Hybrid ensemble modeling for flash flood potential assessment and susceptibility analysis of a Himalayan river catchment

Abstract The occurrence of frequent flash floods in the Indian Himalayan state of Uttarakhand causes massive destruction and damage to life and property every year. In this study, five bivariate statistical models, namely Frequency Ratio, Fuzzy Membership Value, Weights of Evidence (WOE), Statistical Index (SI), and Information Value (IV), were individually integrated with the Index of Entropy (IOE). These models were employed to calculate the flash flood potential index and identify susceptible zones in the Mandakini River Basin. 39 flash flood locations, 39 non-flash flood locations, and 15 flash flood conditioning factors were utilized for training and testing the models with 70% and 30% of the dataset, respectively. The model performances were examined using receiver operating characteristics curves. This best prediction rate performance was featured by SI-IOE and IV-IOE with an AUC = 0.896 followed by WOE-IOE (AUC = 0.889). The results revealed that the areas with high and very high susceptibility cover approximately 40% of the study area.


Introduction
Flash floods are considered among the most catastrophic natural disasters, causing voluminous destruction in fatalities and property loss. The assessment report titled, 'Natural disasters 2018: An opportunity to prepare.' published by the Centre for Research on the Epidemiology of Disasters (CRED) pointed out that 'Floods have affected more people than any other type of disaster in the 21st century, including in 2018'. According to the UN-ESCAP report (Alisjahbana et al. 2019), of the total flood absolute average annual loss (AAL) in the Asia Pacific region, India represents 13 percent.
In the last two decades, India has been experiencing frequent flash flood events, which can be attributed to the changing rainfall pattern and climate change (Rajeevan et al. 2008;Kumar et al. 2018;Ali et al. 2019;Swain et al. 2021). The Northwest Himalayan (NWH) region in India is among the most highly susceptible areas to extreme rainfall or cloud burst-induced flash floods, especially in the monsoon season (Maikhuri et al. 2017;Prasad and Pani 2017).
The highly complex and undulated topography and altitude dependent climate (Bookhagen & Burbank 2006;Bharti et al. 2016) of the region stimulates erosion and debris removal along with large volumes of water flowing through the rivers and streams (Ghosh et al. 2019).
Looking to the aforementioned, researchers around the world have been analyzing flash flood occurrences for susceptibility assessment to develop preventive measures for minimizing the effects of such disasters (Tehrany et al. 2013;Khosravi et al. 2018Khosravi et al. , 2019Zhao et al. 2018;Tien Bui 2019, 2020;Costache 2019a;. Flash Flood Susceptibility (FFS) concept reflects the likelihood of flash flood events occurring in an area based on local terrain, geographical and hydrometeorological factors. FFS modeling can be referred to as a constructive, feasible, and implicit solution for classifying an area into zones where future flash floods may occur, and efforts can be made to attenuate their consequences.
Flash Flood Potential Index (FFPI) has been used by researchers worldwide as a very reliable method to assess the flash flood potential in an area (Popa et al. 2019;Costache and Tien Bui 2020). A wide range of models and techniques have been employed for the flood as well as flash flood susceptibility, such as bivariate statistical techniques viz., frequency ratio (Rahmati et al. 2016;Costache and Zaharia 2017;Samanta et al. 2018;Shafapour Tehrany et al. 2019), the weight of evidence (Khosravi et al. 2016;Costache and Zaharia 2017;Chen et al. 2019;Paul et al. 2019), information value, certainty factor, index of entropy (Costache and Tien Bui 2020) and fuzzy logic . Researchers have also employed multi criteria decision making (MCDM) approaches, viz., Analytical Hierarchy Process (AHP) (Abu El-Magd et al. 2020;Souissi et al. 2020;Abu El-Magd and Eldosouky 2021) and Technique for Order of Prioritization by Similarity to Ideal Solution (TOPSIS) . Machine learning based methods have also been extensively employed for flash flood susceptibility modeling viz., artificial neural networks (Chakrabortty et al. 2021), logistic regression (Nandi et al. 2016), support vector machines (Tehrany Pradhan, Mansor, et al. 2015), and decision trees (Khosravi et al. 2018). Comparative performance evaluation of these approaches in isolation have been satisfactory but can be certainly improved using machine learning techniques Pham et al. 2020) or hybrid combinational approaches and ensembles of multiple models (Tehrany, Pradhan, and Jebur 2015;Mojaddadi et al. 2017;Costache and Tien Bui 2020).
The review of previous research work on susceptibility studies reveals that individual use of techniques like frequency ratio, statistical index, weights of evidence, and information value can analyze the effect of factor classes on the occurrence of flash floods. However, the correlation between the factors must be taken into consideration. On the other hand, the Index of Entropy is a reliable approach that can analyze the association among the parameters without evaluating the factor classes. Therefore, a hybrid ensemble modeling approach is proposed for improving the FFS assessment by combining IOE with FR, FMV, WoE, IV and SI techniques.
Some previous studies attempting FFS assessment in India largely excluded the Himalayan region of Uttarakhand. One of the potential reasons behind this could be a sparse weather monitoring infrastructure in the region and a sparse rain gauge network in the state. Keeping this in consideration, the main aim of this study is to carry out a flash flood potential assessment and susceptibility analysis in the Mandakini river basin of Uttarakhand using hybrid ensemble modeling. The main novelty of the present research is reflected by the application of the hybrid ensemble models to evaluate the flash flood potential and susceptibility in mountainous river basin of Uttarakhand which can be replicated in other flash flood vulnerable watersheds in the region and elsewhere. In this context, the present article may be a valuable reference for future studies.

