# Wind Characteristics in Mountainous Valleys Obtained through Field Measurement
## 3 Results
### Mean Characteristics
#### Wind Profile  
Within the atmospheric boundary layer, when the topography is homogeneous, the distribution pattern of wind speed along height increases nonlinearly. The curve of the wind speed along the height is called the wind profile. The shape of a site's wind profile is highly dependent on the roughness of the surface of the site. Based on the theories of logarithmic rate and exponential law, domestic and foreign scholars have obtained the empirical formulae in each country's norms through statistical analysis of the distribution of the wind field. For windy periods, the formula is generally applicable up to heights of 200 m. Although meteorologists think that the logarithmic law is more accurate, for calculation convenience, the Chinese specification (JTG/T 3360-01-2018) [36] adopts the exponential law form. It is assumed that the distribution of wind speed along the vertical height in the atmospheric boundary layer satisfies the law of exponential change:  
\[U(z_{2})=U(z_{1})(\frac{z_{2}}{z_{1}})^{\alpha} \tag{1}\]  
where \(z_{1}\) and \(z_{2}\) represent the heights from the ground, \(\alpha\) is a dimensionless parameter determined by the surface conditions, and \(U(z_{1})\) and \(U(  
will result in a small number of samples that can be processed, and if the unreliable data from the wind speed at each altitude are removed, sometimes too many data are removed, affecting the accuracy of the fit. Therefore, to ensure the accuracy of the study results, the following principle was adopted in this study: after eliminating invalid data from 18 heights in the same time period, the data greater than or equal to 15 were considered to be available for the sample. These were used to fit the wind profile during the observation period. The sample wind speed is also an important factor affecting wind profile fitting results. If the wind speed is too low, the wind profile often does not have a stable form. Therefore, in this study, the mean wind speed at all altitudes greater than 5 m/s was chosen as a threshold, and a total of 4000 study samples were obtained. According to the exponential law using the least squares method to fit the wind profile, the wind profile data were divided into six forms, as shown in Figure 5. The distribution of form (a) is messy, so it is called messy type. Form (b) complies with the exponential law well. The distribution of form (c) is relatively regular. The distribution of form (d) is opposite to the exponential law, so it is called reverse type. The forms of (e) and (f) are like large and small zigzags, respectively. As the height increases, the mean wind speed shows a gradually increasing law in general. Due to the complex topography, the pattern of wind speed variation with height does not fully comply with the exponential law. Figure 5: _Cont._  
Mathematical statistics on the 4000 samples of wind profiles fitted exponentially yielded a sample mean \(\mu\) of 0.21 and a sample standard deviation \(\sigma\) of 0.11. The frequency distribution histogram is shown in Figure 6. The bridge is located in gentle hilly terrain. According to the Chinese specifications, the surface roughness coefficient for this terrain is 0.22, which is close to the measured value of 0.21. A normal probability plot is used to test whether a set of data obeys a normal distribution. If the sample obeys a normal distribution, the normal probability plot will be a straight line. The shape of the wind profile is the result of many factors, so it was necessary to test whether the \(\alpha\) index obeyed a normal distribution. With a confidence level of 95%, the normal probability plot of the \(\alpha\) index shows that the normal probability plot is typical of a long-tailed distribution, which means that the statistical distribution of the \(\alpha\) index deviates from the mean of the normal distribution. Figure 7 shows the results of the fitting of the wind profile and the corresponding distribution of the wind angle with height for the same time period.