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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Bibliographic Details
Published in:Nonlinear processes in geophysics 2015-08, Vol.22 (4), p.485-497
Main Authors: Kasanický, I., Mandel, J., Vejmelka, M.
Format: Article
Language:English
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
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Summary: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.
ISSN:1607-7946
1023-5809
1607-7946
DOI:10.5194/npg-22-485-2015