Articles | Volume 22, issue 4
Nonlin. Processes Geophys., 22, 485–497, 2015
https://doi.org/10.5194/npg-22-485-2015
Nonlin. Processes Geophys., 22, 485–497, 2015
https://doi.org/10.5194/npg-22-485-2015

Research article 18 Aug 2015

Research article | 18 Aug 2015

Spectral diagonal ensemble Kalman filters

I. Kasanický1, J. Mandel1,2, and M. Vejmelka1 I. Kasanický et al.
  • 1Institute of Computer Science, Academy of Sciences of the Czech Republic, Prague, Czech Republic
  • 2Department of Mathematical and Statistical Sciences, University of Colorado Denver, Denver, CO, USA

Abstract. 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.

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Short summary
A new type of ensemble Kalman filter for data assimilation is developed, based on fast Fourier transform and wavelet transform. The method can work with minimal computational resources. We develop variants for several general types of observations, give a rigorous proof that the method improves the approximation of the state covariance, and present computational experiments showing that the new technique works reliably with very small ensembles and is stable over multiple analysis cycles.