HR: 14:00h
AN: A23A-07    [Abstracts]
TI: Estimating the fractal dimension of the atmosphere and the predictability via Lyapunov exponents for the Caribbean region
AU: * Chadee, X T
EM: xchadee@fsa.uwi.tt
AF: The University of the West Indies, Department of Mathematics and Computer Science, St. Augustine Campus, Trinidad and Tobago
AB: The fractal dimension, Lyapunov-exponent spectrum, and predictability are analyzed for chaotic attractors in the atmosphere by analyzing the time series of daily wind speeds over the Caribbean region. It can be shown that this dimension is greater than 8. However, the number of data points may be too small to obtain a reliable estimate of the Grassberger-Procaccia (1983a) correlation dimension because of the limitations discussed by Ruelle (1990). These results lead us to claim that there probably exist no low-dimensional strange attractors in the atmosphere. Because the fractal dimension has not yet been saturated, the Kolmogorov entropy and the error-doubling time obtained by the method of Grassberger and Procaccia (1983b) are sensitive to the selection of the time delay and are thus unreliable. A practical and more reliable method for estimating the Kolmogorov entropy and error-doubling time involves the computation of the Lyapunov-exponent spectrum using the algorithm of Zeng et al. (1991). Using this method, it is found that the error-doubling time is 2-3 days for time series over the Caribbean region. This is comparable to the predictability time found by Waelbrock (1995) for a single station in Mexico. The predictability time over land is slightly less than that over ocean which tends to have higher climatic signal-to-noise ratio. This analysis impacts on the selection of prediction tools (deterministic chaotic linear and non-linear maps or linear stochastic modeling) for wind speeds in the short term for wind energy farm resource planning and management. We conclude that short term wind predictions in the Caribbean region, for a few days ahead, may be best done with a stochastic model instead of a deterministic chaotic model. References Grassberger, P., and I. Procaccia. 1983a. Measuring the strangeness of attractors. Physica D 9: 189-208. Grassberger, P., and I. Procaccia. 1983b. Estimating the Kolmogorov entropy from a chaotic signal. Phys. Rev. A. 28: 2591-2593. Ruelle, D. 1990. Deterministic chaos: the science and the fiction. Proc. Royal Soc. Lond. A 427: 241-248. Waelbrock, H. 1995. Deterministic chaos in tropical atmospheric dynamics. J. Atmos. Sci. 52: 2404-2415. Zeng, X., R. Eykholt, and R. A. Pielke. 1991. Estimating the Lyapunov-exponent spectrum from short time series of low precision. Phys. Rev. Lett. 66: 3229-3232.
DE: 3238 Prediction (3245, 4263)
DE: 3270 Time series analysis (1872, 4277, 4475)
SC: Atmospheric Sciences [A]
MN: 2007 Joint Assembly