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.

中文翻译：

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表征不同地形条件下风速时间序列的分形维数

摘要 理解时间序列的持续性对于可靠地预测风速至关重要。人们普遍认为，分形分析是一种有用的工具，可以使用分形维数 (D) 作为量化指标来评估风速时间序列的持续性。本文旨在基于 6 年连续风速测量数据揭示在各种地形条件下记录的风速时间序列的持续特征。分形维数分析使用盒计数法进行。结果表明，本研究中分析的 10 分钟风速时间序列表现出明显的分形行为，其特征是每日分形维数介于 1.32 和 1.47 之间。较大的 D 主要出现在城市条件下，而最小值出现在离岸条件下。分形维数的月度模式与湍流强度密切相关，其中分形维数要么保持相对一致，要么在较热的月份表现出明显的月度最大值。此外，分形维数与数据长度密切相关，其中 D 通常随着窗口宽度的增加而增加，并随着测量时间间隔的增加而减小。