Introduction

Every year, various natural disasters such as earthquakes, landslides, and floods cause massive loss of life and property worldwide (Band et al. 2020a). Flood is one of the most dangerous natural hazards, responsible for thousands of deaths, ecosystem damage, communication system disruption, and billions of dollars in economic losses each year (Luu et al. 2018; Aerts et al. 2018; Khosravi et al. 2018; Pham et al. 2021a). Many regions across the world are affected by water excess-related natural events through snow melting or intensified rainfall (Burgan and Icaga 2019), which can be dangerous if they occur unexpectedly. As a natural phenomenon, flash floods occur most commonly in river basins smaller than 200 km2 (Costache and Tien Bui 2020). In recent times, climate change and LULC change have been identified as the primary causes of flash floods (Sekac et al. 2015; Kanani-Sadat et al. 2019). It could happen due to heavy rainfall, sudden ice melting on the upper ridge, or poor infrastructure in the flood risk zone. Several hydrological, meteorological, geomorphological, and flood protection failures are to blame for this hydrological event, as are various human activities such as encroachment on the river catchment, deforestation, and dam development, which increase the frequency of floods (Roy et al. 2020). Climate change has also exacerbated the destructive impact of flash floods (Bubeck and Thieken 2018). This hydrological phenomenon causes catastrophic mudslide and debris flow that is characterized by short response time and results in massive socioeconomic loss all over the world (Peduzzi 2017). The flood assessment studies of Wasko and Sharma (2017) showed that flash flood events of 2013 caused heavy damages with an estimation of more than 50 billion US dollars globally. Additionally, they also forecast it will double within the next 20 years. In the case of flood events, it is estimated that by 2050 the expected potential loss will reach 1 trillion US dollars due to the rapid increase of anthropogenic activities and extreme weather events (Hartnett and Nash 2017). According to the World Meteorological Organization (2016), flash flood has a high mortality rate, accounting for over 5000 lives lost each year, and 85% of flooding cases that result in around 1 million deaths worldwide were due to the deadliest flood events during the 1972–2012 time period. The reports of WHO display that approximately 2 billion people are affected globally between 1998 and 2017. Thus, flash flood event has got substantial attention particularly in monsoon-dominated region. Therefore, flood researchers around the world are constantly looking for new ways to mitigate the hazardous effects of flooding in high-risk areas. Hence, the management of floods is yet subject to a thorough study.

In the modern era, no country is immune to flood hazards, and Asian countries are especially vulnerable due to their dense human populations along river floodplains (Hens et al. 2018; Pham et al. 2021b). Just in the twenty-first century, India has experienced several devastating flash flood events such as the Mumbai flood (2005), Assam flood (2012), Uttarakhand flood (2013), Jammu Kashmir flood (2014), Chennai flood (2015), Kerala flood (2018), and Uttarakhand flood at Chamoli district (2021). All these flood events have caused massive loss of lives and property in India. One of the major causes of increasing flood events and losses is a lack of adequate studies and information about flood-prone areas and lack of flood prevention ideas, and it is evident that flood events cannot be prevented but they can be predicted using appropriate methodologies and analysis (Khosravi et al. 2016). The paradigm has recently shifted from “flood protection” to “flood risk management” (Scheuer et al. 2011; Varu et al. 2020). Hence, to manage the flood risk, flash flood-susceptible zonation is a crucial tool that plays a significant role in flood risk reduction through its predictive flood-prone area identification (Tehrany et al. 2015; Youssef et al. 2015; Pal et al. 2018; Band et al. 2020b; Chowdhuri et al. 2020; Malik and Pal 2021). Thus, West Bengal also experienced significant numbers of severe flood events (1978, 1991, 2000, 2006, 2013, 2017) and many small-scale regional flood occurrences that caused a notable number of deaths and property loss. According to the disaster management department of West Bengal, Bankura district is under a relatively flood-prone district due to two main rivers, namely, Dwarakeswar and Gandheswari. Among them, the Gandheswari River flood has a great impact on Bankura district due to its approximately central location of Bankura town, which has experienced several flood events in 2016, 2018, and 2021. Therefore, in this study, we attempt to make a flash flood-susceptible map (FFSM) to identify specific flood-prone regions of the Gandheswari River basin, which can be very helpful for proper strategy to reduce the severity of flood occurrence. Flash flood events may occur in any region as a result of a variety of factors such as geological, hydrological, and meteorological factors. The analysis of quantitative characteristics of all those factors in the considered basin area is important to know the hydrological behaviour of this river. Using the combined RS–GIS technique, 16 flood conditioning parameters were identified including, geology, geomorphology, soil texture, slope, profile curvature, plan curvature, elevation, aspect, distance to the river, rainfall, land use, and land cover (LULC), and other hydrological parameters to make FFSM in the considered basin area.

