## 3 Results and Discussions
### Impact of Gaussian-Shaped Mountain Height on LIVs  
In this section, we further explore the influence of different heights of Gaussian-shaped mountains on LIVs. The terrain heights are set to 200 m, 250 m, 300 m, and 400 m, with the mountain width fixed at 400 m. Figure 7 presents the calculated LIVs along the distribution line, located at 300 m horizontally from the mountain center. For Configuration A, when lightning strikes at SL1, as shown in Figure 7a, the LIVs at the close end of the line increase with the terrain heights. For the farther observation points, such as the center and the remote end of the line, LIVs decrease as the mountain heights increase. Moreover, an increase in mountain height leads to a corresponding delay in the arrival time of the voltage peak [51]. When lightning strikes at SL2, as shown in Figure 7d-f, at the close end of the line, the increase in induced voltage becomes more pronounced with rising mountain height, and LIVs show increments of 14%, 18%, and 29% relative to 200 m height for mountain height of 250 m, 300 m, and 400 m, as shown in Table 3, respectively. The arrival time of the voltage peak at the center and remote end of the line shows a longer delay due to the longer propagation path. Figure 7g-i depicts the variations in induced overvoltages along the distribution line when lightning strikes at SL3. It can be observed that as the mountain height increases, a reduction exists in the LIVs at the close end of the distribution line [53]. This can be explained by the shielding effect on lightning EM fields nearby is stronger for higher mountains, which, meanwhile, prolongs the propagation path, as concluded by [PERSON] et al. [54]. However, due to the longer propagation distance, the induced voltages at the center of the line and the remote end remain largely unaffected. This can be explained by the reduced shielding effect of mountains in the vicinity of lightning EM fields with increasing observation distance, as demonstrated by [PERSON] et al. [55]. \begin{table}
\begin{tabular}{l l l l l} \hline
**Strike Location** & **Terrains** & **Close End (kV)** & **Center (kV)** & **Remote End (kV)** \\ \hline SL1 & Flat ground & 18.09 & 9.35 & 9.98 \\  & Gaussian-shaped & 16.25 & 8.80 & 10.19 \\  & Cone-shaped & 14.77 & 9.36 & 9.48 \\ SL2 & Flat ground & 11.78 & 33.29 & 11.78 \\  & Gaussian-shaped & 19.42 & 46.95 & 19.42 \\  & Cone-shaped & 17.85 & 44.50 & 17.85 \\ SL3 & Flat ground & 4.18 & 10.57 & 4.18 \\  & Gaussian-shaped & 3.51 & 9.76 & 3.51 \\  & Cone-shaped & 3.55 & 10.45 & 3.55 \\ \hline \end{tabular}
\end{table} 
Table 2: Maximum LIVs of different terrains in Configuration B. \begin{table}
\begin{tabular}{l l l l l} \hline
**Strike Location** & **Height (m)** & **Close End (kV)** & **Center (kV)** & **Remote End (kV)** \\ \hline SL1 & 200 & 15.41 & 5.13 & 16.18 \\  & 250 & 15.58 & 4.59 & 15.89 \\  & 300 & 15.79 & 4.06 & 15.57 \\  & 400 & 15.98 & 3.06 & 14.81 \\ SL2 & 200 & 23.53 & 22.30 & 41.10 \\ \hline \end{tabular}
\end{table} 
Table 3: Maximum LIVs of different mountain heights in Configuration A.  
by the results of [PERSON] et al. (2018), which show that the enhancement of lightning electric fields becomes less pronounced with increasing mountain height. Figure 8g-i illustrates the variations in LIVs for lightning strikes at SL3. As shown in Figure 8g, under the influence of the shielding effect of the mountain, it can be observed that with increasing mountain height, the voltages at the close end are decreased by 8%, 16%, and 31%, respectively, relative to the 200 m height for other corresponding heights. At the center of the line, as shown in Figure 8h, the voltages are decreased by 8%, 10%, and 19%, respectively, when compared to a 200 m height mountain. The results at the remote end of the line are identical to those at the close end as shown in Figure 8g due to the symmetry of terrain. It can be found that the shielding effect is much stronger for SL3 than for SL1, which aligns with the conclusion proposed by [PERSON] et al. (2018).