## 3 Results and Discussions
### Impact of Gaussian-Shaped Mountain Width on LIVs  
As analyzed in Section 3.2, we also compare the calculated LIVs for different Gaussian-shaped mountain widths. The mountain height is fixed to 250 m here, and the mountain widths are set to 200 m, 300 m, 500 m, and 700 m. Figure 9 presents the LIVs calculated along the distribution line, which is located 400 m horizontally from the mountain center, as shown in Figure 1.  
For Configuration A, it can be seen from Figure 9a-c that the LIVs at the center and ends of the line decrease with increasing mountain width. For example, it can be found in Table 5 that the LIVs at the center of the line are reduced by approximately 6%, 27%, and 52% for 300 m, 500 m, and 700 m wide mountains than that of 200 m. Additionally, a larger mountain width leads to a longer peak arrival time. It can be explained that lightning EM waves propagate around the mountain due to terrain obstruction, which extends the propagation path for the case of SL1. In contrast to the case of SL1, as shown in Figure 9d-f for lightning strikes at SL2, the LIVs are significantly affected at the close end of the line only when the mountain width is relatively larger (500 m or 700 m). It is possible that the distance between the mountain base and the distribution line decreases as the mountain width increases. Observation points located closer to the mountain base are more sensitive to the reflection of lightning EM waves, whereas farther observation points are less affected, leading to less significant variation in LIVs at the remote end of the line, as shown in Figure 9e,f. However, the mountain's shielding effect has a certain level of effect on LIVs when lightning strikes at SL3, as shown in Figure 9g-i, as the LIVs at both the line end and center decrease with increasing mountain width. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Strike Location** & **Height (m)** & **Close End (kV)** & **Center (kV)** & **Remote End (kV)** \\ \hline SL1 & 200 & 16.10 & 8.84 & 9.81 \\  & 250 & 16.25 & 8.80 & 10.19 \\  & 300 & 16.40 & 8.55 & 10.55 \\  & 400 & 16.62 & 7.75 & 11.02 \\ SL2 & 200 & 17.59 & 43.74 & 17.55 \\  & 250 & 19.42 & 46.95 & 13.41 \\  & 300 & 20.24 & 49.23 & 14.89 \\  & 400 & 19.04 & 51.22 & 17.09 \\ SL3 & 200 & 3.74 & 10.19 & 3.74 \\  & 250 & 3.51 & 9.76 & 3.51 \\  & 300 & 3.27 & 9.39 & 3.27 \\  & 400 & 2.74 & 8.70 & 2.74 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Maximum LIVs of different mountain heights in Configuration B. \begin{table}
\begin{tabular}{l l l l l} \hline \hline
**Strike Location** & **Width** & **Close End (kV)** & **Center (kV)** & **Remote End (kV)** \\ \hline SL1 & 200 & 14.21 & 6.13 & 16.07 \\  & 300 & 14.22 & 5.72 & 15.70 \\  & 500 & 13.46 & 4.39 & 13.92 \\  & 700 & 12.70 & 3.05 & 12.33 \\ SL2 & 200 & 21.03 & 18.79 & 37.47 \\  & 300 & 20.79 & 19.15 & 37.79 \\  & 500 & 20.27 & 18.71 & 36.86 \\  & 700 & 22.44 & 18.62 & 35.33 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Maximum LIVs of different mountain widths in Configuration A. Figure 10 presents the results of LIVs along the distribution line for Configuration B and the maximum LIVs are presented in Table 6. Figure 10a-c shows the variations in LIVs when lightning strikes at SL1. It can be observed that as the mountain width increases to 500 m, the LIVs exhibit a significant attenuation, particularly at the close end and center of the line. This phenomenon is likely due to the close range between the mountain base and overhead distribution line for a larger mountain width, resulting in enhanced shielding of lightning EM fields by the mountain.