**6. Discussion**

The validation of the SIGMA model for the study area gave satisfactory results by predicting all slow movements events correctly and producing two missed alarms. However, this came at the cost of having a relatively high count of false alarms (22).

As pointed out by Lagomarsino et al. (2015) [27], the most complete form of validation for a threshold model is to compare the skill scores to the ones obtained with the application of other models in the same test site. Several rainfall thresholds for landslides in Kalimpong region has already been defined [2,10,15]. Therefore, the validation statistics of SIGMA were compared to those obtained in the same test site by two already published works, which make use of ED and ID thresholds, as shown in Table 3.


**Table 3.** Comparison of the SIGMA model with other empirical thresholds.

It can be seen that during the validation period, SIGMA outperforms the other models. The terms for evaluating the overall performance of model, efficiency and likelihood ratio, are maximum for SIGMA among the models tested. Efficiency being the ratio of true predictions to a total number of predictions, does not show a significant variation amongst different models. This is often reported in LEWS [27] where the number of true negatives are of a higher order than the other three variables. Specificity measures the ratio of correctly predicted days with no landslides to the total number of days without landslides, and sensitivity denotes the ratio of correctly predicted landslides to the total number of landslides. Likelihood ratio is the ratio of sensitivity to 1-specificity, evaluating the effect of both the parameters. The main reason for the better performance of SIGMA seems to be the effectiveness in predicting the slow movements occurred in 2017: a technique based on detecting antecedent rainfall anomalies. SIGMA is more suited than ID and ED thresholds to forecast slope movements with a complex hydrological response [26]. ID and ED thresholds correctly predicted seven out of eight shallow landslides happened in 2016 but failed to forecast the slow movements in 2017 except for one day. It is also observed that the number of false alarms is also less in the SIGMA model, when compared with the other models. However, before having a definitive response on which would be the threshold model more effective to use in an EWS in Kalimpong, further tests are needed and a larger validation dataset needs to be accounted for.

In addition, the validation showed that SIGMA could need to be improved further, especially concerning the high number of false alarms. That was not a surprising outcome since in the calibration, the optimization procedure aimed at minimizing false negatives (missed alarms) instead of searching for a compromise between missed alarms and correct predictions, thus leading to a high number of false positives. A research direction worth exploring is testing different time intervals in the decisional algorithm: the one used in this research are the one resulted optimal for the Emilia-Romagna region (Italy), and they were defined after a long period of adjustments [26]. The different physical settings of Kalimpong allow for a different optimal set of SIGMA values and time intervals to be defined.

#### **7. Conclusions**

Forecasting of rainfall-induced landslides in Kalimpong town have been carried out using the SIGMA model and considering the historical rainfall and landslide information. A single parameter, the cumulative rainfall, defines the threshold by means of a set of statistical thresholds.

The algorithm was designed to consider a three day rainfall effect for shallow landslides and more days (up to 63) for slow landslides. The time period and standard SIGMA values were decided by trial and error procedure during calibration, minimizing missed alarms and false alarms. A validation procedure showed satisfactory results and proved that SIGMA performed better than other ED and ID thresholds defined for the same region by previous works. For the study area, where both rapid and slow movements are present, the combined use of short-term and long-term antecedent rainfall is thus a point of strength of the model.

It can be concluded that the SIGMA model is a simple and efficient tool which can be used for landslide early warning on regional scale. The model predicts warning levels associated with each day, which can be directly linked to the severity of landslide events predicted. This study proves that the SIGMA model can be exported in parts of the world other than Italy, where the model was originally conceived, with satisfactory performance.

While applying the SIGMA model for a study area different from Italy, in a different hydro-meteo-geological setting, it was found that the values of *Sn*(Δ) of Kalimpong is different from those used for Italy [23]. A simpler algorithm than the one used for Italy was found to provide optimum results, as a smaller area and single rain gauge is considered for the analysis. Being a statistical model, the starting algorithm was decided by trial and error using the meteorological data and was fine-tuned by minimizing false alarms using an optimization procedure. The algorithm correctly predicted warnings on 13 out of 15 days of landslides during the validation period (2016–2017). The events in 2017 were the result of continuous rainfall over a longer time period. It can be concluded that this algorithm-based approach considers the effect of both long-term and short-term rainfall and even slow movements are predicted, providing a performance better than traditional ID and ED thresholds.

The number of false alarms generated has to be reduced either by tuning the SIGMA levels and the time interval lengths, or by improving the model conceptually. As an instance, physical parameters like soil moisture can be considered along with the rainfall data to increase the positive predictive power [18,25]. Also to expand the model for a larger area, spatial variability of meteorological parameters should be considered [36,37]. After further tests and developing standard action plans for each level of warning, this model has the potential to be integrated with rainfall forecasting and to be used as a landslide early warning system on a regional scale.

**Author Contributions:** Conceptualization, M.T.A. and N.S.; data curation, S.K.; formal analysis, M.T.A. and S.K.; methodology, S.S.; supervision, N.S., B.P. and S.S.; validation, M.T.A.; writing—original draft, M.T.A. and A.R.; writing—review and editing, N.S., B.P. and S.S. All authors have read and agreed to the published version of the manuscript.

**Funding:** The work has been carried out with the financial support of Department of Science & Technology (DST), New Delhi, for funding the research project Grant No. (NRDMS/02/31/015(G)); Florence University, in the framework of the project SEGONISAMUELERICATEN20.

**Acknowledgments:** The authors express our sincere gratitude to both the funding agencies. We are also thankful to Praful Rao and Save the Hills organization for their constant support throughout the study.

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

#### **References**


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