• \
    Start Submission Become a Reviewer

    Reading: Ensemble covariances adaptively localized with ECO-RAP. Part 1: tests on simple error models

    Download

     A- A+
    Alt. Display

    Original Research Papers

    Ensemble covariances adaptively localized with ECO-RAP. Part 1: tests on simple error models

    Authors:

    Craig H. Bishop ,

    Naval Research Laboratory, Marine Meteorology Division, 7 Grace Hopper Ave, Stop 2, Building 702, Room 212, Monterey, CA 93943-5502, US
    X close

    Daniel Hodyss

    Naval Research Laboratory, Marine Meteorology Division, 7 Grace Hopper Ave, Stop 2, Building 702, Room 212, Monterey, CA 93943-5502, US
    X close

    Abstract

    In atmospheric data assimilation (DA), observations over a 6–12-h time window are used to estimate the state. Nonadaptive moderation or localization functions are widely used in ensemble DA to reduce the amplitude of spurious ensemble correlations. These functions are inappropriate (1) if true error correlation functions move a comparable distance to the localization length scale over the time window and/or (2) if the widths of true error correlation functions are highly flow dependent. A method for generating localization functions that move with the true error correlation functions and that also adapt to the width of the true error correlation function is given. The method uses ensemble correlations raised to a power (ECO-RAP). A gallery of periodic one-dimensional error models is used to show how the method uses error propagation information and error correlation width information retained by powers of raw ensemble correlations to propagate and adaptively adjust the width of the localization function. It is found that ECORAP localization outperforms non-adaptive localization when the true errors are propagating or the error correlation length scale is varying and is as good as non-adaptive localization when such variations in error covariance structure are absent.In atmospheric data assimilation (DA), observations over a 6–12-h time window are used to estimate the state. Nonadaptive moderation or localization functions are widely used in ensemble DA to reduce the amplitude of spurious ensemble correlations. These functions are inappropriate (1) if true error correlation functions move a comparable distance to the localization length scale over the time window and/or (2) if the widths of true error correlation functions are highly flow dependent. A method for generating localization functions that move with the true error correlation functions and that also adapt to the width of the true error correlation function is given. The method uses ensemble correlations raised to a power (ECO-RAP). A gallery of periodic one-dimensional error models is used to show how the method uses error propagation information and error correlation width information retained by powers of raw ensemble correlations to propagate and adaptively adjust the width of the localization function. It is found that ECORAP localization outperforms non-adaptive localization when the true errors are propagating or the error correlation length scale is varying and is as good as non-adaptive localization when such variations in error covariance structure are absent.

    How to Cite: Bishop, C.H. and Hodyss, D., 2009. Ensemble covariances adaptively localized with ECO-RAP. Part 1: tests on simple error models. Tellus A: Dynamic Meteorology and Oceanography, 61(1), pp.84–96. DOI: http://doi.org/10.1111/j.1600-0870.2007.00371.x
      Published on 01 Jan 2009
    Peer Reviewed
     CC BY 4.0
     Accepted on 30 Sep 2008            Submitted on 17 Apr 2008

    References

    1. Anderson , J. L. 2007. Exploring the need for localization in ensemble data assimilation using a hierarchical ensemble filter. Physica D 230 , 99 - 111 .  

    2. Bishop , C. H. and Hodyss , D. 2007 . Flow adaptive moderation of spuri-ous ensemble correlations and its use in ensemble-based data assimi-lation . Quart. J. R. Meteor. Soc . 133 , 2029 – 2044 .  

    3. Bishop , C. H. and Hodyss , D. 2009 . Ensemble covariances adaptively localized with ECO-RAP. Part 2: a strategy for the atmosphere . Tellus 61A , 97 – 111 .  

    4. Bishop , C. H. , Etherton , B. J. and Majumdar , S. J. 2001 . Adaptive sam-pling with the ensemble transform Kalman Filter, part I: theoretical aspects. Mon. Wea. Rev . 129 , 420 - 436 .  

    5. Bishop , C. H. , Reynolds , C. A. and Tippett , M. K. 2003 . Optimization of the fixed observing network in a simple model. J. Atmos. Sci . 60 , 1471 - 1489 .  

