On optimal solution error in variational data assimilation: Theoretical aspects

Russian Journal of Numerical Analysis and Mathematical Modelling

Volumn 21, Issue 2, 2006, Pages 139-152

  Le Dimet, F X ^a   Shutyaev, V ^b   Gejadze, I ^a  

^a CNRS   (France)

^b INSTITUTE OF NUMERICAL MATHEMATICS   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; DATA PROCESSING; DATA REDUCTION; NONLINEAR EQUATIONS; PROBLEM SOLVING; STATISTICAL METHODS;

NONLINEAR EVOLUTION MODEL; OPTIMAL SOLUTION; STATISTICAL ERRORS; VARIATIONAL DATA ASSIMILATION;

VARIATIONAL TECHNIQUES;

EID: 33744809305     PISSN: 09276467     EISSN: None     Source Type: Journal    
DOI: 10.1163/156939806776369492     Document Type: Article

References (25)

1. V. I. Agoshkov and G. I. Marchuk, On the solvability and numerical solution of data assimilation problems. Russ. J. Numer. Anal. Math. Modelling (1993) 8, No. 1, 1-16.
2. E. Blayo, J. Blum, and J. Verron, Assimilation variationnelle de données en océanographie et réduction de la dimension de l'espace de contrôle. Équations aux Dérivées Partielles et Applications. Elsevier, Paris, 1998, pp. 205-219.
3. G. Chavent, Local stability of the output least square parameter estimation technique. Math. Appl. Comp. (1983) 2, 3-22.
4. A. L. Dontchev, Perturbations, Approximations and Sensitivity Analysis of Optimal Control Systems. Lecture Notes in Control and Information Sciences, Vol. 52. Springer, Berlin, 1983.
5. R. Glowinski and J.-L. Lions, Exact and approximate controllability for distributed parameter systems. Acta Numerica (1994) 1, 269-378.
6. J. R. Gunson and P. Malanotte-Rizzoli, Assimilation studies of open-ocean flows, II. Error measures with strongly nonlinear dynamics. J. Geophys. Res. (1996) 101, No. C12, 28473-28488.
7. A. B. Kurzhanskii and A. Yu. Khapalov, An observation theory for distributed-parameter systems. J. Math. Syst. Estimat. Control (1991) 1, No. 4, 389-440.
8. F.-X. Le Dimet and I. Charpentier, Méthodes du second ordre en assimilation de données. Équations aux Dérivées Partielles et Applications. Articles dédiés à J.-L. Lions. Elsevier, Paris, 1998, pp. 623-639.
9. F.-X. Le Dimet, I. M. Navon, and D. N. Daescu, Second-order information in data assimilation. Monthly Weather Review (2002) 130, No. 3, 629-648.
10. F.-X. Le Dimet, P. Ngnepieba, and V. Shutyaev, On error analysis in data assimilation problems. Russ. J. Numer. Anal. Math. Modelling (2002) 17, No. 1, 71-97.
11. F.-X. Le Dimet, H. E. Ngodock, B. Luong, J. Verron, Sensitivity analysis in variational data assimilation. J. Meteorol. Soc. Japan (1997) 75, No. 1B, 245-255.
12. F.-X. Le Dimet and O. Talagrand, Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus (1986) 38A, 97-110.
13. F.-X. Le Dimet and V. Shutyaev, On deterministic error analysis in variational data assimilation. Nonlinear Processes in Geophysics (2005) 14, 1-10.
14. J.-L. Lions, Contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles. Dunod, Paris, 1968.
15. J.-L. Lions, Contrôlabilité Exacte Perturbations et Stabilisation de Systèmes Distribués. Masson, Paris, 1988.
16. G. I. Marchuk and V. V. Penenko, Application of optimization methods to the problem of mathematical simulation of atmospheric processes and environment. Modelling and Optimization of Complex Systems, Proc. of the IFIP-TC7 Working conf., Springer, New York, 1978, pp. 240-252.
17. G. I. Marchuk, V. I. Agoshkov, and V. P. Shutyaev, Adjoint Equations and Perturbation Algorithms in Nonlinear Problems. CRC Press Inc., New York, 1996.
18. L M. Navon, Variational data assimilation, optimal parameter estimation and sensitivity analysis for environmental problems. Computational Mechanics'95. Springer, New York, 1995, Vol. 1, pp. 740-746.
19. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mischenko, The Mathematical Theory of Optimal Processes. John Wiley, New York, 1962.
20. F. Rabier and P. Courtier, Four-dimensional assimilation in the presence of baroclinic instability. Quart. J. Roy. Meteorol. Soc. (1992) 118, 649-672.
21. Y. K. Sasaki, Some basic formalisms in numerical variational analysis. Monthly Weather Review (1970) 98, 857-883.
22. V. P. Shutyaev, Some properties of the control operator in the problem of data assimilation and iterative algorithms. Russ. J. Numer. Anal. Math. Modelling (1995) 10, No. 4, 357-371.
23. W. C. Thacker, The role of the Hessian matrix in fitting models to measurements. J. Geophys. Res. (1989) 94, No. C5, 6177-6196.
24. J. N. Thepaut and P. Courtier, Four-dimensional variational assimilation using the adjoint of a multilevel primitive equation model. Quart. J. Roy. Meteorol Soc. (1991) 117, 1225-1254.
25. F. Veersé, Variable-storage quasi-Newton operators as inverse forecast/analysis error covariance matrices in variational data assimilation. INRIA Tech. Report No. 3685, 1999.