Chaotic dynamics, Markov processes and climate predictability

C. Nicolis

doi:10.3402/tellusa.v42i4.11886

Chaotic dynamics, Markov processes and climate predictability

Tellus

Volume 42 (1990): Issue 4

By: C. Nicolis

Open Access

|Jan 1990

Abstract

A systematic method for mapping deterministic chaos in general, and atmospheric and climate dynamics in particular, into a Markovian process is developed. The possibility of using the Markovian description for carrying out long-term statistical predictions is suggested, and illustrated on simple models and on data pertaining to sea surface temperature anomalies which can be reduced to one-dimensional maps.

References

Benzi , R. and Speranza , A . 1987 . Dynamics and statistics of atmospheric low frequency variability. In: Irreversible phenomena and dynamical systems analysis in geosciences (eds. C. Nicolis and G . Nicolis ). Reidel , 199 – 239 .
Search in Google Scholar Back to article
Billingsley , P . 1961 . Statistical methods in Markov chains . Ann. Math. Stat . 32 , 12 – 40 .
Search in Google Scholar Back to article
Bowen , R . 1977 . On axiom A diffeomorphisms. Regional Conference Series in Mathematics 35 , 1 - 45.
Search in Google Scholar Back to article
Charney , J. G. and De Yore , J. G. 1979. Multiple flow equilibria in the atmosphere and blocking . J. Atmos. Sci . 36 , 1205 – 1216 .
Search in Google Scholar Back to article
Collet , P. and Eckmann , J. P . 1980 . Iterated maps on the interval as dynamical systems . Brikhäuser , Basel .
Search in Google Scholar Back to article
De Swart , H. E. and Grasman , J . 1987 . Effect of stochastic perturbations on a low-order spectral model of the atmospheric circulation . Tellus 39A , 10 – 24 .
Search in Google Scholar Back to article
Feller , W . 1968 . An introduction to probability theory and its applications . Wiley , New York .
Search in Google Scholar Back to article
Fraedrich , K . 1987a . Estimating weather and climate predictability on attractors . J. Atmos. Sci . 44 , 722 – 728 .
Search in Google Scholar Back to article
Fraedrich , K . 1987b . El Nifio iterations . Beitr. Phys. Atmosph . 60 , 22 – 33 .
Search in Google Scholar Back to article
Fraedrich , K . 1988 . El Nifio/southern oscillation predictability . Mon. Wea. Rev . 116 , 1001 – 1012 .
Search in Google Scholar Back to article
Fraedrich , K. and Muller , K . 1982 . On single station forecasting: sunshine and rainfall Markov chains . Beitr. Phys. Atmosph . 56 , 108 – 134 .
Search in Google Scholar Back to article
Franceschini , V. and Zironi , F . 1985 . On constructing Markov partitions by computer . J. Stat. Phys . 40 , 69 – 91 .
Search in Google Scholar Back to article
Gent , P. R. and McWilliams , J. C . 1982 . Intermediate model solutions to the Lorenz equations: strange attractors and other phenomena . J. Atmos. Sci . 39 , 3 – 13 .
Search in Google Scholar Back to article
Guckenheimer , J. and Holmes , P . 1983 . Nonlinear oscillations, dynamical systems and bifurcations of vector fields . Springer-Verlag.
Search in Google Scholar Back to article
Hemmer , P. C . 1984 . The exact invariant density for a cusp-shaped return map . J. Phys. A: Math. Gen . 17 , 247 – 249 .
Search in Google Scholar Back to article
Keppenne , C. L. and Nicolis , C . 1989 . Global properties and local structure of the weather attractor over Western Europe. J. Atmos. Sc i . 46 , 2356 – 2370 .
Search in Google Scholar Back to article
Lorenz , E. N . 1960 . Maximum simplification of the dynamic equations . Tellus 12 , 243 – 254 .
Search in Google Scholar Back to article
Lorenz , E. N . 1963 . Deterministic nonperiodic flow . J. Atmos. Sci . 20 , 130 – 141 .
Search in Google Scholar Back to article
Lorenz , E. N . 1984a. Some aspects of atmospheric predictability. In: Problems and prospects in long-and medium-range weather forecasting (eds. D. M. Barridge and E. Källen ). Springer-Verlag , 1 – 20 .
Search in Google Scholar Back to article
Lorenz , E. N . 1984b . Irregularity: a fundamental prop-erty of the atmosphere . Tellus 36A , 98 – 110 .
Search in Google Scholar Back to article
Lorenz , E. N . 1987 . Deterministic and stochastic aspects of atmospheric dynamics. In: Irreversible phenomena and dynamical systems analysis in geosciences (eds. C. Nicolis and G . Nicolis ). Reidel , 159 – 179 .
Search in Google Scholar Back to article
Mo , K. C. and Ghil , M . 1987 . Statistics and dynamics of persistent anomalies . J. Atmos. Sci . 44 , 877 – 901 .
Search in Google Scholar Back to article
Nicolis , C. and Keppenne , C. L . 1989 . Climate predictability: a dynamical view . In: Climate and geosciences (eds. A. Berger , S. Schneider and J. C. Duplessy ). Reidel , pp. 241 – 251 .
Search in Google Scholar Back to article
Nicolis , G. and Nicolis , C . 1988 . Master equation approach to deterministic chaos . Phys. Rev . 38A , 427 – 433 .
Search in Google Scholar Back to article
Nicolis , G. and Prigogine , I . 1977 . Self-organization in noneguilibrium systems . Wiley , New-York .
Search in Google Scholar Back to article
Sinai , Ya. G . 1976 . Introduction to ergotic theory . Princeton University Press .
Search in Google Scholar Back to article