• Anderson, J. L., 2001: An ensemble adjustment Kalman filter for data assimilation. Mon. Wea. Rev., 129 , 28842903.

  • 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 , 27412758.

    • Search Google Scholar
    • Export Citation
  • Bouttier, F., 1994: A dynamical estimation of forecast error covariances in an assimilation system. Mon. Wea. Rev., 122 , 23762390.

  • Charron, M., P. L. Houtekamer, and P. Bartello, 2006: Assimilation with an ensemble Kalman filter of synthetic radial wind data in anisotropic turbulence: Perfect model experiments. Mon. Wea. Rev., 134 , 618637.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 1992: Using the extended Kalman filter with a multilayer quasi-geostrophic ocean model. J. Geophys. Res., 97 , (C11). 1790517924.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 2003: The ensemble Kalman filter:Theoretical formulation and practical implementation. Ocean Dyn., 53 , 343367.

  • Furrer, R., and T. Bengtsson, 2007: Estimation of high-dimensional prior and posterior covariance matrices in Kalman filter variants. J. Multivariate Anal., 98 , 227255.

    • Search Google Scholar
    • Export Citation
  • Gauthier, P., P. Courtier, and P. Moll, 1993: Assimilation of simulated wind lidar data with a Kalman filter. Mon. Wea. Rev., 121 , 18031820.

    • Search Google Scholar
    • Export Citation
  • Hamill, T. M., and C. Snyder, 2000: A hybrid ensemble Kalman filter—3D variational analysis scheme. Mon. Wea. Rev., 128 , 29052919.

  • Hamill, T. M., and J. S. Whitaker, 2005: Accounting for the error due to unresolved scales in ensemble data assimilation: A comparison of different approaches. Mon. Wea. Rev., 133 , 31323147.

    • Search Google Scholar
    • Export Citation
  • 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 , 27762790.

    • 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 , 796811.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., and H. L. Mitchell, 2001: A sequential ensemble Kalman filter for atmospheric data assimilation. Mon. Wea. Rev., 129 , 123137.

    • Search Google Scholar
    • Export Citation
  • Houtekamer, P. L., and H. L. Mitchell, 2005: Ensemble Kalman filtering. Quart. J. Roy. Meteor. Soc., 131 , 32693289.

  • Houtekamer, P. L., H. L. Mitchell, G. Pellerin, M. Buehner, M. Charron, L. Spacek, and B. Hansen, 2005: Atmospheric data assimilation with an ensemble Kalman filter: Results with real observations. Mon. Wea. Rev., 133 , 604620.

    • Search Google Scholar
    • Export Citation
  • Karspeck, A. R., and J. L. Anderson, 2007: Experimental implementation of an ensemble adjustment filter for an intermediate ENSO model. J. Climate, 20 , 46384658.

    • Search Google Scholar
    • Export Citation
  • Lawson, W. G., and J. A. Hansen, 2004: Implications of stochastic and deterministic filters as ensemble-based data assimilation methods in varying regimes of error growth. Mon. Wea. Rev., 132 , 19661981.

    • 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 , 27912808.

    • Search Google Scholar
    • Export Citation
  • Orszag, S. A., 1971: Numerical simulation of incompressible flow within simple boundaries (I). Galerkin (spectral) representations. Stud. Appl. Math., 50 , 293327.

    • Search Google Scholar
    • Export Citation
  • Ott, E., and Coauthors, 2004: A local ensemble Kalman filter for atmospheric data assimilation. Tellus, 56A , 415428.

  • Pham, D. T., J. Verron, and M. C. Roubaud, 1998: A singular evolutive extended Kalman filter for data assimilation in oceanography. J. Mar. Syst., 16 , 323340.

    • Search Google Scholar
    • Export Citation
  • Sacher, W., and P. Bartello, 2008: Sampling errors in ensemble Kalman filtering. Part I: Theory. Mon. Wea. Rev., 136 , 30353049.

  • Smith, L. A., and J. A. Hansen, 2004: Extending the limits of ensemble forecast verification with the minimum spanning tree. Mon. Wea. Rev., 132 , 15221528.

    • Search Google Scholar
    • Export Citation
  • Snyder, C., and F. Zhang, 2003: Assimilation of simulated Doppler radar observations with an ensemble Kalman filter. Mon. Wea. Rev., 131 , 16631677.

    • Search Google Scholar
    • Export Citation
  • Tanguay, M., P. Bartello, and P. Gauthier, 1995: Four-dimensional data assimilation with a wide range of scales. Tellus, 47A , 974997.

    • Search Google Scholar
    • Export Citation
  • Tippett, M. K., J. L. Anderson, C. H. Bishop, T. M. Hamill, and J. Whitaker, 2003: Ensemble square root filters. Mon. Wea. Rev., 131 , 14851490.

    • Search Google Scholar
    • Export Citation
  • Tong, M., and M. Xue, 2005: Ensemble Kalman filter assimilation of Doppler radar data with a compressible nonhydrostatic model: OSS experiments. Mon. Wea. Rev., 133 , 17891807.

    • Search Google Scholar
    • Export Citation
  • van Leeuwen, P. J., 1999: Comments on “Data assimilation using an ensemble Kalman filter technique.”. Mon. Wea. Rev., 127 , 13741377.

    • Search Google Scholar
    • Export Citation
  • Whitaker, J. S., and T. M. Hamill, 2002: Ensemble data assimilation without perturbed observations. Mon. Wea. Rev., 130 , 19131924.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 174 174 174
PDF Downloads 0 0 0

Sampling Errors in Ensemble Kalman Filtering. Part II: Application to a Barotropic Model

View More View Less
  • 1 McGill University, Montréal, Québec, Canada
Restricted access

Abstract

In the current study, the authors are concerned with the comparison of the average performance of stochastic versions of the ensemble Kalman filter with and without covariance inflation, as well as the double ensemble Kalman filter. The theoretical results obtained in Part I of this study are confronted with idealized simulations performed with a perfect barotropic quasigeostrophic model. Results obtained are very consistent with the analytic expressions found in Part I. It is also shown that both the double ensemble Kalman filter and covariance inflation techniques can avoid filter divergence. Nevertheless, covariance inflation gives efficient results in terms of accuracy and reliability for a much lower computational cost than the double ensemble Kalman filter and for smaller ensemble sizes.

Corresponding author address: William Sacher, Atmospheric and Oceanic Sciences Department, McGill University, 805 Sherbrooke St. West, Montreal, QC H3A 2K6, Canada. Email: william.sacher@mail.mcgill.ca

Abstract

In the current study, the authors are concerned with the comparison of the average performance of stochastic versions of the ensemble Kalman filter with and without covariance inflation, as well as the double ensemble Kalman filter. The theoretical results obtained in Part I of this study are confronted with idealized simulations performed with a perfect barotropic quasigeostrophic model. Results obtained are very consistent with the analytic expressions found in Part I. It is also shown that both the double ensemble Kalman filter and covariance inflation techniques can avoid filter divergence. Nevertheless, covariance inflation gives efficient results in terms of accuracy and reliability for a much lower computational cost than the double ensemble Kalman filter and for smaller ensemble sizes.

Corresponding author address: William Sacher, Atmospheric and Oceanic Sciences Department, McGill University, 805 Sherbrooke St. West, Montreal, QC H3A 2K6, Canada. Email: william.sacher@mail.mcgill.ca

Save