On extending the limits of variational assimilation in nonlinear chaotic systems

Tellus, Series A: Dynamic Meteorology and Oceanography

Volumn 48, Issue 1, 1996, Pages 96-121

  Pires, Carlos ^a   Vautard, Robert ^a   Talagrand, Olivier ^a  

^a LABORATOIRE DE MÉTÉOROLOGIE DYNAMIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ATMOSPHERIC FLOW MODELLING; CHAOTIC SYSTEM; CHAOTIC SYSTEMS; FLOW MODELLING; NOISY OBSERVATION; OBSERVATION ASSIMILATION; VARIATIONAL ASSIMILATION; WEATHER PREDICTION;

ATMOSPHERE; CHAOS; VARIATIONAL ASSIMILATION; WEATHER SIMULATION;

EID: 0029656548     PISSN: 02806495     EISSN: None     Source Type: Journal    
DOI: 10.3402/tellusa.v48i1.11634     Document Type: Article

References (55)

1. Bennett, A. F. 1992. Inverse methods in physical oceanography. Cambridge University Press, Cambridge, United Kingdom, 346 pp.
2. Bennett, A. F. and BudgeII, W. P. 1989. The Kalman smoother for a linear quasi-geostrophic model of ocean circulation. Dyn. Atmos. Oceans 13, 219-267.
3. Budgell, W. P. 1986. Nonlinear data assimilation for shallow water equations in branched channels. J. Geophys. Res. 91 (C9), 10,633-10,644.
4. Courtier, P. and Talagrand, O. 1990. Variational assimilation of meteorological observations with the direct and adjoint shallow-water equations. Tellus 42A, 531-549.
5. Courtier, P., Derber, J., Errico, R., Louis, J.-F. and Vukicevic, T. 1993. Important literature on the use of adjoint, variational methods and the Kalman filter in meteorology. Tellus 45A, 341-357.
6. Courtier, P., Thépaut, J.-N. and Hollingsworth, A. 1994. A strategy for operational implementation of 4D-VAR, using an incremental approach. Q. J. R. Meteorol. Soc., in press.
7. Daley, R. 1991. Atmospheric data analysis. Cambridge University Press, Cambridge, U.K., 460 pp.
8. Derber, J. C. 1987. Variational four-assimilation analysis using quasi-geostrophic constrains. Mon. Wea. Rev. 115, 998-1008.
9. Devaney, R., and Nitecki, Z. 1979. Shift automorphisms in the Hénon mapping. Comm. Math. Phys. 67, 137-148.
10. Errico, R. M. and Vukicevic, T. 1992. Sensivity analysis using an adjoint of the PSU-NCAR mesoscale model. Mon. Wea. Rev. 120, 1644-1660.
11. Evensen, G. 1992. Using the extended Kalman filter with a multilayer quasigeostrophic ocean model. J. Geophys. Res. 97 (C11), 17,905-17,924.
12. Evensen, G. 1994. Sequential data assimilation with a nonlinear quasi-geostrophic model using Monte Carlo methods to forecast error statistics. J. Geophvs. Res. 99 (C5), 10,143-10,162.
13. Farmer, J. D., and Sidorovich, J. J. 1991. Optimal shadowing and noise reduction. Physica D 47, 373-392.
14. Gaspar, P. and Wunsch, C. 1989. Estimates from altimeter data of barotropic rossby waves in the northwestern atlantic ocean. J. Phys. Oceanogr. 19, 1821-1844.
15. Gauthier, P. 1992. Chaos and quadri-dimensional data assimilation. A study based on the Lorenz model. Tellus 44A, 2-17.
16. Guckenheimer, J. and Holmes, P. 1983. Nonlinear oscillations, dynamical systems, and bifurcations of vector fields. Springer-Verlag, New-York, 453 pp.
17. Ghil, M. and Malanotte-Rizzoli, P. 1991. Data assimilation in meteorology and oceanography. Adv. Geophys. 33, 141-266.
18. Hénon, M. 1976. A two-dimensional mapping with a strange attractor. Comm. Math. Phys. 50, 69-77.
19. Hirsch, M. W. and Pugh, C. C. 1970. Stable manifolds and hyperbolic sets. Proc. Symp. Pure. Math. 14, 133-163.
20. Jazwinski, A. H. 1970. Stochastic processes and filtering theory. Academic Press, New York, USA.
21. Kalman, R. E. 1960. A new approach to linear filtering and prediction problems. J. Basic Eng. 82D, 35-45.
22. Lacarra, J.-F. and Talagrand, O. 1988. Short-range evolution of small perturbations in a barotropic model. Tellus 40A, 81-95.
23. Le Dimet, F.-X. and Talagrand, O. 1986. Variational algorithms for analysis and assimilation of meteorological observations: theoretical aspects. Tellus 38A, 97-110.
24. Legras, B. and Ghil, M. 1985. Persistent anomalies, blocking, and variations in atmospheric predictability. J. Atmos. Sci. 42, 433-471.
25. Lewis, J. and Derber, J. C. 1985. The use of adjoint equations to solve a variational adjustment problem with advective constraints. Tellus 37A, 309-322.
26. Li, Y. 1991. A Note on the uniqueness problem of variational adjustment approach to four-dimensional data assimilation. J. of the Met. Soc. of Japan. 69, 581-585.