Study area
The research work pivots on the Mandakini river basin (MRB) in Uttarakhand's high elevation mountain setting in the Indian Himalayan Region (IHR). It covers an area of 1642 km 2 having geographical coverage spanning over 30 17 0 0.69" to 30 48 0 50.85" latitudes and 78 49 0 1.30" to 79 21 0 59.15" longitudes. Mandakini river emerges from the Chorabari Glacier and is a tributary of river Alaknanda, which further meets river Bhagirathi to form the Mighty Ganges. The entire catchment features a huge variation in the elevation profile ranging from 611 m to 6958 m ( Figure 1). The area represents a rugged topography featuring moderate to steep slopes which are interceded by narrow valleys (Khanduri et al. 2018). Additionally, this area is quite popular across the global water resources community, especially after one of the most dreadful natural disasters (popularly referred to as the Himalayan Tsunami) in India in 2013. The Land Use/Land Cover Database (NRSC 2019) indicates that the study area is dominated by three major land use classes namely, forests, agriculture and snow cover representing approximately 57%, 26% and 16% of the entire area, respectively. The remaining area is shared among water bodies and settlements. The northern part of the study area features the gigantic Himalayas, exhibiting intense monsoon and precipitation patterns. The higher altitudes in the Mandakini catchment (>4500 m) are cold all-round the year and many times become inaccessible due to heavy snowfall (Parida et al. 2017). The summer season in the area spans from April to June, followed by the monsoon season between July and September, which brings the onset of the winter season in October and extends till February. The study area features a peculiar characteristic of the southwest monsoons, which gets 70 to 80 percent of the total rainfall during the monsoon season (Nandargi et al. 2016).

