## 2 Modeling Approach
### Directional Thunderstorm Wind Model  
In order to overcome the shortcomings of the aforementioned classical method, a directional thunderstorm wind model was established [5]. First, the two horizontal components of wind speed were expressed as:  
\[\begin{array}{l}V_{X}(t)=\overline{V}_{X}(t)+V^{\prime}{}_{X}(t)\\ V_{Y}(t)=\overline{V}_{Y}(t)+V^{\prime}{}_{Y}(t)\end{array} \tag{4}\]  
Figure 1: Decomposition of thunderstorm outflow wind speed based on the classical method.  
in which \(\overline{V}_{X}\) and \(\overline{V}_{Y}\) are the slowly-varying mean wind speed in different wind directions, and \(V^{\prime}{}_{X}\) and \(V^{\prime}{}_{Y}\) are residual turbulent fluctuations. The slowly-varying longitudinal mean wind speed \(\overline{u}\) and its direction \(\overline{\pi}\) can be obtained by:  
\[\begin{array}{c}\overline{u}(t)=\sqrt{\overline{V}_{X}^{2}(t)+\overline{V}_{ Y}^{2}(t)}\\ \overline{\alpha}(t)=270-\text{atan}2\big{(}\overline{V}_{Y}(t)/\overline{V}_{ X}(t)\big{)}\end{array} \tag{5}\]  
As shown in Figure 2, the angle range of \(\overline{\alpha}(t)\) is \(0^{\circ}\) to \(360^{\circ}\), while \(V^{\prime}{}_{X}(t)\) and \(V^{\prime}{}_{Y}(t)\) can be projected to the direction of \(\overline{u}(t)\) and its perpendicular direction. Accordingly, the following equation can be generated:  
\[\begin{array}{c}u^{\prime}(t)=-V^{\prime}{}_{X}(t)\sin\overline{\alpha}(t)- V^{\prime}{}_{Y}(t)\cos\overline{\alpha}(t)\\ v^{\prime}(t)=V^{\prime}{}_{X}(t)\cos\overline{\alpha}(t)-V^{\prime}{}_{Y}(t) \sin\overline{\alpha}(t)\end{array} \tag{6}\]  
in which \(u^{\prime}(t)\) and \(v^{\prime}(t)\) are the longitudinal and lateral fluctuating wind speed components, respectively. Similar to the classical method, \(u^{\prime}(t)\) and \(v^{\prime}(t)\) can be simulated as the product of standard deviation and the reduced turbulent fluctuation with stationary Gaussian characteristics:  
\[\begin{array}{c}u^{\prime}(t)=\sigma_{u}(t)\widehat{u}^{\prime}(t)\\ v^{\prime}(t)=\sigma_{v}(t)\widehat{v}^{\prime}(t)\end{array} \tag{7}\]  
Therefore, the longitudinal and lateral wind speed can be expressed as follows:  
\[\begin{array}{c}u(t)=\overline{u}+u^{\prime}(t)=\overline{u}\Big{[}1+I_{u}( t)\widetilde{u^{\prime}}(t)\Big{]}\\ v(t)=v^{\prime}(t)=\overline{u}I_{v}(t)\widehat{v}^{\prime}(t)\end{array} \tag{8}\]  
where the slowly-varying longitudinal and lateral turbulence intensity are:  
\[\begin{array}{c}I_{u}(t)=\sigma_{u}(t)/\overline{u}\\ I_{v}(t)=\sigma_{v}(t)/\overline{u}\end{array} \tag{9}\]  
In addition, the gust factor is:  
\[G_{u}=\hat{u}/\overline{u}_{\max} \tag{10}\]  
where \(\hat{u}\) is the longitudinal peak wind speed, defined as the maximum value of longitudinal average wind speed within a period of 1 s, and \(\overline{u}_{\max}\) is the maximum value of the slowly varying mean wind speed \(\overline{u}\).  
Figure 3 shows the decomposition result of the thunderstorm wind speed signal at a height of 64 m based on the directional thunderstorm wind model by a moving average filter with a period of 30 s. The maximum value of slowly-varying mean wind speeds  
Figure 2: Directional signal decomposition.  
is 18.06 m/s, which is slightly different from \(\overline{U}_{\text{max}}\). The mean values of the longitudinal and lateral slowly-varying turbulence intensity are \(\overline{I}_{u}=0.167\) and \(\overline{I}_{v}=0.165\), respectively, and the ratio \(\overline{I}_{v}/\overline{I}_{u}=0.98\) is greater than the reference value of 0.75 specified in the load code. The cross-correlation between the longitudinal and lateral wind speeds obtained by the decomposition model is 0.021, which means that the wind speeds in two directions are uncorrelated. Thus, the directional thunderstorm wind model is effective.