## 2 Materials and Methods
### Processing and Collection of Rainfall Data: Trigger Factors  
Rainfall is an important debris-flow initiator. The researchers, therefore, gathered rainfall data from 2004 to 2017, as well as SPOT images from each time period, to choose an appropriate event and then established each such event's rainfall statistics. Figure 14 shows the locations of the 12 rain gauge stations that were used for that purpose. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Distance between the** & & **Distance between the** & \\
**Assessment Point and the** & **Score** & **Assessment Point and the** & **Score** \\
**Fault Zone** & & **Fault Zone** & \\ \hline \textless{}100 m & 10 & 600–700 m & 4 \\ 100–200 m & 9 & 700–800 m & 3 \\ 200–300 m & 8 & 800–900 m & 2 \\ 300–400 m & 7 & 900–1000 m & 1 \\ 400–500 m & 6 & \textgreater{}1000 m & 0 \\ 500–600 m & 5 & & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Scoring criteria for fault assessment [40]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Stratum Name** & **Score** & \begin{tabular}{c} **Landslide** \\ **Ratio** \\ \end{tabular} & **Stratum Name** & **Score** & \begin{tabular}{c} **Landslide** \\ **Ratio** \\ \end{tabular} \\ \hline Sanhisa Group and equivalents & 10 & 2.8\% & Tatungshan Formation & 1.91 & 0.28\% \\ Sandstone & 9.76 & 2.73\% & Tableland Deposits & 1.87 & 0.27\% \\ Lushan formation & 7.42 & 2\% & Toukoshan Formation and equivalents & 1.80 & 0.25\% \\ Chinshui Shale and equivalents & 6.73 & 1.78\% & Cholan Formation and equivalents & 1.79 & 0.25\% \\ Kankou Formation & 5.81 & 1.5\% & \
\begin{tabular}{c} Hitsun Formation, Hsinkao \\ Formation \\ \end{tabular} & 1.28 & 0.09\% \\ Juifang Group and equivalents & 3.81 & 0.87\% & Alluvium & 1.03 & 0.01\% \\ Yehliu Group and equivalents & 3.69 & 0.84\% & Lateritic Terrace Deposits & 1.03 & 0.01\% \\ Tananao Schist & 2.21 & 0.38\% &
\begin{tabular}{c} Mafic igneous rocks \\ \end{tabular} & 1.00 & 0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Stratum scoring criteria [40]. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Minimum Value** & \
\begin{tabular}{c} **Maximum** \\ **Value** \\ \end{tabular} & **Average** &
\begin{tabular}{c} **Standard** \\ **Deviation** \\ \end{tabular} \\ \hline Type of stratum & 1.79 & 10.00 & 8.22 & 2.75 \\ Distance from the fault & 0.00 & 10.00 & 5.30 & 3.11 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Values of material factors for all 33 catchment areas. Rainfield Cutting  
As shown in Table 6, rainfall cutting comprises a set of methods that are used to make sense of the relationship between data from major rainfall events and slope damage [41]. In this study, Method 5 was adopted for the division of the rainfalls. This was because Methods 1, 2, and 4 cut rainfalls into time periods that are too long, thus artificially reducing their average intensity value, while Method 3 errs in the opposite direction, making some rainfall data too easy to ignore. Of Methods 5 and 6, the latter has a longer delay time, which also reduces the apparent average intensity of rainfall. Figure 13: Distribution of geological faults in the Ching-Shuei River watershed. Geological Survey and Mining Management Agency, Ministry of Economic Affairs. Available online: [[https://www.gsmma.gov.tw/nss/p/index](https://www.gsmma.gov.tw/nss/p/index)]([https://www.gsmma.gov.tw/nss/p/index](https://www.gsmma.gov.tw/nss/p/index)) (accessed on 5 January 2024). Figure 14: Location map of rainfall stations. Central Weather Administration. Available online: [[https://www.cwa.gov.tw/eng/](https://www.cwa.gov.tw/eng/)]([https://www.cwa.gov.tw/eng/](https://www.cwa.gov.tw/eng/)) (accessed on 5 January 2024).