Flash flood inventory
To evaluate the flash flood susceptibility, a database of past flash flood events in the area of interest holds paramount significance (Tehrany, Pradhan, and Jebur 2015). These locations are used to assess and extract the characteristics of various input layers, which have a strong contributing influence in causing disaster events. These point locations also serve as a perfect evidence-based training input which is very efficiently utilized to identify similar signatures to classify the entire area into various susceptibility zones. Data availability in the Himalayan region is always a major challenge. There is no data released/ shared on flash flood occurrence in the public domain by the government agencies like the Disaster Mitigation & Management Centre of the state (Singh and Pandey 2021). Therefore, in this study, an inventory was created by mapping the past flash flood event locations identified from various sources (Naithani et al. 2002;Joshi and Kumar 2006;Naithani et al. 2011;Rautela and    to collect the data. Figure 2 represents the flash flood event locations mapped for the study. The obtained flash flood inventory included 39 flash flood event locations classified randomly into the training (%70%) dataset and validation (%30%) dataset (Cao et al. 2016;Li et al. 2019;Popa et al. 2019;Ali et al. 2020). An equal number of non-flood event locations were chosen at mountain tops and ridgelines where there is minimal flood occurrence Pham et al. 2020). Considering the aforementioned rationale, the non-flood locations were sampled randomly in the not-yet flood areas (Tehrany, Lee, et al. 2014;Costache and Tien Bui 2019). Costache and Bui in 2019 clearly highlighted that there is no general agreement among the researchers on selection of non-flood points. Thus, for this study keeping the terrain into considering we selected mountain tops and ridgelines for non-flood points.
3.2. Flash flood conditioning factors (methods for generating these data sets) The mainstay for the susceptibility assessment in this study is the selection and mapping of highly influential predictors to detect and appraise the specific areas prone to flash floods Costache 2019b;. In this study, a total of fifteen flash flood conditioning factors namely, aspect, convergence index (CI), Fournier index (FI), hydrological soil group (HSG), lithology, land use/cover (LULC), normalized difference vegetation index (NDVI), plan curvature, profile curvature, slope, stream power index (SPI), topographic position index (TPI), topographic ruggedness index (TRI), topographic wetness index (TWI), distance from the river were considered. All the factors were derived using geospatial techniques. ArcGIS 10.8, SAGA GIS 2.3.2 and QGIS 3.16.3 with GRASS 7.8.5 were used to derive all the above-listed factor layers. Table 1 presents the data sources of various input datasets used to derive the conditioning factors for the analysis. A detailed description of all the conditioning factors and the interpretation of input rasters developed for the susceptibility assessment are presented in Table S1a&b (included in the supplemental material). Figures 3 and 4 presents the input layers prepared for each conditioning factor. Figure 3(f) shows the Lithology map of the study area having 28 soil types represented by numeric codes presented in Table 2.

Methods
Flash flood susceptibility assessment was carried out using five different hybrid couples or ensembles, namely, FR-IOE, WOE-IOE, FMV-IOE, SI-IOE and IV-IOE. The workflow aims to identify the flash flood susceptible areas and classify the entire study area into various zones using geospatial and hydrometeorological data input layers and the areas affected by the flash flood in the past. All these datasets were employed in the following sequence of steps: (i) flash flood events inventory; (ii) partitioning of the inventory points into training and validation data; (iii) preparation of input layers of flash flood conditioning factors; (iv) analysis of the predictive ability of flash flood conditioning factors and their selection; (v) application of stand-alone and coupled models for estimating the FFPI variability and generation of FFSMs; (vi) validation of results using ROC curves; (vii) evaluation of model performance. The methodology developed in the present study is presented schematically in Figure 5.

Multicollinearity assessment of the flash flood conditioning factors
All the conditioning factors were evaluated for multicollinearity using SPSS 25 software.
Multicollinearity results in obtaining inaccurate model results due to the consideration of irrelevant factors in the analysis. Therefore, it is required to eliminate the irrelevant factors. There are several methods available for multicollinearity diagnostics viz., Pearson's correlation coefficients (Sedgwick 2012), variance decomposition proportions (Schuerman 2012), conditional index (Belsley 1991), and Variance Inflation Factors (VIF) and tolerance (Dormann et al. 2013;Ahmad et al. 2021). Khosravi et al. (2018) have strongly recommended preference of VIF and tolerance over the other methods specifically for natural hazards assessment. Variance Inflation Factor (VIF) and Tolerance (TOL) are the two most popularly used indicators to evaluate the multicollinearity among independent   conditioning factor classes to highlight the correlation between the event locations and the factors in consideration. The FR coefficients for each class is calculated using the following formula (Costache 2019b): where FR represents the frequency ratio calculated for a class i of conditioning factor j. Np(LXi) represents the number of flash flood event locations in each class i of factor X, while Np(Xj) represents the number of pixels within a conditioning factor Xj. The total number of classes of each conditioning factor Xi is represented by m, and n is the number of flash flood conditioning factors considered in the study area.

