Skip to main content
Log in

On the chaotic behavior and predictability of the real atmosphere

  • Published:
Advances in Atmospheric Sciences Aims and scope Submit manuscript

Abstract

In this paper the concept of Chaos and its applications to the study of predictability theory is introduced. The author's attempt is to give a general overview of ideas and methods involved in this problem to scientists, who are interested in the problem of predictability but not familiar with the theory of chaos. The problem is discussed in 4 sections. In the first section, the concept of chaos and the study methods are outlined briefly; in the second section, the methods of quantitatively measuring the main characteristics of chaos which are the basis for the predictability theory are in troduced; the third section discusses the time series analysis for directly studying chaotic phenomena in practical problems; and the last section presents some research results on the chaotic characteristics and the predictability of the real atmosphere.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Ben-Mizrachi, A., I. Procacia and P. Grassberger (1984), Characterization of experimental (noisy) strange attractors,Physical Rev.,A,29: 975–977.

    Article  Google Scholar 

  • Eckmann, J.P. and D. Ruelle (1990), Fundamental limitations for estimating dimensions and Liapunov exponents in dynamical systems (preprint).

  • Fraedrich, K. (1986), Estimating the dimensions of weather and climate attractors,J. Atmos. Sci.,43: 331–344

    Google Scholar 

  • Fraedrich, K. (1987), Estimating weather and climate predictability on attractors,J. Atmos. Sci.,44: 722–728

    Article  Google Scholar 

  • Grassberger, P. and I. Procaccia (1983), Measuring the strangeness of strange attractors,Physica 9D: 189–208.

    Google Scholar 

  • Grassberger, P. and I. Procaccia (1984), Dimensions and entropies of strange attractors from a fluctuating dynamics approach.Physica 13D: 34–54.

    Google Scholar 

  • Liu Shida and Liu Shigua (1989),Nonlinear dynamics and complex Phenomena. (Meteor. Press. Beijing), PP. 249.

    Google Scholar 

  • Lorenz, E.N. (1963), Deterministic nonperiodic flow.J. Atmos. Sci.,20: 130–141.

    Article  Google Scholar 

  • Mandelbrot, B.B. (1982),The fractal geometry of nature (W. H. Freeman, San Francisco).

    Google Scholar 

  • Nicolis, C. and G. Nicolis (1984), Is there a climate attractor?Nature,311: 529–532.

    Article  Google Scholar 

  • Packard, N.H., J.P. Crutchfield, J.D. Farmer and R.S. Shaw (1980), Geometry from a time series.Phys. Rev. Lett. 45: 712–716.

    Article  Google Scholar 

  • Takens, F. (1981), Detecting strange attractors in turbulence. InLecture Notes in Mathematics 898. (Springer, Berlin), pp. 366.

    Google Scholar 

  • Wolf, A., J.B. Swift, H.L. Swinney and J.A. Vastano (1985), Determining Lyapunov exponents from a time series,Physica 16D: 285–317.

    Google Scholar 

  • Wolf A. (1986), Quantifying chaos with Lyapunov exponents. InChaos. ed. A. V. Holden (Manchester University Press) 271–190.

  • Yang Peicai (1985), Bifurcation sequence and energy distribution of the higher-dimensional Lorenz system. InProceedings of the International Coference on nonlinear Mechanics (Science Press, Beijing) pp. 1140.

    Google Scholar 

  • Yang Peicai, Liu Jinli and Yang Shuowen (1988), Some features of chaotic motions in the atmospheric boundary layer. InProceedings of the International Conference on Bifurcation theory and its numerical analysis (Xi'AN Jiaotong University Press), pp. 406.

  • Yang Peicai, Lu Daren, Wu Belying, Li Wei, Susumu Kato, Toshitake Tsuda, Shoichiro Fukao, Toru Sato and Mamoru Yamamoto (1988), Chaotic features of the atmospheric motions nearby tropopause revealed by MU radar observation—case study. Paper presented at theFourth MST Radar Workshop. (Kyoto, Japan, Nov. 29–Dec.2, 1988).

  • Yang Peicai and Chen Lieting (1990), On the predictability of El Nino/Southern Oscillation,Chinese J. Atmos. Sci.,14: 77–86.

    Google Scholar 

  • Yan Shaojim, Pong Yingqing and Wang Janzhong (1991), Estimating the entropy of a weather attractor from a single-variable chaotic time series.Adv. in Atmos. Sci., (to be published).

Download references

Author information

Authors and Affiliations

Authors

Additional information

This project is supported by National Natural Science Foundation of China.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Peicai, Y. On the chaotic behavior and predictability of the real atmosphere. Adv. Atmos. Sci. 8, 407–420 (1991). https://doi.org/10.1007/BF02919264

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02919264

Keywords

Navigation