  We propose a data assimilation scheme that produces the analyses for a global
and an embedded limited area model simultaneously, considering forecast
information from both models. The purpose of the proposed approach is twofold.
First, we expect that the global analysis will benefit from incorporation of
information from the higher resolution limited area model. Second, our method
is expected to produce a limited area analysis that is more strongly
constrained by the large scale flow than a conventional limited area analysis.
The proposed scheme minimizes a cost function in which the control variable is
the joint state of the global and the limited area models. In addition, the
cost function includes a constraint term that penalizes large differences
between the global and the limited area state estimates. The proposed approach
is tested by idealized experiments, using `toy' models introduced by Lorenz in
2005. The results of these experiments suggest that the proposed approach
improves the global analysis within and near the limited area domain and the
regional analysis near the lateral boundaries. These analysis improvements lead
to forecast improvements in both the global and the limited area models.
