Convergence of data assimilation by periodic updating in simple Hamiltonian and dissipative systems
By: A. Hannachi and K. Haines
References
-
Bokhove
, O.and T. G., 1996.. 53, 277– 297. -
Browning
, G. L.and H.-O. Kreiss, 1996. Analysis of periodic updating for systems with multiple timescales.. 53, 335– 348. -
Charney
, J., M.and R., 1969. Use of incomplete historical data to infer the present state of the atmosphere.. 26, 1160– 1163. -
Cooper
, M.and K., 1996. Altimetric assimilation with water property conservation. J. Geophys. Res. 101, 1059– 1077. -
Courtier
, P., J. N.and A., 1994. A strategy for operational implementation of 4D-var using an incremental approach. Quart. J.R. Meteor. Soc. 120, 1367– 1388. -
Crutchfield
, J., D., N., R., G.and R. J., 1980. Power spectrum analysis of a dynamical system. Phys. Lett. 76A, 1– 4. -
Gauthier
, P. 1992. Chaos and quadri-dimensional data assimilation: A study based on the Lorenz model. Tellus, 2– 17. -
Gustayson
, F. G., 1966. On constructing formal integrals of a Hamiltonian system near an equilibrium point. Astron. J. 71, 670– 686. -
Hellman
, R. H. G., 1984. Feigenbaum sequences in conservative and dissipative systems. In Chaos and order in nature( H., ed.),– 248. Springer-Verlag. Berlin Heidelberg New York. -
Hénon
, M.and C., 1964. The applicability of the third integral of motion: Some numerical experiments. Astron. J. 69, 73– 79. -
Holmes
, P., 1982. Proof of non-integrability for the Hénon-Heiles Hamiltonian system near an exceptional integrable case. Physica D, 335– 347. -
Horn
, R. A.and C. R., 1988. Matrix analysis . Cambridge Universisty Press. Cambridge. -
Jazwinski
, A. H., 1970.Stochastic processes and filtering. , New York. -
Kalman
, R. E, 1960. A new approach to linear filtering and prediction problems. J. Basic Eng. (Trans. ASME) D, 35– 45. -
Lawden
, D. F., 1975. Analytical methods of optimization. Scottish Academic Press. Edinburgh. -
LeDimet
, F. Xand O., 1986. Variational algo-rithms for analysis and assimilation of meteorological observations., 97- 110. -
Lewis
, J. M.and J. C., 1985. The use of adjoint equations to solve a variational adjustment problem with advective constraints. Tellus, 309– 332. -
Lichtenberg
, A. J.and M. A., 1983. Regular and stochastic motion. Springer-Verlg. New York. -
Lorenz
, E. N. 1963. Deterministic nonperiodic flow.. 20, 130– 141. -
Lorenz
, E. N. 1980. Attractor sets and quasi-geostrophic equilibrium.. 37, 1685– 1699. -
Lorenz
, E. N. 1986. On the existence of a slow manifold.. 43, 1547– 1557. -
Miller
, R. N., M.and F., 1994. Advanced data assimilation in strongly nonlinear dynamical systems.. 51, 1037– 1056. -
Ott.
., 1994. Chaos in dynamical systems. Cambridge University Press. Cambridge. -
Rössler
, O. E., 1976.. 57A, 397- 398. -
Sasaki
, Y. K., 1958. An objective analysis based on the variational method. J. Meteor. Soc. Japan, 738– 742. -
Shepherd
, T. G. 1990. Symmetries laws and Hamiltonian structures in geophysical fluid dynamics . Adv. in Geophys. 32, Academic Press, 287– 338. -
Talagrand
, O., 1981a. A study of the dynamics of four-dimensional data assimilation. Tellus, 43– 60. -
Talagrand
, O., 1981b., 321– 339. -
Williamson
, D.and A., 1971. Adaptation of meteorological variables forced by updating.. 28, 1313– 1324. -
Williamson
, D.and R. E., 1972. Periodic updating of meteorological variables.. 29, 190– 193.
DOI: https://doi.org/10.3402/tellusa.v50i1.14512 | Journal eISSN: 3035-9554
Language: English
Page range: 58 - 75
Submitted on: Dec 27, 1996
Accepted on: Aug 28, 1997
Published on: Jan 1, 1998
Published by: Stockholm University Press
In partnership with: Paradigm Publishing Services
© 1998 A. Hannachi, K. Haines, published by Stockholm University Press
This work is licensed under the Creative Commons Attribution 4.0 License.