Fuzzy membership value (FMV)
Fuzzy logic is an exciting technique to represent and manipulate complex problems. However, in this study, fuzzy logic is implemented using the frequency ratio. The FR values for all the classes of each conditioning factor are normalized using the following equation Feizizadeh 2017, 2021) to obtain the Fuzzy Membership Values (FMV).
where l ij is the FMV of class i of conditioning factor j.

Weights of evidence (WOE)
This technique employs the Bayes' theory of conditional probability to quantify the spatial overlap between the flash flood locations and the conditioning factor classes (Costache and Zaharia 2017). This method involves estimating coefficients based on the association between the presence and absence of flash flood locations and each conditioning factor class. Two types of weights, i.e. positive weight (W þ ) and negative weight (W -), are calculated to obtain the final coefficients. Van Westen et al. in 2003 proposed the above equations were used for computation purposes as follows: where: Npix 1 represent the number of flash flood event pixels in the class; Npix 2 represents the number of flash flood event pixels from outside of the class; Npix 3 represents the number of pixels in the class excluding the flash flood event pixels; Npix 4 represents the number of pixels excluding the flash flood event pixels from outside of the class; W þ and Ware the positive and negative weights, respectively. Finally, the WOE coefficient was calculated as W f using the formula (Van Westen et al. 2003;Costache and Zaharia 2017): Where: W mintotal is the total of all negative weights in a multiclass map.

Statistical index (SI)
SI was originally introduced for landslide susceptibility mapping by Van Westen (1997). This method analyses the statistical correlation between the flash flood inventory locations and the conditioning factors (Yalcin 2008). The following equation is employed to calculate the weights: Where W is the computed weight for a given class i of factor j; L ij represents the number of flash flood locations in class i of factor j, L T is the total flash flood locations in the entire study area, P ij is the number of pixels in class i of the factor j and P L is the total number of pixels in the entire study area.

Information Value (IV)
This method is employed for the probable spatial occurrence of an event based on the conditioning factor and occurrence relationship. This approach has been very effectively applied for landslide susceptibility assessment (Gheshlaghi and Feizizadeh 2021). Information value I i for a factor i is computed using the following equation: A i represents the number of flash flood events in class i, B i represents the factor class i, A is the total number of flash flood events in the study area, and B is the total study area.
Positive values of I i indicate that there is more than average probability of flash flood occurrence, while negative values indicate that there is a less than average probability of flash flood occurrence.

Index of entropy (IOE)
This method is used for evaluating the uncertainty and instability of a system (Shannon 2001). In this study, the entropy of flash flood events indicates the contribution of various conditioning factors in the occurrence of flash floods. This method facilitates the computation of weights for each conditioning factor (W j ) using the following set of equations (Hong et al. 2017): where a and b represent the percentage of flash flood pixels in a class to the total flash flood pixels and the percentage of pixels in a class to the total pixels, respectively. (P ij ) represents the probability density.
where H j and H jmax are the entropy values, S j is the number of classes, I j is the value of the information coefficient, P j is the empirical probability and W j is the weight obtained for each conditioning factor as a whole.

Hybrid integration of the methods
Individual implementation of FR, FMV, WOE, SI and IV feature no provision to evaluate the correlation between the conditioning factors. IOE, on the contrary, is a very effective method to analyze the association among various factors. Therefore, to utilize the effectiveness of all these methods, a hybrid integration approach was adopted wherein the five techniques were paired with IOE method resulting in 5 hybrid models for the FFS assessment. Therefore, the final FFS maps were generated using the following equations for each of the hybrid pair: Where FFPI FR-IOE , FFPI FMV-IOE , FFPI WOE-IOE , FFPI SI-IOE , and FFPI IV-IOE are the flash flood potential indexes, FR ij , FMV ij , WOE ij , SI ij , and IV ij , are the respective weights for each of the five hybrid couple model classes i and factor j, n is the total number of conditioning factors. W j is the weight for each factor derived using the IOE approach.

