A nudging-based data assimilation method: The Back and Forth Nudging (BFN) algorithm

Nonlinear Processes in Geophysics

Volumn 15, Issue 2, 2008, Pages 305-319

  Auroux, D ^a   Blum, J ^b  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b UNIVERSITÉ DE NICE SOPHIA ANTIPOLIS   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; COMPARATIVE STUDY; DATA ASSIMILATION; EQUATION; MODEL TEST; MODELING;

EID: 41549121047     PISSN: 10235809     EISSN: 16077946     Source Type: Journal    
DOI: 10.5194/npg-15-305-2008     Document Type: Article

References (29)

1. Arnold, M. and Datta, B. N.: Single-input eigenvalue assignment algorithms: A close look, SIAM J. Matrix Anal. Appl., 19(2), 444-467, 1998.
2. Auroux, D.: Etude de différentes méthodes d'assimilation de données pour l'environnement, Ph.D. thesis, University of Nice Sophia-Antipolis, 2003.
3. Auroux, D. and Blum, J.: Data assimilation methods for an oceano-graphic problem, vol. XVI of Mathematics in Industry Series: Multidisciplinary methods for analysis, optimization and control of complex systems, pp. 179-194, Springer-Verlag, 2004.
4. Auroux, D. and Blum, J.: Back and forth nudging algorithm for data assimilation problems, C. R. Acad. Sci. Ser. I, 340, 873-878, 2005.
5. Bao, J.-W. and Errico, R. M.: An adjoint examination of a nudging method for data assimilation, Mon. Weather Rev., 125, 1355-1373, 1997.
6. Blayo, E., Verron, J., and Molines, J.-M.: Assimilation of TOPEX/POSEIDON altimeter data into a circulation model of the North Atlantic, J. Geophys. Res., 99(C12), 24 691-24 705, 1994.
7. Bonnans, K. and Rouchon, P.: Commande et optimisation de systèmes dynamiques, Les Éditions de l'École Polytechnique, Palaiseau, 2005.
8. Datta, B. N.: An algorithm, to assign eigenvalues in a Hessenberg matrix: Single-input case, IEEE Trans. Automatic Control, 32(5), 414-417, 1987.
9. Fisher, M. and Courtier, P.: Estimating the covariance matrix of analysis and forecast error in variational data assimilation, Tech. Rep. 220, ECMWF, 1995.
10. Gilbert, J.-C. and Lemaréchal, C.: Some numerical experiments with variable-storage quasi-Newton algorithms, Math. Prog., 45, 407-435, 1989.
11. Hoke, J. and Anthes, R. A.: The initialization of numerical models by a dynamic initialization technique, Mon. Weather Rev., 104, 1551-1556, 1976.
12. Holland, W. R.: The role of mesoscale eddies in the general circulation of the ocean, J. Phys. Ocean., 8(3), 363-392, 1978.
13. Kalnay, E., Ki Park, S., Pu, Z.-X., and Gao, J.: Application of the quasi-inverse method to data assimilation, Mon. Weather Rev., 128, 864-875, 2000.
14. Le Dimet, F.-X. and Talagrand, O.: Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects, Tellus, 38A, 97-110, 1986.
15. Lorenz, E. N.: Deterministic non periodic flow, J. Atmos. Sci., 20, 130-141, 1963.
16. Luenberger, D.: Observers for multivariable systems, IEEE Trans. Autom. Contr., 11, 190-197, 1966.
17. Luong, B., Blum, J., and Verron, J.: A variational method for the resolution of a data assimilation problem, in oceanography, Inverse Problems, 14, 979-997, 1998.
18. Nocedal, J.: Updating quasi-Newton matrices with limited storage, Math. Comput., 35, 773-782, 1980.
19. Pires, C., Vautard, R., and Talagrand, O.: On extending the limits of variational assimilation in nonlinear chaotic systems, Tellus, 48A, 96-121, 1996.
20. Stauffer, D. R. and Bao, J. W.: Optimal determination of nudging coefficients using the adjoint equations, Tellus, 45A, 358-369, 1993.
21. Stauffer, D. R. and Seaman, N. L.: Use of four dimensional data assimilation in a limited area mesoscale model - Part 1 : Experiments with synoptic-scale data, Mon. Weather Rev., 118, 1250-1277, 1990.
22. Talagrand, O.: A study of the dynamics of four-dimensional data assimilation, Tellus, 33A, 43-60, 1981a.
23. Talagrand, O.: On the mathematics of data assimilation, Tellus, 33A, 321-339, 1981b.
24. Trélat, E.: Contrôle optimal: théorie et applications, Vuibert, Paris, 2005.
25. Verron, J.: Altimeter data assimilation into an ocean circulation model: sensitivity to orbital parameters, J. Geophys. Res., 95(C7), 443-459, 1990.
26. Verron, J. and Holland, W. R.: Impact de données d'altimétrie satellitaire sur les simulations numériques des circulations générales océaniques aux latitudes moyennes, Ann. Geophys., 7, 31-46, 1989, http://www.ann-geophys.net/7/31/1989/.
27. Verron, J., Molines, J.-M., and Blayo, E.: Assimilation of Geosat data into a quasigeostrophic model of the North Atlantic between 20°N and 50°N: preliminary results, Oceanol. Acta, 15(5), 575-583, 1992.
28. Vidard, P.-A., Le Dimet, F.-X., and Piacentini, A.: Determination of optimal nudging coefficients, Tellus, 55A, 1-15, 2003.
29. Zou, X., Navon, I. M., and Le Dimet, F.-X.: An optimal nudging data assimilation scheme using parameter estimation, Q. J. Roy. Meteorol. Soc., 118, 1163-1186, 1992.