Treating Model Error in 3-D and 4-D Data Assimilation

  • N. K. Nichols
Part of the NATO Science Series book series (NAIV, volume 26)


The aim of a data assimilation scheme is to use measured observations in combination with a dynamical system model to derive accurate estimates of the current and future states of the system. In operational schemes for atmosphere and ocean forecasting, the model equations are generally assumed to be a ‘perfect’ representation of the true dynamical system and are treated as strong constraints in the assimilation process. The model equations do not, in practice, represent the system behaviour exactly, however, and model errors arise due to lack of resolution and inaccuracies in physical parameters, boundary conditions and forcing terms. Errors also occur due to discrete approximations and random disturbances.


Model Error Data Assimilation Extend Kalman Filter Bias Error Augmented System 
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  1. Bell, M.J., Martin, M.J. and Nichols, N.K. (2001) Assimilation of Data into an Ocean Model with Systematic Errors Near the Equator, The Met Office, Ocean Applications Division, Tech. Note No. 27.Google Scholar
  2. Bierman, G.L. (1977) Factorization Methods for Discrete Sequential Estimation, Mathematics in Science and Engineering, V. 128, Academic Press, New York.Google Scholar
  3. Derber, J.C. (1989) A variational continuous assimilation technique, Monthly Weather Review, 117, 2437–2446.CrossRefGoogle Scholar
  4. Dee, D.P. and da Silva, A.M. (1998) Data assimilation in the presence of forecast bias, Quart. J. Roy. Met. Soc., 117, 269–295.CrossRefGoogle Scholar
  5. Griffith, A.K. (1997) Data Assimilation for Numerical Weather Prediction Using Control Theory, The University of Reading, Department of Mathematics, PhD Thesis.Google Scholar
  6. Griffith, A.K., Martin, M.J. and Nichols, N.K. (2000) Techniques for treating systematic model error in 3D and 4D data assimilation, in Proceedings of the Third WMO Int. Symposium on Assimilation of Observations in Meteorology and Oceanography, World Meteorological Organization, WWRP Report Series No. 2, WMO/TD — No. 986, pp. 9–12.Google Scholar
  7. Griffith, A.K. and Nichols, N.K. (1996) Accounting for model error in data assimilation using adjoint methods, in M. Berz, C. Bischof, G. Corliss and A. Greiwank (eds.), Computational Differentiation: Techniques, Applications and Tools, SIAM, Philadelphia, pp. 195–204.Google Scholar
  8. Griffith, A.K. and Nichols, N.K. (2000) Adjoint techniques in data assimilation for estimating model error, Journal of Flow, Turbulence and Combustion, 65, 469–488.CrossRefGoogle Scholar
  9. Kalman, R.E. (1961) A new approach to linear filtering and prediction problems, Transactions of the ASME, Series D, 83, 35–44.Google Scholar
  10. Martin, M.J. (2001) Data Assimilation in Ocean Circulation Models with Systematic Errors, The University of Reading, Department of Mathematics, PhD Thesis.Google Scholar
  11. Martin, M.J., Bell, M.J. and Nichols, N.K. (2001) Estimation of systematic error in an equatorial ocean model using data assimilation, in M.J. Baines (ed.), Numerical Methods for Fluid Dynamics VII, ICFD, Oxford, pp. 423–430.Google Scholar
  12. Martin, M.J., Nichols, N.K. and Bell, M.J. (1999) Treatment of Systematic Errors in Sequential Data Assimilation, The Met Office, Ocean Applications Division, Tech. Note No. 21.Google Scholar
  13. Miller, R.N., Ghil, M. and Gauthiez, F. (1994) Advanced data assimilation in strongly nonlinear dynamical systems, J. Atmos. Sc., 51, 1037–1056.CrossRefGoogle Scholar
  14. Zupanski, D. (1997) A general weak constraint applicable to operational 4DVAR data assimilation systems, Monthly Weather Review, 123, 1112–1127.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2003

Authors and Affiliations

  • N. K. Nichols
    • 1
  1. 1.Department of MathematicsThe University of ReadingReadingUK

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