On Some Aspects of the Definition of Initial Conditions for Ensemble Prediction

L. Descamps Laboratoire de Météorologie Dynamique, Ecole Normale Supérieure, CNRS, UPMC, Paris, France

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O. Talagrand Laboratoire de Météorologie Dynamique, Ecole Normale Supérieure, CNRS, UPMC, Paris, France

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Abstract

Four methods for initialization of ensemble forecasts are systematically compared, namely the methods of singular vectors (SV) and bred modes (BM), as well as the ensemble Kalman filter (EnKF) and the ensemble transform Kalman filter (ETKF). The comparison is done on synthetic data with two models of the flow, namely, a low-order model introduced by Lorenz and a three-level quasigeostrophic atmospheric model. For the latter, both cases of a perfect and an imperfect model are considered. The performance of the various initialization methods is assessed in terms of the statistical reliability and resolution of the ensuing predictions. The relative performance of the four methods, which is statistically significant to a range of about 6 days, is in the order EnKF > ETKF > BM > SV. The difference between the former two methods and the latter two is on the whole more significant than the differences between EnKF and ETKF, or between BM and SV separately. The general conclusion is that, if the quality of ensemble predictions is assessed by the degree to which the predicted ensembles statistically sample the uncertainty on the future state of the flow, the best initial ensembles are those that best statistically sample the uncertainty on the present state of the flow.

Corresponding author address: L. Descamps, Laboratoire de Météorologie Dynamique, Ecole Normale Supérieure, CNRS, UPMC, EP, 24 rue Lhomond, 75231 Paris, CEDEX 05, France. Email: descamps@lmd.ens.fr

Abstract

Four methods for initialization of ensemble forecasts are systematically compared, namely the methods of singular vectors (SV) and bred modes (BM), as well as the ensemble Kalman filter (EnKF) and the ensemble transform Kalman filter (ETKF). The comparison is done on synthetic data with two models of the flow, namely, a low-order model introduced by Lorenz and a three-level quasigeostrophic atmospheric model. For the latter, both cases of a perfect and an imperfect model are considered. The performance of the various initialization methods is assessed in terms of the statistical reliability and resolution of the ensuing predictions. The relative performance of the four methods, which is statistically significant to a range of about 6 days, is in the order EnKF > ETKF > BM > SV. The difference between the former two methods and the latter two is on the whole more significant than the differences between EnKF and ETKF, or between BM and SV separately. The general conclusion is that, if the quality of ensemble predictions is assessed by the degree to which the predicted ensembles statistically sample the uncertainty on the future state of the flow, the best initial ensembles are those that best statistically sample the uncertainty on the present state of the flow.

Corresponding author address: L. Descamps, Laboratoire de Météorologie Dynamique, Ecole Normale Supérieure, CNRS, UPMC, EP, 24 rue Lhomond, 75231 Paris, CEDEX 05, France. Email: descamps@lmd.ens.fr

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  • Anderson, J. L., 1997: Impact of dynamical constraints on the selection of initial conditions for ensemble predictions: Low-order perfect model results. Mon. Wea. Rev., 125 , 29692983.

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

    • Search Google Scholar
    • Export Citation
  • Bowler, N., 2006: Comparison of error breeding, singular vectors, random perturbations and ensemble Kalman filter perturbation strategies on a simple model. Tellus, 58A , 538548.

    • Search Google Scholar
    • Export Citation
  • Buizza, R., and T. N. Palmer, 1995: The singular-vector structure of the atmospheric global circulation. J. Atmos. Sci., 52 , 14341456.

    • Search Google Scholar
    • Export Citation
  • Buizza, R., M. Miller, and T. N. Palmer, 1999: Stochastic representation of model uncertainties in the ECMWF Ensemble Prediction System. Quart. J. Roy. Meteor. Soc., 125 , 28872908.

    • Search Google Scholar
    • Export Citation
  • Buizza, R., P. Houtekamer, Z. Toth, G. Pellerin, M. Wei, and Y. Zhu, 2005: A comparison of the ECMWF, MSC, and NCEP global ensemble prediction systems. Mon. Wea. Rev., 133 , 10761097.

    • Search Google Scholar
    • Export Citation
  • Candille, G., and O. Talagrand, 2005: Evaluation of probabilistic prediction systems for a scalar variable. Quart. J. Roy. Meteor. Soc., 131 , 21312150.

    • Search Google Scholar
    • Export Citation
  • Candille, G., C. Côté, P. Houtekamer, and G. Pellerin, 2007: Verification of an ensemble prediction system against observations. Mon. Wea. Rev., 135 , 26882699.

    • Search Google Scholar
    • Export Citation
  • Ehrendorfer, M., 1994a: The Liouville equation and its potential usefulness for the prediction of forecast skill. Part I: Theory. Mon. Wea. Rev., 122 , 703713.

