Elias D. Nino

Elias D. Nino, Adrian Sandu, Xinwei Deng

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.

Elias D. Nino, Adrian Sandu

This study develops a hybrid ensemble-variational approach for solving data assimilation problems. The method, called TR-4D-EnKF, is based on a trust region framework and consists of three computational steps. First an ensemble of model runs is propagated forward in time and snapshots of the state are stored. Next, a sequence of basis vectors is built and a low-dimensional representation of the data assimilation system is obtained by projecting the model state onto the space spanned by the ensemble deviations from the mean. Finally, the low-dimensional optimization problem is solved in the reduced-space using a trust region approach; the size of the trust region is updated according to the relative decrease of the reduced order surrogate cost function. The analysis state is projected back onto the full space, and the process is repeated with the current analysis serving as a new background. A heuristic approach based on the trust region size is proposed in order to adjust the background error statistics from one iteration to the next. Experimental simulations are carried out using the Lorenz and the quasi-geostrophic models. The results show that TR-4D-EnKF is an efficient computational approach, and is more accurate than the current state of the art 4D-EnKF implementations such as the POD-4D-EnKF and the Iterative Subspace Minimization methods.