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.

在多种应用中，对风的时间行为进行建模和预测非常重要，这在很大程度上取决于对风的可变性的理解和量化。现有关于风速可变性的文献主要与水平风分量有关，而有关垂直风分量的知识则文献较少。本文在分形维分析的背景下研究了垂直风速的变化。结果表明，垂直风速的时间序列是单分形的，反持久性较弱。分形维数的中值从10m高度的1.582降低到320m高度的1.547。分形维数的垂直剖面在大小和剖面形状方面都与大气稳定性条件密切相关，偏差在较高水平时最明显。此外，发现分形维数随平均水平风速的增加而增加，这可以部分归因于大气稳定性的影响。这种关系也是高度相关的。与水平风分量类似，垂直风分量的分形维数也与窗口宽度呈正相关。