  In this paper, we introduce a new, local formulation of the ensemble Kalman
Filter approach for atmospheric data assimilation. Our scheme is based on the
hypothesis that, when the Earth's surface is divided up into local regions of
moderate size, vectors of the forecast uncertainties in such regions tend to
lie in a subspace of much lower dimension than that of the full atmospheric
state vector of such a region. Ensemble Kalman Filters, in general, assume that
the analysis resulting from the data assimilation lies in the same subspace as
the expected forecast error. Under our hypothesis the dimension of this
subspace is low. This implies that operations only on relatively low
dimensional matrices are required. Thus, the data analysis is done locally in a
manner allowing massively parallel computation to be exploited. The local
analyses are then used to construct global states for advancement to the next
forecast time. The method, its potential advantages, properties, and
implementation requirements are illustrated by numerical experiments on the
Lorenz-96 model. It is found that accurate analysis can be achieved at a cost
which is very modest compared to that of a full global ensemble Kalman Filter.
