The Use of an Ensemble Approach to Study the Background Error Covariances in a Global NWP Model

Margarida Belo Pereira DVM, Instituto de Meteorologia, Lisbon, Portugal

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Loïk Berre Météo-France, CNRM-GMAP, Toulouse, France

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Abstract

The estimation of the background error statistics is a key issue for data assimilation. Their time average is estimated here using an analysis ensemble method. The experiments are performed with the nonstretched version of the Action de Recherche Petite Echelle Grande Echelle global model, in a perfect-model context. The global (spatially averaged) correlation functions are sharper in the ensemble method than in the so-called National Meteorological Center (NMC) method. This is shown to be closely related to the differences in the analysis step representation. The local (spatially varying) variances appear to reflect some effects of the data density and of the atmospheric variability. The resulting geographical contrasts are found to be partly different from those that are visible in the operational variances and in the NMC method. An economical estimate is also introduced to calculate and compare the local correlation length scales. This allows for the diagnosis of some existing heterogeneities and anisotropies. This information can also be useful for the modeling of heterogeneous covariances based, for example, on wavelets. The implementation of the global covariances and of the local variances, which are provided by the ensemble method, appears moreover to have a positive impact on the forecast quality.

Corresponding author address: Margarida Belo, DVM, Instituto de Meteorologia, Rua C ao Aeroporto, Lisbon 1749-077, Portugal. Email: margarida.belo@meteo.pt

Abstract

The estimation of the background error statistics is a key issue for data assimilation. Their time average is estimated here using an analysis ensemble method. The experiments are performed with the nonstretched version of the Action de Recherche Petite Echelle Grande Echelle global model, in a perfect-model context. The global (spatially averaged) correlation functions are sharper in the ensemble method than in the so-called National Meteorological Center (NMC) method. This is shown to be closely related to the differences in the analysis step representation. The local (spatially varying) variances appear to reflect some effects of the data density and of the atmospheric variability. The resulting geographical contrasts are found to be partly different from those that are visible in the operational variances and in the NMC method. An economical estimate is also introduced to calculate and compare the local correlation length scales. This allows for the diagnosis of some existing heterogeneities and anisotropies. This information can also be useful for the modeling of heterogeneous covariances based, for example, on wavelets. The implementation of the global covariances and of the local variances, which are provided by the ensemble method, appears moreover to have a positive impact on the forecast quality.

Corresponding author address: Margarida Belo, DVM, Instituto de Meteorologia, Rua C ao Aeroporto, Lisbon 1749-077, Portugal. Email: margarida.belo@meteo.pt

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  • Andersson, E., and M. Fisher, 1998: Background errors for observed quantities and their propagation in time. Proc. ECMWF Workshop on Diagnosis of Data Assimilation Systems, Reading, United Kingdom, ECMWF, 81–89.

  • Berre, L., 2000: Estimation of synoptic and mesoscale forecast error covariances in a limited area model. Mon. Wea. Rev., 128 , 644667.

    • Search Google Scholar
    • Export Citation
  • Berre, L., S. E. Ştefănescu, and M. Belo Pereira, 2006: The representation of the analysis effect in three error simulation techniques. Tellus, 58A , 196209.

    • Search Google Scholar
    • Export Citation
  • Bouttier, F., 1993: The dynamics of error covariances in a barotropic model. Tellus, 45A , 408423.

  • Bouttier, F., 1994: Sur la prévision de la qualité des prévisions météorologiques. Ph.D. dissertation, Université Paul Sabatier, 240 pp. [Available from Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex, France.].

  • Daley, R., 1991: Atmospheric Data Analysis. Cambridge University Press, 460 pp.

  • Deckmyn, A., and L. Berre, 2005: A wavelet approach to representing background error covariances in a limited area model. Mon. Wea. Rev., 133 , 12791294.

    • Search Google Scholar
    • Export Citation
  • Derber, J., and F. Bouttier, 1999: A reformulation of the background error covariance in the ECMWF global data assimilation system. Tellus, 51A , 195221.

    • Search Google Scholar
    • Export Citation
  • Desroziers, G., V. Mathiot, and F. Orain, 1995: A study of ARPEGE forecast error covariances. Proc. WMO Second Int. Symp. on Assimilation of Observations in Meteorology and Oceanography, Vol. I, Tokyo, Japan, WMO, 263–268.

