Editorial Type:
Article
Article Type:
Research Article

An Adaptive Compensatory Approach of the Fixed Localization in the EnKF

Xinrong Wu Key Laboratory of Marine Environmental Information Technology, State Oceanic Administration, National Marine Data and Information Service, Tianjin, China

Search for other papers by Xinrong Wu in
Current site
Google Scholar
PubMed Close
,
Wei Li Key Laboratory of Marine Environmental Information Technology, State Oceanic Administration, National Marine Data and Information Service, Tianjin, China

Search for other papers by Wei Li in
Current site
Google Scholar
PubMed Close
,
Guijun Han Key Laboratory of Marine Environmental Information Technology, State Oceanic Administration, National Marine Data and Information Service, Tianjin, China

Search for other papers by Guijun Han in
Current site
Google Scholar
PubMed Close
,
Lianxin Zhang Key Laboratory of Marine Environmental Information Technology, State Oceanic Administration, National Marine Data and Information Service, Tianjin, China

Search for other papers by Lianxin Zhang in
Current site
Google Scholar
PubMed Close
,
Caixia Shao Key Laboratory of Marine Environmental Information Technology, State Oceanic Administration, National Marine Data and Information Service, Tianjin, China

Search for other papers by Caixia Shao in
Current site
Google Scholar
PubMed Close
,
Chunjian Sun Key Laboratory of Marine Environmental Information Technology, State Oceanic Administration, National Marine Data and Information Service, Tianjin, China

Search for other papers by Chunjian Sun in
Current site
Google Scholar
PubMed Close
, and
Lili Xuan Key Laboratory of Marine Environmental Information Technology, State Oceanic Administration, National Marine Data and Information Service, Tianjin, China

Search for other papers by Lili Xuan in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Nov 2015
DOI:
https://doi.org/10.1175/MWR-D-15-0060.1
Page(s):
4714–4735
Restricted access

Abstract

Although the fixed covariance localization in the ensemble Kalman filter (EnKF) can significantly increase the reliability of background error covariance, it has been demonstrated that extreme impact radii can cause the EnKF to lose some useful information. Tuning an optimal impact radius, on the other hand, is always difficult for a general circulation model. The EnKF multiscale analysis (MSA) approach was presented to make up for the above-mentioned drawback of the fixed localization. As a follow-up, this study presents an adaptive compensatory approach to further improve the performance of the EnKF-MSA. The new method adaptively triggers a multigrid analysis (MGA) to extract multiscale information from the observational residual after the EnKF without inflation is completed at each analysis step. Within a biased twin experiment framework consisting of a barotropic spectral model and an idealized observing system, the performance of the adaptive method is examined. Results show that the MGA reduces the computational cost of the MSA by 93%. On the assimilation quality, the adaptive method has an incremental improvement over the EnKF-MSA. That is, the adaptive EnKF-MGA reduces to the EnKF without inflation, which is better than the EnKF-MSA, for moderate impact radii. The proposed scheme works for a broader range of impact radii than the standard EnKF (i.e., the EnKF with inflation). For extreme impact radii, the adaptive EnKF-MGA can produce smaller assimilation errors than the standard EnKF and shorten the spinup period by 53%. In addition, the computational cost of the MGA is negligible relative to that of the standard EnKF.

Corresponding author address: Xinrong Wu, 93 Liuwei Road, Hedong District, Tianjin 300171, China. E-mail: xinrong_wu@yahoo.com

Abstract

Although the fixed covariance localization in the ensemble Kalman filter (EnKF) can significantly increase the reliability of background error covariance, it has been demonstrated that extreme impact radii can cause the EnKF to lose some useful information. Tuning an optimal impact radius, on the other hand, is always difficult for a general circulation model. The EnKF multiscale analysis (MSA) approach was presented to make up for the above-mentioned drawback of the fixed localization. As a follow-up, this study presents an adaptive compensatory approach to further improve the performance of the EnKF-MSA. The new method adaptively triggers a multigrid analysis (MGA) to extract multiscale information from the observational residual after the EnKF without inflation is completed at each analysis step. Within a biased twin experiment framework consisting of a barotropic spectral model and an idealized observing system, the performance of the adaptive method is examined. Results show that the MGA reduces the computational cost of the MSA by 93%. On the assimilation quality, the adaptive method has an incremental improvement over the EnKF-MSA. That is, the adaptive EnKF-MGA reduces to the EnKF without inflation, which is better than the EnKF-MSA, for moderate impact radii. The proposed scheme works for a broader range of impact radii than the standard EnKF (i.e., the EnKF with inflation). For extreme impact radii, the adaptive EnKF-MGA can produce smaller assimilation errors than the standard EnKF and shorten the spinup period by 53%. In addition, the computational cost of the MGA is negligible relative to that of the standard EnKF.

Corresponding author address: Xinrong Wu, 93 Liuwei Road, Hedong District, Tianjin 300171, China. E-mail: xinrong_wu@yahoo.com
Save
Cover Monthly Weather Review
Monthly Weather Review

  • Anderson, J. L., 2001: An ensemble adjustment Kalman filter for data assimilation. Mon. Wea. Rev., 129, 2884–2903, doi:10.1175/1520-0493(2001)129<2884:AEAKFF>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Anderson, J. L., 2007: Exploring the need for localization in ensemble data assimilation using a hierarchical ensemble filter. Physica D, 230, 99–111, doi:10.1016/j.physd.2006.02.011.

