Data assimilation (DA) combines a given model and observations to generate the optimal estimates of model states and initialize forecasts. DA methods from simple to complex are all applied in various studies according to de facto interests and resources. Methods include nudging, the 3-dimensional variational (3D-Var) method (Derber & Rosati, 1989) and ensemble optimal interpolation (EnOI; Evensen, 2003) are adopted mainly because they are cost-effective. State-of-the-art DA methods include the 4-dimensional variational (4D-VAR) (Kalnay

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