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Spectral Diagonal Ensemble Kalman Filters : Volume 2, Issue 1 (27/01/2015)

By Kasanický, I.

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Book Id: WPLBN0004020123
Format Type: PDF Article :
File Size: Pages 29
Reproduction Date: 2015

Title: Spectral Diagonal Ensemble Kalman Filters : Volume 2, Issue 1 (27/01/2015)  
Author: Kasanický, I.
Volume: Vol. 2, Issue 1
Language: English
Subject: Science, Nonlinear, Processes
Collections: Periodicals: Journal and Magazine Collection (Contemporary), Copernicus GmbH
Publication Date:
Publisher: Copernicus Gmbh, Göttingen, Germany
Member Page: Copernicus Publications


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Mandel, J., Vejmelka, M., & Kasanický, I. (2015). Spectral Diagonal Ensemble Kalman Filters : Volume 2, Issue 1 (27/01/2015). Retrieved from

Description: Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, Czech Republic. A new type of ensemble Kalman filter is developed, which is based on replacing the sample covariance in the analysis step by its diagonal in a spectral basis. It is proved that this technique improves the aproximation of the covariance when the covariance itself is diagonal in the spectral basis, as is the case, e.g., for a second-order stationary random field and the Fourier basis. The method is extended by wavelets to the case when the state variables are random fields which are not spatially homogeneous. Efficient implementations by the fast Fourier transform (FFT) and discrete wavelet transform (DWT) are presented for several types of observations, including high-dimensional data given on a part of the domain, such as radar and satellite images. Computational experiments confirm that the method performs well on the Lorenz 96 problem and the shallow water equations with very small ensembles and over multiple analysis cycles.

Spectral diagonal ensemble Kalman filters

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