    6. Bowler , N. E. 2006 . Comparison of error breeding, singular vectors, ran-dom perturbations and ensemble Kalman filter perturbation strategies on a simple model . Tellus 58A , 538 – 548 .  

    7. Cohn , S. E. 1997 . An introduction to estimation theory . J. Meteorol. Soc. Jpn . 1B , 257 – 288 .  

    8. Daley , R. 1991 . Atmospheric Data Analysis . Cambridge University Press , Cambridge , 457 pp .  

    9. Daley , R. 1992 . Forecast-error statistics for homogeneous and inhomo-geneous observation networks . Mon. Wea. Rev . 120 , 627 – 643 .  

    10. Eady , E. T. 1949 . Long waves and cyclone waves . Tellus 1 , 17 – 31 .  

    11. Evensen , G. 2003 . The ensemble Kalman filter: theoretical formulation and practical implementation . Ocean Dyn . 53 , 343 – 367 .  

    12. Gaspari , G. and Cohn , S. E. 1999 . Construction of correlation functions in two and three dimensions . Quart. J. R. MeteoroL Soc . 125 , 723 – 757 .  

    13. Hamill , T. M. , Whitaker , J. S. and Snyder , C. 2001 . Distance-dependent filtering of background error covariance estimates in an ensemble Kalman filter. Mon. Wea. Rev . 129 , 2776 - 2790 .  

    14. Houtekamer , P. L. and Mitchell , H. L. 1998 . Data assimilation using an ensemble Kalman Filter technique . Mon. Wea. Rev . 126 , 796 – 811 .  

    15. Houtekamer , P. L. , Mitchell , H. L. , Pellerin , G. , Buehner , M. Charron , M., and co-authors . 2005 . Atmospheric data assimilation with an ensemble Kalman Filter: results with real observations. Mon. Wea. Rev . 133 , 604 - 620 .  

    16. Hunt , B. R. , Kalnay , E. , Kostelich , E. , Ott , E. , Patil , D., and co-authors . 2004. Four-dimensional ensemble Kalman filtering. Tellus A 56 , 273 - 277 .  

    17. Khare , S. P. and Anderson , J. L. 2006 . An examination of ensemble filter based adaptive observation methodologies. Tellus 58A , 179 - 195 .  

    18. Khare , S. P. , Anderson , J. L. , Hoar , T. J. and Nychka , D . 2008 . An investigation into the application of an ensemble Kalman smoother to high-dimensional geophysical systems. Tellus 60A , 97 - 112 .  

    19. Lorene , A. C. 2003 . The potential of the ensemble Kalman filter for NWP-a comparison with 4D-VAR . Quart. J. R. MeteoroL Soc . 129 , 3183 – 3203 .  

    20. Lorenz , E. N. 1996 . ECMWF Seminar on Predictability Volume 1 , Read-ing , United Kingdom , 1 pp .  

    21. Majumdar , S. J. , Bishop , C. H. , Szunyogh , I., and Toth , Z . 2001 . Can an Ensemble Transform Kalman Filter predict the reduction in fore-cast error variance produced bytargeted observations? Quart. J. R. MeteoroL Soc . 127 , 2803 - 2820 .  

    22. Miyoshi , T. and Yamane , S. 2007 . Local ensemble transform Kalman filtering with an AGCM at a T159/L48 resolution . Mon. Wea. Rev . 135 , 3841 – 3861 .  

    23. Pedlosky , J. 1987 . Geophysical Fluid Dynamics . Springer-Verlag , New York , 710 pp .  

    24. Szunyogh , I. , Kostelic , E. J. , Gyarmati , G. , Kalnay , E. , Hunt , B. R. , and co-authors . 2008 . A local ensemble transform Kalman filter data assimilation system for the NCEP global model . Tellus 60A , 113 - 130 .  

    25. Whitaker , J. S. , Hamill , T. M. , Wei , X. , Song , Y. and Toth , Z. 2008 . Ensemble data assimilation with the NCEP Global Forecast System. Mon. Wea. Rev . 136 , 463 - 482 .  

    Jump to Discussions Related content
    comments powered by Disqus