Fractal Characteristics of Tall-Tower Wind Data in Missouri

The Hurst exponent is used to determine the measure of predictability of a time series. The H value is between 0 and 1 with 0.5 representative of a random or uncorrelated series, H > 0.5 and H < 0.5 reflect a dataset which is persistent and anti-persistent respectively. The fractal dimensions can be given from the Hurst exponent. The fractal dimension is a factor of the complexity of which the system is being repeated at various scales. If the fractal dimension does not change with scale it is deemed monofractal if not, multifractal. The Hurst exponents were determined in this study using the Rescale Range Analysis (R/S Analysis) and Multifractal Detrended Fluctuation Analysis (MF-DFA) for monofractal and multifractal investigations respectively. These methods were applied to wind speed daily 10-minute time series data for the year 2009 from three locations within Missouri: Columbia, Neosho and Blanchard in the year 2009 for three different heights. The results obtained from the monofractal analysis showed minor variations in the Hurst exponents for the three stations and its six channels for all the months in 2009. This value varied from approximately 0.8 and 0.9 and its corresponding fractal dimensions were 1.2 and 1.1. The results for the MF-DFA showed that the wind speed time series was multifractal in nature as the Hurst exponent was a function of the scaling parameter. Also, the plots of the Renyi Exponent were non-linear for the stations and the various channels; this is representative of multifractal signals.