**4. Method**

This section explains the procedure to determine thresholds. The determination of thresholds using empirical methods can be divided into two primary steps. The first step is the collection of rainfall and landslide data, and the next step is to apply empirical models to determine the thresholds. An event rainfall is determined by the number of consecutive days of rainfall before the landslide incident. This helps in calculating the number of days of rainfall before landslide and the total rainfall. Thereafter, the rainfall events leading to landslides are plotted in a log(E) vs log(D) graph and the distribution fitted to the power law equation. The equation of the threshold is *<sup>E</sup>* = (<sup>α</sup> <sup>±</sup> <sup>Δ</sup>α). *<sup>D</sup>*(γ±Δγ), where E is cumulated event rainfall (mm), D is duration (h), α is intercept, and γ is the slope of threshold curve [4]. The uncertainties Δα and Δγ are determined using a bootstrap nonparametric statistical technique [32]. This uncertainties measure the variation of the threshold around a central tendency line, which depends on multiple factors, but primarily on the number and the distribution of the empirical data points representing different rainfall conditions that have resulted in landslides [33]. The distribution of rainfall conditions which have resulted to triggering of landslides is fitted the power law equation in a log-log graph. The thresholds were determined using the methodology proposed by [4] and further modified by [32] for various exceedance probabilities ranging from 1% to 50%.

The equation involves the discrete and continuous maximum likelihood function estimation to fit the data in agreement with the equation. There are two assumptions involved with the use of power law equation. (1) With the increase in the cumulated rainfall, there is a nonlinear increase in the probability of landslides. It asserts that the possibility of landslide decreases when threshold reduces and vice versa. (2) With the increase in rainfall duration, the occurrences of slope failure reduce [27].

The study of antecedent rainfall for landslide incidences is important as it may lead to an increase in soil moisture content leading to slope instability. The impact of antecedent rainfall should be a site-specific study and may not always hold good for other regions with similar geological and rainfall conditions [34]. The variation in soil moisture content across an area is difficult to accurately determine as it depends on various factors like the variation in soil type, depth, climatic variation, etc. [7]. Various authors have used different periods to determine the correlation between antecedent rainfall and number of days for landslide triggering. [35–38] examined for 3, 4, 18, and 180 days respectively. [14] used 7, 10, and 15 days, whereas [39] assessed 2, 5, 15, and 25 days based on a trial and error basis. In this study, we considered 3, 7, 10, 15, 20, and 30 days.
