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This study considers the data assimilation problem in coupled systems, whichconsists of two components (sub-systems) interacting with each other throughcertain coupling terms. A straightforward way to tackle the assimilationproblem in such systems is to concatenate the states of the sub-systems intoone augmented state vector, so that a standard ensemble Kalman filter (EnKF)can be directly applied. In this work we present a divided state-spaceestimation strategy, in which data assimilation is carried out with respect toeach individual sub-system, involving quantities from the sub-system itself andcorrelated quantities from other coupled sub-systems. On top of the dividedstate-space estimation strategy, we also consider the possibility to run thesub-systems separately. Combining these two ideas, a few variants of the EnKFare derived. The introduction of these variants is mainly inspired by thecurrent status and challenges in coupled data assimilation problems, and thusmight be of interest from a practical point of view. Numerical experiments witha multi-scale Lorentz 96 model are conducted to evaluate the performance ofthese variants against that of the conventional EnKF. In addition, specific forcoupled data assimilation problems, two prototypes of extensions of thepresented methods are also developed in order to achieve a trade-off betweenefficiency and accuracy.

Ensemble Kalman filtering with a divided state-space strategy for coupled data assimilation problems