The High-Rank Ensemble Transform Kalman Filter
Abstract
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.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Jul 31, 2019
- Source ID
- 10.1175/mwr-d-18-0210.1
Entities
People
- Bo Huang
- Craig H Bishop
- Xuguang Wang
Organizations
- National Oceanic and Atmospheric Administration
- Office of Naval Research
- United States Naval Research Laboratory
- University of Melbourne
- University of Oklahoma