*4.2. Soil Water Index–Rainfall Duration (SWI–D) Threshold for Large-Scale Landslides (LSLs) and Verification*

Unlike other consolidated approaches, we have defined soil water index–rainfall duration (SWI–*D*) thresholds, instead of the popular average rainfall intensity–rainfall duration thresholds. In this study, the SWI–*D* rainfall threshold curve at 5% exceedance probability was estimated by the method proposed by Brunetti et al. [48]. This threshold was expected to leave 5% of the data points below the threshold line. In general, a threshold requires verification with a certain number of cases. The verification cases are usually randomly selected from the total cases and excluded from the database used to build the threshold. Since the number of LSLs is inconsistent every year and the number of samples used to establish the threshold is limited, the random sampling method was not used to select the verification cases in this study; instead, the LSLs occurring in the last two years of the study period were selected as the threshold verification cases. Figure 8 depicts the SWI–*D* conditions associated with LSLs and SSLs in Taiwan and the threshold lines. The threshold for LSLs is determined as SWI = 155.20 − 1.56*D* and *D* ≥ 24 h. Figure 9 presents the ratios of water depth in the third tank (*S*3) to the SWIs for LSLs and SSLs. The 50th-percentile of *S*3/SWI is 0.41, which indicates that when *S*<sup>3</sup> occupies more than 40% of the SWI, there is a higher potential of LSL initiation. This result implies the importance of the water content of the deeper layer.

**Figure 8.** Soil water index–rainfall duration (SWI–*D*) thresholds for (**a**) LSLs and (**b**) SSLs.

**Figure 9.** (**a**) Data distribution of the ratios of *S*<sup>3</sup> to SWI for (**a**) LSLs and (**b**) SSLs. (**c**) Probability distribution of the ratios of *S*<sup>3</sup> to SWI for LSLs and SSLs. Duration was calculated from the beginning of rainfall to landslide occurrence.

The SWI–*D* threshold built with LSL data for 2001–2013 was validated with eight LSLs triggered by heavy rainfall in 2015 and 2016 (Figure 10). Six of them accorded with the SWI–*D* conditions for 2001–2013, verifying that the SWI can be treated as an indicator for triggering LSLs. However, two cases were lower than the SWI–*D* threshold. Even so, the two lower values were relatively close to the threshold line. The verification confirmed the advantage of using the SWI. For instance, the SWI often increases rapidly before landslide occurrence, and this phenomenon can be used for a warning system.

**Figure 10.** Validation of the SWI–*D* threshold using the data for six LSLs occurring during 2015–2016. Dashed line represents the SWI–*D* threshold.

## *4.3. Comparison with Small-Scale Landslides*

For comparison, we used an inventory dataset including 174 small-scale landslides (<0.1 km2) provided by the Soil and Water Conservation Bureau, Taiwan. The inventory reports occurrence times and rainfall records. One evident contrast between the rainfall conditions for SSLs and those for LSLs in Taiwan is that the LSLs primarily occur with higher cumulative rainfall. However, SSLs are more likely with shorter but intense rainfall events.

For further comparison, Figure 8 shows the SWI–*D* conditions for triggering SSLs and LSLs. Although the variations of the SWI–*D* conditions for the two types of landslide are challenging to distinguish, we note that the SWI–*D* threshold for LSLs is much higher than that for SSLs. The slope materials require a more substantial amount of water content to evolve into a massive landslide. Figure 9 displays the variation of the ratio of *S*<sup>3</sup> to SWI for SSLs and LSLs. We also noted that each percentile of *S*3/SWI for LSLs was significantly higher than that for SSLs. For the 50th percentile, SSLs can potentially occur when *S*<sup>3</sup> occupies 27% of the SWI; however, LSLs can potentially occur when *S*<sup>3</sup> occupies 41% of the SWI. A rainfall event that raises the SWI and *S*<sup>3</sup> to high values is critical for triggering LSLs. Therefore, identifying changes in the SWI is conducive to determining the lowest rainfall thresholds for landslides of different scales. Based on the data for 2001–2016, Figure 7 shows the hourly changes of the SWI from the beginning of the rainfall events to LSL occurrences. We used non-parametric median regressions to determine the general trend of the SWI for triggering these LSLs. In addition to an LSL with a duration greater than 200 h, the general SWI curve for the remaining 82 LSLs was obtained by calculating the 50th-percentile of SWIs per each 1-hour increasing interval of duration. Figure 7 also displays the general trends of SSLs in Taiwan, reported by Chen, et al. [27]. Saito, et al. [3] classified rainfall conditions for triggering SSLs into two types, shorter duration–high intensity (SH) and long duration–low intensity (LL). The general trend of the time-varying changes in the SWI for the LSLs in Taiwan is located between the SH type and the LL type. Among the 83 LSLs, only one LSL, occurring in 2006, was triggered by an LL type rainfall event. Comparing SSLs with LL types, the rainfall conditions for triggering LSLs are associated with high average intensity. Furthermore, comparing SSLs with SH types, rainfall conditions for triggering LSLs are associated with a slightly longer duration.
