*2.2. Methodology*

The main objective of this paper is to determine flood-susceptible areas based on the combination of MCDM and GIS. Afterward, the Importance Weights (IWs) value of the qualitative criteria and *FHI* are calculated using the AHP method, respectively [21]. The AHP approach is one of the MCDM models that address the complexity involved in the decision-making process using Pairwise comparisons and considering the effects of quantitative criteria [9,22]. The Saaty's scale is proposed in this technique for scoring the importance value of criteria [23] (see Table 1).

**Table 1.** The Saaty's scale for scoring the importance value of criteria [9].


Combining the AHP method and a GIS tool into a decision support system holds significant promise for enhancing decision-making in the planning process [15]. The GISbased hierarchical mode, incorporating qualitative spatial layers and expert opinions, allows the prioritizing of criteria by utilizing the Pairwise Comparison Matrix (PCM) [15]. Moreover, there are different criteria in this study, and there is a lack of agreemen<sup>t</sup> among experts within this field due to the presence of uncertainty. In these situations, applying fuzzy memberships to reduce uncertainties is highly recommended. Therefore, in this study, a hierarchical model has been applied based on a combination of AHP methods and GIS in the form of fuzzy sets. First of all, various spatial layers and maps were used and introduced in ArcGIS. However, the present study selected eight criteria, including drainage density, land use/land cover, precipitation, slope, soil-type, elevation, geology, and distance from the river, according to their essential role in flood region selection.

In the next stage, the weight assigned to each criterion has been established through the application of a GIS-based hierarchical integration model [15], respectively. The weighting procedure has been fully implemented in ArcGIS software based on raster layer analysis with 30m cell size. Having selected the criteria, it is imperative to carry out the subsequent

steps sequentially. The arrangemen<sup>t</sup> of the hierarchical model based on GIS is depicted in Figure 2.

**Figure 2.** The arrangemen<sup>t</sup> of the GIS-based hierarchical model.

In the following, the classification of the layers has been redefined in accordance with common interval scales, which are depicted in Table 1 [24]. The subsequent phase entails computing the criteria weights by applying the AHP based on the PCM [9]. Employing the fuzzy membership tool to establish the nature of the fuzzy membership function is advisable. Lastly, the "fuzzy overlay tool" is utilized to combine the specific weights of each raster layer. Then, the validity of the PCM must be examined. The AHP employs the inconsistency ratio to assess the compatibility of the experts' opinions with the questionnaire. Prior to commencing data processing within a GIS framework, it is crucial to calculate the Inconsistency Index (*I.I*), the Random Inconsistency Index (*R.I.I*), and *λ*max. The calculation of *I.I* can be performed as follows:

$$I.I = \frac{\lambda\_{\text{max}} - n}{n - 1} \tag{1}$$

The maximum eigenvalue of the matrix, denoted as *λ*max and the number of criteria by the variable *n*, are represented in the Equation (1).

The Ratio of Inconsistency (*I.R*) is obtained by dividing the value of *I.I* by the value of *R.I.I* as stated in Equation (2). The values of *R.I.I* for the matrix are presented in Table 2.

$$I.R = \frac{I.I}{R.I.I} \tag{2}$$

The Inconsistency ratio must be 0.1 or less for the comparisons to be consistent and the respondents to be valid.


**Table 2.** The Random Inconsistency Index values of matrices.

The GIS tool was utilized for specifying the weight of criteria in the subsequent step due to its remarkable ability to store and integrate spatial layers. The spatial layers for each criterion were created using ArcGIS software. Each layer was considered the main quantitative criterion for the flood susceptibility mapping process. The primary classification of the critical criteria for flood sustainability mapping in the Ottawa district and their attributed requirements for converting to raster layers are briefly introduced in Table 3. It should be noted that preparing the precipitation data layer involved gathering statistical and synoptic gauge data from the study area, covering the period from 1985 to 2022, focusing on obtaining the long-term annual average. The process of interpolating precipitation data was carried out using the Kriging method, which resulted in the transformation of the data into a raster layer. Furthermore, the drainage density criterion was determined by dividing the total length of the river network by the area of the watershed. The drainage density is calculated using Equation (3) [15].

$$
\Omega I = \frac{\sum L\_i}{A} \tag{3}
$$

where *Li* stands for the length of the river system measured in kilometers, while *A* represents the watershed area in square kilometers.