In proper flood disaster management, it is crucial for the identification of real-time flood inundation maps (Chang et al. 2018) and to forecast this systematically and scientifically. Numerous approaches have been used that help to forecast the different features of flood events: the statistical correlation of flood characteristics with the physical properties of the watershed (Wheater et al. 1993) and various evidential methods such as the multi-criteria decision analysis (MCDA) and analytical hierarchy process (AHP) used to identify the flood-susceptibility zones. But to handle the complexities of data structure and to make high accuracy in recent time, the machine learning (ML) approach has gained more attention from researchers across the globe (Tehrany et al. 2015; Khosravi et al. 2018; Band et al. 2020b). Several ML algorithms such as random forest (RF), logistic regression (LR), support vector machine (SVM), artificial neural network (ANN) and various ensemble approaches have been used to identify flood-susceptibility mapping (Luu et al. 2018; Bui et al. 2018; Costache and Tien Bui 2020; Malik et al. 2020; Saha et al. 2021a). Hybrid and combined modeling approaches are beneficial for mapping flash flood susceptibility. Most of the researchers have used multiple ML approaches rather than a single ML approach to obtain better results (Band et al. 2020b). A literature review revealed that the application of pragmatic kernel-based models, such as support vector regression (SVR), is one of the most popular tools for mapping flash flood susceptibility, especially in data-limited regions such as West Bengal, India (Paul et al. 2019; Roy et al. 2020). However, the support vectors identified the optimal hyperplane; a certain kernel function was adopted to convert the input dataset into two distinct categories and also avoid developing a linear association between two training and validation datasets (Choubin et al. 2019). Recently, more advanced algorithm of short-term hybrid memory (LSTM) and ant lion optimizer (ALO) modeling has been used in streamflow analysis with good accuracy (Yuan et al. 2018). Dynamic evolving neural fuzzy inference system (DENFIS) model was used in evaluating the performance of relationship between the capturing rainfall-runoff and rainfall-water level (Chang et al. 2019). Furthermore, group method of data handling (GMDH) approach has been applied in flood (Dodangeh et al. 2020) and landslide (Panahi et al. 2022) susceptibility analysis. Studies also show that least squares support vector machine (LSSVM) and gravitational search algorithm (GSA) have been widely used in various prediction analysis. Among them Yuan et al. (2015) used LSSVM and GSA model in short-term wind prediction analysis and their outcomes gives good prediction result. The hybrid algorithm of extreme learning machine (ELM) and PSOGWO was used in monthly runoff-based streamflow prediction analysis in Mangla watershed of Pakistan (Adnan et al. 2021). All of the above-mentioned methods have been used in several research studies and their outcomes are also very good. In addition to this, state-of-the-art meta-heuristic algorithm has been widely used by several researchers across the world for prediction analysis in different fields. In this study, flash flood-susceptibility mapping was performed using SVR, coupled with the particle swarm optimization (PSO) method (SVM–PSO) and grasshopper optimization algorithm (GOA) method (SVM–GOA) as two meta-heuristic algorithms, to optimize the SVR model. The above selected learning algorithms have great capacity in the field of prediction analysis and is more suitable for large dataset analysis; therefore, we have selected these models. State of the art generally refers to the highest level of achievement in a specific purpose, i.e. performance analysis. State-of-the-art algorithm is used in the field of landslide susceptibility (Mehrabi et al. 2020), groundwater potential zoning (Arabameri et al. 2021), flood studies (Arora et al. 2021) and many more. Overall, the predictive accuracy of flash flood susceptibility has been enhanced substantially by applying these ensemble models. However, no common consensus has still been established on choosing the optimal model for flash flood-susceptibility mapping; therefore, novel models are required and should be verified. Nevertheless, our study intended to answer the two research questions: firstly, what are the influential variables attributing to flash flood susceptibility? Secondly, what are the areas flooded most frequently? To answer the two questions, the primary goal was to (i) identify the influential variable for flash flood events using the multicollinearity test in the Gandheswari River basin and (ii) to prepare FFSM using state-of-the-art ensemble and standalone machine learning methods (SVR, SVR–PSO, and SVR–GOA) and (iii) compare the results to produce the region's accurate FFSM. The novel aspect of our study is that it couples with the ensemble (SVR–PSO and SVR–GOA) for FFSM. As we know, the ensemble approach is the best for any kind of susceptibility analysis than any single model. Therefore, an ensemble of SVR–GOA and SVR–PSO was chosen in this study to predict flood-susceptibility analysis. As our study revealed that the used ensemble of SVR–PSO and SVR–GOA models for predicting flood-susceptibility mapping is the first, and those will be significant modeling approaches in identifying flash flood-susceptible zone. The reason for choosing the SVR is that its computational complexity does not depend on the dimensionality of the input space, along with its high prediction accuracy with complex capacity. Although other learning models also have good analysis capacity, SVR has been used in flood-susceptibility analysis and gives optimal prediction, so here we have chosen this model. Additionally, PSO and GOA have been widely used in several fields of prediction analysis due to their unique performance analysis, so here we have selected this model for ensemble with SVR. Lastly, it is worth mentioning that the proposed model is limited to not only flash flood susceptibility, but also can be used in any natural hazards.

