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

  • Anderson, J. L., 2007a: Exploring the need for localization in ensemble data assimilation using a hierarchical ensemble filter. Physica D, 230, 99111.

    • Search Google Scholar
    • Export Citation
  • Anderson, J. L., 2007b: An adaptive covariance inflation error correction algorithm for ensemble filters. Tellus, 59A, 210224.

  • Anderson, J. L., 2009: Spatially and temporally varying adaptive covariance inflation for ensemble filters. Tellus, 61A, 7283.

  • 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
  • Anderson, J. L., , T. Hoar, , K. Raeder, , H. Liu, , N. Collins, , R. Torn, , and A. Avellano, 2009: The Data Assimilation Research Testbed: A community facility. Bull. Amer. Meteor. Soc., 90, 12831296.

    • 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, 8496.

    • 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, 97111.

    • Search Google Scholar
    • Export Citation
  • Bishop, C. H., , B. J. Etherton, , and S. J. Majumdar, 2001: Adaptive sampling with the ensemble transform Kalman filter. Part I: Theoretical aspects. Mon. Wea. Rev., 129, 420436.

    • Search Google Scholar
    • Export Citation
  • Bonavita, M., , L. Torrisi, , and F. Marcucci, 2008: The ensemble Kalman filter in an operational regional NWP system: Preliminary results with real observations. Quart. J. Roy. Meteor. Soc., 134, 17331744.

    • Search Google Scholar
    • Export Citation
  • Bonavita, M., , L. Torrisi, , and F. Marcucci, 2010: Ensemble data assimilation with the CNMCA regional forecasting system. Quart. J. Roy. Meteor. Soc., 136, 11321145.

    • Search Google Scholar
    • Export Citation
  • Bowler, N. E., , A. Arribas, , K. R. Mylne, , K. B. Robertson, , and S. E. Beare, 2008: The MOGREPS short-range ensemble prediction system. Quart. J. Roy. Meteor. Soc., 134, 703722.

    • Search Google Scholar
    • Export Citation
  • Campbell, W. F., , C. H. Bishop, , and D. Hodyss, 2010: Vertical covariance localization for satellite radiances in ensemble Kalman filters. Mon. Wea. Rev., 138, 282290.

    • Search Google Scholar
    • Export Citation
  • Daley, R., 1992: Estimating model-error covariances for application to atmospheric data assimilation. Mon. Wea. Rev., 120, 17351746.

  • Desroziers, G., , L. Berre, , B. Chapnik, , and P. Poli, 2005: Diagnosis of observation, background and analysis-error statistics in observation space. Quart. J. Roy. Meteor. Soc., 131, 33853396.

    • Search Google Scholar
    • Export Citation
  • Evensen, G., 1994: Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophys. Res., 99 (C5), 10 14310 162.

    • Search Google Scholar
    • Export Citation
  • Fertig, E. J., , B. R. Hunt, , E. Ott, , and I. Szunyogh, 2007: Assimilating non-local observations with a local ensemble Kalman filter. Tellus, 59A, 719730.

    • Search Google Scholar
    • Export Citation
  • Fertig, E. J., and Coauthors, 2009: Observation bias correction with an ensemble Kalman filter. Tellus, 61A, 210226.

  • Gaspari, G., , and S. E. Cohn, 1999: Construction of correlation functions in two and three dimensions. Quart. J. Roy. Meteor. Soc., 125, 723757.

    • 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, 511522.

    • 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
  • Harlim, J., , and B. R. Hunt, 2007: Four-dimensional local ensemble transform Kalman filter: Numerical experiments with a global circulation model. Tellus, 59A, 731748.

    • 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
  • Houtekamer, P. L., , H. K. Mitchell, , and X. Deng, 2009: Model error representation in an operational ensemble Kalman filter. Mon. Wea. Rev., 137, 21262143.

    • 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, 112126.

    • Search Google Scholar
    • Export Citation
  • Kang, J.-S., 2009: Carbon cycle data assimilation using a coupled atmosphere-vegetation model and the local ensemble transform Kalman filter. Ph.D. dissertation, University of Maryland, College Park, 164 pp.

    • Search Google Scholar
    • Export Citation
  • Kang, J.-S., , E. Kalnay, , J. Liu, , I. Fung, , T. Miyoshi, , and K. Ide, 2011: “Variable localization” in an Ensemble Kalman Filter: Application to the carbon cycle data assimilation. J. Geophys. Res., in press.

    • Search Google Scholar
    • Export Citation
  • Li, H., , E. Kalnay, , and T. Miyoshi, 2009: Simultaneous estimation of covariance inflation and observation errors within an ensemble Kalman filter. Quart. J. Roy. Meteor. Soc., 135, 523533.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E., 1996: Predictability: A problem partly solved. Proc. ECMWF Seminar on Predictability, Vol. 1, Reading, United Kingdom, ECMWF, 1–18.

    • Search Google Scholar
    • Export Citation
  • Lorenz, E., , and K. Emanuel, 1998: Optimal sites for supplementary weather observations: Simulation with a small model. J. Atmos. Sci., 55, 399414.

