*3.1. Landslide Data*

The main parameters of landslides include disturbed area, location, time of occurrence, failure mechanism, and type. In this study, we collected landslide data from the annual inventory of the Forestry Bureau of Taiwan. The information on the disturbed area and location of each landslide was integrated into the annual landslide inventory, but the failure mechanisms and types of landslides were not investigated. To delimit landslides of different scales, the criterion of a disturbed area of 0.1 km2 was adopted in this study to separate LSLs from SSLs [20].

Since the mass movement of an LSL may generate ground motion, such ground motion can be recorded by nearby seismic stations [36,37]. In the frequency domain, the natural energy of landslide-induced ground-motion (called a landslide-quake) is mainly below 5 Hz, and the distribution pattern of energy in a spectrogram is triangular due to a gradual increase–decay process over time [36]. The triangular pattern in the spectrogram is the particular property that discriminates landslide-quakes from those of earthquakes and other background noise [20]. The Soil and Water Conservation Bureau (SWCB) of Taiwan extracts the occurrence times of LSLs triggered by heavy rainfall from seismic records through identifying landslide-quakes. The occurrence times of 83 LSLs triggered by rainfall over a period of 16 years (2001–2016) were observed from the landslide-induced seismic records of the SWBC and used to locate their sources using a locating approach proposed by Chen et al. [38]. Manconi, et al. [37] proposed a similar approach to detect, locate, and estimate the volumes of rockslides by analyzing waveforms acquired from broadband regional seismic networks in the eastern Italian Alps [37]. The types and failure mechanisms of the LSLs are not mentioned in the SWCB reports. However, according to some in situ investigations, the most recurrent types of LSLs in Taiwan are rock slides and debris avalanches. We collected the occurrence times and locations of LSLs from the reports of the SWCB. According to the SWCB reports, the identification error of landslide-quakes might occur due to the interference from local tremors or anthropogenic noise. A double-check conducted jointly with the analysis of remote-sensing imagery should be implemented to avoid misdetection. This study carefully compared the locations of 83 LSLs with the annual landslide inventory of the Forestry Bureau to create an LSL dataset containing the information on LSL location, disturbed area, and time (accuracy in minutes) (Figure 2 and Table 1). These 83 LSLs occurred in Taiwan during the typhoon season: 1 in June, 12 in July, 63 in August, and seven in September. This study used 75 LSLs during the period between 2001 and 2013 to analyze rainfall conditions and used 8 LSLs that occurred in 2015 and 2016 to verify the results.

The alignment of the LSLs with the geological map showed that of these 83 LSLs, 16 were located in the Western Foothills, where the lithology mainly consists of sedimentary rocks. Ten LSLs were situated in the Hsuehshan Range, where the rock formation mainly consists of alternating meta-sandstone and shale. Forty-seven LSLs occurred on the west flank of the Central Range, where the strata mainly consist of argillite and slate. Nine LSLs occurred in the eastern flank of the Central Range, where the lithology mainly comprises schist and marble. Only one LSL occurred in the Coastal Range, where the strata mainly comprise sedimentary rocks and igneous rock. The slope gradients of these LSLs were mainly distributed in the range between 20◦ and 40◦. The LSLs primarily occurred on slopes with elevations ranging from 500 to 2000 m, but the distributions of the highest and lowest elevations of these LSLs showed that their average vertical displacement was greater than 500 m [20].

Most of the 83 LSLs occurred in metamorphic rock areas, indicating that metamorphic rock slopes were likely to be massively unstable, which could be attributed to the active tectonics in Taiwan's mountainous area inducing intense rock deformation and displacement. In contrast, the sedimentary rock areas in Taiwan have a relatively more moderate relief than the metamorphic rock area. Although massively unstable slopes still develop on sedimentary rocks, the number of LSLs was significantly lower than that on metamorphic rocks. Although the difference in LSL numbers between sedimentary rock slopes and metamorphic rock slopes seems to indicate that the geological and topographic features

would influence the evolution of a massively unstable slope, the limited number of LSLs and SSLs considered in the study should be noted.

