Singapore Rainfall Behavior: Chaotic?
Publication: Journal of Hydrologic Engineering
Volume 4, Issue 1
Abstract
The possibility of making short-term prediction of rainfall is studied by investigating the existence of chaotic behavior in the rainfall data series. The minimum number of variables essential and the number of variables sufficient to model the dynamics of the rainfall process are identified. The behavior of rainfall over different record lengths is studied. The effects of the data size and the delay time on the correlation dimension estimate are also analyzed. Daily rainfall data of different record lengths from each of six stations in Singapore are analyzed. The correlation dimension method, the inverse approach of the nonlinear prediction method, and the method of surrogate data (to detect nonlinearity) are used in the analysis. The results indicate that the rainfall data exhibit nonlinear behavior and possibly low-dimensional chaos, which imply that short-term prediction based on nonlinear dynamics might be possible. The minimum number of variables essential is identified as 3 and the number of variables sufficient lies in the range between 11 and 18. The results also indicate that the attractor dimensions of data of longer record lengths are greater than that of data of shorter record lengths. The study suggests that a minimum of ∼1,500 data points is required for the computation of the correlation dimension. Recommendation on the selection of the delay time is also provided.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Abarbanel, H. D. I., Brown, R., and Kadtke, J. B. ( 1990). “Prediction in chaotic nonlinear systems: Methods for time series with broadband Fourier spectra.” Phys. Rev. A, 41(4), 1782–1807.
2.
Casdagli, M. ( 1989). “Nonlinear prediction of chaotic time series.” Physica D, 35, 335–356.
3.
Casdagli, M. ( 1991). “Chaos and deterministic versus stochastic non-linear modeling.” J. Royal Stat. Soc. B, 54(2), 303–328.
4.
Farmer, J. D., and Sidorowich, J. J. ( 1987). “Predicting chaotic time series.” Phys. Rev. Lett., 59(8), 845–848.
5.
Fraedrich, K. ( 1986). “Estimating the dimensions of weather and climate attractors.” J. Atmos. Sci., 43(5), 419–132.
6.
Frazer, A. M., and Swinney, H. L. ( 1986). “Independent coordinates for strange attractors from mutual information.” Phys. Rev. A, 33(2), 1134–1140.
7.
Frison, T. ( 1994). “Nonlinear data analysis techniques.” Trading on the edge: Neural, genetic, and fuzzy systems for chaotic financial markets, G. J. Deboeck, ed., Wiley, New York, 280–296.
8.
Grassberger, P, and Procaccia, I. ( 1983). “Measuring the strangeness of strange attractors.” Physica D, 9, 189–208.
9.
Hao, B.-L. ( 1984). Chaos . World Scientific, Singapore.
10.
Havstad, J. W., and Ehlers, C. L. ( 1989). “Attractor dimension of nonstationary dynamical systems from small data sets.” Phys. Rev. A, 39(2), 845–853.
11.
Holzfuss, J. W., and Mayer-Kress, G. ( 1986). “An approach to error estimation in the application of dimension algorithms.” Dimension and entropies in chaotic systems, G. Mayer-Kress, ed., Springer, New York, 114–117.
12.
Jayawardena, A. W., and Lai, F. ( 1994). “Analysis and prediction of chaos in rainfall and stream flow time series.” J. Hydro., Amsterdam, 153, 23–52.
13.
Kostelich, E. J., and Yorke, J. A. ( 1988). “Noise reduction in dynamical systems.” Phys. Rev. A, 38(3), 1649–1652.
14.
Kurths, J., and Herzel, H. ( 1987). “An attractor in a solar time series.” Physica D, 25, 165–172.
15.
Muller-Jerking, J., Martinerie, J., Neuenschwander, S., Pezard, L., Ranault, B., Varela, F. J. ( 1996). “Detecting non-linearities in neuro-electrical signals: A study of synchronous local field potentials.” Physica D, 94, 65–91.
16.
Nerenberg, M. A. H., and Essex, C. ( 1990). “Correlation dimension and systematic geometric effects.” Phys. Rev. A, 42(12), 7065–7074.
17.
Packard, N. H., Crutchfield, J. P., Farmer, J. D., and Shaw, R. S. ( 1980). “Geometry from a time series.” Phys. Rev. Lett., 45(9), 712–716.
18.
Ramsey, J. B., and Yuan, H. J. ( 1990). “The statistical properties of dimension calculations using small data sets.” Nonlinearity, 3, 155–176.
19.
Rodriguez-Iturbe, I. ( 1991). “Exploring complexity in the structure of rainfall.” Adv. Water Resour., 14(4), 162–167.
20.
Rodriguez-Iturbe, I., De Power, B. F., Sharifi, M. B., and Georgakakos, K. P. ( 1989). “Chaos in rainfall.” Water Resour. Res., 25(7), 1667–1675.
21.
Sangoyomi, T. B., Lall, U., and Abarbanel, H. D. I. ( 1996). “Nonlinear dynamics of the Great Salt Lake: Dimension estimation.” Water Resour. Res., 32(1), 149–159.
22.
Schreiber, T. ( 1993). “Extremely simple nonlinear noise-reduction method.” Phys. Rev. E, 47(4), 2401–2404.
23.
Schuster, H. G. ( 1984). Deterministic chaos . VCH, Weinheim, Germany.
24.
Sharifi, M. B., Georgakakos, K. P., and Rodriguez-Iturbe, I. ( 1990). “Evidence of deterministic chaos in the pulse of storm rainfall.” J. Atmos. Sci., 47(7), 888–893.
25.
Smith, L. A. ( 1988). “Intrinsic limits on dimension calculations.” Phys. Lett. A, 133(6), 283–288.
26.
Sugihara, G., and May, R. M. ( 1990). “Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series.” Nature, 344, 734–741.
27.
Takens, F. ( 1981). “Detecting strange attractors in turbulence.” Dynamical systems and turbulence, D. A. Rand and L. S. Young, eds., Springer, Warwick, 366–381.
28.
Theiler, J. ( 1987). “Efficient algorithm for estimating the correlation dimension from a set of discrete points.” Phys. Rev. A, 36(9), 4456–4462.
29.
Theiler, J., Galdrikian, B., Longtin, A., Eubank, S., and Farmer, J. D. ( 1992a). “Using surrogate data to detect nonlinearity in time series.” Proc., Workshop on Nonlinear Modeling and Forecasting, 163–185.
30.
Theiler, J., Eubank, S., Longtin, A., Galdrikian, B., and Farmer, J. D. ( 1992b). “Testing for nonlinearity in time series: The method of surrogate data.” Physica D, 58, 77–94.
31.
Tsonis, A. A. ( 1992). Chaos: From theory to applications . Plenum, New York.
32.
Tsonis, A. A., and Elsner, J. B. ( 1988). “The weather attractor over very short timescales.” Nature, 333, 545–547.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 4 • Issue 1 • January 1999
Pages: 38 - 48
History
Received: Sep 27, 1996
Published online: Jan 1, 1999
Published in print: Jan 1999
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.