## 2 Materials and Methods
### Validation of Flood Hazard Susceptibility Maps  
After the calculation of the closeness coefficient with Euclidean, Manhattan, Chebyshev, Jaccard, and Soergel distances at 25,000 random points in TOPSIS, the flood hazard susceptibility map was generated using Krigging interpolation in the study area. Flood susceptibility values at flooded and non-flooded points were extracted from the estimated flood susceptibility maps to determine the prediction capability of the models using various statistical indicators. Among the most widely used measures for analyzing model categorization accuracy are the Receiver Operating Characteristic (ROC) curve and the Seed Cell Area Index (SCAI) [64]. The ROC curve is the plot of the true positive rate (TPR) against the false positive rate (FPR) and the area under the ROC curve (AUC) gives an idea about the performance of distance-based measures in TOPSIS models. A maximum ROC value close to 1 indicates a very good prediction capability of a model. The flooded and non-flooded training (70%) and testing (30%) data points are extracted to evaluate the achievement and prediction ability of the models for each process. In the ROC analysis, 1-specificity in the x-direction (Equation (19)) vs. sensitivity in the y-direction (Equation (20)) was presented as follows:  
\[x=1-specificity=1-\frac{TN}{TN+FP} \tag{19}\]  
\[y=sensitivity=\frac{TN}{TP+FN} \tag{20}\]  
where _TN_s are true negatives, _FP_s are false positives, _TP_s are true positives, and _FN_s are false negatives.  
True Skill Statistics (TSS) is a simple and one of the most practical measures to assess the accuracy of the predictions [82]. TSS is defined as  
\[TSS=sensitivity+specificity-1=\frac{TP}{TP+FN}+\frac{TN}{TN+FP}-1 \tag{21}\]  
In the current study, the number of true and false predictions of flood occurrence (_TP_, _FP_) and non-occurrence (_TN_, _FN_) was used to compute the AUC and TSS using the maximum value of [PERSON]'s index. Thus, the sensitivity of the estimated results that involved the assessment of both more and less susceptible zones to flooding was investigated. As the values of AUC and TSS increase, the accuracy of the predicted results is found to be improved [83]. The AUC is also associated with the efficiency of the predicted susceptibility maps, especially for flooded pixels. These values can be interpreted as weak (0.5-0.6), moderate (0.6-0.7), good (0.7-0.8), very good (0.8-0.9), and excellent (0.9-1) [84].  
Flood susceptibility maps were categorized using four different classification methods: equal, quantile, natural break, and geometric intervals. By using those methods, the flood susceptibility values were clustered in five categories, very low (VL), low (L), moderate (M), high (H), and very high (VH), in ArcGIS. Thus, the consistency of the spatial distribution of the predictions was better understood.  
Another measure in evaluating the consistency of the flood susceptibility maps is the Seed Cell Area Index (\(SCAI\)), which was used to determine the categorized class density per flood pixel density in that class as given in Equation (22). If the flood susceptibility map classes are high and very high, then the \(SCAI\) values should be small whereas if the flood susceptibility map classes are low and very low then the \(SCAI\) values should be higher.  
\[SCAI=\frac{\textit{Percentage of the class pixels}}{\textit{Percentage of the flood hazards pixels on each class}} \tag{22}\]