    • Search Google Scholar
    • Export Citation

  • Anderson, J. L., 2008: Spatially and temporally varying adaptive covariance inflation for ensemble filters. Tellus, 61A, 72–83, doi:10.1111/j.1600-0870.2008.00361.x.

    • Search Google Scholar
    • Export Citation

  • Anderson, J. L., and S. L. Anderson, 1999: A Monte Carlo implementation of the nonlinear filtering problem to produce ensemble assimilations and forecasts. Mon. Wea. Rev., 127, 2741–2758, doi:10.1175/1520-0493(1999)127<2741:AMCIOT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Anderson, J. L., and L. L. Lei, 2013: Empirical localization of observation impact in ensemble Kalman filters. Mon. Wea. Rev., 141, 4140–4153, doi:10.1175/MWR-D-12-00330.1.

    • Search Google Scholar
    • Export Citation

  • Asselin, R., 1972: Frequency filter for time integrations. Mon. Wea. Rev., 100, 487–490, doi:10.1175/1520-0493(1972)100<0487:FFFTI>2.3.CO;2.

    • Search Google Scholar
    • Export Citation

  • Berre, L., and G. Desroziers, 2010: Filtering of background error variance and correlations by local spatial averaging: A review. Mon. Wea. Rev., 138, 3693–3720, doi:10.1175/2010MWR3111.1.

    • Search Google Scholar
    • Export Citation

  • Bishop, C. H., and D. Hodyss, 2007: Flow adaptive moderation of spurious ensemble correlations and its use in ensemble-based data assimilation. Quart. J. Roy. Meteor. Soc., 133, 2029–2044, doi:10.1002/qj.169.

    • Search Google Scholar
    • Export Citation

  • Bishop, C. H., and D. Hodyss, 2009a: Ensemble covariances adaptively localized with ECO-RAP. Part 1: Tests on simple error models. Tellus, 61A, 84–96, doi:10.1111/j.1600-0870.2008.00371.x.

    • Search Google Scholar
    • Export Citation

  • Bishop, C. H., and D. Hodyss, 2009b: Ensemble covariances adaptively localized with ECO-RAP. Part 2: A strategy for the atmosphere. Tellus, 61A, 97–111, doi:10.1111/j.1600-0870.2008.00372.x.

    • Search Google Scholar
    • Export Citation

  • Bishop, C. H., and D. Hodyss, 2011: Adaptive ensemble covariance localization in ensemble 4D-VAR state estimation. Mon. Wea. Rev., 139, 1241–1255, doi:10.1175/2010MWR3403.1.

    • Search Google Scholar
    • Export Citation

  • Bishop, C. H., D. Hodyss, P. Steinle, H. Sims, A. M. Clayton, A. C. Lorenc, D. M. Barker, and M. Buehner, 2011: Efficient ensemble covariance localization in variational data assimilation. Mon. Wea. Rev., 139, 573–580, doi:10.1175/2010MWR3405.1.

    • Search Google Scholar
    • Export Citation

  • Briggs, W. L., V. E. Henson, and S. F. McCormick, 2000: A Multigrid Tutorial. 2nd ed. Society for Industrial and Applied Mathematics, 193 pp.

    • Search Google Scholar
    • Export Citation

  • Evensen, G., 2007: Data Assimilation: The Ensemble Kalman Filter. Springer, 187 pp.

  • Gaspari, G., and S. E. Cohn, 1999: Construction of correlation functions in two and three dimensions. Quart. J. Roy. Meteor. Soc., 125, 723–757, doi:10.1002/qj.49712555417.

    • Search Google Scholar
    • Export Citation

  • Greybush, S. J., E. Kalnay, T. Miyoshi, K. Ide, and B. R. Hunt, 2011: Balance and ensemble Kalman filter localization techniques. Mon. Wea. Rev., 139, 511–522, doi:10.1175/2010MWR3328.1.

    • Search Google Scholar
    • Export Citation

  • Haltiner, G. J., and R. T. Williams, 1980: Numerical Prediction and Dynamic Meteorology. 2nd ed. Wiley, 477 pp.

  • Hamill, T. M., J. S. Whitaker, and C. Snyder, 2001: Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter. Mon. Wea. Rev., 129, 2776–2790, doi:10.1175/1520-0493(2001)129<2776:DDFOBE>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Houtekamer, P. L., and H. L. Mitchell, 1998: Data assimilation using an ensemble Kalman filter technique. Mon. Wea. Rev., 126, 796–811, doi:10.1175/1520-0493(1998)126<0796:DAUAEK>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Houtekamer, P. L., H. L. Mitchell, and X. Deng, 2009: Model error representation in an operational ensemble Kalman filter. Mon. Wea. Rev., 137, 2126–2143, doi:10.1175/2008MWR2737.1.