Material and methods

Study area

The designated area of the study to implement the proposed method is the Gandheswari River basin which is located in the Bankura district of West Bengal, India, with an absolute location of 23º13′28"N to 23º30′25"N latitude and 86º53′13"E to 87º07′30"E longitude (Fig. 1). This river basin covers approximately 364.9km2, is elongated in shape and structurally controlled (Mondal and Mistri 2015). Gandheswari is a tributary of the Dwarakeswar River, which flows through the Bankura district. From the north-western to the south-eastern part of the district, the Gandheswari River flows through four blocks: Bankura, Saltora, Chhatna, and Gangajalghati, before joining the Dwarakeswar River. Geologically, this area is dominated by Chotonagpur gneissic complex, and pediment pediplain complex is the significant geomorphic characteristic with an 11–383 m elevation range (GSI). The average rainfall in the study area is 1400 mm, and it is located in a monsoonal climatic region. Because of the SW monsoon, a considerable amount of precipitation falls during July and August. In the last few years, substantial changes in LULC along the river channel make this region vulnerable to flash floods; population and settlement density in this region have increased day by day due to socioeconomic development in this region that significantly increased encroachment toward the river channel that increased pressure on river flow. These geographical conditions and anthropogenic pressure are responsible for accelerating flash flood events. The disaster management department of West Bengal identified the Bankura district as a relatively floodprone district; as a result, the identification of flash flood-prone region is more essential and can help to take necessary steps to reduce the adverse effect of flash flood in this river basin.

Fig. 1
figure 1

Location map of the study area and flood inventory map

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Methodology

The exact FFSM and its level of accuracy are determined by the size and availability of the data, as well as the methods used to create this map. It is necessary to develop a proper methodological framework (Fig. 2) that aids in determining flood-prone areas. In this study, we adopted the following steps for this assessment:

  1. (I)

    A flood inventory map was prepared based on 140 flood points; of those, 70 were flood areas and 70 non-flood areas.

  2. (II)

    Sixteen appropriate flash flood causative factors were identified based on an extensive literature survey and local geo-environmental conditions.

  3. (III)

    Multicollinearity test was adopted among various flash flood causative factors by using variance inflation factor (VIF) and tolerance (TLT) methods.

  4. (IV)

    Support vector regression (SVR), particle swarm optimization (PSO), and grasshopper optimization algorithm (GOA) models were used to model the FFSM.

  5. (V)

    Support vector regression (SVR), ensemble method of SVR–PSO, and SVR–GOA were used in flash flood-susceptibility mapping.

  6. (VI)

    The projected result of these models was validated by six statistical techniques such as sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), and receiver operating characteristics (ROC) – AUC, kappa coefficient analysis and one graphical technique of Taylor diagram.

Fig. 2
figure 2

Methodological framework of FFSM

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Flood inventory map

Flash flood inventory mapping plays a significant role in establishing the relationship between flood and various causative factors. It is the most important requirement in FFSM (Arabameri et al. 2019). Various methods are used to make it, but it depends on several parameters such as the environmental condition of the study area, research purpose, and access of RS–GIS data (Pradhan 2013; Arabameri et al. 2019). To create an FFSM, first, we gather the necessary data and create a spatial database. It is necessary to provide the necessary data with high accuracy. The inventory area has previously been affected by torrential flash floods and can detect areas where flash floods may occur in the future. This area is also prone to rapid surface runoff, which contributes to flash flood events on the downslope. It is justified by the fact that the accuracy of FFSM mostly depends on proper inventory mapping, which is based on extensive historical data analysis (Band et al. 2020b; Saha et al. 2021a). In this study, a total of 140 points were identified, among them, 70 points depict flood areas and 70 were non-flood areas. Google Earth's image of the time of flood events and the extensive field inventories were the main basis of flood area selection. In the same way, non-flood areas have been randomly selected using ArcGIS software.

