**5. Results and discussion**

In this study, an event rainfall–duration threshold has been determined using available rainfall and landslide data [32,40]. The definition of rainfall and landslide event to determine any kind of threshold is very critical [18]. In the present study, to determine the thresholds, the landslides after the initial failure were not considered, i.e., if, on a particular day, five landslides occur, they will be recognized as one landslide event. This approach is similar to other works [40] and reduces the number of rainfall events with landslides. After that, landslide events which initiated due to very low rainfall values (lower than 25th percentile) were discarded to determine more accurate thresholds [25] as such landslide incidences may not be solely initiated by rainfall. Thus, the number of landslides reduced to 51 landslide events. With the method explained in the previous section, the threshold came out to be *<sup>E</sup>* = (5.68 <sup>±</sup> 1.80). *<sup>D</sup>*(0.70±0.04). Figure 5a depicts the 51 rainfall conditions, which led to landslides, threshold at 5% (T5,B) exceedance probability and the associated uncertainty (Figure 5b,c). The relative uncertainties for the γ parameter are less than the acceptable value of 10% [32]. However, the uncertainty for α is slightly higher at 31.7%, which can be attributed to limited number of empirical data used to determine thresholds [25]. The power-law function and maximum likelihood estimations are used to get the best fitted curve by utilization the present set of data. The lower boundary points are determined using regression analysis and a standard deviation is used to understand the distribution of normally distributed data from the mean value [27]. The graph is drawn on a logarithmic scale. [25] also defined ED thresholds for Chukha region using a semi-automatic empirical approach and defined

threshold as E = (7.3 <sup>±</sup> 2.0). D(0.71 <sup>±</sup> 0.06) using 43 landslide data points for 2004–2014. The thresholds defined for Kalimpong region, India by [11] depicted ED relationship as E = 3.52. D0.41.

**Figure 5.** (**a**) Event rainfall–duration (ED) threshold for 51 rainfall conditions in log–log coordinates (**b**) Variation in parameter α, and associated uncertainty Δα, as a function of the number of events. (**c**) Variation in parameter γ, and associated uncertainty Δγ, as a function of the number of events.

To evaluate the importance of antecedent rainfall the rainfall events during the monsoon of year 2012 were analyzed, a total of 50 rainfall events occurred which led to eight landslide events. As there were more than 1000 rainfall events during 2004–2014, the landslide events of 2012 were selected to understand the significance of antecedent rainfall. Figure 6 depicts the daily (Rday) and 30-day (R30-day) antecedent precipitation values for 2012. The daily rainfall values were comparatively higher on the day of landslide occurrence. Adopting the calculated threshold for triggering landslide, the number of daily rainfall events exceeding the reference period is high which depicts that antecedent precipitation plays an important role in landslide initiation [41]. The landslide events during this period were characterized by an R30-day value of 350 mm. Considering the R30-day value of 350 mm, the number of rainfall events exceeding it is 14. This analysis resulted in fewer data points, which depict the significance of antecedent rainfall, and thus its effect on the distribution of soil moisture during the initiation of triggering rainfall [41].

Event Number

**Figure 6.** Cumulated rainfall during 2012 monsoon period.

To determine the number of antecedent rainfall days significant for landslide triggering, a trial and error approach considering various days was used [11,27]. The daily rainfall on the day of rainfall for landslide events was plotted against antecedent rainfall for various time durations of 3, 7, 10, 20, and 30 days (Figure 7). The diagonal line divides the graph to differentiate the scattering bias of daily rainfall (ordinate) and antecedent rainfall (abscissa). The diagonal depicts that the daily precipitation data on the day of failure and the antecedent precipitation prior to failure are same [27]. Figure 7 shows graphs of daily rainfall corresponding to antecedent rainfall of various periods. As observed in Figure 7, the majority of the landslide events are biased towards antecedent rainfall as compared to daily rainfall. In the case of 3-day antecedent rainfall, 19.6% of the landslides are biased towards daily rainfall and the remaining 80.4% (41 of the 51 landslides) are biased towards 3-day antecedent rainfall prior to failure. Similarly, for 7-day antecedent conditions, the biasness of daily rainfall towards landslide initiation decreases to 13.7%. In the remaining cases (10-day, 20-day, and 30-day) the effect decreases to 1.9%. Such a comparison between the daily and antecedent rainfall data would give more clarity with the availability of hourly data. The observation of plots for similar bias antecedent conditions shows that a greater number of points in the case of 10 days is concentrated along the abscissa in comparison to other cases where a scattering of points along the abscissa is prevalent [27]. Therefore, it can be concluded that an antecedent rainfall of 88.35 mm for a minimum of 10 days provides the best correlation for triggering of landslides in the region.