27. Lorenc, A. C. 1981. A global three-dimensional multivariate statistical interpolation scheme. Mon. Wea. Rev. 109, 701-721.
28. Lorenc, A. C. 1986. Analysis methods for numerical weather prediction. Q. J. R. Meteorol. Soc. 112, 1177-1194.
29. Lorenz, E. N. 1963. Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130-141.
30. Lorenz, E. N. 1965. A study of the predictability of a 28-variable atmospheric model. Tellus 27, 321-333.
31. Lorenz, E. N. 1969. Atmospheric predictability as revealed by naturally occurring analogues. J. Atmos. Sci. 26, 636-646.
32. Miller, R. N., Ghil, M. and Gauthiez, F. 1994. Advanced data assimilation in strongly nonlinear dynamical systems. J. Atmos. Sci. 51, 1037-1056.
33. Molteni, F. and Palmer, T. 1993. Predictability and finite-time instability of the northern winter circulation. Quart. J. R. Meteor. Soc. 119, 269-298.
34. Nese, J. M., Dutton, J. A. and Wells, R. 1987. Calculated attractor dimensions for low-order spectral models. J. Atmos. Sci. 44, 1950-1972.
35. Oseledec, V. I. 1968. A multiplicative ergodic theorem: Lyapunov characteristic numbers for dynamical systems. Trans. Moscow Math. Soc. 19, 197-231.
36. Palmer, T. 1988. Medium and extended-range predictability and the stability of the Pacific/North American mode. Quart. J. R. Meteor. Soc. 114, 691-713.
37. Palmer, T. 1993. Extended-range atmospheric prediction and the Lorenz model. Bull. Am. Meteor. Soc. 74, 49-65.
38. Parrish, D. and Derber, D. 1992. The National Meteorological Center's Spectral Statistical-Interpolation Analysis System. Mon. Wea. Rev. 120, 1747-1763.
39. Rabier, F. and Courtier, P. 1992. Four-dimensional assimilation in the presence of baroclinic instability, Q. J. R. Meteorol. Soc. 118, 649-672.
40. Robertson, D. H., Brown, F. B. and Navon, I. M. 1989. Determination of the structure of mixed-xenon clusters using a finite-temperature, lattice-based Monte Carlo method, J. Chem. Phys. 90, 3221-3229.
41. Ruelle, D. 1989. Chaotic evolution and strange attractors. Cambridge University Press, Cambridge, 95 pp.
42. Sheinbaum, J. and Anderson, D. L. T. 1990a. Variational assimilation of XBT data. Part I. J. Phys. Oceanogr. 20, 672-688.
43. Sheinbaum, J. and Anderson, D. L. T. 1990b. Variational assimilation of XBT data. Part II. Sensitivity studies and use of smoothing constraints. J. Phys. Oceanogr. 20, 689-704.
44. Sparrow, C. 1982. The Loren: equations. Springer-Verlag, New-York, 269 pp.
45. Stensrud, D. J. and Bao, J. W. 1992. Behaviors of variational and nudging assimilation techniques with a chaotic low-order model. Mon. Wea. Rev. 120, 3016-3028.
46. Talagrand, O. 1992. Data assimilation problems. In: Proceedings, NATO Advanced Study Institute, Energy and water cycles in the climate system, (Glücksburg, Germany, October 1991), E. Raschke and D. Jacob, eds. Forschungszentrum Geesthacht, Geesthacht, Germany, 187-213.
47. Talagrand, O. and Courtier, P. 1987. Variational assimilation of meteorological observations with the adjoint vorticity equation (I). Theory. Quart. J. R. Met. Soc. 113, 1311-1328.
48. Thacker, W. C. and R. B. Long, 1988. Fitting dynamics to data. J. Geophys. Res. 93, 1227-1240.
49. Thépaut, J.-N., Vasiljevic, D., Courtier, P. and Pailleux, J., 1993. Variational assimilation of conventional meteorological observations with a multilevel primitive-equation model. Q. J. R. Meteorol. Soc. 119, 153-186.
50. Tibaldi, S. and Molteni, F. 1990. On the operational predictability of blocking. Tellus 42A, 343-365.
51. Toth, Z. and Kalnay, E. 1993. Ensemble forecasting at NMC. The generation of perturbations. Bull. Amer. Meteor. Soc. 74, 2317-2330.
52. Toth, Z. and Kalnay, E. 1994. Ensemble forecasting at NMC. The use of the breeding method for generating perturbations. Proceedings, 10th AMS Conference on Numerical Weather Prediction, Portland, Oregon, USA, July 1994. Published by the American Meteorological Society.
53. Vautard, R. and Legras, B. 1988. On the source of midlatitude low-frequency variability. Part II. Non-linear equilibration of weather regimes. J. Atmos. Sci. 45, 2845-2867.
54. Vautard, R. 1990. Multiple weather regimes over the north Atlantic: analysis of precursors and successors. Mon. Wea. Rev. 118, 2056-2081.
55. Zou, X. Navon, I. M. and Le Dimet, F.-X. 1992. Incomplete observations and control of gravity waves in variational data assimilation. Tellus 44A, 273-296.