Towards Strongly-coupled Ensemble Data Assimilation with Additional Improvements from Machine Learning

Abstract. We assessed different coupled data assimilation strategies with a hierarchy of coupled models, ranging from the simple coupled Lorenz model to the state-of-the-art coupled general circulation model CFSv2. 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 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 the 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 oceans, 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.