Map grading
Each of the Five flash flood susceptibility rasters generated using each of the hybrid approaches were graded into five susceptibility classes viz., very low, low, medium, high and very high. The maximum and minimum values of the flash flood potential indexes from each method are different (Costache and Zaharia 2017). This variation is attributed to different statistical formulae used for computation in each approach (Eq. 1-7). Consequently, the grading cannot be fixed and the range from each method can be split using a statistical classification method. There are four popular classification approaches namely natural breaks (NB), quantile (Q), equal interval (EI), and geometric interval (GI). Therefore, all four approaches were tested by conducting a systematic analysis of the presence of flash flood locations in each susceptibility class (Costache and Zaharia 2017). Percentage of the number of training and validating flash flood event locations for each of the ensemble approaches in different susceptibility classes for all four classification methods was estimated. The approach showing maximum percentage of flash flood events (training and validation) in the high and very high susceptibility zones was chosen for the grading.

Validation and comparison of FFS models
Two methods were used to evaluate the models' performance and validation of results. The first method involves estimating the flash flood event pixel density (Costache and Another approach to appreciate the significance of model results is the receiver operating characteristic curve (ROC curve). This is the most reliable and extensively used validation approach being used in hazard susceptibility studies (Chen et al. 2018;Khosravi et al. 2019;Du et al. 2020).

Multicollinearity analysis (importance of FF conditioning factors)
The multicollinearity test of the conditioning factors was carried out using two statistical parameters viz., VIF and Tolerance (Table 3). VIF values varied between 1.005 and 3.340 for convergence index and Fournier index for July. The tolerance values range between 0.299 and 0.995. The analysis indicates that no problem of multicollinearity exists in the selected variables. Therefore, all conditioning factors were employed to assess the flash flood susceptibility in the study area. Table S2 (supplemental material) presents the FR values calculated for a total of 111 classes of conditioning factors. 39 of the 111 classes didn't experience any flash flood event and thus feature an FR equal to 0. The land cover class of settlements exhibits an FR of 29.93, which is the maximum among all factors and classes. Furthermore, IOE weights for each conditioning factor presented in Table S2 (supplemental material) were integrated with FRs using Eq. (15) to obtain the flash flood potential index for the study area (Figure 6(a)). The computed FFPI values range from 0.83 to 118.70. The FFS map was categorized into five classes using the quantile classification approach: very low (0.83 À 4.07), low (4.07 À 4.99), moderate (4.99 À 8.23), high (8.23 À 9.62), and very high (9.62 À 118.70). Table S2 (supplemental material) presents the FMV values (ranging between 0 and 1) computed for all the classes of conditioning factors. Furthermore, IOE weights were integrated with the FMV values using Eq. (16) to obtain the FFPI for the study area ( Figure  6(b)). The computed FFPI values range from 0.34 to 3.28. The FFS map was categorized into five classes using the quantile classification approach: very low (0.34 -1.16), low (1.16 -1.43), moderate (1.43 -1.61), high (1.61 -1.78), and very high (1.78 -3.28). Table S2 (supplemental material) presents W f values computed for all the classes of conditioning factors. The classes with no flash flood events exhibit zero value for W f . Furthermore, IOE weights were integrated with the WOE values using Eq. (17) to obtain the FFPI for the study area as shown in Figure 6(c). The computed FFPI values range from À8.45 to 14.77. The FFS map was categorized into 5 classes using quantile classification approach: very low (À8.45 -À4.34), low (À4.34 -À3.43), moderate (À3.43 -À2.89), high (À2.89 À 3.49), and very high (3.49 À 14.77).  Figure 6(d). The computed FFPI values range from À3.05 to 6.20. The FFS map was categorized into 5 classes using quantile classification approach: very low (À3.05 -À1.02), low (À1.02 -À0.73), moderate (À0.73 -À0.55), high (À0.55 À 1.01), and very high (1.01 À 6.20).  Figure 7 shows donut charts to express the percentage area distribution of the FFS classes for all five hybrid coupled models. Except for the FR-IOE model, the remaining four models have a relatively similar area distribution among the various susceptibility levels.

