# Characterization of Wind Guests: A Study Based on Meteorological Tower Observations
## 2 Materials and Methodology
### Definition of Wind Gust Descriptors  
As mentioned above, the main objective of this study was to examine and discuss the gust characteristics through various gust descriptors. In light of the studies by [PERSON] et al. [5], the major gust descriptors involved in the study are summarized as follows:  
Gust peak magnitude \(u_{t,T}^{max}\) denotes the maximum 3 s moving average longitudinal wind speed u every 10-min period [8]. The amplitude of gust \(u_{t,T}^{a}\) represents the difference between the peak 3-s moving average gust speed and the 10-min average wind velocity \(U_{T}\) (see Figure 2):  
\[u_{t,T}^{a}=u_{t,T}^{max}-U_{T} \tag{1}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Instrument** & **Height (m)** & **Observation Element** & **Output Frequency** \\ \hline
3D (Three dimensional) sonic anemometer (CSAT3) & 10, 40, 160, 320 above the level of ground temperature (Is) & Three orthogonal wind components (\(u_{x}\), \(u_{y}\), \(u_{z}\)), sonic virtual temperature (Is) & 10 Hz \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Information of the observation data. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Year** & **Start** & **End** \\ \hline
2018 & 15 September 00:00 & 17 September 23:59 \\
2018 & 8 January 20:00 & 8 January 23:59 \\
2018 & 9 January 00:00 & 9 January 11:00 \\
2018 & 8 March 00:00 & 8 March 11:00 \\
2018 & 7 April 00:00 & 7 April 09:00 \\
2019 & 4 March 20:00 & 4 March 23:59 \\
2019 & 5 March 00:00 & 5 March 04:00 \\
2019 & 22 September 06:00 & 22 September 11:00 \\
2019 & 7 October 00:00 & 7 October 08:00 \\
2020 & 16 February 00:00 & 16 February 17:00 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Outline of the observation period involved in the current study. The gust coefficient \(G_{t,T}\) is the ratio of the maximum value of peak gust \(u_{t,T}^{max}\) to the average wind speed in 10 min:  
\[G_{t,T}=u_{t,T}^{max}/U_{T} \tag{2}\]  
Likewise, the peak coefficient \(k_{t,T}\) is the ratio of the gust amplitude \(u_{t,T}^{a}\) to the standard deviation \(\sigma_{T}\) of the wind speed in 10 min:  
\[k_{t,T}=u_{t,T}^{a}/\sigma_{T} \tag{3}\]  
Turbulence intensity \(TI\) is the standard deviation of the 10 Hz longitudinal wind speeds, which is normalized by the 10 min average wind speed:  
\[TI=\sigma_{T}/U_{T} \tag{4}\]  
In addition to the aforementioned gust descriptors, the discrete gust events' evolution in a time series can also be represented by four additional parameters, namely, the rise time \(t_{r}\), the lapse time \(t_{l}\), the rise magnitude \(u_{r}\), the lapse magnitude \(u_{l}\)[5]. The rise time represents the time from the starting valley (i.e., the local minimum 3-s moving average immediately following below \(U_{T}\)) to the gust peak; the lapse time represents the time from the peak to trough (i.e., the next minimum value below \(U_{T}\) in the moving average of 3-s). The increase was defined as the wind speed difference from the initial valley to the peak, whereas the drop was defined as the wind speed difference from the peak to the end valley (see Figure 2). Based on these four parameters, a gust asymmetrical factor (GAF) can be determined as:  
\[GAF=\frac{u_{r}/t_{r}}{u_{l}/t_{l}} \tag{5}\]  
Figure 2: A diagram of a single gust event showing the gust descriptors. Moreover, the gust length scale \(L_{g}\) is an estimate of the physical degree of a wind gust, which is described as the integral of the 3-s moving average of longitudinal wind speed throughout the gust:  
\[L_{g}=\int_{t_{start}}^{t_{end}}u_{3s}dt \tag{6}\]  
where \(t_{start}\) and \(t_{end}\) are the time of the start-valley and end-valley of the gust event, respectively. It is worth mentioning that the entire gust period is defined using the times of start-valley and end-valley, rather than the crossing times of \(U_{T}\) and \(u_{3s}\), which ensures that the whole process of flow acceleration and deceleration is fully encapsulated [5].