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Spectral diagonal ensemble Kalman filters
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 approximation of the covariance when the covariance itself is diagonal in the spectral basis, a...
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| Published in: | Nonlinear processes in geophysics 2015-08, Vol.22 (4), p.485-497 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
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| cited_by | cdi_FETCH-LOGICAL-c404t-b79a680b48bd047640ebc29ce7396b0163ebcf50b6ba2580331642342935c63c3 |
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| cites | cdi_FETCH-LOGICAL-c404t-b79a680b48bd047640ebc29ce7396b0163ebcf50b6ba2580331642342935c63c3 |
| container_end_page | 497 |
| container_issue | 4 |
| container_start_page | 485 |
| container_title | Nonlinear processes in geophysics |
| container_volume | 22 |
| creator | Kasanický, I. Mandel, J. Vejmelka, M. |
| description | 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 approximation 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. |
| doi_str_mv | 10.5194/npg-22-485-2015 |
| format | article |
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| ispartof | Nonlinear processes in geophysics, 2015-08, Vol.22 (4), p.485-497 |
| issn | 1607-7946 1023-5809 1607-7946 |
| language | eng |
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| source | EZB Electronic Journals Library |
| subjects | Algorithms Approximation Covariance Data assimilation Discrete Wavelet Transform Fast Fourier transformations Fields (mathematics) Fourier transforms Kalman filters Localization Probability distribution Proof theory Radar Radar imaging Random variables Satellite imagery Shallow water Shallow water equations Spaceborne remote sensing Spectra State variable Wavelet transforms Weather forecasting |
| title | Spectral diagonal ensemble Kalman filters |
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