Susceptibility classification assessment
The spatial distribution of the susceptibility levels using different models has already been presented in Figure 6. The choice of an optimal classification approach was made using a systematic analysis of the presence of flash flood locations in each susceptibility class. Table 4 presents the percentage distribution of flash flood event locations used to train and validate all five hybrid models. The analysis was carried out using four different classification approaches, namely natural breaks (NB), quantile (Q), equal interval (EI), and geometric interval (GI). Table 4 also shows that the maximum percentage of flash flood events (training and validation) are grouped in the high and very high susceptibility zones using the quantile classification scheme for all the five models. Thus, taking into consideration the variation in range of FFPI generated through the 5 hybrid models and testing of the four statistical classification techniques, quantile method was adopted.

Comparative evaluation of models
A pair-wise pixel distribution comparison among all the 5 approaches was performed by cross tabulating the number of pixels classified in each class for each of the 10 paired combinations. The cross tabulations resulted in 10 two-dimensional confusion matrices (Ahmad et al. 2021). Figure 8 presents the confusion matrices for all 10 combinations. Each matrix represents the spatial distribution of susceptibility classes in terms of number of pixels and accounted percentage in each map pair.
Additionally, each matrix is summarized by presenting the total percentage of pixels/ area which represents the same spatial distribution (sum of the diagonal elements) of susceptibility classes in both maps of the pair, for example in Figure 8(a), 62.25% pixels/area  is classified exactly same by both FR-IOE and FMV-IOE approach. Also, the percentage spatial distribution of dissimilarities is represented in two categories viz., Figure 8(a) shows 19.99% pixels/area (sum of upper diagonal elements) shows higher susceptibility categories by the map prepared using FR-IOE model and 17.76% pixels/area (sum of lower diagonal elements) shows lower susceptibility categories compared to the map prepared using FMV-IOE model. Similarly, Figure 8(b-j) represents the results for each model pair. The dissimilarities in the spatial distribution of flash floods among the maps (Figures 6, 7) are due the influence of the flash flood susceptibility factors considered for the analysis (Ahmad et al. 2021).
The performance of all the hybrid models was evaluated using ROC curves. Also, these curves were used to validate the obtained results. The Success Rate (Figure 9(a)) was constructed for the performance evaluation of the models using the training flash flood locations. Success Rate is a measure of the capability of the models to accurately classify the flash flood-prone areas by comparing them with training points. FMV-IOE featured the best performance (AUC ¼ 0.986), followed by FR-IOE (AUC ¼ 0.871), IV-IOE (AUC ¼ The results validation of all the five hybrid models was conducted by analyzing the Prediction Rate. ROC curves for the prediction rate were constructed by employing the flash flood locations reserved for the validation purpose. The curves presented in Figure  9(b) represent the Prediction Rate and indicate the agreement between the observed and predicted values of FFPI. This time the best performance was featured by SI-IOE and IV-IOE with an AUC ¼ 0.896 followed by WOE-IOE (AUC ¼ 0.889), FMV-IOE (AUC ¼ 0.861), and FR-IOE (AUC ¼ 0.847) as indicated in Figure 9(b). The values indicate that all the models produce results with high accuracy.

