Data Sheet 1_Causality-driven localization method for improving ensemble-based Kalman filters in strongly coupled data assimilation system.pdf

Strongly coupled data assimilation (SCDA) is a critical tool for improving Earth system predictions by directly integrating observational data into coupled numerical models that simulate interactions among atmospheric, oceanic, and terrestrial components. However, SCDA faces significant challenges, including high sensitivity to hyperparameters such as localization and difficulties in diagnosing cross-component interactions. These challenges can arise in ensemble-based Kalman filters, a primary category method used in SCDA, due to limited ensemble sizes. This study introduces a novel causality-driven localization method for SCDA utilizing the Liang-Kleeman (LK) information flow. By transforming the empirical determination of localization parameters, as done in the conventional Gaspari-Cohn (G-C) localization method, into a quantitative assessment of causal dependence strength, the LK information flow generates an anisotropic localization method that provides a physically constrained framework for SCDA. Through twin experiments using the Ensemble Adjustment Kalman Filter (EAKF) based on an intermediate atmosphere-ocean-land coupled model, the LK-based SCDA is found to outperform the G-C localization method. The LK method captures variable heterogeneity, directional asymmetry, and spatial heterogeneity in component interactions, leading to faster stabilization and more accurate assimilation results, with these improvements being particularly pronounced in small ensemble sizes. These findings highlight the potential of causality-driven localization to enhance the robustness and efficiency of SCDA, particularly in complex, multi-component systems.