The use of thresholds for an operational early warning system can be justified by validating it with an independent dataset which is lacking in various studies conducted, as mentioned in the review article by [19]. The present study validates the determined thresholds using the rainfall data of 2015 by determining the threat score [3,42]. Threat score (TS) is defined as the number of true positive cases (TP) divided by the summation of true positive (TP), false negative (FN), and false positive (FP) cases [43].

$$TS = \frac{TP}{TP + FN + FP} \tag{1}$$

During this period, eight landslide events occurred due to a total of 46 rainfall events. As determined earlier, a R30-day precipitation value of 350 mm could be used as a pre-filter, and it was found that only 11 of the 46 rainfall events exceeded the value. Thereafter, the biasness of the landslide events with respect to daily and antecedent rainfall was carried out and the results show that only one case was slightly biased towards the daily rainfall whereas the rest were biased towards antecedent rainfall. This analysis shows that a R30-day value could be used as a pre-filter for determining thresholds and antecedent rainfall plays a significant part for landslide initiation in the

region. Finally, the threat score for 2015 landslide event was calculated using the ED threshold value of 53.3 mm. The results determined were TP equal to six, FN and FP were two and three respectively, and so TS was found to be 0.54. The result shows that the rainfall thresholds can be used the first step and eventually the threshold effectiveness will be improved in time when additional data will be collected, as shown in other long-term projects [12]. However, when using as an early warning system the effect of daily as well as antecedent rainfall needs to be considered.

**Figure 7.** Relation between antecedent rainfall before failure (3, 7, 10, 20, and 30 days) and daily rainfall for landslide occurrences.

#### **6. Conclusions**

Rainfall-induced landslides are one of the major destructive natural disasters in Bhutan. However, minimal study has been conducted to develop a landslide early warning system, either regionally or locally. This paper attempts to determine rainfall thresholds in terms of event rainfall–rainfall duration and antecedent rainfall for landslide incidences using daily rainfall data for Chukha region located in the south-western part of Bhutan Himalayas. The analysis was carried out from the available rainfall and landslide occurrences between 2004 to 2014. The majority of the landslide occurrences are along the Phuentsholing–Thimphu highway, which is an important road connection for the country as it connected the capital with India and used for trade purposes. The thresholds determined for the region depicts a minimum event rainfall of 55 mm for short duration of 24 h can trigger landslides. Thereafter, the significance of antecedent rainfall was carried out using the rainfall events of 2012 monsoon. The analysis revealed the importance of antecedent rainfall and therefore it was necessary to determine the antecedent time window necessary for landslide occurrence. The biasness of the rainfall events which resulted in landslides revealed that a 10-day antecedent rainfall would provide the best correlation for landslide occurrences in the study region. Further, it can be stated that R30-day value of 350 mm could be used as a pre-filter before the use of ED thresholds. The derived rainfall thresholds can be improved with the availability of hourly rainfall data to use for an effective warning system.

**Author Contributions:** A.D. and R.S. carried out the analysis and wrote the article, B.P. provided technical assistance and contributed in writing the article, S.A. carried out the GIS work and K.D. provided the data for carrying out analysis.

**Funding:** The research was funded from BRACE project (NERC/GCRF NE/P016219/1) granted to Raju Sarkar.

**Acknowledgments:** The authors are thankful to National Center for Hydrology and Meteorology, Royal Government of Bhutan for providing rainfall data and the Border Roads Organization (Project DANTAK), Government of India for providing landslide data. Authors are also thankful to staff of College of Science and Technology, Royal University of Bhutan, who helped directly or indirectly while carrying out the present study. The authors acknowledge the two anonymous reviewers for their useful comments and suggestions.

**Conflicts of Interest:** The authors declare no conflict of interest.