Discussion
Flash flood susceptibility assessment is considered as the primary stage to plan for and deal with flash flood hazard mitigation. Therefore, an accurate or reliable FFS map can prove to be a very effective input to plan for hazard management. Thus far, several studies have been conducted for FFS assessment, and various methods and techniques have been employed to obtain reliable maps in different topographical and climatic settings (Khosravi et al. 2016(Khosravi et al. , 2018Costache and Zaharia 2017;Popa et al. 2019;Band et al. 2020). However, no such study has so far been reported for the mountainous river basins of Uttarakhand, which are prone to frequent flash floods. Previous studies (Bhambri et al. 2016;Singh and Pandey 2021) have highlighted the vulnerability of Mandakini River Basin to frequent flash floods. This river basin has been experiencing frequent flash flood events triggered by extreme rainfall (Bhambri et al. 2016;Singh and Pandey 2021) and has been widely analyzed in context of the Kedarnath tragedy in 2013 (Bhambri et al. 2016). Therefore, it is necessary to investigate the application of novel techniques for FFS assessment in the region. Weights of Evidence (WOE), Frequency ratio (FR), Information value (IV), Certainty factor (CF), Index of entropy (IOE), Fuzzy logic and Neuro-fuzzy logic are some of the most popularly used methods for addressing many real-world problems specifically flood and flash flood susceptibility as well as landslide susceptibility (Costache and Zaharia 2017;Costache 2019b;Costache and Tien Bui 2020). Researchers worldwide have been using hybrid models designed by integrating various bivariate statistical techniques to harness the advantages of the combination and, consequently, obtain more reliable outputs (Costache 2019a;Pham et al. 2020). These hybrid ensemble models have proven to be promisingly reliable in solving complex real-world problems Gheshlaghi and Feizizadeh 2021). However, it may be argued that modern machine algorithms could outperform the bivariate statistical models. But, here it becomes necessary to point out that in Uttarakhand state of India the availability of historical data pertaining to locations of flash flood events is a major limitation (Singh and Pandey 2021). Consequently, in this study, number of flash flood event locations were limited and thus modern machine learning algorithms were not considered, as they require large number of training data points.
This study attempts a comparison of performance evaluation of some hybrid ensemble models, namely, FR-IOE, FMV-IOE, WOE-IOE, SI-IOE and IV-IOE, in identifying flash flood-prone areas. The major contribution of this study is the synchronized use of the fuzzy system and bivariate statistics and their hybrid combination for the FFS assessment.
Gheshlaghi & Feizizadeh in 2021 employed integration of FMV, FR and IV with IOE for landslide susceptibility assessment in the Azarshahr Chay Basin of Iran. They concluded that FMV-IOE generated higher accuracy of prediction and performed the best followed by FR-IOE and IV-IOE. On the contrary, the application of these hybrid models for flash flood susceptibility in Mandakini River Basin revealed that SI-IOE and IV-IOE are the best performing models, followed by WOE-IOE and FMV-IOE. FR-IOE showed the weakest performance of the five hybrid models.
Each approach, if individually used for the susceptibility assessment, has certain limitations. Therefore, all five models were paired with the IOE approach to improve their performance. Previous studies have shown that the hybrid approach of pairing the models has increased the accuracy (Costache 2019b;Ali et al. 2020). The results for predictive capability indicate that among the 5 hybrid ensemble models, the combination of SI and IV with the IOE approach was the most efficient.
One of the most critical and important aspects of FFS assessment is identifying and choosing the most significant conditioning factors. Therefore, in this study, a total of fifteen flash flood conditioning factors (aspect, convergence index (CI), Fournier index (FI), hydrological soil group (HSG), lithology, land use/cover (LULC), normalized difference vegetation index (NDVI), plan curvature, profile curvature, slope, stream power index (SPI), topographic position index (TPI), topographic ruggedness index (TRI), topographic wetness index (TWI), distance from the river) were considered. A multicollinearity assessment was conducted for all these factors to identify redundant factors using VIF and tolerance values. The analysis revealed that none of the factors possess redundancy, and hence all 15 parameters were chosen for the susceptibility modeling and mapping. These factors have also been identified as the most important flash flood conditioning factors in previous studies as well (Costache and Tien Bui 2019;Costache 2019a;Band et al. 2020).
A major geographical implication of this study is the uneven distribution of sample points. In particular, there are no sampling points in the Northwestern and Northeastern parts of the study area. This observation is attributed to the fact that these regions have not experienced (not reported) any flash floods in the past. Additionally, Singh & Pandey in 2021 conducted a study on flash flood vulnerability for the Upper Ganga Basin in Uttarakhand wherein the Mandakini River Basin emerged as a critically vulnerable subwatershed. Also, the LULC map suggests that the northwestern and northeastern regions are forested with no built-up areas. The LULC map confirms that these regions are inhabited and hence are not vulnerable in terms of population exposure. Therefore, keeping in-view the vulnerability of the sub-watershed and existing LULC it is ascertained that despite the sample points being unevenly distributed in the area, the results obtained are justifiable.
The success rate and predictive capability of the hybrid models were determined graphically using the ROC curves for both training as well as testing flash flood event locations, respectively (Figure 8(a, b)). The maximum AUC for the prediction capability was acquired by SI-IOE and IV-IOE with an AUC ¼ 0.896, followed by WOE-IOE, FMV-IOE, and FR-IOE. FFS maps obtained by each hybrid ensemble are presented in Figure 6. Interestingly the AUC values for training (0.986) and testing (0.861) for FMV-IOE are not similar but, the model performance in the testing dataset is very well comparable with other four models. This outcome may be considered as a limitation and may be attributed to the complexity of the model. Since it is a predictive model, the performance on the testing (unseen) data is reasonably good. Moreover, the training and testing datasets are completely different, this observation may be attributed as an inherent characteristic of the model itself considering the influence of conditioning factors.
These are the final outputs generated after the analysis, and each map depicts the study area in five (very low, low, medium, high and very high) susceptibility zones. Furthermore, Figure 7 shows the percentage area distribution of the FFS classes for all the five hybrid coupled models. The visualization suggests that except for the FR-IOE model, the percentage area distribution of susceptibility classes in the remaining four models is more or less similar with a very slight variation. However, the physical location of the zones on the ground is not exactly the same. Therefore, AUC values are the deciding factor to choose the best model based on prediction capability performance.
In general, the AUC values suggest that all the hybrid approaches have performed well, with four out of five models representing an AUC of more than 0.85 and FR-IOE with an AUC of 0.847. The ensemble models employed in this study have successfully demonstrated a solid methodology for obtaining FFS maps for the Mandakini River Basin in the mountain state of Uttarakhand. Therefore, similar studies can be conducted to map the entire state for generating FFS maps which can be very useful for the decision-makers for planning, management, and mitigation of damages in future disaster events.