**Table 3.** Categorization of spatial layers of each criterion with their requirements.


In the next stage, the reclassification tool is employed to categorize the raster layers according to the available classification system. A fuzzy membership tool based on linear fuzzy sets is utilized to transform the raster layers into fuzzy numbers to accomplish this task. Subsequently, the resulting fuzzified raster layers are subjected to reclassification utilizing the Saaty scale, as presented in Table 1. Then, the reclassified fuzzy raster layers are evaluated using an AHP-based GIS approach to calculate the weight of the fuzzy raster layers. Additionally, the Inconsistency Ratio of PCM is determined using Equations (1) and (2). Furthermore, a demonstration of how to calculate the weighted elevation criterion and form a weighted layer can be seen in Figure 3.

**Figure 3.** The process of fuzzy weighted Elevation layer within a hierarchical GIS model: (**a**) Elevation

raster layer, (**b**) Fuzzy Elevation layer, (**c**) Reclassified

In the next step, the *FHI* is calculated with the following Equation (4) to evaluate the floodingprobabilityrate:

 AHP layer, (**d**) Weighted Elevation layer.

$$FHI \sum\_{i=1}^{n} WiRi \tag{4}$$

where *Ri* is each criterion's raster layer, *Wi* is each criterion's weight, and *n* corresponds to the number of the criteria. Therefore, Equation (5) is written in the following form:

$$\begin{array}{l} FH = W\_{EL}R\_{EL} + W\_{LILL\subset}R\_{LIL\subset} + W\_{DD}R\_{DD} + W\_{GEO}R\_{GEO} \\ \quad + W\_{SL}R\_{SL} + W\_{SP}R\_{SP} + W\_{PR}R\_{PR} + W\_{DR}R\_{DR} \end{array} \tag{5}$$

In this research, to attain *FHI* within a GIS environment, the weights of each criterion are calculated by multiplying them in their respective raster layer through the utilization of the Raster Calculator tool.

Finally, to determine the final flood susceptibility map of the study area, all the fuzzy weighted layers are integrated using the Fuzzy Overlay tool. In the following, the categorization of weighted fuzzy overlay layers of criteria is shown in Figure 4.

**Figure 4.** Classification of overlaying weighted fuzzy layers' process based on the criteria specified.

### **3. Results and Discussion**

Table 4 presents the results of the PCM and the average weight per layer. Furthermore, Table 4 showcases the calculated inconsistency ratios of each PCM, which were determined using Equations (1) and (2). In this study, the criteria are eight and the result *R.I.I* = 1.41. Finally, the consistency ratio has been calculated *I.R* = 0.041, since the *I.R* value was inferior to 0.1 and the consistency of the weight was accepted. Based on the obtained IWs of criteria in Table 4, the precipitation, slope, and soil criteria with the values of 0.298, 0.162, and 0.143 have the highest IW for the flood assessment, respectively. In addition, the geology and elevation criteria with values of 0.018 and 0.041 are the least important in assessing food susceptible areas of the case study.


**Table 4.** The results of the PCM for the spatial layers and their respective weights.

In addition, the *FHI* was found to evaluate the rate of flooding probability [25], which was calculated as follow:

$$\begin{aligned} FH &= 0.041R\_{EL} + 0.121R\_{LILIC} + 0.109R\_{DD} + 0.018R\_{GEO} \\ &+ 0.143R\_{SL} + 0.162R\_{SP} + 0.298R\_{PR} + 0.107R\_{DR} = 5.23 \end{aligned} \tag{6}$$

The proposed method, which considers a multitude of quantitative criteria, is utilized to achieve the mapping of flood susceptibility. The final map of the flood susceptibility mapping of the study area was constructed and classified into five major classes with flood potentiality from very low to very high (see Figure 5). Based on Figure 5, 3.18% of the study area represents the very low class, 40.93% of the area represents the low class, 24.37% of the area represents the moderate class, 15.27% of the area represents the high class, and 16.24% of the area represents the very high class.

**Figure 5.** The flood susceptibility map of the Ottawa district.
