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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
Historic
Publication Date:
2015
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 http://hawaiilibrary.net/


Description
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.

Summary
Spectral diagonal ensemble Kalman filters

Excerpt
Anderson, B. D. O. and Moore, J. B.: Optimal Filtering, Prentice-Hall, Englewood Cliffs, NJ, 1979.; Anderson, J. L.: An ensemble adjustment Kalman filter for data assimilation, Mon. Weather Rev., 129, 2884–2903, doi:2.0.CO;2>10.1175/1520-0493(2001)129<2884:AEAKFF>2.0.CO;2, 2001.; Beezley, J. D., Mandel, J., and Cobb, L.: Wavelet ensemble Kalman filters, in: Proceedings of IEEE IDAACS'2011, Prague, 15–17 September 2011, Vol. 2, IEEE, 514–518, doi:10.1109/IDAACS.2011.6072819, 2011.; Berre, L.: Estimation of synoptic and mesoscale forecast error covariances in a limited-area model, Mon. Weather Rev., 128, 644–667, doi:2.0.CO;2>10.1175/1520-0493(2000)128<0644:EOSAMF>2.0.CO;2, 2000.; Boer, G. J.: Homogeneous and isotropic turbulence on the sphere, J. Atmos. Sci., 40, 154–163, doi:2.0.CO;2>10.1175/1520-0469(1983)040<0154:HAITOT>2.0.CO;2, 1983.; Buehner, M. and Charron, M.: Spectral and spatial localization of background-error correlations for data assimilation, Q. J. Roy. Meteor. Soc., 133, 615–630, doi:10.1002/qj.50, 2007.; Burgers, G., van Leeuwen, P. J., and Evensen, G.: Analysis scheme in the ensemble Kalman filter, Mon. Weather Rev., 126, 1719–1724, 1998.; Courtier, P., Andersson, E., Heckley, W., Vasiljevic, D., Hamrud, M., Hollingsworth, A., Rabier, F., Fisher, M., and Pailleux, J.: The ECMWF implementation of three-dimensional variational assimilation (3D-Var). I: Formulation, Q. J. Roy. Meteor. Soc., 124, 1783–1807, doi:10.1002/qj.49712455002, 1998.; Da Prato, G.: An Introduction to Infinite-Dimensional Analysis, Springer-Verlag, Berlin, doi:10.1007/3-540-29021-4, 2006.; Daubechies, I.: Ten Lectures on Wavelets, Vol. 61, CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, doi:10.1137/1.9781611970104, 1992.; Evensen, G.: Data Assimilation: The Ensemble Kalman Filter, 2nd Edn., Springer, Berlin, doi:10.1007/978-3-642-03711-5, 2009.; Furrer, R. and Bengtsson, T.: Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants, J. Multivariate Anal., 98, 227–255, doi:10.1016/j.jmva.2006.08.003, 2007.; Gaspari, G. and Cohn, S. E.: Construction of correlation functions in two and three dimensions, Q. J. Roy. Meteor. Soc., 125, 723–757, doi:10.1002/qj.49712555417, 1999.; Hunt, B. R., Kostelich, E. J., and Szunyogh, I.: Efficient data assimilation for spatiotemporal chaos: a local ensemble transform Kalman filter, Physica D, 230, 112–126, doi:10.1016/j.physd.2006.11.008, 2007.; Kalman, R. E.: A new approach to linear filtering and prediction problems, J. Basic Eng.-T. ASME, 82, 35–45, doi:10.1115/1.3662552, 1960.; Kalnay, E.: Atmospheric Modeling, Data Assimilation and Predictability, Cambridge University Press, 2003.; Kelly, D. T. B., Law, K. J. H., and Stuart, A. M.: Well-posedness and accuracy of the ensemble Kalman filter in discrete and continuous time, Nonlinearity, 27, 2579–2603, doi:10.1088/0951-7715/27/10/2579, 2014.; Kwiatkow

 

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