Characterization of vertical wind velocity variability based on fractal dimension analysis

Modelling and forecasting the temporal behaviour of wind is of substantial importance in a variety of applications, which depend largely on the understanding and quantification of its variability. Existing literature focusing on wind speed variability is predominantly associated with horizontal wind component, whereas the knowledge of vertical wind component is much less documented. This paper investigates the variability of vertical wind velocity in the context of fractal dimension analysis. It is shown that the time series of vertical wind velocity are monofractals and weak anti-persistent. The median value of fractal dimension decreases from 1.582 ​at 10 ​m height to 1.547 ​at 320 ​m height. The vertical profile of fractal dimension is strongly tied with atmospheric stability condition, in terms of both magnitude and profile shape, and the deviation is most pronounced at higher levels. Moreover, the fractal dimension is found to increase with the increase in the mean horizontal wind speed, which can be partly attributed to the effect of atmospheric stability. Such relationship is also height-dependent. Similar to the horizontal wind component, the fractal dimension of vertical wind component also exhibits a positive correlation with window width.