  This study considers the data assimilation problem in coupled systems, which
consists of two components (sub-systems) interacting with each other through
certain coupling terms. A straightforward way to tackle the assimilation
problem in such systems is to concatenate the states of the sub-systems into
one augmented state vector, so that a standard ensemble Kalman filter (EnKF)
can be directly applied. In this work we present a divided state-space
estimation strategy, in which data assimilation is carried out with respect to
each individual sub-system, involving quantities from the sub-system itself and
correlated quantities from other coupled sub-systems. On top of the divided
state-space estimation strategy, we also consider the possibility to run the
sub-systems separately. Combining these two ideas, a few variants of the EnKF
are derived. The introduction of these variants is mainly inspired by the
current status and challenges in coupled data assimilation problems, and thus
might be of interest from a practical point of view. Numerical experiments with
a multi-scale Lorentz 96 model are conducted to evaluate the performance of
these variants against that of the conventional EnKF. In addition, specific for
coupled data assimilation problems, two prototypes of extensions of the
presented methods are also developed in order to achieve a trade-off between
efficiency and accuracy.