We also collected data on 174 SSLs occurring from 2006 to 2013 from the annual reports of the SWCB. The SSLs were investigated carefully with fieldwork, particularly in the cases of events that caused damage to public utilities or private property. The reports contained detailed information on the location, disturbed area, and approximate occurrence time of each SSL. These 174 SSLs occurred during the typhoon season: 2 in May, 32 in June, 36 in July, 39 in August, 24 in September, and 41 in October. The distribution of the slope gradients of the SSLs was similar to that of the LSLs. Unlike the LSLs, a large portion of the SSLs took place on slopes with elevations ranging from 750 to 1250 m. The occurrence times were estimated based on real-time videos and interviews with residents. Unfortunately, the accuracy of the time points was not mentioned in the reports. We have carefully double-checked the landslide data to exclude any SSLs that were not triggered by rainfall.

**Figure 2.** (**a**) Distribution of the 83 large-scale landslides (LSLs) that occurred between 2001 and 2016. (**b**) Example of satellite image of an LSL occurring in 2009 with a disturbed area of 2.3 km2. (**c**) Original seismic waveform induced by the LSL. (**d**) Spectrogram of the vertical component of the seismic waveform induced by the LSL.

#### *3.2. Rainfall Data*

There are 594 rain gauge stations installed by the Central Weather Bureau (CWB) around Taiwan (Figure 1). Among these, 328 rainfall gauge stations were established in mountainous areas above 100 m a.s.l. The density of rain gauges is approximately one per 73 km2. All rainfall gauges record hourly rainfall intensity. Due to the lack of rain gauge stations in the vicinity of landslide sites, we converted the records of the three nearest rain gauge stations into the representative rainfall data for each landslide site. This rainfall conversion involved conducting a deterministic interpolation using inverse distance weighting (IDW). IDW interpolation determines rainfall values on a landslide site using a weighted combination of a set of rainfall gauges. The weight is a function of the inverse distance from the landslide site to each rain gauge station. The interpolated rainfall should be a locational-dependent variable. The rainfall data of the nearest rainfall gauge stations will have the most significant influence in the interpolation. Chen and Liu [39] have proposed that a scan radius of 10–30 km would be the optimal parameter for IDW in interpolating rainfall data in Taiwan. In this study, we adopted a scan radius of 10 km from each landslide to collect rainfall data. If fewer than three rain gauge stations corresponded to this principle, we then adopted the record of the nearest rain gauge station. To determine the duration of a rainfall event, many previous studies have determined the length of a rainfall event using different non-rainfall intervals [40]. In this study, the starting-time of a rainfall event is defined as the time when the hourly rainfall exceeds 1 mm. The ending-time of the rainfall event is the time when the hourly rainfall becomes zero, but that level must be maintained for at least 24 h.



To confirm the rainfall threshold for triggering landslides, the rainfall conditions corresponding to the occurrence time of each landslide are necessary. Consequently, we counted the average rainfall intensity (*I*, mm/h), rainfall duration (*D*, h), and cumulative event rainfall (*E*, mm) from the starting-time of a rainfall event until the time point when the landslide occurred. If a landslide occurred after the peak hourly rainfall, the calculation of average rainfall intensity for the landslide would involve the value of the maximum hourly rainfall.

#### *3.3. Soil Water Index*

The soil water index (SWI) is a conceptual model which uses a three-layer tank model to estimate the depth of remaining water in three simulated soil layers during a rainfall event [41] (Figure 3). During a massive rainfall event, the water continues to infiltrate into the ground surface, and the moisture of the soil layers increases, which is strongly related to the potential for slope failure disasters. However, it is not an easy task to obtain the actual water contents in the soil layers if there are not enough hydrological instruments. Determining the physical or statistical relationship between rainfall, surface runoff, and groundwater is a compromise method for assessing underground water storage [42,43]. The tank model is a simple concept that uses three tanks, which represent reservoirs in a watershed. It considers rainfall as the input and generates output as the surface runoff, subsurface flow, intermediate flow, and sub-base flow. The tank model also explains the phenomena of infiltration, percolation, and water storage in the tanks. Thus, the SWI is established as a rainfall-runout model with some fixed parameters to estimate the permeation of water in the soil layers. This method was used to assess and predict potential landslides and to construct early warning systems in Japan [22].

**Figure 3.** Schematic layout of the soil water index (SWI) tank model. The SWI represents the summation of water depth in the three tanks.