Conclusions
The Himalayan state of Uttarakhand in India experiences frequent flash floods in the monsoon season every year. Consequently, such circumstances lead to human casualties as well as infrastructure and property damage. Therefore, identification of areas prone to flash flood occurrences can prove to be highly beneficial for the state's residents and the state and government authorities' decision-makers. In addition, the results can be employed to issue flash flood forecasts and warnings, and consequently, be effectively used by the Uttarakhand state disaster management authority. Therefore, spatial prediction of flash flood occurrence must be carried out in this highly flood susceptible region to assist government authorities in disaster mitigation/prevention and effective land use planning. In this study, an attempt has been made to obtain the flash flood potential index of the Mandakini River Basin using five hybrid models. The FFPI was further used to create FFS maps of the study area. FFPI was calculated based on the flash flood events inventory database signatures for all the 15 conditioning factors, namely aspect, CI, FI, HSG, lithology, LULC, NDVI, plan curvature, profile curvature, slope, SPI, TPI, TRI and TWI followed by using five hybrid models in a GIS environment. The predictive ability and importance of these factors were tested using the VIF and tolerance diagnostics. The performance evaluation and validation of the models were done using ROC curves.
The Upper Ganga Basin in Uttarakhand has multiple sub-watersheds categorized under critical flash flood vulnerability zones (Singh and Pandey 2021). The present study carried out for the Mandakini river basin, would provide valuable information regarding the methodology that can be adopted to identify flash flood susceptible areas in various vulnerable watersheds. Additionally, using these maps the decision-makers and local authorities can identify most susceptible towns and villages in the region and plan the future expansion accordingly. Preferences for construction and infrastructural development should be given to low and very low susceptible areas. Availability of limited historical data (flash flood event locations) is a limitation in this study, which was not favourable for implementation of data intensive machine learning techniques. A long-term inventory of past flash flood events can be very beneficial to take up flash flood susceptibility studies in the area using advance machine learning methods. It may further facilitate in increasing the accuracy obtained by the hybrid models used in this study. The following conclusions are drawn from the present study: All the five hybrid models showed good predictive capability performance for FFS in assessment of the MRB the northwestern Himalayan region. However, SI-IOE and IV-IOE methods generated the highest accuracy of prediction. Therefore, four out of five methods can be used to create FFS maps in the MRB and other mountainous basins in the Himalayan region. The presented methodology has been efficiently implemented to identify the high and very high susceptible areas to flash floods. The methodology demonstrated in this study can be applied in the data-scarce mountainous catchments to develop FFS maps. Hybrid models are suggested to be used for flash flood susceptibility mapping and assessment because of their capability to generate reliable results.