**5. Landslide Susceptibility Mapping**

Landslide susceptibility can be defined as the probability of spatial occurrences of slope failures for a given set of geo-environmental conditions [48], and its determination is one of the crucial steps needed to understand identify potentially landslide-prone sections for any study region. Several studies around the world have been conducted towards the development of landslide susceptibility maps (LSM) using various methods [8]; however, there seems to be no consensus as to the best method for analysis [49]. Aleotti and Chowdhury [50] categorized LSM methods as either quantitative or qualitative. Qualitative models are mostly based on expert opinion, whereas quantitative models are data-driven, which makes them more reliable. The quantitative approaches include several kinds of techniques such, including statistical, deterministic, and other approaches [51–53]. In the case of statistical approaches, it is assumed that the parameters affecting landslide events in the past will be the same in future [54], and these analyses can be categorized into bivariate and multivariate [49]. In bivariate analysis, the factors affecting landslides are compared with landslide inventory data by providing weights based on landslide causative factors. The most frequently used methods in bivariate models are overlay, index-based, and weight-of-evidence analyses [8,51,55]. Bui et al. [6] performed a comparison between a bivariate approach (statistical index) and a multivariate approach (logistic regression) for Vietnam, and found equal forecasting capability. However, one of the main issues with the use of a quantitative approach is the assignment of weights to the landslide-affecting factors [56–58]. The use of GIS has been proven to be a powerful tool with which to validate the significance of factors, and it has been used for multi-criterion decision analysis [49,59]. The decision

analysis technique combines primary- and secondary-level weights for every causative factor, where primary weights are similar to the bivariate approach and secondary weights are expert-opinion-based. For secondary weights, the analytic hierarchy process (AHP) has become popular and has been successfully applied for decision-making systems [60,61]. AHP uses a pairwise relative comparison between every landslide-causative factor. Generally, AHP consists of five key steps: (a) simplify the decision process into its component factors, (b) distribute the factors in a hierarchy process, (c) allocate numerical values to analyze the relative significance of each factor, (d) compose a comparison matrix, and (e) provide weights to every factor by calculating normalized principal eigenvectors [62].

To determine susceptibility, a variety of factors responsible for landslides in the study region were considered. Parameter selection depends on various factors, such as landslide type, data availability and reliability, and adopted methods [63]. For the present study, we used eight landslide-conditioning factors based on the characteristics of the area and prepared from various data sources (Table 2). Figure 9a–f represents all the maps used for the analysis, derived from the Shuttle Radar Topography Mission (SRTM) digital elevation model (DEM) with 30 × 30 m resolution, which was the only terrain data source available for this region. The factors with continuous values were reclassified into categories based on Jenks' natural breaks optimization method [64] and developed using ArcGIS 10.4.1.


**Table 2.** Parameters Used for Landslide Susceptibility Mapping.

The above-mentioned thematic layers were combined by using a weight-of-factors approach determined by AHP to develop the landslide susceptibility map. The use of AHP to develop landslide susceptibility maps has been successfully applied in various regions [61,66,67]. The weights required to carry out AHP were calculated by performing pairwise comparisons for each landslide factor and assigning values from 1 to 9 [63,68–70]. Table 3 shows the pairwise comparison and priority calculation, along with rankings of all indicators. These values were based on an expert's opinion and were placed in n × n matrix, where n is the number of factors.

**Table 3.** Parameter Wise Weights, Matrix, and Consistency Ratio as Determined Using AHP.


Consistency Ratio = 0.039.

**Figure 9.** *Cont.*

(**d**)

**Figure 9.** *Cont.*

(**f**)

**Figure 9.** *Cont.*

**Figure 9.** Landslide-conditioning factor maps: (**a**) slope, (**b**) elevation, (**c**) aspect, (**d**) mean daily rainfall, (**e**) proximity to road, (**f**) proximity to stream, (**g**) geology, and (**h**) land use and land cover (LULC).

The AHP reduced the inconsistencies formed due to the subjectivity of different experts' opinions by computing a consistency index (CI) and consistency ratio (CR), which were determined by

$$\text{CI} = (\lambda\_{\text{max}} - \text{n}) / (\text{n} - 1) \tag{3}$$

$$\text{CR} = \text{CL/RI} \tag{4}$$

where λmax represents the largest Eigenvector of the matrix and n represents the total causative factors (order of the matrix) used in the generation of the LSM. RI (random index) is the average value of CI for a randomly generated pairwise matrix and can be accepted only when CR values are less than 10% [71]. For the present study, the average consistency index was estimated for a sample size of 500 and its value was 0.039 (3.9%), which was considered acceptable. Several authors have calculated and estimated different RIs based on various simulation methods and the total number of matrices involved in the process (Table 4). However, we have used Satty's [71] RI values of n = 11 and up to 500 matrices, where the values are 0, 0, 0.58, 0.9, 1.12, 1.24, 1.32, 1.41, 1.45, 1.49, and 1.51.

**Table 4.** RI Values Obtained by Various Authors (Adopted from Reference [72]).


The values of CR cannot be negative and can attain a maximum value of 0.3. Values of CR less than 0.1 are considered acceptable; if this is not achieved, new attempts are made until the value is acceptable [80]. However, the values of CR are dependent on the analysis type and the number of criteria being considered. In some cases, CR > 0.1 may not be considered critical, and values of CR ranging from 0.15 to 0.3 can also be considered acceptable. A matrix will be considered consistent, according to Saaty [71], if

$$
\lambda \text{max} < \mathbf{n} + 0.1((\lambda \text{max}) - \mathbf{n}) \tag{5}
$$

Finally, all the landslide-causative factors and classes were integrated by a method of weighted overlay in ArcGIS to generate the landslide susceptibility index (LSI).

$$\text{LSI} = \sum\_{\mathbf{k}=1} \,^\text{n} \,^\text{W}\_{\mathbf{k}} \mathbf{W}\_{\mathbf{jk}} \tag{6}$$

where Wk is the weight of the causative factor, Wjk is the rank value for factor class j of causative factor k, and n represents the total causative factors selected. Ranks of criteria were calculated based on priority or weight values. The highest priority considered was Rank 1, while the lowest priority considered was the last rank in the AHP.
