A parallel implementation of the ensemble Kalman filter based on modified Cholesky decomposition

Nino, Elias D.; Sandu, Adrian; Deng, Xinwei

doi:10.1016/j.jocs.2017.04.005

Cited by 34 publications

(18 citation statements)

References 13 publications

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“…In practice, localization methods can be utilized in order to mitigate the impact of sampling errors during the assimilation steps [8]. For instance, in the EnKF implementation based on a modified Cholesky decomposition (EnKF-MC) [9,10], the covariance matrix estimator proposed by Bickel and Levina in [11] and the conditional independence of model components regarding their spatial distances are exploited in order to estimate a sparse precision matrix of the background distribution, to reduce the computational cost of the analysis step, and to mitigate the impact of spurious correlations during the assimilation of observations. Given the relation between A and B −1 in (7b) and by using the Bickel and Levina estimator, we think that a sparse precision matrix of the analysis distribution can be estimated without the needing of actually computing (7b), and therefore, the assimilation of observations can be efficiently performed.…”

Section: Introductionmentioning

confidence: 99%

A Matrix-Free Posterior Ensemble Kalman Filter Implementation Based on a Modified Cholesky Decomposition

Niño-Ruiz

2017

Atmosphere

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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.

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Section: Introductionmentioning

confidence: 99%

A Matrix-Free Posterior Ensemble Kalman Filter Implementation Based on a Modified Cholesky Decomposition

Niño-Ruiz

2017

Atmosphere

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“…In practice, localization methods are often used to artificially increase the degrees of freedom of P b and to mitigate the impact of sampling errors [12][13][14][15]. An efficient EnKF implementation which accounts for implicit localization during the assimilation step is the EnKF method based on a modified Cholesky decomposition (EnKF-MC) [16]. In this filter, the vanilla covariance (7d) is replaced by the Bickel and Levina estimator [17]:…”

Section: Ensemble Kalman Filters Based On Modified Cholesky Decomposimentioning

confidence: 99%

A Robust Non-Gaussian Data Assimilation Method for Highly Non-Linear Models

2018

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Abstract:In this paper, we propose an efficient EnKF implementation for non-Gaussian data assimilation based on Gaussian Mixture Models and Markov-Chain-Monte-Carlo (MCMC) methods. The proposed method works as follows: based on an ensemble of model realizations, prior errors are estimated via a Gaussian Mixture density whose parameters are approximated by means of an Expectation Maximization method. Then, by using an iterative method, observation operators are linearized about current solutions and posterior modes are estimated via a MCMC implementation. The acceptance/rejection criterion is similar to that of the Metropolis-Hastings rule. Experimental tests are performed on the Lorenz 96 model. The results show that the proposed method can decrease prior errors by several order of magnitudes in a root-mean-square-error sense for nearly sparse or dense observational networks.

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“…In the EnKF implementation based on a modified Cholesky decomposition (EnKF-MC) [10,11], the covariance matrix estimator proposed by Bickel and Levina in [12] and the conditional independence of model components regarding their spatial distances are exploited in order to obtain sparse Cholesky factors of the precision background error covariance matrix. This is done in order to reduce the computational cost of the analysis step, and to mitigate the impact of spurious correlations during the assimilation of observations.…”

Section: Efficient Formulation and Implementation Of Data Assimilatiomentioning

confidence: 99%

Efficient Formulation and Implementation of Data Assimilation Methods

2018

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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.

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A parallel implementation of the ensemble Kalman filter based on modified Cholesky decomposition

Cited by 34 publications

References 13 publications

A Matrix-Free Posterior Ensemble Kalman Filter Implementation Based on a Modified Cholesky Decomposition

A Matrix-Free Posterior Ensemble Kalman Filter Implementation Based on a Modified Cholesky Decomposition

A Robust Non-Gaussian Data Assimilation Method for Highly Non-Linear Models

Efficient Formulation and Implementation of Data Assimilation Methods

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