## 3 Results
### Time Series Analysis of Wind Speed at Different Heights
Power Law Wind Profile Theory is a common method used in wind engineering to express the relationship between wind speed and altitude, as shown in Equation (1). The magnitude of the \(\alpha\) value reflects the rate of increase in wind speed with altitude. We use the least squares method to fit the data. Since the calculation process of the optimal parameter values is quite dependent on the initial parameter values due to its nonlinearity, we transform Equation (1) into a linear model, Equation (13), through logarithmic change:  
\[logv(z)=logv\Big{(}z_{ref}\Big{)}+\alpha log\bigg{(}\frac{z}{z_{ref}}\bigg{)} \tag{13}\]  
Subsequently, we fit the average wind speed for each month, calculating the optimal \(\alpha\) value for each month. Taking January 2000 as an example, we visualize the original height and wind speed scale to demonstrate the actual nonlinear relationship, as shown in Figure 6. \begin{table}
\begin{tabular}{c c c c} \hline \hline \(\mathbf{S_{n}}\) & \(\mathbf{RE_{i}}\) & \(\mathbf{RE_{m}}\) & \(\mathbf{RE_{u}}\) \\ \hline Spring & y = 54.03 – 0.0258x & y = 51.85 – 0.0238x & y = 21.16 – 0.0107x \\ Summer & y = 34.92 – 0.0165x & y = 25.85 – 0.0114x & y = 10.49 – 0.0033x \\ Autumn & y = 35.73 – 0.0169x & y = 58.19 – 0.0274x & y = 36.80 – 0.0160x \\ Winter & y = 17.78 – 0.0078x & y = 32.23 – 0.0143x & y = \(-\)0.15 + 0.0025x \\ \hline \hline \end{tabular} RE.—low-level regression equations; RE.—middle-level regression equations; RE.—upper-level regression equations.  
\end{table} 
Table 4: Fitting functions for different altitude levels in different seasons. Figure 6: Optimal fitting of the wind shear index \(\alpha\) for monthly average wind speed: an example from January 2000. Using the least squares method and Mann-Kendall trend analysis, we examined monthly wind shear index values in Beijing over the past 30 years. Both methods revealed a statistically significant upward trend. Specifically, the least squares analysis showed an average annual increase of 0.003 in the wind shear index, and the Mann-Kendall analysis yielded a Z value of 5.617. This trend could be influenced by factors such as climate change, atmospheric circulation changes, and human activities. Increased wind shear might affect atmospheric stability, potentially causing instability when warm, moist air interacts with swiftly moving upper cold air. This could increase convective activities and the likelihood of extreme weather events like thunderstorms and heavy precipitation. Furthermore, a higher wind shear index could enhance vertical mixing, helping transport ground-level pollutants to higher altitudes and impacting weather patterns and climate, as shown in Figure 7.  
After obtaining the optimal \(\alpha\) value for each month, the wind speed is adjusted to the standard statistical height (10 m) specified in the regulations. When calculating the basic wind speed, the maximum wind speed value in the time sequence segment is used. The maximum wind speed for each month is obtained through maximum value sampling, and then compared with the monthly average time series for trend analysis, as shown in Figure 8.  
From the trend line, the change trend of the maximum wind speed is like that of the overall average wind speed, and it also shows a downward trend (Z value is \(-3.71\), \(p\) value is less than 0.05). The maximum wind speed has more pronounced seasonal fluctuation  
Figure 8: Overall trend of wind speed at 10 m height. Figure 7: Time series of \(\alpha\) values from 1991 to 2020 with trend line. characteristics compared to the average wind speed. To more visually demonstrate this characteristic, the maximum wind speed is integrated into a monthly scale for fitting, as shown in Figure 9.  
Maximum wind speed is significantly affected by seasonal factors, with peaks mainly occurring in winter and early spring. In the seasonal trend fitting, only a sine function was initially used for analysis. However, the results show that the variability of maximum wind speed is high.