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Sonechkin D. M., Dacenko N. M., Ivashchenko N. N. New method of chaotic теме series extrapolation by means of wavelets with an application to climate dynamics. Izvestiya VUZ. Applied Nonlinear Dynamics, 1996, vol. 4, iss. 4, pp. 108-121.

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Russian
Heading: 
Deterministic Chaos
Article type: 
Article
UDC: 
551.509+621.317

New method of chaotic теме series extrapolation by means of wavelets with an application to climate dynamics

Autors: 
Sonechkin Dmitrij Mihajlovich, Hydrometeorological Research Centre of Russian Federation
Dacenko N. M., Hydrometeorological Research Centre of Russian Federation
Ivashchenko Nadezhda Nazarovna, Hydrometeorological Research Centre of Russian Federation
Abstract: 

Basing on the so-called frame of the wavelet transform one can split any chaotic time series of interest to statistically stationary oscillations and a trend-like component. Such splitting seems to be useful in order to continue the time series into future because extrapolation of the trend-like component usually is a trivial procedure. As far as the oscillations are concerned, those can be predicted with some success by means of а special mapping of their running extreme (a maximum and a minimum) onto the corresponding next ones. Both procedures (splitting and mapping) are illustrated on an example of the current climate change problem. As a result of these procedures using, the conclusion has been obtained that the current global warming probably will be checked during the next several years.

Key words: 
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Acknowledgments: 
This work was carried out with partial support from the Russian Foundation for Basic Research (grant 94-05-16341).
Reference: 
  1. Lorenz EN. Deterministic nonperiodic flow. J. Atmospheric Sciences. 1963;20(2):130-141. DOI: 10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2.
  2. Lorenz EN. On the prevalence of aperiodicity in simple systems. In: Grmela M, Marsden JE, editors. Global Analysis. Lecture Notes in Mathematics. Vol. 755. Berlin: Springer; 1979. P. 53-75. DOI: 10.1007/BFb0069804.
  3. Schertzer Р, Lovejoy S. Non-Linear Variability in Geophysics. Dordrecht: Springer; 1990. 318 p. DOI: 10.1007/978-94-009-2147-4.
  4. Abarbanel HDI, Brown R, Kadtke JB. Prediction in chaotic nonlinear systems: methods for time series with broadband Fourier spectra. Phys. Rev. А. 1990;41(4):1782-1807. DOI: 10.1103/physreva.41.1782.
  5. Broomhead DS, Lowe D. Multivariable functional interpolation and adaptive networks. J. Complex Syst. 1988;2:321-355.
  6. Casadagli M. Nonlinear prediction of chaotic time series. Physica D. 1989;35:335-356. DOI: 10.1016/0167-2789(89)90074-2.
  7. Crutchfield J, McNamara BS. Equations of motion from а data series. J. Complex Syst. 1987;1:417-452.
  8. Elsner JB, Tsonis AA. Empirically derived climate predictability over the extratropical northern hemisphere. Nonlin. Processes Geophys. 1994;1:41-44. DOI: 10.5194/npg-1-41-1994.
  9. Farmer D, Sidorowich JJ. Predicting chaotic time series. Phys. Rev. Lett. 1987;59(8):845-848. DOI: 10.1103/PhysRevLett.59.845.
  10. Smith L. Quantifying chaos with predictive flows and maps: locating unstable periodic orbits. In: Abraham NB, editor. Measures of Complexity and Chaos. Boston: Springer; 1990. P. 359-366. DOI: 10.1007/978-1-4757-0623-9_51.
  11. Sugihara G, May RM. Nonlinear forecasting as a way distinguishing chaos from measurement error in time series. Nature. 1990;344(6268):734-741. DOI: 10.1038/344734a0.
  12. Tsonis AA, Triantafyllos GN, Elsner JB. Searching for determinism in observed data: а review of the issue involved. Nonlin. Processes Geophys. 1994;1:12-25. DOI: 10.5194/npg-1-12-1994.
  13. Wales DJ. Calculating the rate of loss of information from chaotic time series by forecasting. Nature. 1991;350:485-488. DOI: 10.1038/350485a0.
  14. Vinogradskaya AA, Zimin NE, Sonechkin DМ. Ultimate possibilities of long-term weather forecast based on archived data. Meteorology and Hydrology. 1990;10:5.
  15. Chui CK. An Introduction to Wavelets. Boston: Academic Press; 1992. p. 264.
  16. Datsenko NМ, Sonechkin DМ. Wavelet analysis of time series and atmospheric dynamics. Izvestiya VUZ. Applied Nonlinear Dynamics. 1993;1(1-2):9-14.
  17. Mallat S. А theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans. Pattern Analysis Machine Intelligence. 1989;11(7):674-693. DOI: 10.1109/34.192463.
  18. Daubechies I. Orthogonal bases of compactly supported wavelets. Communications Pure and Applied Mathematics. 1988;41(7):909-996. DOI: 10.1002/cpa.3160410705.
  19. Mandelbrot BB, Van Ness JW. Fractional Brownian motion, fractional noises and applications. SIAM Review. 1968;10(4):422-437. DOI: 10.1137/1010093.
  20. Meyer Y. Wavelets. Algorithms and Applications. Philadelphia: SIAM Pub.; 1993. 133 p.
  21. Elemker PW, Plantevin Е. Wavelet bases adapted to inhomogeneous cases. In: Koornwinder TH, editor. Wavelets: An Elementary Threatment of Theory and Applications. Singapore: World Scientific; 1993. P. 107-128. DOI: 10.1142/9789814503747_0007.
  22. Meyer SD, Kelly BG, O Brien JJ. An introduction to wavelet analysis in oceanography and meteorology: with application to the dispersion of Yanai waves. Monthly Weather Review. 1993;121(10):2858-2866. DOI: 10.1175/1520-0493(1993)121<2858:AITWAI>2.0.CO;2.
  23. TRENDS’91 - Highlights. A Compendium of Data on Global Change, CDIAC, Oak Ridge National Laboratory, 1992. 665 p.
  24. Sneyers В. Use and misuse of statistical methods for the detection of climate change. In: Report on the informal planning meeting on statistical procedures for climate change detection. WMO, WCDMP-20. 25 June 1992, Toronto. Canada. P. j76-j81.
  25. Woodward WA, Gray HL. Global warming and the problem of testing for trend in time series data. J. Climate. 1993;6(5):953-962. DOI: 10.1175/1520-0442(1993)006<0953:gwatpo>2.0.co;2.
  26. Plaut G, Ghil M, Vautard R. Interannual and interdecadal variability in 335 years of Central England temperatures. Science. 1995;268(5211):710-713. DOI: 10.1126/science.268.5211.710.
Received: 
31.07.1995
Accepted: 
20.08.1996
Published: 
10.12.1996
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