The High-Rank Ensemble Transform Kalman Filter
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The High-Rank Ensemble Transform Kalman Filter

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Details:

  • Journal Title:
    Monthly Weather Review
  • Personal Author:
  • NOAA Program & Office:
    NWS (National Weather Service)
  • Description:
    The ensemble Kalman filter is typically implemented either by applying the localization on the background error covariance matrix (B-localization) or by inflating the observation error variances (R-localization). A mathematical demonstration suggests that for the same effective localization function, the background error covariance matrix from the B-localization method shows a higher rank than the R-localization method. The B-localization method is realized in the ensemble transform Kalman filter (ETKF) by extending the background ensemble perturbations through modulation (MP-localization). Specifically, the modulation functions are constructed from the leading eigenvalues and eigenvectors of the original B-localization matrix. Because of its higher rank than the classic R-localized ETKF, the B-/MP-localized ETKF is termed as the high-rank ETKF (HETKF). The performances of the HETKF and R-localized ETKF were compared through cycled data assimilation experiments using the Lorenz model II. The results show that the HETKF outperforms the R-localized ETKF especially for a small ensemble. The improved analysis in the HETKF is likely associated with the higher rank from the B-/MP-localization method, since its higher rank is expected to contribute more positively to alleviating the rank deficiency issue and thus improve the analysis for a small ensemble. The HETKF is less sensitive to the localization length scales and inflation factors. Furthermore, the experiments suggest that the above conclusion comparing the HETKF and R-localized ETKF does not depend on how the analyzed ensemble perturbations are subselected in the HETKF.
  • Keywords:
  • Source:
    Monthly Weather Review, 147(8), 3025-3043
  • DOI:
  • ISSN:
    0027-0644;1520-0493;
  • Format:
    PDF
  • Publisher:
    American Meteorological Society
  • Document Type:
    Journal Article
  • Funding:
    Grant no. NA15NWS4680022
  • Rights Information:
    Other
  • Compliance:
    Library
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