Vertical Localization for Strongly Coupled Data Assimilation: Experiments in a Global Coupled Atmosphere-Ocean Model

Strongly coupled data assimilation allows observations of one Earth system component (e.g., the ocean) to directly update another component (e.g., the atmosphere). The majority of the information transfer in strongly coupled atmosphere-ocean systems is passed through vertical correlations between atmospheric boundary layer and ocean mixed layer fields. In this work we use correlations from a global, coupled model to study vertical observation-space localization techniques for strongly coupled data assimilation. We generate target correlations using a bootstrapping approach from a single 24 hr forecast from a realistic global, weakly coupled atmosphere-ocean cycling system with an 80-member ensemble, which is the ensemble size currently used by the NOAA operational global data assimilation system. We compare data assimilation methods with different localization schemes using single-update, offline experiments. We develop a new strategy for optimal observation space localization, called Empirical Optimal R-localization (EORL), to give an upper bound on the improvement we can expect with any localization scheme. We then evaluate Gaspari-Cohn localization, which is a commonly used parametric localization function and review its performance with respect to the optimal localization scheme. We investigate how the performance of these localization strategies changes with increasing ensemble sizes. Our results show that strongly coupled data assimilation has the potential to be an improvement over weakly coupled data assimilation when large ensembles are used. We also show that the Gaspari-Cohn localization function does not appear to be a particularly good choice for cross-fluid vertical localization.