    • Search Google Scholar
    • Export Citation
  • Mitchell, H. L., , and P. L. Houtekamer, 2009: Ensemble Kalman filter configurations and their performance with the logistic map. Mon. Wea. Rev., 137, 43254343.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., 2005: Ensemble Kalman filter experiments with a primitive-equation global model. Ph.D. dissertation, University of Maryland, College Park, 197 pp.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., , and S. Yamane, 2007: Local ensemble transform Kalman filtering with an AGCM at a T159/L48 resolution. Mon. Wea. Rev., 135, 38413861.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., , S. Yamane, , and T. Enomoto, 2007: Localizing the error covariance by physical distances within a local ensemble transform Kalman filter (LETKF). SOLA, 3, 8992, doi:10.2151/sola.2007-023.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., , Y. Sato, , and T. Kadowaki, 2010: Ensemble Kalman filter and 4D-Var intercomparison with the Japanese operational global analysis and prediction system. Mon. Wea. Rev., 138, 28462866.

    • Search Google Scholar
    • Export Citation
  • Miyoshi, T., , and M. Kunii, 2011: The local ensemble transform Kalman filter with the Weather Research and Forecasting model: Experiments with real observations. Pure Appl. Geophys., in press.

    • Search Google Scholar
    • Export Citation
  • Molteni, F., 2003: Atmospheric simulations using a GCM with simplified physical parametrizations. I: Model climatology and variability in multi-decadal experiments. Climate Dyn., 20, 175191.

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

  • Szunyogh, I., , E. J. Kostelich, , G. Gyarmati, , D. J. Patil, , B. R. Hunt, , E. Kalnay, , E. Ott, , and J. A. Yorke, 2005: Assessing a local ensemble Kalman filter: Perfect model experiments with the National Centers for Environmental Prediction global model. Tellus, 57A, 528545.

    • Search Google Scholar
    • Export Citation
  • 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, 113130.

    • Search Google Scholar
    • Export Citation
  • Torn, R. D., 2010a: Ensemble-based sensitivity analysis applied to African Easterly Waves. Wea. Forecasting, 25, 6178.

  • Torn, R. D., 2010b: Performance of a mesoscale ensemble Kalman filter (EnKF) during the NOAA high-resolution hurricane test. Mon. Wea. Rev., 138, 43754392.

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

  • Whitaker, J. S., , T. M. Hamill, , X. Wei, , Y. Song, , and Z. Toth, 2008: Ensemble data assimilation with the NCEP Global Forecast System. Mon. Wea. Rev., 136, 463482.

    • 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, 12381253.

    • Search Google Scholar
    • Export Citation
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The Gaussian Approach to Adaptive Covariance Inflation and Its Implementation with the Local Ensemble Transform Kalman Filter

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  • 1 Department of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, Maryland
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Abstract

In ensemble Kalman filters, the underestimation of forecast error variance due to limited ensemble size and other sources of imperfection is commonly treated by empirical covariance inflation. To avoid manual optimization of multiplicative inflation parameters, previous studies proposed adaptive inflation approaches using observations. Anderson applied Bayesian estimation theory to the probability density function of inflation parameters. Alternatively, Li et al. used the innovation statistics of Desroziers et al. and applied a Kalman filter analysis update to the inflation parameters based on the Gaussian assumption. In this study, Li et al.’s Gaussian approach is advanced to include the variance of the estimated inflation as derived from the central limit theorem. It is shown that the Gaussian approach is an accurate approximation of Anderson’s general Bayesian approach. An advanced implementation of the Gaussian approach with the local ensemble transform Kalman filter is proposed, where the adaptive inflation parameters are computed simultaneously with the ensemble transform matrix at each grid point. The spatially and temporally varying adaptive inflation technique is implemented with the Lorenz 40-variable model and a low-resolution atmospheric general circulation model; numerical experiments show promising results both with and without model errors.

Corresponding author address: Takemasa Miyoshi, Department of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, MD 20742. E-mail: miyoshi@atmos.umd.edu

Abstract

In ensemble Kalman filters, the underestimation of forecast error variance due to limited ensemble size and other sources of imperfection is commonly treated by empirical covariance inflation. To avoid manual optimization of multiplicative inflation parameters, previous studies proposed adaptive inflation approaches using observations. Anderson applied Bayesian estimation theory to the probability density function of inflation parameters. Alternatively, Li et al. used the innovation statistics of Desroziers et al. and applied a Kalman filter analysis update to the inflation parameters based on the Gaussian assumption. In this study, Li et al.’s Gaussian approach is advanced to include the variance of the estimated inflation as derived from the central limit theorem. It is shown that the Gaussian approach is an accurate approximation of Anderson’s general Bayesian approach. An advanced implementation of the Gaussian approach with the local ensemble transform Kalman filter is proposed, where the adaptive inflation parameters are computed simultaneously with the ensemble transform matrix at each grid point. The spatially and temporally varying adaptive inflation technique is implemented with the Lorenz 40-variable model and a low-resolution atmospheric general circulation model; numerical experiments show promising results both with and without model errors.

Corresponding author address: Takemasa Miyoshi, Department of Atmospheric and Oceanic Science, University of Maryland, College Park, College Park, MD 20742. E-mail: miyoshi@atmos.umd.edu
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