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

被引:15
作者
Nino-Ruiz, Elias D. [1 ]
机构
[1] Univ Norte, Dept Comp Sci, Appl Math & Computat Sci Lab, Barranquilla 080001, Colombia
关键词
ensemble kalman filter; posterior ensemble; modified cholesky decomposition; VARIATIONAL DATA ASSIMILATION; ERROR COVARIANCES; CHAOS; MODEL; NWP;
D O I
10.3390/atmos8070125
中图分类号
X [环境科学、安全科学];
学科分类号
08 ; 0830 ;
摘要
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.
引用
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页数:17
相关论文
共 45 条
[1]   Localization and Sampling Error Correction in Ensemble Kalman Filter Data Assimilation [J].
Anderson, Jeffrey L. .
MONTHLY WEATHER REVIEW, 2012, 140 (07) :2359-2371
[2]  
Anderson JL, 2001, MON WEATHER REV, V129, P2884, DOI 10.1175/1520-0493(2001)129<2884:AEAKFF>2.0.CO
[3]  
2
[4]  
[Anonymous], J COMPUT SCI
[5]  
[Anonymous], 2003, Ocean Dynamics, DOI [10.1007/s10236-003-0036-9, DOI 10.1007/S10236-003-0036-9]
[6]  
[Anonymous], 2005, Proceedings of the 16th Annual Workshop on Circuits, Systems and Signal Processing
[7]   Regularized estimation of large covariance matrices [J].
Bickel, Peter J. ;
Levina, Elizaveta .
ANNALS OF STATISTICS, 2008, 36 (01) :199-227
[8]  
Bishop CH, 1999, J ATMOS SCI, V56, P1748, DOI 10.1175/1520-0469(1999)056<1748:ETAAO>2.0.CO
[9]  
2
[10]   Ensemble-derived stationary and flow-dependent background-error covariances: Evaluation in a quasi-operational NWP setting [J].
Buehner, M .
QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, 2005, 131 (607) :1013-1043