## 2 Collation and Analysis of Measured Data of Temperature and Wind
### Probability Model Fitting of Wind Speed and Direction
#### 2.3.3 Basic Wind Speed Calculation and Result Analysis  
After determining the three probability parameters of the joint distribution of wind speed and direction, the basic wind speed in a certain return period of different wind directions can be obtained. The basic wind speed calculation formulae, for the Gumbel distribution are as follows [24]:  
\[ \begin{array}{l}\frac{1}{R}=Nf(\theta)\Big{\{}1-\exp\Big{[}\frac{U_{R}-B( \theta)}{A(\theta)}\Big{]}\Big{\}}\\ U_{R}=-A(\theta)LnLn\frac{FNf(\theta)}{FNf(\theta)-1}+B(\theta)\end{array}  \tag{8}\]  
In the formula, \(R\) is the return period, and \(N\) is the number of strong winds in any one year. In this study, \(N\) is 365. \(U_{R}\) is the basic wind speed of the \(R\)-year return period. The basic wind speed of 16 wind directions in different return periods can be obtained by Formula (8), as shown in Table 2.  
It can be seen from Table 2 that the Gumbel distribution has the maximum basic wind speed in the NNE wind direction, and the maximum value is 30.69 m/s. In most cases, the basic wind speed obtained by considering the effect of wind direction is smaller than that obtained by ignoring the effect of wind direction. However, there are exceptions, that is, the basic wind speed considering the influence of wind direction is larger than that ignoring the influence of wind direction, such as NNE and SSW wind direction. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Wind Direction**} & \multirow{2}{*}{**Wind Frequency**} & \multicolumn{2}{c}{**Gumbel Distribution**} & \multicolumn{2}{c}{**Frechet Distribution**} & \multicolumn{2}{c}{**Weibull Distribution**} \\ \cline{2-10}  & & \(A\) & \(B\) & \(r\) & \(A\) & \(C\) & \(r\) & \(A\) & \(C\) & \(r\) \\ \hline N & 2.00\% & 0.929 & 5.842 & 0.856 & 5.875 & 6.131 & 0.886 & 6.551 & 5.255 & 0.716 \\ NNE & 8.00\% & 2.982 & 6.893 & 0.786 & 7.045 & 2.243 & 0.786 & 9.163 & 2.554 & 0.738 \\ NE & 4.75\% & 1.101 & 4.895 & 0.849 & 4.968 & 4.152 & 0.834 & 5.349 & 5.846 & 0.844 \\ ENE & 4.25\% & 1.129 & 5.224 & 0.920 & 5.323 & 4.528 & 0.938 & 5.850 & 4.739 & 0.859 \\ E & 2.00\% & 1.158 & 5.500 & 0.846 & 5.866 & 4.211 & 0.797 & 6.304 & 4.331 & 0.859 \\ ESE & 5.00\% & 0.966 & 3.679 & 0.808 & 3.742 & 3.599 & 0.869 & 4.268 & 3.877 & 0.718 \\ SE & 11.00\% & 2.667 & 4.475 & 0.636 & 4.379 & 1.797 & 0.715 & 6.891 & 1.983 & 0.634 \\ SSE & 14.75\% & 0.585 & 3.284 & 0.793 & 3.240 & 5.851 & 0.851 & 3.728 & 6.583 & 0.725 \\ S & 12.25\% & 1.380 & 3.316 & 0.840 & 3.493 & 2.292 & 0.928 & 4.492 & 2.446 & 0.744 \\ SSW & 10.75\% & 3.014 & 5.285 & 0.747 & 5.302 & 1.548 & 0.703 & 7.555 & 2.144 & 0.749 \\ SW & 12.25\% & 2.827 & 5.379 & 0.711 & 5.314 & 1.881 & 0.717 & 7.610 & 2.306 & 0.713 \\ WSW & 4.50\% & 1.212 & 5.942 & 0.740 & 6.035 & 4.771 & 0.726 & 6.308 & 7.286 & 0.742 \\ W & 2.25\% & 1.253 & 5.821 & 0.762 & 5.956 & 4.673 & 0.739 & 6.392 & 5.562 & 0.861 \\ WNW & 1.75\% & 1.158 & 4.888 & 0.896 & 4.881 & 4.039 & 0.851 & 5.706 & 5.019 & 0.946 \\ NW & 2.00\% & 0.694 & 3.398 & 0.932 & 3.345 & 4.959 & 0.924 & 3.878 & 5.889 & 0.937 \\ NNW & 2.50\% & 0.343 & 3.021 & 0.882 & 3.053 & 7.774 & 0.877 & 3.591 & 6.297 & 0.818 \\ \(\Sigma\) & 1 & 2.398 & 5.014 & 0.980 & 5.199 & 1.962 & 0.934 & 6.796 & 2.422 & 0.948 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Fitting parameters of wind speed probability density curve under discrete wind direction. Compared with the basic wind speed of 26.9 m/s in the 100-year return period of Guyuan area in the General Specifications for Design of Highway Bridges and Culverts (JTGD60-2015), it is found that it is smaller than the basic wind speed of 30.21 m/s in the 100-year return period of the whole wind direction calculated in this study. Because the basic wind speed of the 100-year return period in the specification generally adopts conservative design criteria to ensure the safety of the structure, this means that the basic wind speed in the specification may be lower than the actual observed wind speed, and there is a certain safety margin.