**1. Introduction**

In a global database of landslide disasters given by Froude and Petley (2018) [1], three–quarters of all landslide events between 2004 to 2016 occurred in Asian countries, with substantial events in the Himalayas. Indian Himalayas are highly susceptible to landslides which are triggered primarily by rainfall [2] and Sikkim and Darjeeling Himalayas are among the most highly vulnerable landslide

zones. Due to rapid urbanization and increase in population in such areas, landslides and associated loss are an increasing concern [3] and early warning systems are regarded as a promising tool for landslide forecasting and risk management [4].

Rainfall being the most common triggering factor for landslides, early warning systems are typically based on empirical rainfall thresholds that describe the interaction between the primary cause (rainfall) and the final effect (landslide). In a few words, a triggering threshold is represented by a mathematical equation describing the critical rainfall condition above which landslides are triggered. The only input data used for the threshold definition are a dataset of rainfall recordings and a catalogue of landslides for which the time and location of occurrence are known with sufficient approximation. This approach completely bypasses the physical mechanism of triggering, thus simplifying the modeling effort, the computational resources required, and the amount of data needed for the analysis [5].

During the last few decades, many attempts were made across the world to define critical rainfall thresholds based on a number of different rainfall parameter, but the most common are intensity and duration (ID thresholds) [6–13], total event rainfall and duration (ED thresholds) [14–18] and antecedent rainfall [19–22]. The selection of the optimal rainfall parameters which are used for defining the threshold depends mainly on the landslide typology and physical characteristics of the region. It is well accepted that shallow landslides and debris flows are triggered by high intensity-short rainfalls and deep-seated landslides occur as a result of less intense rain over a long time [16,23,24]

When an area is prone to both shallow and rapid and deep-seated and slow moving landslides, a threshold model which can accommodate the effect of both the cases should be defined. A model that holds this characteristic is SIGMA (sistema integrato gestione monitoraggio allerta—integrated system for management, monitoring and alerting), which was developed for managing the risk associated with landslides triggered by rainfall in the Emilia-Romagna Region, Italy [23,25,26]. The model takes cumulative rainfall as input, and it considers the long-term and short-term behavior in order to account for shallow and deep landslides, respectively. Another important advantage of this method is the indication of warning level. The model can be calibrated with respect to the severity of landslides and can be used for developing regional site specific thresholds.

An ongoing research continuously produced new upgrades and optimization of the model SIGMA [19,26,27], making it possible to be used across the world for landslide hazard warning. However, to our knowledge, the model has never been applied outside Italy, thus leaving the claimed flexibility of application only theoretical. Hence, this study applies the SIGMA model to Kalimpong town in the Darjeeling Himalayas and thus tests the exportability of the SIGMA model in different climatic and geomorphological settings.

## **2. Study Area and Input Data**

Kalimpong town is a part of the Kalimpong district of West Bengal state, India, as shown in Figure 1. This hilly town belongs to Darjeeling Himalayas, hemmed between rivers Tista in the west and Relli in the east, with an elevation ranging from 355 m to 1646 m above mean sea level. The slopes in the western face of the town are steep, while the eastern slopes are gentle.

The geological setting of the region is associated with the evolution of Darjeeling Himalayan ranges. Precambrian high-grade gneiss and quartzite, calc–silicate and quartzite, high-grade schist phyletic etc. are the dominant rock types found in the region [28]. Upper sedimentary layers of the young folded mountains get eroded during heavy rainfalls. The area consists of several joints and cracks that accelerates the weathering of the rock and the formation of unconsolidated matter [29]. The bedrock throughout the study area is composed of Daling series quartz mica schist of golden to silver colors [30]. The inclination of bed towards the east and northeast varies from 20◦ near river Tista to about 40◦ towards town. These slopes in can be morphometrically classified into escarpment category A (>45◦), steep slope category B (30◦–45◦), moderate steep slope category C (20◦–30◦) and gentle slope category D (10◦–20◦). Silt to medium grained sand and loam constitutes a major portion of the topsoil of the area. According to GSI, more than 60% of the region comprises colluvium followed

by older debris (24%) and young debris (2.5%). This geomorphological setting makes the region very prone to landslides, and rainfall is the main triggering factor.

**Figure 1.** Location details (**a**) India; (**b**) West Bengal; (**c**) digital elevation model of Kalimpong (modified after [31]).

The geology of the area allows rainwater to percolate, increasing the pore pressure, therefore the shear strength of the soil decreases. The change in water content due to intense rainfall leads to the saturation of material and a sudden increase in the unit weight. This mechanism reduces the stability and resistance of parent rocks. The average annual precipitation in this area was observed to be 1872 mm during the study period, and the drainage density of the region is also very high. The area is drained by numerous mountainous natural streams (kholas) and their tributaries (jhoras). The precipitation with daily accuracy was collected for this study from the rain gauge maintained in Tirpai, Kalimpong (Save The Hills). The months from June to September are considered a monsoon period and the monthly rainfall from 2010 to 2017 is given in Table 1.


