**4. Analysis**

The rainfall and landslide data for Kalimpong town have been used to develop (2010–2015) and validate (2016 and 2017) rainfall thresholds for the region. The spatial distribution of landslide events during the study period is shown in Figure 3.

**Figure 3.** Spatial distribution of rain gauges and landslide events during the study period. (modified after [15]).

For each day, '*n*'-day cumulative rainfall values were calculated with *n* ranging from 1 to 365. Cumulative probability distribution curves were plotted after sorting the values in ascending order. For small values of '*n*', the distributions were found to be closer to log-normal, and for higher values of '*n*', the distributions tend towards normal. The asymmetric distribution of data sets has been observed by other researchers as well [23]. Choosing Gaussian distribution as a target function, cumulative values corresponding to multiples of SIGMA were calculated by applying the transformation, as shown in Figure 4a.

After applying the transformation, a probability of not overcoming a particular 'aσ' value can be calculated using the reverse procedure. For each value of 'aσ', cumulative values for *n*-days varying from 1 to 365 were plotted as SIGMA curves. The values of standard curves were initially taken as 1.5σ, 1.75σ, 2σ and 2.5σ and are plotted in Figure 4b.

**Figure 4.** (**a**) Transformation of original cumulative distribution in the target distribution for Kalimpong town; (**b**) An example of SIGMA (sistema integrato gestione monitoraggio allerta—integrated system for management, monitoring and alerting) curves (σ curves) for cumulative periods up to 100 days (2010–2015).

From the probability distribution plots, SIGMA curves have been combined using an algorithm, which is the crucial part of the SIGMA model. The algorithm defines four different levels of alert, such as "red", "orange", "yellow" and "green". These values are used to delineate exceptional rainfall values. The starting algorithm for the proposed model is as shown in Figure 5. It considers the effect of short-term rainfall first, and exceedance of threshold will give high criticality alert for the day. If a red alert case does not exist, first orange alert level and then yellow alert level were checked for each day. If the result is negative in all cases, absent criticality (green color) is defined for the day. Hence, if a landslide happens to continue for a number of days, an effective model should predict the corresponding warning level on each day. The block diagram proposed in Figure 5 has to be considered as a starting point for the work, since it was then calibrated as described in the following paragraphs.

**Figure 5.** Algorithm used for calibration of the SIGMA model for Kalimpong town.

A threshold is considered to be exceeded if any of the elements in the vector crosses the value. Once a threshold is exceeded, the algorithm defines the level of warning on each day. These outputs were used to calibrate the model (data from 2010 to 2016). A trial and error procedure has been adopted in the optimization module of the algorithm, which relates the daily warning levels with landslide occurrences, as in Martelloni et al. (2012) [23]. The value of threshold is progressively raised so that false alarms are avoided. A visualization of the procedure is shown in Figure 6 where standard SIGMA value of 1.75 was optimized to 1.95. Using the same procedure, other standard values of 1.5 and 2 were optimized to 1.65, and 2.05, respectively. The standard value of 2.5 remained the same after optimization. The thresholds values were increased to minimize false alarms for each event, such that no true alarms are missed. The execution of this module terminates once the algorithm catches an event with an observed warning level conforming to the considered threshold. The standard SIGMA curves remain the same, but the calibration process gives a modified set of SIGMA curves for the region.

**Figure 6.** Visualization of calibration algorithm. The threshold value was raised till the cumulative rainfall curve of the event (F) is not crossing the threshold curve (standard threshold of 1.75 is optimized to 1.95).
