• Burgers, G., , P. J. Van Leeuwen, , and G. Evensen, 1998: Analysis scheme in the ensemble Kalman filter. Mon. Wea. Rev, 126 , 17191724.

  • Cañizares, R., 1999: On the application of data assimilation in regional coastal models. Ph.D. thesis, Delft University of Technology, Delft Netherlands, 133 pp.

    • Search Google Scholar
    • Export Citation
  • Cohn, S. E., , and R. Todling, 1995: Approximate Kalman filters for unstable dynamics. Second Int. Symp. on Assimilation of Observations in Meteorology and Oceanography, Tokyo, Japan, WMO, 241–246.

    • Search Google Scholar
    • Export Citation
  • ——, and ——,. 1996: Approximate data assimilation schemes for stable and unstable dynamics. J. Meteor. Soc. Japan, 74 , 6375.

  • Dee, D. P., 1991: Simplification of the Kalman filter for meteorological data assimilation. Quart. J. Roy. Meteor. Soc, 117 , 365384.

  • Evensen, E., 1994: Sequential data assimilation with a nonlinear QG model using Monte Carlo methods to forecast error statistics. J. Geophys. Res, 99 , 10 14310 162.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., , and P. J. Van Leeuwen, 1996: Assimilation of geosat altimiter data for the agulhas current using the Ensemble Kalman filter with a quasigeostrophic model. Mon. Wea. Rev, 124 , 8596.

    • Search Google Scholar
    • Export Citation
  • Ghil, M., , and P. Malanotte-Rizzoli, 1991: Data assimilation in meteorology and oceanography. Advances in Geophysics, vol. 33, Academic Press, 141–266.

    • Search Google Scholar
    • Export Citation
  • Hammersley, J., , and D. Handscomb, 1964: Monte Carlo Methods. Wiley and Sons.

  • Heemink, A. W., , K. Bolding, , and M. Verlaan, 1997: Storm surge forecasting using Kalman filtering. J. Meteor. Soc. Japan, 75 , 305318.

  • Houtekamer, P. L., , and A. L. Mitchel, 1998: Data assimilation using ensemble Kalman filter technique. Mon. Wea. Rev, 126 , 796811.

  • Lermusiaux, P. F. J., 1997: Error subspace data assimilation methods for ocean field estimation: Theory, validation and applications. Ph. D. thesis, Harvard University, 402 pp.

    • Search Google Scholar
    • Export Citation
  • Maybeck, P. S., 1979: Stochastic Models, Estimation and Control. Vol. 141–1, Mathematics in Science and Engineering, Academic Press, 423 pp.

    • Search Google Scholar
    • Export Citation
  • Pham, D., , J. Verron, , and M. Rouband, 1998: A singular evolutive extended Kalman filter for data assimilation in oceanography. J. Mar. Syst, 16 , 323340.

    • Search Google Scholar
    • Export Citation
  • Verlaan, M., , and A. W. Heemink, 1995: Data assimilation schemes for non-linear shallow water flow models. Proc. Second Int. Symp. on Assimilation of Observations, Tokyo, Japan, WMO, 247–252.

    • Search Google Scholar
    • Export Citation
  • ——, and ——,. 1997: Tidal flow forecasting using reduced-rank square root filters. Stochastic Hydro. Hydraul, 11 , 349368.

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Variance Reduced Ensemble Kalman Filtering

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  • 1 Faculty of Information Technology and Systems, Department of Applied Mathematical Analysis, Delft University of Technology, Delft, Netherlands
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Abstract

A number of algorithms to solve large-scale Kalman filtering problems have been introduced recently. The ensemble Kalman filter represents the probability density of the state estimate by a finite number of randomly generated system states. Another algorithm uses a singular value decomposition to select the leading eigenvectors of the covariance matrix of the state estimate and to approximate the full covariance matrix by a reduced-rank matrix. Both algorithms, however, still require a huge amount of computer resources. In this paper the authors propose to combine the two algorithms and to use a reduced-rank approximation of the covariance matrix as a variance reductor for the ensemble Kalman filter. If the leading eigenvectors explain most of the variance, which is the case for most applications, the computational burden to solve the filtering problem can be reduced significantly (up to an order of magnitude).

Corresponding author address: A. W. Heemink, Delft University of Technology, Department of Applied Mathematical Analysis, Mekelweg 4, 2628 CD Delft, Netherlands. Email: a.w.heemink@math.tudelft.nl

Abstract

A number of algorithms to solve large-scale Kalman filtering problems have been introduced recently. The ensemble Kalman filter represents the probability density of the state estimate by a finite number of randomly generated system states. Another algorithm uses a singular value decomposition to select the leading eigenvectors of the covariance matrix of the state estimate and to approximate the full covariance matrix by a reduced-rank matrix. Both algorithms, however, still require a huge amount of computer resources. In this paper the authors propose to combine the two algorithms and to use a reduced-rank approximation of the covariance matrix as a variance reductor for the ensemble Kalman filter. If the leading eigenvectors explain most of the variance, which is the case for most applications, the computational burden to solve the filtering problem can be reduced significantly (up to an order of magnitude).

Corresponding author address: A. W. Heemink, Delft University of Technology, Department of Applied Mathematical Analysis, Mekelweg 4, 2628 CD Delft, Netherlands. Email: a.w.heemink@math.tudelft.nl

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