  • Fisher, M., 2003: Background error covariance modelling. Proc. ECMWF Seminar on Recent Developments in Data Assimilation for Atmosphere and Ocean, Reading, United Kingdom, ECMWF, 45–63.

  • Gauthier, P., C. Charette, L. Fillion, P. Koclas, and S. Laroche, 1999: Implementation of a 3D variational data assimilation system at the Canadian Meteorological Centre. Part I: The global analysis. Atmos.–Ocean, 37 , 103156.

    • Search Google Scholar
    • Export Citation
  • Gustafsson, N., L. Berre, S. Hörnquist, X-Y. Huang, M. Lindskog, B. Navascués, K. S. Mogensen, and S. Thorsteinsson, 2001: Three-dimensional variational data assimilation for a limited area model. Part I: General formulation and the background error constraint. Tellus, 53A , 425446.

    • Search Google Scholar
    • Export Citation
  • Hollingsworth, A., 1987: Objective analysis for numerical weather prediction: Short- and medium-range numerical weather prediction. Proc. WMO/IUGG NWP Symp., Tokyo, Japan, Meteorological Society of Japan, 11–59.

  • Houtekamer, P. L., L. Lefaivre, J. Derome, H. Ritchie, and H. L. Mitchell, 1996: A system simulation approach to ensemble prediction. Mon. Wea. Rev., 124 , 12251242.

    • Search Google Scholar
    • Export Citation
  • Ingleby, N. B., 2001: The statistical structure of forecast errors and its representation in the Met. Office global 3-D variational data assimilation scheme. Quart. J. Roy. Meteor. Soc., 127 , 209231.

    • Search Google Scholar
    • Export Citation
  • Lindzen, R. S., and M. Fox-Rabinovitz, 1989: Consistent vertical and horizontal resolution. Mon. Wea. Rev., 117 , 25752583.

  • Lorenc, A. C., and Coauthors, 2000: The Met. Office global 3-dimensional variational data assimilation scheme. Quart. J. Roy. Meteor. Soc., 126 , 29913012.

    • Search Google Scholar
    • Export Citation
  • McNally, A., 2000: Estimates of short-term forecast-temperature error correlations and the implications for radiance-data assimilation. Quart. J. Roy. Meteor. Soc., 126 , 361373.

    • 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
  • Parrish, D. F., and J. C. Derber, 1992: The National Meteorological Center’s spectral statistical interpolation analysis system. Mon. Wea. Rev., 120 , 17471763.

    • Search Google Scholar
    • Export Citation
  • Rabier, F., A. McNally, E. Andersson, P. Courtier, P. Undén, J. Eyre, A. Hollingsworth, and F. Bouttier, 1998: The ECMWF implementation of three-dimensional variational assimilation (3D-Var). Part II: Structure functions. Quart. J. Roy. Meteor. Soc., 124 , 18091829.

    • Search Google Scholar
    • Export Citation
  • Rabier, F., H. Järvinen, E. Klinker, J-F. Mahfouf, and A. J. Simmons, 2000: The ECMWF operational implementation of four-dimensional variational assimilation. Part I: Experimental results with simplified physics. Quart. J. Roy. Meteor. Soc., 126 , 11431170.

    • Search Google Scholar
    • Export Citation
  • Ştefănescu, S. E., L. Berre, and M. Belo Pereira, 2006: The evolution of dispersion spectra and the evaluation of model differences in an ensemble estimation of error statistics for a limited area analysis. Mon. Wea. Rev., in press.

    • Search Google Scholar
    • Export Citation
  • Veersé, F., and J-N. Thépaut, 1998: Multiple-truncation incremental approach for four-dimensional variational data assimilation. Quart. J. Roy. Meteor. Soc., 124 , 18891908.

    • Search Google Scholar
    • Export Citation
  • Wu, W-S., R. Purser, and D. Parrish, 2002: Three-dimensional variational analysis with spatially inhomogeneous covariances. Mon. Wea. Rev., 130 , 29052916.

    • Search Google Scholar
    • Export Citation
  • Žagar, N., E. Andersson, and M. Fisher, 2004: Balanced tropical data assimilation based on a study of equatorial waves in ECMWF short-range forecast errors. ECMWF Tech. Memo. 437, 30 pp.

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