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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
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The references below have been chosen because of their educational value. It does not necessarily mean that they are the original historical references. These can usually be found in the reference lists of the paper below.

Bennett, A. and M. Thornburn, 1992: The generalized inverse of a non-linear quasi-geostrophic ocean circulation model. J. Phys. Oceanogr., 3, 213-230.

Derber, J. and F. Bouttier, 1999: A reformulation of the background error covariance in the ECMWF global data assimilation system. Accepted for publication in Tellus.

Courtier, P., J.-N. Thépaut and A. Hollingsworth, 1994: A strategy for operational implementation of 4D-VAR, using an incremental approach. Quart. J. Roy. Meteor. Soc., 120, 1367-1387.

Courtier, P.,1997: Dual formulation of four-dimensional variational assimilation. Quart. J. Roy. Meteor. Soc., 123, 2449-2461.

Courtier, P., E. Andersson, W. Heckley, J. Pailleux, D. Vasiljevic, M. Hamrud, A. Hollingsworth, F. Rabier and M. Fisher, 1998: The ECMWF implementation of three-dimensional variational assimilation (3D-Var). Part 1: formulation. Quart. J. Roy. Meteor. Soc., 124, 1783-1807.

Daley, R., 1991: Atmospheric Data Analysis. Cambridge Atmospheric and Space Science Series, Cambridge University Press. ISBN 0-521-38215-7, 457 pages.

Errico, R. and T. Vukicevic, 1992: Sensitivity Analysis using an Adjoint of the PSU-NCAR Mesoscale Model. Mon. Wea. Rev., 120, 1644-1660.

Errico, R., T. Vukicevic and K. Raeder, 1993: Examination of the accuracy of a tangent linear model. Tellus, 45A, 462-477.

Eyre, J., 1987: Inversion of cloudy satellite sounding radiances by nonlinear optimal estimation: theory and simulation for TOVS. Quart. J. Roy. Meteor. Soc., 113.

Ghil, M., 1989: Meteorological Data Assimilation for Oceanographers. Part I: Description and Theoretical Framework. Dyn. of Atmos. Oceans, 13, 171-218.

Gilbert, J.-C. and C. Lemaréchal, 1989: Some numerical experiments with variable storage quasi-Newton algorithms. Mathematical Programming.

Hollingsworth, A., and P. Lonnberg, 1986: The statistical structure of short-range forecast errors as determined from radiosonde data. Part I: The wind field. Tellus, 38A, 111-136.

Hollingsworth, A., D. Shaw, P. Lonnberg, L. Illari, K. Arpe and A. Simmons, 1986: Monitoring of observation and analysis quality by a data-assimilation system. Mon. Wea. Rev., 114, 1225-1242.

Lacarra, J.-F., and O. Talagrand, 1988: Short-Range Evolution of Small Perturbations in a Barotropic Model. Tellus, 40A, 81-95.

Lorenc, A., 1986: Analysis methods for numerical weather prediction. Quart. J. Roy. Meteor. Soc., 112, 1177-1194.

Lorenc, A., 1981: A Global Three-Dimensional Multivariate Statistical Interpolation Scheme. Mon. Wea. Rev.,

Parrish, D. and J. Derber, 1992: The National Meteorological Center's spectral statistical-interpolation analysis system. Mon. Wea. Rev., 120, 1747-1763.

Rabier, F., and P. Courtier, 1992: Four-dimensional assimilation in the presence of baroclinic instability. Quart. J. Roy. Meteor. Soc., 118, 649-672.

Talagrand, O. and P. Courtier, 1987: Variational assimilation of meteorological observations with the adjoint vorticity equation. I: Theory. Quart. J. Roy. Meteor. Soc., 113, 1311-1328.

Thepaut, J.-N. and P. Courtier, 1991: Four-dimensional data assimilation using the adjoint of a multi-level primitive-equation model. Quart. J. Roy. Meteor. Soc., 117, 1225-1254.

Vukicevic, T., 1991: Nonlinear and Linear Evolution of Initial Forecast Errors. Mon. Wea. Rev., 119, 1602-1611

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