Data assimilation as a nonlinear dynamical systems problem: Stability and convergence of the prediction-assimilation system

Chaos

Volumn 18, Issue 2, 2008, Pages

  Carrassi, Alberto ^a   Ghil, Michael ^b,c   Trevisan, Anna ^d   Uboldi, Francesco ^e  

^a ROYAL METEOROLOGICAL INSTITUTE OF BELGIUM   (Belgium)

^b ECOLE NORMALE SUPÉRIEURE   (France)

^c UNIVERSITY OF CALIFORNIA   (United States)

^d CNR   (Italy)

^e NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 46449116212     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.2909862     Document Type: Article

References (38)

1. A. H. Jazwinski, Stochastic Processes and Filtering Theory (Academic, New York, 1970).
2. Applied Optimal Estimation, edited by, A. Gelb, (MIT Press, Cambridge, MA, 1974).
3. Dynamic Meteorology: Data Assimilation Methods, edited by, L. Bengtsson, M. Ghil, and, E. Kälĺn, (Springer-Verlag, New York, 1981).
4. M. Ghil and P. Malanotte-Rizzoli, Adv. Geophys. 33, 141 (1991).
5. O. Talagrand, J. Meteorol. Soc. Jpn. 75, 191 (1997).
6. R. Kalman, J. Basic Eng. 82, 35 (1960).
7. R. Kalman, J. Basic Eng. 83, 95 (1961).
8. M. Ghil, J. Meteorol. Soc. Jpn. 75, 289 (1997).
9. E. Kalnay, Atmospheric Modeling, Data Assimilation and Predictability (Cambridge University Press, Cambridge, UK, 2003).
10. R. Todling and S. E. Cohn, Mon. Weather Rev. 122, 2530 (1994).
11. M. K. Tippet, S. E. Cohn, R. Todling, and D. Marchesin, SIAM J. Matrix Anal. Appl. 22, 56 (2000).
12. I. Fukumori, Mon. Weather Rev. 130, 1370 (2002).
13. G. Evensen, J. Geophys. Res. 99, 143 (1994).
14. C. L. Keppenne and M. M. Rienecker, Mon. Weather Rev. 130, 2951 (2002).
15. S. E. Cohn and D. P. Dee, SIAM (Soc. Ind. Appl. Math.) J. Numer. Anal. 25, 586 (1988).
16. E. Ott, C. Grebogi, and J. A. Yorke, Phys. Rev. Lett. 64, 1196 (1990).
17. S. Boccaletti, C. Grebogi, Y.-C. Lai, H. Mancini, and D. Maza, Phys. Rep. 329, 103 (2000).
18. M. Chen and J. Kurths, Phys. Rev. E 76, 027203 (2007).
19. E. Tziperman, H. Scher, S. E. Zebiak, and M. A. Cane, Phys. Rev. Lett. 79, 1034 (1997).
20. G. S. Duane and J. J. Tribbia, Phys. Rev. Lett. 86, 4298 (2002).
21. G. S. Duane, J. J. Tribbia, and J. B. Weiss, Nonlinear Processes Geophys. 13, 601 (2006).
22. S.-C. Yang, D. Baker, H. Li, K. Cordes, M. Huff, G. Nagpal, E. Okereke, J. Villafane, E. Kalnay, and G. S. Duane, J. Atmos. Sci. 63, 2340 (2006).
23. A. Trevisan and F. Uboldi, J. Atmos. Sci. 61, 103 (2004).
24. F. Uboldi and A. Trevisan, Nonlinear Processes Geophys. 13, 67 (2006).
25. A. Carrassi, A. Trevisan, and F. Uboldi, Tellus, Ser. A 59A, 101 (2007).
26. M. Ghil, S. Cohn, J. Tavantzis, K. Bube, and E. Isaacson, " Applications of estimation theory to numerical weather prediction.," (Ref.), pp. 139-224.
27. K. Ide, P. Courtier, M. Ghil, and A. Lorenc, J. Meteorol. Soc. Jpn. 75, 181 (1997).
28. Z. Toth and E. Kalnay, Bull. Am. Meteorol. Soc. 74, 2317 (1993).
29. D. J. Patil, B. R. Hunt, E. Kalnay, J. A. Yorke, and E. Ott, Phys. Rev. Lett. 86, 5878 (2001).
30. E. N. Lorenz, J. Atmos. Sci. 20, 130 (1963).
31. R. N. Miller, M. Ghil, and F. Gauthiez, J. Atmos. Sci. 51, 1037 (1994).
32. E. N. Lorenz and K. A. Emanuel, J. Atmos. Sci. 55, 399 (1998).
33. " The 'Fermi-Pasta-Ulam' Problem-The First 50 Years.," edited by, D. K. Campbell, P. Rosenau, and, G. Zaslavsky, Chaos 15 (1) (Special Issue) (2005).
34. R. Rotunno and J. W. Bao, Mon. Weather Rev. 124, 1051 (1996).
35. D. Ruelle, Chaotic Evolution and Strange Attractors (Cambridge University Press, New York, 1989).
36. J. Kao, D. Flicker, R. Henninger, S. Frey, M. Ghil, and K. Ide, J. Comput. Phys. 196, 705 (2004).
37. J. Kao, D. Flicker, K. Ide, and M. Ghil, J. Comput. Phys. 214, 725 (2006).
38. M. J. Galmiche Sommeria, E. Thivolle-Cazat, and J. Verron, C. R. Acad. Sci., Ser. IIb: Mec., Phys., Chim., Astron. 331, 843 (2003).