On the Localization in Strongly Coupled Ensemble Data Assimilation Using a Two‐Scale Lorenz Model

For coupled numerical models with different components (domains), there are two kinds of assimilation strategies applied for producing ocean analysis and initial condition of predictions: the strongly coupled data assimilation (SCDA) and weakly coupled data assimilation (WCDA). The former needs to accurately estimate cross‐component error covariances, which is much challenging, especially when a small ensemble size's Kalman filter‐based algorithm is used and a coupled model has the components of different spatiotemporal scales. In this study, we propose a new scheme for the ensemble adjustment Kalman filter (EAKF) to address cross‐component localization, a critical issue in estimating the cross‐component error covariance in SCDA, based on a two‐scale Lorenz ’96 coupled mode with different temporal and spatial scales. Emphasis places on designing the cross‐component localization factors in the framework of multiple spatial scales. The result shows that the SCDA can provide much more accurate estimations of the states than the WCDA when the new proposed cross‐component localization is used. A further analysis reveals that the advantage of the SCDA over the WCDA is attributed to the assimilation of observations from the small‐scale model in the coupled system, whereas the contribution of the assimilation of observations from the large‐scale model is not obvious. This study offers a useful technique to develop SCDA system in operational prediction models, which is being pursued in the prediction community. Plain Language Summary For the data assimilaton of the coupled models, there are two kind of assimilation strategies. The strongly coupled data assimilation (SCDA) can update the variables of a different model component than the observation, and has the potential to be better than weakly coupled data assimilation (WCDA). The effectiveness of SCDA highly depends on the quality of cross‐compoent covariance, especially when the model components are with different spatial scales. We have developed a new localization strategy for the cross‐component covariance. New formulas are proposed to compute the localization factors for the variables and observations with different scales. With the new localization strategy, we have shown that SCDA can provide much more accurate analyses than WCDA in a twin experiment using the two‐scale Lorenz model. Key Points We have developed new formula to compute the cross‐domain localization factors for the strongly coupled data assi