Abstract
This study investigates the filtering problem with one-way coupled (OWC) state-space systems, for which the joint ensemble Kalman filter (EnKF) is the standard solution. In this approach, the states of the two coupled sub-systems are jointly updated with all incoming observations. This enables transfer of the information across the sub-systems, which should provide coupled-state estimates in better agreement with the observations. The state estimates of the joint EnKF highly depend on the relevance of the joint ensembles' cross-covariances between the sub-systems' variables. In this work, we propose a new joint EnKF scheme based on the One-Step-Ahead (OSA) smoothing formulation of the filtering problem for efficient assimilation into OWC systems. The scheme introduces an extra smoothing step for both states' sub-systems with the future observations, followed by an analysis step for each sub-system state using only its own observation, all within a Bayesian-consistent framework. The extra OSA smoothing step enables us to more efficiently exploit the observations, to enhance the representativeness of the EnKF covariances, and to mitigate for reported inconsistencies in the joint EnKF analysis step. We demonstrate the relevance of the proposed approach by presenting and analyzing results of various numerical experiments conducted with a OWC Lorenz-96 model.