# Analysis of the Near-Ground Wind Field Characteristics during Typhoon Soulik
## 3 Quantitative Analysis of Mean Wind Properties
### Profiles of Wind Velocity  
The wind speed profile represents the vertical arrangement of transverse wind speed and is a crucial factor in calculating wind loads on buildings. Multiple ideas and models have been developed to elucidate the variations in average wind speed with height inside the atmospheric boundary layer. These include the power law [20], the logarithmic law [20], and the Deaves-Harries model [21]. (1) Power law  
Through extensive empirical research, [PERSON] [20] conducted an analysis of wind profiles across various terrains. The findings indicate that the exponential function provides a more accurate representation of the variations in average wind height. The power law expression is  
\[\frac{U(z)}{U\Big{(}z_{ref}\Big{)}}=\big{(}\frac{z}{z_{ref}}\big{)}^{a} \tag{7}\]  
where \(z_{ref}\) represents the standard height, \(U\Big{(}z_{ref}\Big{)}\) represents the average wind velocity at the standard height, and \(a\) represents the power law constant. (2) Logarithmic law  
In a state of neutral atmospheric circumstances, there exists a region where the inner and outer boundary layers overlap. Within this region, the wind velocity adheres to both the boundary layer law and the velocity deficit law. The logarithmic law expression is  
\[U(z)=\frac{u^{*}}{\kappa}In(\frac{z}{z_{0}}) \tag{8}\]  
where \(z_{0}\) is the roughness length. This study employs the 0.02 m measurement based on the landform characteristics and the Class C site conditions under the American specification [22]; \(\kappa\) is the von Karman constant, usually 0.4; \(u^{*}\) represents friction speed. Its commonly used mathematical formula is as follows [23]. \[u^{*}=\left[\left(\overline{u^{\prime}w^{\prime}}\right)^{2}+\left(\overline{ v^{\prime}w^{\prime}}\right)^{2}\right]^{1/4} \tag{9}\]  
Figure 2: Changes in average wind velocity and direction over time. (3) Deaves-Harries model  
The Deaves-Harries model is optimized on the basis of the logarithmic law and can be well applied to the whole boundary layer. The expression is  
\[\frac{U(z)}{u^{*}}=\left(\frac{1}{\kappa}\right)\left\{In\left(\frac{z}{z_{0}} \right)+5.75\left(\frac{z}{z_{g}}\right)-1.88\left(\frac{z}{z_{g}}\right)^{2}-1.33\left(\frac{z}{z_{g}}\right)^{3}+0.25\left(\frac{z}{z_{g}}\right)^{4}\right\} \tag{10}\]  
where \(z_{g}\) denotes the boundary layer height, which is computed as follows:  
\[z_{g}=\frac{u^{*}}{B^{\prime}f} \tag{11}\]  
where \(B^{\prime}\) is the empirical parameter, generally six, and \(f\) is the Coriolis parameter, which is taken as \(7.554\times 10^{-5}s^{-1}\) in this study. Figure 3a displays variation trends in average wind speed with height in five distinct groups. From the figure, the measured wind speed profile presents two different changing trends. As the wind speed is below 12 m/s, the average wind speed exhibits a very gradual variation with height. However, as it exceeds 12 m/s, the variation becomes more pronounced. Figure 3b displays the comparative graph of the measured wind profile and each standard. The findings indicate that as the average wind speed exceeds 12 m/s, the power law and the logarithmic law demonstrate a closer fit to the observed variation pattern of Typhoon Soulik's average wind speed with height, but the Deaves-Harris model exhibits some disparities. To establish a quantitative assessment of the degree of concurrence between the theoretical model and the measured wind profile, the power law, the logarithmic law, and the Deaves-Harries model are evaluated with the measured wind profile. The wind speed correlation coefficient and standard deviation of the theoretical model are represented by a Taylor diagram, as shown in Figure 4. From the figure, the Deaves-Harris model shows the lowest correlation coefficient with measured wind profiles at 0.49 and the highest normalized standard deviation at 0.44. The power law and the logarithmic law both exhibit correlation coefficients of around 0.7 with measured wind profiles, while their normalized standard deviations are 0.11 and 0.09, respectively.