  This paper discusses an efficient parallel implementation of the ensemble
Kalman filter based on the modified Cholesky decomposition. The proposed
implementation starts with decomposing the domain into sub-domains. In each
sub-domain a sparse estimation of the inverse background error covariance
matrix is computed via a modified Cholesky decomposition; the estimates are
computed concurrently on separate processors. The sparsity of this estimator is
dictated by the conditional independence of model components for some radius of
influence. Then, the assimilation step is carried out in parallel without the
need of inter-processor communication. Once the local analysis states are
computed, the analysis sub-domains are mapped back onto the global domain to
obtain the analysis ensemble. Computational experiments are performed using the
Atmospheric General Circulation Model (SPEEDY) with the T-63 resolution on the
Blueridge cluster at Virginia Tech. The number of processors used in the
experiments ranges from 96 to 2,048. The proposed implementation outperforms in
terms of accuracy the well-known local ensemble transform Kalman filter (LETKF)
for all the model variables. The computational time of the proposed
implementation is similar to that of the parallel LETKF method (where no
covariance estimation is performed). Finally, for the largest number of
processors, the proposed parallel implementation is 400 times faster than the
serial version of the proposed method.
