The application of Kalman smoother theory to the estimation of 4DVAR error statistics

Tellus, Series A: Dynamic Meteorology and Oceanography

Volumn 48, Issue 2, 1996, Pages 221-237

  Ménard, Richard ^a,d   Daley, Roger ^b,c  

^a MCGILL UNIVERSITY   (Canada)

^b ENVIRONMENT CANADA   (Canada)

^c NAVAL RESEARCH LABORATORY   (United States)

^d NASA GODDARD SPACE FLIGHT CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ATMOSPHERIC ASSIMILATION DATA; DATA ASSIMILATION; ERROR ANALYSIS; ERROR STATISTICS; FOUR DIMENSIONAL VARIATIONAL ALGORITHM; KALMAN FILTERS; KALMAN SMOOTHING; PONTRYAGIN OPTIMISATION; SMOOTHER THEORY;

EID: 0029775260     PISSN: 02806495     EISSN: None     Source Type: Journal    
DOI: 10.3402/tellusa.v48i2.12056     Document Type: Article

References (33)

1. Bennett, A. 1992. Inverse methods in physical oceanography. Cambridge University Press, New York, 346 pp.
2. Bennett, A. and Budgell, P. 1989. The Kalman smoother for a linear quasi-geostrophic model of ocean circulation. Dyn. Atmos. Oceans 13, 219-267.
3. Bennett, A. and Thorburn, M. 1992. The generalized inverse of a nonlinear quasigeostrophic ocean circulation model. J. Phys. Oceanogr. 22, 213-230.
4. Bouttier, F. 1994. Sur la prévision de la qualité des prévision météorologiques. PhD Thesis, Université Paul Sabatier à Toulouse.
5. Cohn, S. E. 1993. Dynamics of short-range univariate forecast error covariances. Mon. Wea. Rev. 121, 3123-3149.
6. Cohn, S. E., Sivakumaran, N. S. and Todling, R. 1994. A fixed-lag Kalman smoother for retrospective atmospheric data assimilation. Mon. Wea. Rev. 122, 2838-2867.
7. Courtier, P. and Talagrand, O. 1990. Variational assimilation of meteorological observations with the direct and adjoint shallow water equations. Tellus 42A, 531-549.
8. Daley, R. 1991. Atmospheric data analysis. Cambridge University Press. 457 pp.
9. Daley, R. 1992a. The lagged innovation covariance: a performance diagnostic for atmospheric data assimilation. Mon. Wea. Rev. 120, 178-196.
10. Daley, R. and Ménard, R. 1993. Spectral characteristics of Kalman filter systems for atmospheric data assimilation. Mon. Wea. Rev. 121, 1554-1565.
11. Dee, D. 1995. On-line estimation of error covariance parameters for atmospheric data assimilation. Mon. Wea. Rev. 123, 1182-1196.
12. Evensen, G. 1994. Inverse methods and data assimilation in non-linear ocean models. Physica D 77, 108-129.
13. Fraser, D. and Potter, J. 1969. The optimum linear smoother as a combination of two optimum linear filters. IEEE Trans. Automat. Contr. AC-14, 387-390.
14. Gauthier, P., Courtier, P. and Moll, P. 1993. Assimilation of simulated wind lidar data with a Kalman filter. Mon. Wea. Rev. 121, 1803-1820.
15. 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.
16. Gelb, A. 1974. Applied optimal estimation. Cambridge University Press. 374 pp.
17. Gel'fand, I. and Fomin, S. 1963. Calculus of variations. Prentice-Hall, Englewood Cliffs, 582 pp.
18. Hollingsworth, A. and Lönnberg, P. 1986. The statistical structure of short-range forecast errors as determined from radiosonde data. Part I: the wind field. Tellus 38A, 111-136.
19. Jazwinski, A. 1970. Stochastic processes and filtering theory. Academic Press, New York, 343 pp.
20. Ménard, R. 1994. Kalman filtering of Burgers' equation and its application to atmospheric data assimilation. PhD Thesis, McGill University, Montréal.
21. Ménard, R., Lyster, P., Chang, L.-P. and Cohn, S. E. 1995. Middle atmosphere assimilation of UARS constituent data using a Kalman filter. Proceedings of the 2nd International Symposium on Assimilation of observations in meteorology and oceanography. Tokyo, Japan. World Meteorological Organization, pp. 235-238.
22. Moiseenko, A. and Saenko, O. 1992. Using the Kalman smoother to analyze and process oceanographic data. Russ. J. Numer. Anal. Math. Modelling 1, 241-255.
23. Molteni, F. and Palmer, T. 1993. Predictability and finite-time instability of the northern winter circulation. Quart. J. Roy. Meteor. Soc. 119, 269-298.
24. Parrish, D. and Derber, J. 1992. The National Meteorological Center's spectral statistical interpolation analysis system. Mon. Wea. Rev. 120, 1747-1763.
25. Pontryagin, L., Boltyanskii, V., Gamkrelidge, R. and Mishchenko, E. 1962. The mathematical theory of optimal processes. Translation by K. Trogonoff, edited by L. Neustadt, Wiley-Interscience, New York, 357 pp.
26. Rabier, F., Courtier, P., Pailleux, J., Talagrand, O. and Vasiljevic, D. 1993. A comparison between four-dimensional variational assimilation and simplified sequential assimilation, relying on three-dimensional variational analysis. Quart. Journ. Roy. Met. Soc. 119, 845-880.
27. Rauch, H., Tung, F. and Striebel, C. 1965. Maximum likelihood estimates of linear dynamic systems. AIAA Journal 3, 1445-1450.
28. Thacker, W. 1986. Relationship between statistical and deterministic methods of data assimilation. Variational methods in the geosciences (ed. Y. Sasaki). Elsevier, Amsterdam, 173-179.
29. Thépaut, J.-N., Vasiljevic, D., Courtier, P. and Pailleux, J. 1993. Variational assimilation of conventional observations with a multi-level primitive equations model. Quart. Journ. Roy. Met. Soc. 119, 153-186.
30. Todling, R. and Cohn, S. E. 1994. Sub-optimal schemes for atmospheric data assimilation based on the Kalman filter. Mon. Wea. Rev. 122, 2530-2557.
31. Wergen, W. 1992. The effect of model errors in variational assimilation. Tellus 44A, 297-313.
32. Wunsch, C. 1988. Transient tracers as a problem in control theory. J. Geophys. Res. 93, 8099-8110.
33. Zupanski, M. 1993. Regional four-dimensional variational data assimilation in a quasi-operational forecasting environment. Mon. Wea. Rev. 121, 2396-2408.