3.2.1. Application of the Analytical Hierarchy Process (AHP) model
AHP is a popular MCDA method for hazard zonation. There are many other weight estimating methods, but AHP is thought to be a promising method that can deliver quick, most accurate, and economical performance (Murmu et al., 2019). Using ArcGIS software, the present study's process involves gathering and developing all the eleven thematic layers. To provide easy data handling in the GIS environment, all thematic parameters were projected and geo-rectified to UTM zone 45 North. The AHP assigned a weight to the geo-referenced map. When the database was made for all the layers, the weights and ranks assigned to all eleven parameters and their sub-classes respectively were determined by using the AHP. Hydrogeology, geomorphology, and all the data are collected as a vector layer. After collecting all vector data, which are transformed into a raster layer in the GIS environment. Soil data for the present study was extracted from FAO-DSMW (Digital Soil Map of the World. ASTER DEM was adopted from NASA for preparing drainage density and slope maps and flow accumulation of the present study area. For generating drainage density, DEM data was first processed through the flowing steps such as sink-filling, flow accumulation, and flow direction, line density. For preparing a rainfall map, at first, rainfall data were gathered from the agriculture office of the Alipurduar district then the IDW interpolation method was selected for rainfall zonation mapping. Subsequently, Landsat 8 OLI (30m) satellite data were adopted for preparing the LULC from USGS Earth Explorer. After the collection of the two Landsat satellite images, mosaic them into a single Image, and finally, the LULC map was done by using supervised classification. Ultimately, all thematic layers and sub-classes of every parameter have been done, then all calculated weights and ranks are given to all parameter and their sub-classes, respectively, by using MCDA-AHP techniques. Then weighted overlay Analysis was enacted, and finally, flash flood susceptibility mapping of the Alipurduar district was prepared.
Using Saaty's 1–9 scale, where a score of 1 indicates parity between the importance of the two parameters and a score of 9 illustrates the outrageous relevance of one parameter in comparison to the other, the relative significance for each individual layer is determined (Saaty, 1980). Every parameter's weights were computed using Saaty's scale of relative relevance values (1–9) (Table 3). The majority of the reciprocal factors in the comparison matrix are represented mathematically as n(n1)/2, where n is the number of parameters in the comparison matrix (Saaty, 1980; Pramanik, 2016). The AHP approach has four very important steps:
To analyze every alternative in accordance with its relative importance to every criterion, pair-wise comparisons are performed. Many academics have long been interested in a pair-wise comparison method that Saaty (1980) first suggested. Pair-wise comparisons are quantified by using a scale. According to this scale, the available values for the pair-wise comparisons are in nonzero values 9, 8, 7, 6, 5, 4, 3, 2, 1, 1/2, 1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9 (See also Table 2). For the pair-wise matrix following formula is used:
\(AW=\left[\begin{array}{ccccc}{a}_{11}& {a}_{12}& {a}_{13}& \cdots & {a}_{1n}\\ {a}_{21}& {a}_{22}& {a}_{23}& \cdots & {a}_{2n}\\ ⋮& ⋮& ⋮& ⋮& ⋮\\ ⋮& ⋮& ⋮& ⋮& ⋮\\ {a}_{n1}& {a}_{n2}& {a}_{n3}& \cdots & {a}_{nn}\end{array}\right]\) × \(\left[\begin{array}{c}{w}_{1}\\ {w}_{2}\\ ⋮\\ ⋮\\ {w}_{n}\end{array}\right]\)
Where, AW is the Pair-wise comparison matrix, and ann is the indicator of the pair-wise matrix element. Table 4 represents the pair-wise comparison matrix of the thematic layers.
In this matrix system, land use compared to drainage has been assigned importance value 3 which determined that drainage is moderately more important than land use which is moderately less important. Thus, all the corresponding relative importance has been made in this eleven-criteria matrix system to delineate the flash flood susceptibility mapping.
The division of each cell prepares the normalized pair-wise comparison matrix by the total of each column, and normalized weights are obtained for each factor by the average of each row. Table 5 shows the normalized pair-wise comparison matrix and corresponding weights of each factor.
The consistency index is computed based on the following formula:
$$\text{C}\text{I}=\frac{\left({\lambda }_{max}-n\right)}{n-1}$$
Where, λmax represents the principal eigenvalue and is computed from the matrix that comes to 11.983 for the present study, and n represents the number of parameters for the flash flood susceptible, which is 11. Thus, the consistency index is 0.0986.
The consistency ratio is computed based on the following formula:
$$\text{C}\text{R}=\frac{CI}{RI}$$
Hence, the consistency ratio result must be less than 0.1 in order to maintain the consistency of the judgement; in this case, the determined consistency Ratio (RC) is 0.0646, which is < 1, so this matrix is deemed to be perfectly consistent. Hence, the 121 significant pair-wise matrixes are valid for the present study.
Weighted Overlay Analysis is a method for producing an incorporated assessment depending on a pair-wise comparison matrix of AHP by using a similar range of values to input elements (ESRI, 2015).
$$\text{W}\text{O}\text{A}={\sum }_{i=1}^{n}{\text{W}}_{\text{i}}\times {\text{R}}_{\text{i}}$$
Where Wi is considered as a particular decision criterion, Ri is the raster layer of that particular criterion, and n is the number of the decision matrix.
In the final step, the model was validated through the flash flood inventory data (2017–2020) of the Alipurduar district and field-based observations. The methodological flow chart is shown in Fig. 2.