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Home > Newsevents > Training > Rcourse_notes > DATA_ASSIMILATION > ASSIM_CONCEPTS >  
   

Data assimilation concepts and methods
March 1999

By F. Bouttier and P. Courtier


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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APPENDIX D. Main symbols
  model state vector
  true value of the model state i.e. perfect analysis
  background model state
  analysed model state
  observation vector
  observation operator (maps into the space by providing model equivalents of the observed values)
  linearized observation operator (in the vicinity of a predefined model state)
  background error covariances (estimation error covariance matrix of )
  analysis error covariances (estimation error covariance matrix of )
  observation error covariances (error covariance matrix of
  analysis gain matrix
  identity matrix
  cost function of the variational analysis
  background term of the cost function
  observation term of the cost function
  penalization term of the cost function


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