**1. Introduction**

Rainfall or earthquake triggered landslides are common in some parts of the world, causing loss of human life and property [1]. A global dataset of landslide disasters [2] showed that three-quarters of all landslide events occurred in the Himalayan arc between 2004 and 2016. Bhutan is one of the highly susceptible landslide zones in the Himalayan region [3]. The majority of landslides in Bhutan are initiated due to heavy monsoon precipitation and aggravated due to the increase in human activities. The increasing number of landslide events in Bhutan can be attributed to complex geological conditions,

steep slopes, climate change, type of soil, and tectonic activity. Landslides in Bhutan mostly occur during the monsoons during which the torrential rainfall leads to several flash floods and landslide triggering, cutting off many parts of south Bhutan from the rest.

The relationship between the amount of rainfall associated with landslide occurrences is generally studied using either an empirical or physical based approach [4–7]. Physical process models are based on numerical models which study the relationship between rainfall, pore water pressure, soil type, and volumetric water content that can lead to slope instability. Such a study is usually site specific due to variation in soil properties. It is a challenge to extend this approach to large areas, as the extensive data that is required are usually not available, and their use for an early warning system is either experimental or prototype based [8–10]. On the other hand, empirical methods study the landslides that are caused by rainfall events—both massive downpour that triggers instantaneous landslides and the low but continuous antecedent rain that destabilizes the slope and triggers the landslide. Although, there are many factors like rainfall, earthquake, geology, soil type etc. involved for landslide triggering, in the present study, precipitation rates have been considered as this is the primary cause of several changes in soil properties, pressure variations, etc. The minimum quantity of precipitation requisite for landslide occurrences known as thresholds can be determined using empirical models. The limit is defined by lower-bound lines to the precipitation conditions causing landslides and plotted in Cartesian, semi-logarithmic, or logarithmic coordinates [11]. Contingent upon the kind of available rainfall data, empirical thresholds can be summarized as follows: (1) thresholds which combine rainfall data obtained from specific rainfall events [12], (2) thresholds involving antecedent parameters [6], and (3) alternating thresholds, like hydrological thresholds [13]. Therefore, several works can be found depicting rainfall thresholds based on empirical techniques [4,7,14–18]. The present study highlights the importance of antecedent rainfall along with the determination of cumulative event-rainfall–duration thresholds for an operational early warning system. A recent review on rainfall thresholds [19] showed that the thresholds could be used to predict landslide events at various geographical extents and also in a broad spectrum of physical settings [10]. The study also found that, for setting up an early warning system using empirical rainfall thresholds, various factors needs to be taken care of: (i) collection of reliable and large rainfall and landslide datasets, (ii) selecting threshold parameters depending on landslide characteristics and precipitation data, (iii) defining the events and using an objective and standardized methodology, (iv) validation of the thresholds determined. The recent development is on defining objective thresholds using semi-automated algorithms [20–23].

In the context of Bhutan, it is difficult to study the relationship using the physical based approach as the data required is not available. Therefore, this study is lying on an empirically based approach, which defines thresholds using available records of daily rainfall and landslide data in the period 2004–2014. The available scientific literature for landslides in Bhutan is very sparse with no operating landslide early warning system [24,25]. Only one study has been carried out to determine site-specific rainfall thresholds [25], which determined thresholds using an algorithm-based approach, CTRL-T (Calculation of Thresholds for Rainfall-Induced Landslides Tool). However, more extensive work can be found for the Indian Himalayas [11,26–28] and Nepal Himalayas [29]. The study also discusses the significance of antecedent rainfall and the possibility to use the output as a decision tool for landslide determination. The effect of antecedent rainfall on landslides was analysed for various time durations: 3, 7, 10, 20, and 30 days. Further, the analysis has been validated using a statistical indicator, i.e., threat score for 2015 rainfall data. The paper is presented in five sections; the first two sections are listed as 'Study Area' and 'Rainfall and Landslide data'. The third section is listed as 'Methodology' where explanation on threshold calculation and the uncertainty associated with it are described. The fourth heading is marked as 'Results and Discussions' summarizing threshold determination along with understanding the importance of antecedent rainfall. The findings of the present study are summarized in section five 'Conclusions'.
