Advances in Atmospheric Sciences

, Volume 26, Issue 1, pp 154–160 | Cite as

An adaptive estimation of forecast error covariance parameters for Kalman filtering data assimilation

Article

Abstract

An adaptive estimation of forecast error covariance matrices is proposed for Kalman filtering data assimilation. A forecast error covariance matrix is initially estimated using an ensemble of perturbation forecasts. This initially estimated matrix is then adjusted with scale parameters that are adaptively estimated by minimizing −2log-likelihood of observed-minus-forecast residuals. The proposed approach could be applied to Kalman filtering data assimilation with imperfect models when the model error statistics are not known. A simple nonlinear model (Burgers’ equation model) is used to demonstrate the efficacy of the proposed approach.

Key words

data assimilation Kalman filter ensemble prediction estimation 

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References

  1. Anderson, J. L., 2001: An ensemble adjustment Kalman filter for data assimilation. Mon. Wea., Rev., 129, 2844–2903.Google Scholar
  2. Bengtsson, T., D. Nychka, and C. Snyder, 2003: A frame work for data assimilation and forecasting in high dimensional non-linear dynamic systems. J. Geophys. Res., 108(D), 8875.CrossRefGoogle Scholar
  3. Burgers, J. M., 1974: The Nonlinear Diffusion. D. Reidel Publ. Co., Dordrecht, Holland, 173pp.Google Scholar
  4. Cohn, S. E. 1997: An introduction to estimation theory. J. Meteor. Soc. Japan, 75, 257–288.Google Scholar
  5. Constantinescu, M., A. Sandu, T. Chai, and G. R. Carmichael, 2007: Ensemble-based chemical data assimilation. I: General approach. Quart. J. Roy. Meteor. Soc., 133, 1229–1243.CrossRefGoogle Scholar
  6. Dee, D. P., and A. M. da Silva, 1999: Maximumlikelihood estimation of forecast and observation error covariance parameters. Part 1: Methodology. Mon. Wea. Rev., 127, 1822–1849.CrossRefGoogle Scholar
  7. Hamill, T. M., 2006: Ensemble-based atmospheric data assimilation. Predictability of Weather and Climate, Cambridge press, 123–156.Google Scholar
  8. Ide, K., P. Courtier, G. Michael, and A. C. Lorenc, 1997: Unified notation for data assimilation: operational, sequential and variational. J. Meteor. Soc. Japan, 75, 71–79.Google Scholar
  9. Julier, S. J., and K. Uhlmann, 2004: Unscented filtering and nonlinear estimation. Proc. IEEE Aeroscience and Electronic Systems, 92, 410–422.Google Scholar
  10. Miller, R. N., M. Ghil, and F. Gauthiez, 1994: An advanced data assimilation in strongly nonlinear dynamical systems. J. Atmos. Sci., 15, 1037–1056.CrossRefGoogle Scholar
  11. Ozaki, T., J. C. Jimenez, and V. H. Ozaki, 2000: The role of the likelihood function in the estimation of chaos models. Journal of Time Series Analysis, 21, 363–387.CrossRefGoogle Scholar
  12. Uboldi, F., and M. Kamachi, 2000: Time-space weakconstraint data assimilation for nonlinear models. Tellus, 52A, 412–421.Google Scholar
  13. Zhu, J. and M. Kamachi, 2000: An adaptive variational method for data assimilation with imperfect models. Tellus, 52A, 265–279.Google Scholar

Copyright information

© Chinese National Committee for International Association of Meteorology and Atmospheric Sciences, Institute of Atmospheric Physics, Science Press and Springer-Verlag GmbH 2009

Authors and Affiliations

  1. 1.National Institute of Water and Atmospheric ResearchWellingtonNew Zealand

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