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Data assimilation concepts and methods
March 1999
By F. Bouttier and P. Courtier
Table of contents
1. Basic concepts in data assimilation
2. The state vector, control space and observations
3. The modelling of errors
4. Statistical interpolation with least-squares estimation
5. A simple scalar illustration of least-squares estimation
6. Models of error covariance
7. Optimal interpolation (OI) analysis
8. Three-dimensional variational analysis (3D-Var)
9. 1D-Var and other variational analysis systems
10. Four-dimensional variational assimilation (4D-Var)
11. Estimating the quality of the analysis
12. Implementation techniques
13. Dual formulation of 3D/4D-Var (PSAS)
14. The extended Kalman filter (EKF)
15. Conclusion
Appendix A. A primer on linear matrix algebra
Appendix B. Practical adjoint coding
Appendix C. Exercises
Appendix D. Main symbols
References
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15 . Conclusion
This presentation of analysis algorithms has been centred on the algebra of the least-squares analysis method. However one shall not forget the importance of other issues like observation screening and physical consistency of the assimilation, including bias correction, which can be of great importance for the quality of the assimilation system taken as a whole.
The recent trend in data assimilation is to combine the advantages of 4D-Var and the Kalman filter techniques. In a real-time assimilation system, 4D-Var over a short time interval is a very efficient analysis method. A Hessian estimation method can provide a good estimate of the analysis error covariance matrix. A simplified version of the extended Kalman filter forecast step is then used (SKF) to estimate the forecast error covariances at the time of the next analysis, which must then be combined with an empirical, more static model of the background error covariances. It is hoped that a good compromise between these algorithms can be achieved. There can be some constructive interactions with the problems of ensemble prediction, and specific studies of analysis quality like sensitivity studies and observation targeting. These new methods provide many by-products which still remain to be used as diagnostic tools for improving the assimilation and forecast system.
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03.12.2001
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