# Full-Scale Measurements of Wind Characteristics on a High- Rise Building during Typhoon Sarika
## 3 Wind Characteristics of Typhoon Sarika
### Gust Factor  
The gust factor \(G(t_{g})\) is defined as the ratio of the gust speed \(\hat{U}\) in gust duration \(t_{g}\) to the 10-min mean wind speed \(\overline{U}\), which can be written as:  
\[G(t_{g})=\frac{\hat{U}(t_{g})}{\overline{U}}=1+\frac{\text{max}(\overline{u }(t_{g}))}{\overline{U}} \tag{9}\]  
where the gust speed \(\hat{U}\) is the largest mean wind speed within the gust duration \(t_{g}\). \(\text{max}(\overline{u(t_{g})})\) is the largest mean wind speed in duration \(t_{g}\) of the longitudinal fluctuating wind speed within 10-min. It can seem that the longer the gust duration \(t_{g}\) is, the smaller difference between the gust duration and the gust duration is, and the results of the gust factor are closer to 1. Taking \(t_{g}\) = 3 s and \(T\) = 10 min as examples, this paper investigates the variations of the longitudinal and lateral gust factors concerning mean wind speed. Figure 9 shows that the longitudinal and lateral gust factors are prone to decrease when the 10-min mean wind speed is less than 7 m/s, and the longitudinal and lateral gust factors are basically (1.2, 3.2) and (0.2, 1.5) in sequence. Moreover, the longitudinal and lateral gust factors remain stable after the 10-min mean wind speed reaches 7 m/s; the longitudinal and lateral gust factors are basically (1.2, 1.8) and (0.2, 0.6) in sequence during the passage of Typhoon Sarika.  
The gust factor is obviously correlated with turbulence intensity. [PERSON] [14] suggest the following formula to establish the relationship between gust factor and turbulence intensity,  
\[G_{u}(t_{g})=1+k_{1}t_{u}^{k_{2}}\ln(T/t_{g}) \tag{10}\]  
where \(T\) is a different sample duration. [PERSON] suggested \(k_{1}\) = 0.5, \(k_{2}\) = 1.0; Equation (10) shows that the main factors of gust factors are turbulence intensity, sample duration, and gust duration. Taking \(t_{g}\) = 3 s and \(T\) = 10 min as example, Equation (10) is adopted to fit the relationship between gust factor and turbulence intensity during the passage of Typhoon Sarika, and to compare with the linear model proposed by [PERSON] [14] Figure 10 demonstrates that the gust factor increases with the increasing turbulence intensity, and shows a linear relationship between turbulence intensity and gust factor. The results show that the prediction values of the linear model proposed by [PERSON] [14] are larger than the measured values. Based on the measured values of longitudinal and lateral gust factors and turbulence intensity during Typhoon Sarika, an empirical formula concerning longitudinal and lateral gust factor and turbulence intensity are proposed:  
\[G_{u}(t_{g})=1+0.42I_{u}^{0.97}\ln(T/t_{g}) \tag{11}\]  
\[G_{v}(t_{g})=0.40I_{v}^{0.95}\ln(T/t_{g}) \tag{12}\]  
This study investigates the variation of gust factor during the passage of Typhoon Sarika obtained for different sample duration \(T\) (1, 10, 30, and 60 min) and gust duration \(t_{g}\) (0.1, 0.2, 0.3, 0.5, 1.0, 2.0, 3.0, 5.0, 10, 30, 60,120, 180, 600, 1200, and 1800 s). Figure 11a,b shows that, the gust factor decreases as the gust duration \(t_{g}\) increases when the sample duration \(T\) is 10-min during different wind speeds. Figure 11c,d illustrates that the gust factor increases with the increasing sample duration \(T\).  
Figure 9: The variation of gust factor with respect to 10-min wind speed and direction. (**a**) \(G_{u,v}\) with respect to 10-min \(\overline{U}\); (**b**) \(G_{u,v}\) with respect to 10-min \(\alpha\).