448
Views
10
CrossRef citations to date
0
Altmetric
Original Articles

Chaotic dynamics, Markov processes and climate predictability

Pages 401-412 | Received 23 Sep 1988, Accepted 11 Sep 1989, Published online: 15 Dec 2016

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.
  • Billingsley, P. 1961. Statistical methods in Markov chains. Ann. Math. Stat. 32, 12–40.
  • Bowen, R. 1977. On axiom A diffeomorphisms. Regional Conference Series in Mathematics 35, 1-45.
  • Charney, J. G. and De Yore, J. G. 1979. Multiple flow equilibria in the atmosphere and blocking. J. Atmos. Sci. 36, 1205–1216.
  • Collet, P. and Eckmann, J. P. 1980. Iterated maps on the interval as dynamical systems. Brikhäuser, Basel.
  • 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.
  • Feller, W. 1968. An introduction to probability theory and its applications. Wiley, New York.
  • Fraedrich, K. 1987a. Estimating weather and climate predictability on attractors. J. Atmos. Sci. 44, 722–728.
  • Fraedrich, K. 1987b. El Nifio iterations. Beitr. Phys. Atmosph. 60, 22–33.
  • Fraedrich, K. 1988. El Nifio/southern oscillation predictability. Mon. Wea. Rev. 116, 1001–1012.
  • Fraedrich, K. and Muller, K. 1982. On single station forecasting: sunshine and rainfall Markov chains. Beitr. Phys. Atmosph. 56, 108–134.
  • Franceschini, V. and Zironi, F. 1985. On constructing Markov partitions by computer. J. Stat. Phys. 40, 69–91.
  • 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.
  • Guckenheimer, J. and Holmes, P. 1983. Nonlinear oscillations, dynamical systems and bifurcations of vector fields. Springer-Verlag.
  • Hemmer, P. C. 1984. The exact invariant density for a cusp-shaped return map. J. Phys. A: Math. Gen. 17, 247–249.
  • Keppenne, C. L. and Nicolis, C. 1989. Global properties and local structure of the weather attractor over Western Europe. J. Atmos. Sci. 46,2356–2370.
  • Lorenz, E. N. 1960. Maximum simplification of the dynamic equations. Tellus 12, 243–254.
  • Lorenz, E. N. 1963. Deterministic nonperiodic flow. J. Atmos. Sci. 20, 130–141.
  • 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.
  • Lorenz, E. N. 1984b. Irregularity: a fundamental prop-erty of the atmosphere. Tellus 36A, 98–110.
  • 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.
  • Mo, K. C. and Ghil, M. 1987. Statistics and dynamics of persistent anomalies. J. Atmos. Sci. 44, 877–901.
  • 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.
  • Nicolis, G. and Nicolis, C. 1988. Master equation approach to deterministic chaos. Phys. Rev. 38A, 427–433.
  • Nicolis, G. and Prigogine, I. 1977. Self-organization in noneguilibrium systems. Wiley, New-York.
  • Sinai, Ya. G. 1976. Introduction to ergotic theory. Princeton University Press.