    • Search Google Scholar
    • Export Citation

  • Hunt, B. R., E. J. Kostelich, and I. Szunyogh, 2007: 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.

    • Search Google Scholar
    • Export Citation

  • Jun, M., I. Szunyogh, M. G. Genton, F. Zhang, and C. H. Bishop, 2011: A statistical investigation of the sensitivity of ensemble-based Kalman filters to covariance filtering. Mon. Wea. Rev., 139, 3036–3051, doi:10.1175/2011MWR3577.1.

    • Search Google Scholar
    • Export Citation

  • Lei, L. L., and J. L. Anderson, 2014: Empirical localization of observations for serial ensemble Kalman filter data assimilation in an atmospheric general circulation model. Mon. Wea. Rev., 142, 1835–1851, doi:10.1175/MWR-D-13-00288.1.

    • Search Google Scholar
    • Export Citation

  • Li, W., Y. Xie, Z. He, G. Han, K. Liu, J. Ma, and D. Li, 2008: Application of the multigrid data assimilation scheme to the China Seas’ temperature forecast. J. Atmos. Oceanic Technol., 25, 2106–2116, doi:10.1175/2008JTECHO510.1.

    • Search Google Scholar
    • Export Citation

  • Li, W., Y. Xie, S.-M. Deng, and Q. Wang, 2010: Application of the multigrid method to the two-dimensional Doppler radar radial velocity data assimilation. J. Atmos. Oceanic Technol., 27, 319–332, doi:10.1175/2009JTECHA1271.1.

    • Search Google Scholar
    • Export Citation

  • Liu, D. C., and J. Nocedal, 1989: On the limited memory BFGS method for large scale optimization. Math. Program., 45, 503–528, doi:10.1007/BF01589116.

    • Search Google Scholar
    • Export Citation

  • Mitchell, H. L., P. L. Houtekamer, and G. Pellerin, 2002: Ensemble size, balance, and model-error representation in an ensemble Kalman filter. Mon. Wea. Rev., 130, 2791–2808, doi:10.1175/1520-0493(2002)130<2791:ESBAME>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Miyoshi, T., 2011: The Gaussian approach to adaptive covariance inflation and its implementation with the local ensemble transform Kalman filter. Mon. Wea. Rev., 139, 1519–1535, doi:10.1175/2010MWR3570.1.

    • Search Google Scholar
    • Export Citation

  • Miyoshi, T., and K. Kondo, 2013: A multi-scale localization approach to an ensemble Kalman filter. SOLA, 9, 170–173, doi:10.2151/sola.2013-038.

    • Search Google Scholar
    • Export Citation

  • Ott, E., and Coauthors, 2004: A local ensemble Kalman filter for atmospheric data assimilation. Tellus, 56A, 415–428, doi:10.1111/j.1600-0870.2004.00076.x.

    • Search Google Scholar
    • Export Citation

  • Robert, A., 1969: The integration of a spectral model of the atmosphere by the implicit method. Proc. WMO/IUGG Symp. on Numerical Weather Prediction, Tokyo, Japan, Japan Meteorological Society, 19–24.

  • Szunyogh, I., E. J. Kostelich, G. Gyarmati, E. Kalnay, B. R. Hunt, E. Ott, E. Satterfield, and J. A. Yorke, 2008: A local ensemble transform Kalman filter data assimilation system for the NCEP global model. Tellus, 60A, 113–130, doi:10.1111/j.1600-0870.2007.00274.x.

    • Search Google Scholar
    • Export Citation

  • Wu, X., W. Li, G. Han, S. Zhang, and X. Wang, 2014: A compensatory approach of the fixed localization in EnKF. Mon. Wea. Rev., 142, 3713–3733, doi:10.1175/MWR-D-13-00369.1.

    • Search Google Scholar
    • Export Citation

  • Xie, Y., S. Koch, J. McGinley, S. Albers, P. E. Bieringer, M. Wolfson, and M. Chan, 2011: A space–time multi-scale analysis system: A sequential variational analysis approach. Mon. Wea. Rev., 139, 1224–1240, doi:10.1175/2010MWR3338.1.

    • Search Google Scholar
    • Export Citation

  • Yang, S.-C., E. Kalnay, and B. R. Hunt, 2012: Handling nonlinearity in an ensemble Kalman filter: Experiments with the three-variable Lorenz model. Mon. Wea. Rev., 140, 2628–2646, doi:10.1175/MWR-D-11-00313.1.

    • Search Google Scholar
    • Export Citation

  • Zhang, F., C. Snyder, and J. Sun, 2004: Impacts of initial estimate and observation availability on convective-scale data assimilation with ensemble Kalman filter. Mon. Wea. Rev., 132, 1238–1253, doi:10.1175/1520-0493(2004)132<1238:IOIEAO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Zhang, S., J. L. Anderson, A. Rosati, M. J. Harrison, S. P. Khare, and A. Wittenberg, 2004: Multiple time level adjustment for data assimilation. Tellus, 56A, 2–15, doi:10.1111/j.1600-0870.2004.00040.x.

    • Search Google Scholar
    • Export Citation
All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 575 214 14
PDF Downloads 173 57 1