*4.1. Rainfall Threshold Estimation*

A rainfall threshold determines the minimum rainfall conditions necessary for landslide initiation in a specific region [39], and various researchers have attempted to quantify thresholds using several approaches [39–41]. A recent review article [40] on rainfall threshold estimation explained in detail the various approaches currently in use, along with their merits and demerits. Of the various techniques, empirically based approaches are widely used because of the simplicity and ease with which they can provide an accurate approximation of minimum precipitation conditions. Various rainfall thresholds using different parameters have been developed, such as ID (intensity–duration) [21], ED (cumulative event rainfall duration) [4], and AD (antecedent rainfall duration) [16,42]. The most commonly used rainfall variables for threshold estimation are daily rainfall, antecedent rainfall, and cumulative rainfall [40]. However, the choice of rainfall variable with which to determine thresholds is primarily dependent on the type of landslides in the region [20].

For the S-T highway, monsoonal rainfall occurs with interruptions and can be characterized mostly low-intensity and long-duration events along with occasional extreme events, making the choice of antecedent rainfall appropriate [30]. Antecedent rainfall is a significant factor for landslide triggering, especially in less impermeable soils, as it lowers soil suction and increases pore water pressure [13]. The use of antecedent rainfall was based on analysis of historical landslide pattern, the field visit, and previous studies conducted in other regions of Bhutan. Although estimation of the number of days to be considered to analyze the effect of antecedent rainfall was a challenge, it has been widely accepted that antecedent rainfall over 15 days to 30 days plays a crucial role for landslide initiation in the Himalayas [43]. The calculation of the antecedent period prior to landslide incidence is usually based on a trial-and-error approach, ranging from 3 days to 120 days [30,44,45].

For this study, the correlation between daily and antecedent rainfall conditions was analyzed for six different time periods (3, 5, 7, 10, 15, and 30 days) (Figure 5a–f). The analysis of the various antecedent rainfall time periods was conducted using the method proposed by Zezere et al. [42]. Blue dots represent the daily rainfall, whereas the orange points depict the antecedent rainfall values for respective time periods. The best discrimination between daily and antecedent conditions, according to the method suggested by Reference [42], was observed for 30 day antecedent rainfall and was accepted as the metric for threshold calculation.

**Figure 5.** *Cont.*

**Figure 5.** Relationship between daily (blue) and antecedent (orange) rainfall in 2014–2017.

The threshold determination was performed using a scatter chart for daily (RTH) and 30 day antecedent rainfall (R30ad), and was calculated for all three zones. The graph was generated using the rainfall and landslide data from 2014–2017. The threshold equation was obtained by using the lower

end points in the scattered graph [13,16]. The threshold equations of various zones are depicted in Figure 6.

**Figure 6.** Threshold equation between daily rainfall and 30 day antecedent rainfall for all the three zones.
