Exploring the influence of spatio-temporal scale differences in Coupled Data Assimilation

Abstract. Identifying the optimal strategy for initializing coupled climate prediction systems is challenging due to the spatio-temporal scale separation and disparities in the observational network. We aim to clarify when strongly coupled data assimilation (SCDA) is preferable to weakly coupled data assimilation (WCDA). We use a two-components coupled Lorenz-63 system and the Ensemble Kalman Filter (EnKF) to compare WCDA and SCDA for diverse spatio-temporal scale separations and observational networks – only in the atmosphere, the ocean, or both components. When both components are observed, SCDA and WCDA yield similar performances. However, sometimes SCDA performs marginally worse due to its higher sensitivity (as opposed to WCDA) to key approximations in the EnKF – linear analysis update and sampling error. When observations are only in one of the components, SCDA systematically outperforms WCDA. The spatio-temporal scale separation determines SCDA's performance in this scenario and the largest improvements are found when the observed component has a smaller spatial scale. This suggests that SCDA of fast atmospheric observations can potentially improve the large-slow ocean component. Conversely, observations of the fine ocean can improve the large atmosphere at a comparable temporal scale. However, when both components are highly chaotic, and the observed component's spatial scale is the largest, SCDA does not improve over WCDA. In such a case, the cross-updates may become too sensitive to data assimilation approximations.