**Table 1.** The monthly rainfall (mm) during monsoon seasons in the study area town (2010–2017).

A landslide catalogue was prepared from the reports of the Geological Survey of India, newspapers and field surveys. The database contains the spatial and temporal distribution of rainfall-induced landslide events during 2010–2017. The dataset from 2010 to 2015 was used for model calibration and the dataset from 2016 to 2017 was used for model validation. The major fatal landslides happened in the region were shallow and rapid in nature, but there are some areas which experience continuous sinking because of slow, deep-seated movements, especially near major jhoras [32]. The movements are occurring gradually and are observed as cracks in buildings and roads after each monsoon. Since 2017, these slow movements are monitored using micro-electro-mechanical tilt sensors installed at Chibo [33]. During the validation period (years 2016–2017), ground displacements were observed on 7 days at two locations [2].

The annual cumulative rainfall for these years is plotted in Figure 2a and the temporal distribution of landslides along with the average rainfall is shown in Figure 2b. It is observed that the number of landslide events is maximum in the month of July where the rainfall peak is recorded. From Figure 2b, it is clear that the number of landslides is directly related to the rainfall amount. Landslides are becoming an increasing menace in the region during monsoon season. The havocs related to landslides have multilevel impacts on the livelihood of population. Loss of farm lands and disruption of roads are affecting the income sources of the people. The socioeconomic development of the region is throttled by the disasters and associated setbacks. Hence, it is critical to adopt measures to minimize the impact of landslides in the region. An effective approach is to develop an early warning system using rainfall thresholds to forecast the occurrence of landslides. Since the area is affected by landslides of mixed typology (rapid shallow slides and slow deep seated movements), we took into account the SIGMA model [23], specifically conceived for similar settings, and we customized it for an application in the study area.

**Figure 2.** (**a**) Yearly cumulative rainfall; (**b**) Monthly distribution of landslide occurrence and average rainfall, (2010–2017) in mm.

#### **3. The SIGMA Model**

The SIGMA model was developed for the Emilia-Romagna region in Italy [23]. This model uses the standard deviation of a statistical distribution as the key parameter for the analysis and defines thresholds as a function of standard deviation, predicting the potential of rainfall to initiate landslide events in the study area. Since the model is based on statistical distribution, it is easily exportable to other regions [23]. Adopting the methodology from Martelloni et al. (2012) [23], a customized SIGMA model for Kalimpong town is derived in this study. The modifications are in accordance with the historical database collected for the study area, thus making SIGMA compatible for a different hydro-meteo-geological setting than the area for which it is originally developed. The daily precipitation data were added at '*n*' days, with an '*n*' day wide shifting window which moves at everyday time steps throughout rainfall data. The values of '*n*' will vary from 1 to 365. To calculate the cumulative probability distribution for each data set, a standard distribution, which is the target function is chosen as a model [34].This transformation relates the cumulative rainfall (z) with the target distribution (y = a,σ) ('σ' is the standard deviation of the series and 'a' is a multiplication constant). For each '*n*' day cumulative rainfall series, the values are sorted in ascending order such that

$$z\_1 \prec z\_2 \prec z\_3 \prec \cdots \prec z\_k \prec \cdots \prec z\_n \tag{1}$$

and a cumulative sample frequency is defined as

$$P\_k = \frac{k}{n} - \frac{0.5}{n} = G(y) \tag{2}$$

where, 1 ≤ *k* ≤ *n*.

The conversion is carried out using the cumulative distribution function of z, termed as F(z). For each value of zk, F(zk) defines the probability that the variable z takes a value less than zk, where *k* varies between 1 to *n*.

The original data z transformed to y is obtained as:

$$\mathbf{G}^{-1}(\mathbf{F}(\mathbf{z})) \to \mathbf{G}^{-1}(P\_k) = \mathbf{y} \tag{3}$$

After applying the transformation function, from a particular value of standard deviation or its multiple, cumulative sample frequency and precipitation can be calculated. The same procedure is repeated for all values of *n* from 1 to 365 and precipitation curves (σ curves) are plotted. The probability curves derived are used as the input values in the algorithm. A level of warning is predicted for everyday based on the rainfall thresholds. Rainfall recordings were cumulated with one day time steps for a particular time interval. These values are compared with the precipitation curves, from shorter to longer time frames [23]. In the case of shallow landslides, the analysis should focus on the immediate effect of rainfall: the cumulative rainfall values up to two days before the day of analysis is considered. The decisional algorithm used is given in Equation 4:

$$C\_{1-3} = \left[\sum\_{i=1}^{n} P(t+1-i)\right]\_{n=1,2,3} \ge \left[S\_n(\Delta)\right]\_{n=1,2,3} \tag{4}$$

where, Δ = a,σ, *C*1–3 is the vector indicating the cumulated rainfall at time t and *Sn*(Δ) are the thresholds relative to number of days *n* and Δ [23]. In the case of slow movements, the algorithm ponders the effect of cumulative rainfall from 4 days up to 63 days [23]. The condition for crossing the threshold is given by:

$$\mathbb{C}\_{4-63} = \left[\sum\_{i=1}^{n+3} P(t-2-i)\right]\_{n=1,2,\ldots,60} \ge [\mathbb{S}\_{n+3}(\Delta)]\_{n=1,2,\ldots,60} \tag{5}$$

The definitions of vector *C* are kept the same and have been used in the study for the analysis. The analysis was carried out in the same method proposed by the developers of the SIGMA model, to define the thresholds for Kalimpong town.
