*6.2. Importance of Factors Using Correlation-Based Feature Selection*

– Relative importance analysis of factors affecting flash floods was carried out using correlation-based feature selection method as shown in Table 4. It can be seen that distance from rivers is the most important factor for flash floods as the value of *AM* (0.608) is the highest compared with other factors. Following factors are slope (*AM* = 0.484), elevation (*AM* = 0.337), lithology (*AM* = 0.125), soil (*AM* = 0.099), rainfall (*AM* = 0.049), land use (*AM* = 0.024), aspect (*AM* = 0.022), and distance from faults (*AM* = 0.007), respectively. The feature selection results are reasonable as the areas close to the river are more likely to be affected by floods. This is true for normal river floods and also for flash floods in case of torrential rains within short period in this area [112,113]. Slope is also important as it influences surface runoff, volume, and velocity of flow. In the study area (Tafresh), there is more accumulation than outflow due to gentle topography (slope factor) resulting in the rapid rise of the flood water level within short time during torrential rain. Therefore, slope factor is the second most influential factor in the flood modeling (Table 4), which is consistent with many studies [114,115]. At higher elevation, slope factor is important resulting in higher velocity and runoff thus draining the water rapidly towards lower levels [116–118]. Other factors, namely lithology, soil, rainfall, land use, and aspect are also important factors for modeling of flash floods though their *AM* value varies as mentioned in Table 4. Here, we would like to mention that though *AM* of rainfall factor is only 0.049, it is the main and also triggering factor on which flash flood depends, especially in this area. However, the feature selection results show that distance to faults is the least important factor to flash flood occurrence and modeling (*AM* = 0.007), and thus this factor has a very small contribution to the performance of the models, and it should be removed from the datasets for further analysis of the models. Therefore, out of nine factors, only eight factors (distance from river, aspect, elevation, slope, rainfall, soil types, land use, and lithology) were reasonably selected for modeling of flash floods in this study.


**Table 4.** Importance of factors using correlation based feature selection.

#### *6.3. Validation of Di*ff*erent Models*

Performance of the machine learning models was validated using various criteria on both training and testing datasets (Figures 6–9). Validation of all the models was done by the ROC method (Figure 6). Results indicated very high AUC value during both training (ABM-CDT = 0.995; Bag-CDT = 0.972; Dag-CDT = 0.947; MBAB-CDT = 0.986; and CDT= 0.933) and testing phase (ABM-CDT = 0.96; Bag-CDT = 0.93; Dag-CDT = 0.47; MBAB-CDT = 0.933; and CDT = 0.90). Among all five models, ABM-CDT shows the maximum level of AUC compared with other models. All the models indicate a very low value of RMSE, both on the training dataset (ABM-CDT = 0.168; Bag-CDT = 0.245; Dag-CDT = 0.316; MBAB-CDT = 0.206; and CDT = 0.279) and testing dataset (ABM-CDT = 0.291; Bag-CDT = 0.307; Dag-CDT = 0.329; MBAB-CDT = 0.31; and CDT = 0.323) period, which clearly indicate high reliability of the proposed models (Figure 7). However, the ABM-CDT model indicates the best performance in comparison to other models, and it has the lowest RMSE value. –

**Figure 6.** *Cont.*

**Figure 6.** Analysis of Receiver Operating Characteristic (ROC) of the models: (**a**) training dataset and (**b**) validating dataset.

Figure 8 indicates performance of the models using other validation criteria. It can be observed that all models have good performance with high values of PPV, NPV, SST, SPF, and ACC. Out of these, the ABM-CDT model has high values of PPV (95.81% for training and 94.37% for testing), NPV (96.41% for training and 85.92% for testing), SST (96.39% for training and 87.01% for testing), SPF (95.83% for training and 93.85% for testing), and ACC (96.11% for training and 90.14% for testing), the Bag-CDT model has values of PPV (88.62% for training and 94.37% for testing), NPV (97.01% for training and 85.92% for testing), SST (96.73% for training and 87.01% for testing), SPF (89.5% for training and 93.85% for testing), and ACC (92.81% for training and 90.14% for testing), the Dag-CDT model has values of PPV (89.82% for training and 91.55% for testing), NPV (88.02% for training and 81.69% for testing), SST (88.24% for training and 83.33% for testing), SPF (89.63% for training and 90.63% for testing), and ACC (88.92% for training and 86.62% for testing), the MBAB-CDT model has values of PPV (92.22% for training and 94.37% for testing), NPV (96.41% for training and 84.51% for testing), SST (96.25% for training and 85.9% for testing), SPF (92.53% for training and 93.75% for testing), and ACC (94.31% for training and 89.44% for testing) and the CDT model has values of PPV (90.42% for training and 94.37% for testing), NPV (91.02% for training and 81.69% for testing), SST (90.96% for training and 83.75% for testing), SPF (90.48% for training and 93.55% for testing), and ACC (90.72% for training and 88.03% for testing). Kappa statistics also show a satisfactory accuracy in both the case of training (ABM-CDT = 0.922; Bag-CDT = 0.856; Dag-CDT = 0.788; MBAB-CDT = 0.898; and CDT = 0.814) and testing (ABM-CDT = 0.803; Bag-CDT = 0.803; Dag-CDT = 0.732; MBAB-CDT = 0.789; and CDT = 0.761) (Figure 9).