    • Search Google Scholar
    • Export Citation
  • Ehrendorfer, M., 1994b: The Liouville equation and its potential usefulness for the prediction of forecast skill. Part II: Applications. Mon. Wea. Rev., 122 , 714728.

    • Search Google Scholar
    • Export Citation
  • Epstein, E. S., 1969: Stochastic dynamic predictions. Tellus, 21 , 739759.

  • 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. 4362.

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

  • Evensen, G., 2004: Sampling strategies and square root analysis schemes for the EnKF. Ocean Dyn., 54 , 539560.

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

    • Search Google Scholar
    • Export Citation
  • Hamill, T. M., C. Snyder, and R. E. Morss, 2000: A comparison of probabilistic forecasts from bred, singular-vector, and perturbed observation ensembles. Mon. Wea. Rev., 128 , 18351851.

    • Search Google Scholar
    • Export Citation
  • Hansen, J., and C. Penland, 2007: On stochastic parameter estimation using data assimilation. Physica D, 230 , 8898.

  • Houtekamer, P. L., and J. Derome, 1995: Methods for ensemble prediction. Mon. Wea. Rev., 123 , 21812196.

  • 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
  • Leith, C. E., 1974: Theoretical skills of Monte Carlo forecasts. Tellus, 38A , 97110.

  • Lorenz, E. N., 1963: Deterministic nonperiodic flow. J. Atmos. Sci., 20 , 130141.

  • Lorenz, E. N., 1996: Predictability: A problem partly solved. Proc. Workshop on Predictability, Vol. 1, Reading, United Kingdom, ECMWF, 1–18.

  • Lorenz, E. N., and K. A. Emanuel, 1998: Optimal sites for supplementary weather observations: Simulation with a small model. J. Atmos. Sci., 55 , 399414.

    • Search Google Scholar
    • Export Citation
  • Marshall, J., and F. Molteni, 1993: Toward a dynamical understanding of planetary-scale flow regimes. J. Atmos. Sci., 50 , 17921818.

  • Molteni, F., and T. N. Palmer, 1993: Predictability and finite-time instability of the northern winter circulation. Quart. J. Roy. Meteor. Soc., 119 , 269298.

    • Search Google Scholar
    • Export Citation
  • Molteni, F., R. Buizza, T. N. Palmer, and T. Petroliagis, 1996: The ECMWF Ensemble Prediction System: Methodology and validation. Quart. J. Roy. Meteor. Soc., 122 , 73119.

    • Search Google Scholar
    • Export Citation
  • Pellerin, G., L. Lefaivre, P. Houtekamer, and C. Girard, 2003: Increasing the horizontal resolution of ensemble forecasts at CMC. Nonlinear Proc. Geophys., 10 , 463468.

    • Search Google Scholar
    • Export Citation
  • Reynolds, C., and T. Palmer, 1998: Decaying singular vectors and their impact on analysis and forecast correction. J. Atmos. Sci., 55 , 30053023.

    • Search Google Scholar
    • Export Citation
  • Stanski, H., J. Wilson, and W. Burrows, 1989: Survey of common verification methods in meteorology. Environment Canada Research Tech. Rep. 89-5, 114 pp.

  • Talagrand, O., R. Vautard, and B. Strauss, 1999: Evaluation of probabilistic prediction system. Proc. Workshop on Predictability, Reading, United Kingdom, ECMWF, 1–25.

  • Toth, Z., and E. Kalnay, 1993: Ensemble forecasting at NMC: The generation of perturbations. Bull. Amer. Meteor. Soc., 74 , 23172330.

  • Toth, Z., and E. Kalnay, 1997: Ensemble forecasting at NCEP and the breeding method. Mon. Wea. Rev., 125 , 32973319.

  • Toth, Z., O. Talagrand, G. Candille, and Y. Zhu, 2003: Forecast verification. A Practitioner’s Guide in Atmospheric Science, I. T. Jolliffe and D. B. Stephenson, Wiley and Sons, 137–163.

  • Vannitsem, S., and C. Nicolis, 1997: Lyapunov vectors and error growth patterns in a T21L3 quasigeostrophic model. J. Atmos. Sci., 54 , 347361.

    • Search Google Scholar
    • Export Citation
  • Wang, X., and C. Bishop, 2003: A comparison of breeding and ensemble transform Kalman filter ensemble forecast schemes. J. Atmos. Sci., 60 , 11401158.

    • Search Google Scholar
    • Export Citation
  • Wang, X., C. Bishop, and S. Julier, 2004: Which is better, an ensemble of positive–negative pairs or a centered spherical simplex ensemble? Mon. Wea. Rev., 132 , 15901605.

    • Search Google Scholar
    • Export Citation
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