Enhancing ensemble data assimilation into one‐way‐coupled models with one‐step‐ahead smoothing

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.

Strongly Versus Weakly Coupled Data Assimilation in Coupled Systems With Various Inter‐Compartment Interactions

“…First, we revealed when sCDA is superior to wCDA, which is the primary objective of this study. In the perfect model settings, in addition to the well‐known importance of large ensemble sizes (see e.g., Kirchgessner et al., 2014 and especially for sCDA, compare Figures 3 and 4 in Raboudi et al., 2021), sCDA works better when the absolute value of the inter‐compartment interaction parameter β is large. Since the accurate estimation of both intra‐compartment and inter‐compartment covariances is necessary for sCDA, the small number of ensemble members is not preferrable in sCDA because it increases the sampling error.…”

“…Liu et al (2013) found that in a simplified coupled atmosphere-ocean model, assimilating observation of the dominant compartment (namely atmosphere) to update oceanic variables was effective. Raboudi et al (2021) used the one-way coupled multiscale Lorenz96 model to indicate that sCDA is superior to wCDA when the ensemble size is large. Tondeur et al (2020) used Modular Arbitrary Order Ocean-Atmospheric Model (De Cruz et al, 2016), an atmosphere-ocean model with arbitrary spatial resolutions.…”

“…Raboudi et al. (2021) used the one‐way coupled multiscale Lorenz96 model to indicate that sCDA is superior to wCDA when the ensemble size is large. Tondeur et al.…”