In this model, the SWI is defined as the total storage water height *Sk*, which is the sum of three tanks, and the formula can be written as [22]: s

$$\text{SWI}\left(t+\Delta t\right) = \sum\_{k} S\_{k}(t+\Delta t) \tag{1}$$

where *t* represents the time in hours; Δ*t* expresses the passed time in hours; (*k* = 1,2,3) represents the tanks from top to bottom. Every *Sk*, the remaining water (mm) for each tank, is computed every hour (Δ*t* = 1(h)) by:

$$\mathcal{S}\_{k}\left(t+\Delta t\right) = \begin{cases} \mathcal{S}\_{k}(t) - \left[\sum\_{I} Q\_{kl}(t) + Z\_{k}(t)\right] + \mathcal{R}(\Delta t), & (k=1) \\\\ \mathcal{S}\_{k}(t) - \left[\sum\_{I} Q\_{kl}(t) + Z\_{k}(t)\right] + \left[Z\_{k-1}(t+\Delta t) - Z\_{k-1}(t)\right], & (k \ge 2) \end{cases} \tag{2}$$

where *R*(Δ*t*) represents the hourly rainfall amount in mm. *Qkl* means the leakage height from the *l*th side tube of each tank (the top tank has two side tubes, and the others have one). *Zk* is the water that permeates from the base tube of the *k*th tank. *Zk*−<sup>1</sup> is the water that permeates from the base tube of the (*k* − 1) th tank. Both *Qkl* and *Zk* vary with *t* and can be calculated as follows:

$$Q\_{kl}(t) = \begin{cases} \, \_{kl} \{ S\_k(t) - L\_{kl} \} \, \left( S\_k(t) > L\_{kl} \right) \\ 0 \qquad \left( S\_k(t) \le L\_{kl} \right) \end{cases} \tag{3}$$

where *akl* and *bk* are the coefficients of seepage for the side holes and the base holes of the *k*th tank, respectively. *Lkl* represents the height (mm) of the leakage water flowing through the *l*th side hole of the *k*th tank.

In the three-layer tank model, the sum of *Q*<sup>11</sup> and *Q*<sup>12</sup> represents surface runoff, *Q*<sup>21</sup> represents intermediate flow, and *Q*<sup>31</sup> represents baseflow, respectively. In addition, *Z*<sup>1</sup> represents the infiltration amount from the first tank. *Z*<sup>2</sup> and *Z*<sup>3</sup> represent the percolation amounts from the second and third layers. *S*1, *S*2, and *S*<sup>3</sup> denote the depths of water storage in the first, second, and third tanks. Some previous studies performed statistical analysis of the relationship between river discharge and precipitation, and the constants *akl*, *bk*, and *Lkl* (Table 2) were determined and used in the SWI model [22]. It may be true that the discharging rate and saturation capability would vary between distinct geological and topographic settings. However, the SWI is representative of conceptual water content. Furthermore, the variations of time series of the SWI using parameters adjusted with different areas have similar trends [41]. Thus, the Japanese government adopted the constant parameters developed by Okada, et al. [41] for the whole nation regardless of the various geological conditions [44]. Chen, et al. [27] applied the SWI model to calculate the rainfall characteristics for triggering shallow landslides in Taiwan and used the previous rainfall data over one month to inspect the effect of the antecedent rainfall. In this study, the SWI values of large-scale landslides and other rainfall factors were calculated and combined to find the hydrological conditions for triggering large-scale landslides. Figure 4 displays a paradigm for obtaining the time-varying SWI and its conditions for triggering an LSL. The hourly rainfall records of the three nearest rainfall gauge stations were used to estimate the representative hourly rainfall for the LSL (Figure 4a,b). Then the time-varying rainfall was interpolated to the landslide site using the IDW method and adopted to calculated *S*1, *S*2, and *S*<sup>3</sup> (Figure 4c). The time-varying SWI could be obtained by summing *S*1, *S*2, and *S*3. The total remaining depths of the three tanks represent the water stored underground [45]. The concept of the tank model is easily understandable. In addition, the SWI can be used as a proxy for both meteorological trigger and hydrological cause. For the three-layer tank model, outputs through the outlets of the first tank, second tank, and third tank represent surface runoff, intermediate runoff, and baseflow [46,47]. Since most of the 83 LSLs were found to have depths of tens of meters by the SWCB, the remaining water depths in the deepest tank might be the critical hydrological causes for triggering LSLs. In this study, we calculated the time-varying values of the SWI for one month before the targeted rainfall event and in the period of the rainfall event.


**Table 2.** Parameters for calculating SWI.

**Figure 4.** Example of three selected rain gauge stations and an LSL site. (**a**) Distribution of three rain gauges and the LSL No.41. (**b**) Rainfall records at the three stations and the estimated hourly rainfall using the inverse distance weighting (IDW) method. (**c**) Example of change in the SWI for the LSL.
