Characterising the fractal dimension of wind speed time series under different terrain conditions

Abstract

Understanding the persistence in time series is of crucial importance relating to the reliable forecast of wind speed. It has been widely acknowledged that fractal analysis is a useful tool to evaluate the persistence in wind speed time series using the fractal dimension (D) as a quantitative indicator. This paper aims to unveil the persistent characteristics of wind speed time series recorded under various terrain conditions based on 6-year continuous anemometric data. Fractal dimension analysis is carried out using box-counting method. The results indicate that the 10-min wind speed time series analysed in this study exhibit clear fractal behaviour, characterizing a daily fractal dimension between 1.32 and 1.47. Larger D occurs mostly at urban conditions, while the minimum is obtained at offshore condition. The monthly pattern of fractal dimension is strongly correlated with the turbulence intensity, in which the fractal dimension either remains relatively consistent or exhibits marked monthly maxima during hotter months. Furthermore, the fractal dimension is closely tied with the length of data, in which D typically increases with increasing window-width, and decreases as the measurement time interval increases.