Browsing by Author "Nino-Ruiz, Elias D."
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- Efficient Formulation and Implementation of Data Assimilation MethodsNino-Ruiz, Elias D.; Sandu, Adrian; Cheng, Haiyan (MDPI, 2018-07-06)This Special Issue presents efficient formulations and implementations of sequential and variational data assimilation methods. The methods address three important issues in the context of operational data assimilation: efficient implementation of localization methods, sampling methods for approaching posterior ensembles under non-linear model errors, and adjoint-free formulations of four dimensional variational methods.
- An Efficient Implementation of the Ensemble Kalman Filter Based on Iterative Sherman Morrison FormulaNino-Ruiz, Elias D.; Sandu, Adrian; Anderson, J. L. (Elsevier, 2012-01-01)
- An Ensemble Kalman Filter Implementation Based on Modified Cholesky Decomposition for Inverse Covariance Matrix EstimationNino-Ruiz, Elias D.; Sandu, Adrian; Deng, Xinwei (2016-05-31)This paper develops an efficient implementation of the ensemble Kalman filter based on a modified Cholesky decomposition for inverse covariance matrix estimation. This implementation is named EnKF-MC. Background errors corresponding to distant model components with respect to some radius of influence are assumed to be conditionally independent. This allows to obtain sparse estimators of the inverse background error covariance matrix. The computational effort of the proposed method is discussed and different formulations based on various matrix identities are provided. Furthermore, an asymptotic proof of convergence with regard to the ensemble size is presented. In order to assess the performance and the accuracy of the proposed method, experiments are performed making use of the Atmospheric General Circulation Model SPEEDY. The results are compared against those obtained using the local ensemble transform Kalman filter (LETKF). Tests are performed for dense observations ($100\%$ and $50\%$ of the model components are observed) as well as for sparse observations (only $12\%$, $6\%$, and $4\%$ of model components are observed). The results reveal that the use of modified Cholesky for inverse covariance matrix estimation can reduce the impact of spurious correlations during the assimilation cycle, i.e., the results of the proposed method are of better quality than those obtained via the LETKF in terms of root mean square error.
- Ensemble Kalman filter implementations based on shrinkage covariance matrix estimationNino-Ruiz, Elias D.; Sandu, Adrian (Springer, 2015-11-01)
- A Matrix-Free Posterior Ensemble Kalman Filter Implementation Based on a Modified Cholesky DecompositionNino-Ruiz, Elias D. (MDPI, 2017-07-18)In this paper, a matrix-free posterior ensemble Kalman filter implementation based on a modified Cholesky decomposition is proposed. The method works as follows: the precision matrix of the background error distribution is estimated based on a modified Cholesky decomposition. The resulting estimator can be expressed in terms of Cholesky factors which can be updated based on a series of rank-one matrices in order to approximate the precision matrix of the analysis distribution. By using this matrix, the posterior ensemble can be built by either sampling from the posterior distribution or using synthetic observations. Furthermore, the computational effort of the proposed method is linear with regard to the model dimension and the number of observed components from the model domain. Experimental tests are performed making use of the Lorenz-96 model. The results reveal that, the accuracy of the proposed implementation in terms of root-mean-square-error is similar, and in some cases better, to that of a well-known ensemble Kalman filter (EnKF) implementation: the local ensemble transform Kalman filter. In addition, the results are comparable to those obtained by the EnKF with large ensemble sizes.
- A Parallel Implementation of the Ensemble Kalman Filter Based on Modified Cholesky DecompositionNino-Ruiz, Elias D.; Sandu, Adrian; Deng, Xinwei (2016-06-03)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.
- Robust data assimilation using L1 and Huber normsRao, Vishwas; Sandu, Adrian; Ng, Michael; Nino-Ruiz, Elias D. (2015-11-06)Data assimilation is the process to fuse information from priors, observations of nature, and numerical models, in order to obtain best estimates of the parameters or state of a physical system of interest. Presence of large errors in some observational data, e.g., data collected from a faulty instrument, negatively affect the quality of the overall assimilation results. This work develops a systematic framework for robust data assimilation. The new algorithms continue to produce good analyses in the presence of observation outliers. The approach is based on replacing the traditional Ł2 norm formulation of data assimilation problems with formulations based on Ł1 and Huber norms. Numerical experiments using the Lorenz-96 and the shallow water on the sphere models illustrate how the new algorithms outperform traditional data assimilation approaches in the presence of data outliers.