Fractal characteristics of tall tower wind speeds in Missouri. (July 2020) - Balkissoon, Sarah; Fox, Neil; Lupo, Anthony
Abstract: The Hurst exponent H is used to determine the measure of predictability of a time series. The value between 0 and 1 with 0.5 representative of a random or uncorrelated series, H > 0.5 and H < 0.5 reflect a data set which is persistent and anti-persistent respectively. The fractal dimension 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 daily 10 min wind speed time series data for the year 2009 from three locations within Missouri: Columbia, Neosho and Blanchard for three tall tower stations. The results obtained from the monofractal analysis showed minor variations in the Hurst exponents for the three stations and heights for all the months in 2009. These values ranged from 0.7 to 0.9 and its corresponding fractal dimension was ranged between 1.3 and 1.1. The results for the MF-DFA showed that the wind speed time series were multifractal in nature as the Hurst exponents were functions of the scaling parameters. Also, the plots of the Renyi Exponent were non-linear for the stations and the various channels; this is representative of multifractal signals. The fractal dimensions of the time series using multifractal analysis were determined to be greater than these values determined using monofractal analysis. However, there were no indications of consistent increases in the complexity of the systems' multifractality with increasing heights for the various stations' tall towers. Graphical abstract: Image 1 Highlights: Fractal characteristics of wind speeds were studied for tall towers in Missouri. R/S method: Hurst exponent did not change significantly with months and heights. MFDFA method: wind speeds are multifractal and anti-persistent. No dominant trend in multifractal parameters with increasing heights.