Flash flood causative factors

As a complex natural incident, the flash flood in a particular watershed does not only depend on the hydro-meteorological factors, but also on the geomorphological condition of that watershed (Tien Bui et al. 2019); Thus, it is necessary to identify the flash flood causative factors and their relationship with flash flood events (Khosravi et al. 2016). It means the sensitivity analysis and the relation of each causative factor should be estimated (Twele et al. 2016; Arabameri et al. 2019). In the present study, based on the environmental condition of the study area, historical flood events, and various studies (Khosravi et al. 2016, 2018; Chapi et al. 2017; Arabameri et al. 2019; Band et al. 2020b; Chowdhuri et al. 2020; Roy et al. 2020; Malik and Pal 2021), 16 flood causative factors were used. Furthermore, the 16 flood-susceptibility factors were chosen for this study area depending upon the various local topo-hydrological, climatological, geological, environmental and geomorphological condition. In flood-susceptibility analysis, local conditioning factors are very important for accurate analysis and to understand the flood condition. Alongside, various literature reviews have also been conducted for the selection of appropriate flood conditioning factors. These factors were geology, geomorphology, soil texture, normalized difference vegetation index (NDVI), normalized difference water index (NDWI), land use and land cover (LULC), profile curvature, rainfall, distance from the river, plan curvature, stream power index (SPI), drainage density, aspect, topographic wetness index (TWI), elevation and slope, which have direct and indirect relation with flash flood events in the considered area.

All these considered parameters were prepared from different sources and by using the GIS environment including geology and geomorphology maps prepared from the Geological Survey of India (GSI) and soil texture map collected from the National Bureau of Soil Survey and Land Use Planning (NBSS and LUP), Government of India. The rainfall map of this study area was prepared by the inverse distance weighting (IDW) method with the help of the Indian Meteorological Department rainfall data. ALOS PALSAR DEM (https://asf.alaska.edu/) with 12.5-m resolution helps to extract slope, elevation, aspect, plan curvature, and profile curvature in Arc GIS 10.4 where SPI and TWI are developed by SAGA-GIS. ALOS PALSAR also helps to extract distance from the river and drainage density in Arc hydro environment. LULC, NDVI, and NDWI map were prepared from Landsat 8 (https://earthexplorer.usgs.gov/).

Elevation was a significant causative factor of a flash flood that controls the natural flow of a river, and it can regulate the microclimatic conditions of a region that leads to development in plant coverage which has a significant impact on runoff formation (Tien Bui et al. 2020). Higher elevation was usually safe from flash floods, whereas lower elevation was highly vulnerable to flash flood events (Malik et al. 2020; Islam et al. 2021; Malik and Pal 2021), so it has an inverse association with height. The elevation ranges from 11 to 383 m (Fig. 3a) in the present study and the northern and southern portions are characterized with higher and lower elevations, respectively.

Fig. 3
figure 3figure 3figure 3

Flood causative factors: a elevation, b slope, c aspect, d topographic wetness index TWI, e stream power index SPI, f drainage density, g distance to river, h plan curvature, i profile curvature, j rainfall, k NDVI, l NDWI, m geology, n geomorphology, o soil texture and p LULC

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Slope defines the intensity and magnitude of water percolation and water accumulation (Choubin et al. 2019). According to Florinsky (2016), the slope of the Earth's surface can influence several hydrogeological processes such as infiltration and runoff that have a great impact on the occurrence of the flash flood. An adverse relationship is present between slope and flood. The heavy rainfall in the steep slope region helps to originate high energy in the surface runoff that leads to faster flow toward low land, resulting in a flash flood (Ngo et al. 2021). Very low slope with high surface rainfall causes low surface runoff which leads to flooding (Rahmati et al. 2016). On the other hand, a high slope is prone to high runoff that is less susceptible to flood. The slope ranges from 0° to 43.18° (Fig. 3b); the higher slope is found in the central region, and the lower part along the river of the study area is characterized with a lower slope.

Aspect of slope is an angle between the north and horizontal direction and has substantial influence on soil water (Ragab et al. 2003). Thus, the aspect is considered an important flood-susceptibility forecasting parameter (Zhao et al. 2018). This shows the orientation of the slope (Choubin et al. 2019). In this study, the slope aspect varies from −1 to 359.23 (Fig. 3c).

