## 2 Materials and Methods
### Processing and Collection of Rainfall Data: Trigger Factors
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Method** & **Correction Method** & **Start of Rain** & **End of Rain** \\ \hline
1 & No rain for previous 24 h & No rain for 24 consecutive hours \\
2 & 1 & No rain for previous 12 h & No rain for 12 consecutive hours \\
3 & Hourly rainfall is greater than 4 mm & Rainfall is less than 4 mm for three \\  & Cumulative rainfall is at least 10 mm in the first 24 h & Cumulative rainfall is less than 10 mm for 24 consecutive hours \\
5 & 3 & Hourly rainfall is greater than 4 mm & Rainfall is less than 4 mm for six consecutive hours \\
6 & 4 & Cumulative rainfall is at least 10 mm in the first 12 h & Cumulative rainfall is less than 10 mm for 24 consecutive hours \\ \hline \hline \end{tabular}
\end{table} 
Table 6: The six rainfall-cutting methods. Because their centers were dispersed, the temporal and spatial distributions of the rainfall events in each of the 12 above-mentioned rain gauge stations' records were inconsistent with one another. Therefore, the structural properties of the known spatial distribution of observed values are used in an approach known as kriging, which provides estimations closer to real-world events than conventional estimation techniques do. After classifying each event's rainfall, a Pearson correlation-coefficient test was run. Table 7 shows the correlation matrix among the various debris flows following the normalization of four separate sets of rainfall data. The eigenvalues for cumulative rainfall, maximum daily rainfall, and rainfall intensity (RI) are all greater than 0.7, demonstrating a strong correlation between these three factors. Maximum hourly rainfall can only be determined after a rainfall event has ended; however, the cumulative rainfall and rainfall intensity, which also have a significant impact on debris flows, can be computed while a rainfall event is still in progress. Extrapolating maximum daily rainfall from cumulative rainfall is quicker and more practical than measuring maximum daily rainfall directly. Therefore, using the maximum daily and hourly rainfall of the event as the key debris-flow triggers is more in line with the primary goal of this study: developing a basis for a real-time early warning of such flows. Tables 8-10 display the maximum daily rainfall and maximum hourly rainfall associated with each of the focal rainfall events. Rainfall distribution maps based on those data (Figures 15 and 16) were then created in QGIS using the kriging algorithm. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Factors**} & \multicolumn{2}{c}{**Maximum Daily**} & \multicolumn{2}{c}{**Maximum**} & \multicolumn{1}{c}{**Cumulative**} & \multicolumn{1}{c}{**Rainfall**} \\  & **Rainfall** & **Hourly Rainfall** & **Rainfall** & **Intensity** \\ \hline Maximum Daily & \multirow{2}{*}{1.00} & \multirow{2}{*}{0.59} & \multirow{2}{*}{0.89} & \multirow{2}{*}{0.89} \\ Rainfall & & & & \\ Maximum Hourly & & & & \\ Rainfall & & & & \\ Cumulative Rainfall & & & & \\ Rainfall Intensity & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Pearson correlation coefficients. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Event**} & \multicolumn{2}{c}{**Typhoon Mindulle in 2004**} & \multicolumn{2}{c}{**Typhoon Sinlaku in 2008**} \\
**Event** & **Maximum Daily** & **Maximum Hourly Rainfall** & **Maximum Daily** & **Maximum Daily** & **Maximum Hourly Rainfall** \\  & **Rain (mm)** & **(mm)** & **Rain (mm)** & **Rain (mm)** \\ \hline Alishan & 616 & 84.5 & 738 & 53 \\ Ruili & 423 & 76.5 & 481.5 & 41 \\ Shipanlong & 525.5 & 77.5 & 984 & 68 \\ Fengliulu & 499 & 87 & 889 & 62.5 \\ Da-an & 0 & 0 & 441.5 & 46.5 \\ Dapu & 180.5 & 33 & 184 & 24 \\ Shenmu Village & 513 & 72.5 & 630.5 & 41 \\ Zhongxinlun & 217 & 50.5 & 345 & 33 \\ Tongtou & 293.5 & 44 & 408 & 44.5 \\ Caoling & 370 & 53 & 568.5 & 46.5 \\ Fengshan & 424 & 73.5 & 856 & 56 \\ Meishan & 0 & 0 & 0 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Rainfall data from the typhoons Mindulle and Sinlaku.