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**Figure 7***.* Analysis of RMSE of models*.*  **Figure 7.** Analysis of RMSE of models.

**Figure 8.** Analysis of accuracy of the models using: (**a**) training dataset and (**b**) validating dataset.

**Figure 9.** Kappa values for the models.

Considering analysis of the above results, it can be stated that all these developed and applied models performed well for flash flood susceptibility mapping in this study. In particular, the prediction capability of the CDT model has been enhanced by more than 5% with AdaBoost, about 3% with Bagging and MultiBoostAB, and 5% with Dagging. In general, CDT algorithm is one of the good data mining models built on the decision tree and uses IDM and general uncertainty measures [69]. However, it has a low accuracy as the built tree decides to categorize a new sample of data, especially with incomplete or missing values of the data. Therefore, the use of ensemble frameworks like AdaBoostM1, Bagging, Dagging, and MultiboostAB is a great help in improving performance of the CDT as these techniques have the capability to condense the bias as well as the variance and avoid the problem of overfitting [119]. Comparison results of different ensemble frameworks used in this study (ABM-CDT, Bag-CDT, Dag-CDT, and MBAB-CDT) showed that ABM-CDT outperforms other ensemble frameworks (Bag-CDT, Dag-CDT, and MBAB-CDT). Thus, it can be stated that AdaBoostM1 is more effective than other ensemble techniques (Dagging, Bagging, and MultiBoostAB) in improving performance of the CDT for flash flood susceptibility assessment of this study. This result is reasonable as AdaBoostM1 can be considered to make a classification of the binary classes and enhance the prediction accuracy [120,121]. It is a very well-known fact that among all these ensembles, AdaBoostM1 is an interpretable and highly robust algorithm that prevents noise in order to make significant improvement in classifying error in comparison to the base decision tree classifier [122]. Our results are comparable to the previous ensemble model-based studies, which report that the ensemble models lead to a boost in the performance of a standalone model [123–125].

#### *6.4. Development of Flash Flood Susceptibility Maps*

Flash flood susceptibility maps of the research area were produced using ABM-CDT, Bag-CDT, Dag-CDT, MBAB-CDT, and CDT models (Figure 10). Figure 11 shows the comparison of results of all the models of flash flood susceptibility classes and their percentage of class pixels and flash flood pixels. All the models indicated that more than 50% of past flash floods were observed on very high susceptibility class of the maps (ABM-CDT = 51.3%; Bag-CDT = 53.8%; CDT = 61.8%; Dag-CDT = 69.7%; and MBAB-CDT = 86.1%). Evaluation of the frequency ratio data of the historical flash flood locations and the generated flash flood maps for the very high susceptible pixel class was done. The maximum FR was observed for ABM-CDT (3.46) followed by Bag-CDT (3.44); Dag-CDT (3.4); CDT (2.88), and MBAB-CDT (2.66), which clearly indicated higher degree of reliability of ABM-CDT and Bag-CDT algorithms.

Analysis of the results of flash flood susceptibility maps shows that the Tafresh city area, which is located in the Tafresh watershed, belongs to very high susceptibility class. This is due to rapid development and expansion of the city area by encroaching topographically vulnerable areas to flash floods. Moreover, construction of buildings and roads in urban areas resulted in the increase of surface areas of impermeable structures and thus less infiltration and more runoff, causing flash floods in the event of intense rainfall during short periods [40,126,127]. The results of flood susceptibility zoning in Tafresh watershed showed that the southeastern parts have high to very high susceptibility to flash floods. The most important causes of flood susceptibility in these areas are related with anthropogenic activities causing drastic changes in catchment morphology, such as leveling of the land, altering the natural drainage, and increasing the impervious surfaces in the city. This has exacerbated the risk of floods and flooding of the infrastructure facilities thus increasing the potential threat to life and financial losses.

**Figure 10.** Flash flood susceptibility maps of the models: (**a**) ABM-CDT, (**b**) Bag-CDT, (**c**) Dag-CDT, (**d**) MBAB-CDT, and (**e**) CDT.

**Figure 11.** Analysis of performance of flash flood susceptibility maps using different models. **Figure 11.** Analysis of performance of flash flood susceptibility maps using different models.
