than the weakly coupled and plain strongly coupled EnKF regardless of the ensemble size. To extend the correlation-cutoff method to operational coupled models, a neural network approach is proposed to systematically acquire the observation localization functions for all pairs between the model state and observation types. The following strongly coupled EnKF experiments with an intermediate-complexity coupled model show promising results with this method.