Extended Kalman filtering for vortex systems. Part I: Methodology and point vortices

Dynamics of Atmospheres and Oceans

Volumn 27, Issue 1-4, 1998, Pages 301-332

  Ide, Kayo ^a   Ghil, Michael ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ATMOSPHERE; FILTER; VORTEX; VORTICITY;

ATMOSPHERIC DYNAMICS; ATMOSPHERIC FLOW; DATA ASSIMILATION; KALMAN FILTER; VORTEX SYSTEM; VORTICITY;

EID: 0031881635     PISSN: 03770265     EISSN: None     Source Type: Journal    
DOI: 10.1016/s0377-0265(97)00016-x     Document Type: Article

References (33)

1. Anderson, J.L., 1995. Selection of initial conditions for ensemble forecasts in a simple perfect framework. J. Atmos. Sci. 53, 22-36.
2. Aref, H., 1984. Integrable, chaotic, and turbulent vortex motion in two-dimensional flow. Ann. Rev. Fluid Mech. 15, 345-389.
3. Bengtsson, L., Ghil, M., Källén, E. (Eds.), 1981. Dynamic Meteorology: Data Assimilation Methods, Appl. Math. Sci. Ser. Vol. 36. Springer-Verlag, 330 pp.
4. Buizza, R., Tribbia, J., Molteni, F., Palmer, T., 1993. Computation of optimal unstable structures for a numerical weather prediction model. Tellus 45A, 388-406.
5. Cohn, S., 1993. Dynamics of short-term univariate forecast error covariance. Won. Weather Rev. 121, 3123-3149.
6. Daley, R., 1991. Atmospheric Data Analysis. Cambridge University Press, 420 pp.
7. Gelb, A. (Ed.), 1974. Applied Optimal Estimation. The MIT Press, 374 pp.
8. Gandin, L.S., 1965. Objective Analysis of Meteorological Fields (Israel Program for Scientific Translations, Jerusalem, Trans.). Gidrometeorol. Izd., 242 pp. (original work published 1963).
9. Ghil, M., 1989. Meteorological data assimilation for oceanographers. Part I: Description and theoretical framework. Dyn. Atmos. Oceans 13 (3-4), 171-218.
10. Ghil, M., Balgovind, R., 1979. A fast Cauchy-Riemann solver. Math. Comput. 33, 585-635.
11. Ghil, M., Ide, K., 1994. Extended Kalman filtering for vortex systems: an example of observing system design. In: Brasseur, P., Nihoul, J.C.J. (Eds.), Data Assimilation for Modelling Ocean in a Global Change Perspective. Springer-Verlag, New York, pp. 167-193.
12. Ghil, M., Malanotte-Rizzoli, P., 1991. Data assimilation in meteorology and oceanography. Adv. Geophys. 33, 141-226.
13. Ghil, M., Cohn, S.E., Taventzis, J., Bube, K., Isaccson, E., 1981. Application of estimation theory to numerical weather prediction. In: Bengtsson, L., Ghil, M., Källén, E. (Eds.), Dynamic Meteorology: Data Assimilation Methods, Appl. Math. Sci. Ser. Vol. 36. Springer-Verlag, pp. 139-224.
14. Greenside, H.S., Helfand, H., 1981. Numerical integration of stochastic differential equations - II. Bell Syst. Tech. J. 60, 1927-1940.
15. Hao, Z., Ghil, M., 1995. Sequential parameter estimation for a coupled ocean-atmosphere model. In: Proceedings of the Second WMO International Symposium on Assimilation of Observations in Meteorology and Oceanography, Tokyo, vol. 1. pp. 181-186.
16. Ide, K., Ghil, M., 1997a. Extended Kalman filtering for vortex systems. Part II: Rankine vortices and Eulerian data. Dyn. Atmos. Oceans 27, 333-350.
17. Ide, K., Ghil, M., 1997b. Evolution of prediction errors in nonlinear systems, deterministic and stochastic. (In preparation.)
18. Jazwinski, A.M., 1970. Stochastic Processes and Filtering Theory. Academic Press, 376 pp.
19. Kalman, R.E., 1960. A new approach to linear filtering and prediction problems. Trans. ASME, Ser. D, J. Basic Eng. 82D, 35-45.
20. Kalman, R.E., Bucy, R.S., 1961. New results in linear filtering and prediction problems. Trans. ASME, Ser. D, J. Basic Eng. 83D, 95-108.
21. Legras, B., Vautard, R., 1996. A guide to Liapunov vectors. In: Palmer, T. (Ed.), Proc. 1995 ECMWF Seminar on Predictability. ECMWF, Reading, UK, pp. 143-156.
22. Lorenc, A., 1981. A global three-dimensional multivariate statistical interpolation scheme. Mon. Weather Rev. 109, 701-721.
23. Mariano, A.J., 1990. Contour analysis: a new approach for melding geophysical fields. J. Atmos. Ocean. Tech. 7, 285-295.
24. McWilliams, J.C., 1980. An application of equivalent modons to atmospheric blocking. Dyn. Atmos. Oceans 5, 43-66.
25. McWilliams, J.C., 1991. Geostrophic vortices. In: Osborne, A.R. (Ed.), Nonlinear Topics in Ocean Physics: Proceedings of the International School of Physics "Enrico Fermi" Course 109. Elsevier Science Publishers B.V., Amsterdam, pp. 5-50.
26. Miller, R., Ghil, M., Gauthiez, F., 1994. Advanced data assimilation in strongly nonlinear dynamical systems. J. Atmos. Sci. 51, 1037-1056.
27. Panel on Model-Assimilated Data Sets for Atmospheric and Oceanic Research, 1991. Four-Dimensional Model Assimilation of Data: A Strategy for the Earth System Sciences. National Academy Press, 78 pp.
28. Provost, C., Salmon, R., 1986. A variational method for inverting hydrographic data. J. Mar. Res. 44, 1-34.
29. Robinson, A.R. (Ed.), 1983. Eddies in Marine Science. Springer-Verlag, 609 pp.
30. Sasaki, Y., 1970. Some basic formalisms in numerical variational analysis. Mon. Weather Rev 98, 875-883.
31. Smedstad, O.M., O'Brien, J., 1991. Variational data assimilation and parameter estimation in an equatorial Pacific Ocean model. Prog. Oceanogr. 26, 179-241.
32. Talagrand, O., Courtier, P., 1987. Variational assimilation of meteorological observations with the adjoint vorticity equation. I. Theory. Q.J.R. Meteorol. Sci. 113, 1311-1328.
33. Toth, K., Kalnay, E., 1993. Ensemble forecasting at NMC: the generation of perturbations. Bull. Am. Met. Soc. 74, 2317-2330.