## 5 Results
\begin{array}{ll}\alpha k&\qquad\text{when }0\leq k\leq k_{i}\\ \alpha*k_{i}exp(-\beta(k-k_{i}))&\qquad\text{when }k>k_{i}\end{array} \right. \tag{12}\]  
where \(h\) is the function of rainfall response changing with time. The coefficients \(\alpha\) and \(\beta\) are constant, and the lag time \(k_{i}\) at which has a maximum value of \(h(k)\) are needed to be  
Figure 5: Rainfall impact functions of the DARB station are divided into two groups based on the rainfall responses. Basemap shows the proportion of discrete data of Group II within certain timespan. Group I includes the runoff and river-hydrological impact caused by rainfall (brown circles) and group II comprises the impact of debris avalanches on the observation stations caused by heavy rainfall (blue squares). The data of group II were stacked; the unit amounts were counted and shown as the results on the base diagram in which the darker blue area contains 65% and the lighter one contains more than 90% discrete data. determined. Due to the sampling frequency, it is impossible to obtain the exact lag time under half an hour. Since the response of all stations quickly reached the peak after the rain, all \(k_{i}\) were set to be one. We calculated and concluded the results of all BSMs in Table 2 and all fitted curves are plotted in Figure 6. More, the response of RNT and RST was smaller than the others, and it might be because a different BSM model, GTSM100, was used here. It is the earlier developed version than GTSM21, and is reported to have low sensitivity to the vertical strain in earlier studies [40]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**BSM**} & \multicolumn{2}{c}{**Fitted Kernel Curve Parameters**} & \multicolumn{2}{c}{**Time to Decay to 10\% of Max.**} & \multirow{2}{*}{**Terrain**} \\  & \(\alpha\) & \(\beta\) & \(k_{i}\) & & **Response, Hr** & **Viciuity of BSM** \\ \hline JING & \(-8.80\times 10^{-10}\) & 0.045 & 1 & 26.5 & 1.02 \\ SANS & \(-2.03\times 10^{-10}\) & 0.012 & 1 & 95 & 1.03 \\ CINT & \(-2.97\times 10^{-10}\) & 0.013 & 1 & 93 & 1.28 \\ PFMT & \(-6.56\times 10^{-10}\) & 0.036 & 1 & 33 & 1.11 \\ BMMT & \(-5.23\times 10^{-10}\) & 0.025 & 1 & 47 & 1.13 \\ TAIS & \(-7.80\times 10^{-10}\) & 0.007 & 1 & 178 & 1.16 \\ TSUN & \(-4.15\times 10^{-10}\) & 0.008 & 1 & 140 & 1.14 \\ DARB & \(-1.53\times 10^{-10}\) & 0.011 & 1 & 105 & 1.21 \\ RNT & \(-1.22\times 10^{-10}\) & 0.022 & 1 & 53 & 1.19 \\ RST & \(-7.58\times 10^{-11}\) & 0.028 & 1 & 42 & 1.18 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Coefficient of the kernel fitting function. Figure 6: The kernel curves of all BSMs plotted on the same scale diagram. Base on Equation (12), the constant \(\alpha\) means the maximum response at the time of \(k_{i}\), and \(\beta\) describe the behavior of strain decay by time. According to the results, all maximum responses were under ten nanostrains per hectopascal and were different individually. There was no significant relation between the maximum response and elasticity, the reason causing such a difference was not clear. Besides, the decay constant, \(\beta\) describes the time that a rainfall impact persisted. The quick response of rainfall mainly reflected the additional strain caused by the rainwater, which had not infiltrated into the groundwater after rainfall. The influence of runoff was declining gradually as the rainwater flowed out of the adjacent region of the station. One of the major factors for influence of runoff was terrain roughness, which involves the process of generation, convergence, channelization, and concentration of runoff [54]. The terrain roughness is generally defined as the ratio of the surface area of a surface unit to its projected area on a horizontal plane [55]. It is an important quantitative indicator to measure the degree of surface erosion. In some studies, terrain roughness has a certain impact on the collection and dissipation of surface runoff [56; 57].