TWI mainly indicates the moisture condition of the soil, saturation level, and water depth of topography (Band et al. 2020b), influence to plant diversities and distribution. This can closely regulate the depletion and spatial spreading of surface runoff (Bui et al. 2018). Generally, high TWI values indicate more vulnerability to flooding compared to low TWI values. In the current study, the range is from 6.94 to 27.78. (Fig. 3d); high TWI is found mainly along the river that implies this region is significantly prone to flash floods. TWI is calculated from the following equation:

$${\text{TWI}} = \ln \left( {\frac{{A_{s} }}{{\tan \left( {{\text{slope}}} \right)}}} \right),$$
(1)

where \(A_{s}\) represents the area of the basin (\(km^{2}\))and tan (slope) is the slope of the basin.

Stream power index (SPI) can be described as the erosive power and surface runoff of an area (Malik et al. 2020). High SPI represents the high surface runoff, whereas the low SPI represents the low surface runoff of a river basin. Low SPI with high intensity of rainfall makes the area flood susceptible. In this study, SPI ranges from 0.34 to 19.75 (Fig. 3e); the higher value location of SPI implies that the immediate location of the stream is highly vulnerable to flash floods. The following equation has been used to calculate SPI:

$${\text{SPI}} = A_{S} *\tan \left( {{\text{slope}}} \right),$$
(2)

where \(A_{s}\) describes the catchment area (km2) and tan (slope) is the slope of the catchment.

Drainage density plays a significant role in FFSM which is determined by the drainage length per unit area (Horton 1932); this has a crucial role in storage and transfer of water of a watershed, and it is evident that higher river density causes higher flood events (Khosravi et al. 2018). A drainage system is the natural flow of the runoff, and when the channelized flow exceeds its channel potential, it makes the area flooded. Figure 3f shows the drainage condition of the study area where the middle to a lower portion of the study area is characterized by higher drainage density.

Distance to the river can easily describe which region is more susceptible to flood and which is less (Malik et al. 2020). The high velocity of stream flow occurs at the time of heavy and stormy runoff period and at that time it reaches its maximum limit and makes the area flooded. The area which is close to the river is most vulnerable to flood compared to the high distant area from the river (Fig. 3g).

Plan curvature is the terrain’s curvature concerning the slope direction which plays a significant role in predicting flood susceptibility. A positive value represents a convex profile where the flat profile is described by zero and a negative value indicates a concave profile; the plan curvature of the study area ranges between −3.18 and 2.96. (Fig. 3h). Plan curvature affects the runoff pattern; therefore, it has valuable insight into FFSM.

Profile curvature is the surface curvature against the cliff which is very close to the plan curvature. It has a substantial influence on surface runoff and is a significant indicator of flood events (Arabameri et al. 2019).The profile curvature of this area is between −3.32 and 2.61(Fig. 3i).

Rainfall is a significant parameter in the magnitude of the flash flood events, which has a direct relation between the intensity of rainfall and flash flood. According to Guardiola-Albert et al. (2020) and Gaume et al. (2004), high-intensity rainfall in small watershed regions triggers flash flood occurrence. The rainfall amount varies from 515 to 537 mm (Fig. 3j) and a higher amount of rainfall is mainly found in the southern portion of the study area which mainly occurs due to SW monsoon. As a primary driving force, the short duration, high intensity, high frequency, and small spatial distribution of rainfall make the watershed more vulnerable to flooding with the association of other flood-causing factors.

NDVI represents the vegetation status of an area. Vegetation characteristics are different based on their geomorphological location. Flood area’s plants are significantly different from the other plants in the surrounding region that can help to identify the flood-susceptible areas (Paul et al. 2019). In this study, NDVI (Fig. 3k) can be calculated through the following equation:

$${\text{NDVI}} = \frac{{\left( {{\text{NIR}} - {\text{RED}}} \right)}}{{\left( {{\text{NIR}} + {\text{RED}}} \right)}},$$
(3)

where NIR refers to the near-infrared band.

NDWI is the index that indicates the amount of water in an area. This is very useful to monitor drought conditions and other studies (Gu et al. 2007) as well as control the flood events. NDWI ranges from −1 to + 1, where high values represent the high water content and low to very low water contents in an area. In this study, NDWI ranges from − 0.10 to + 0.31 (Fig. 3l). It has been calculated from the following equation

$${\text{NDWI}} = \frac{{\left( {{\text{NIR}} - {\text{SWIR}}} \right)}}{{\left( {{\text{NIR}} + {\text{SWIR}}} \right)}} ,$$
(4)

where NIR represents the near-infrared band and SWIR represents the short wave near-infrared band.

The geological structure of an area has great control on the channel properties, runoff development, and infiltration rate of a river of an area (Malik et al. 2020). So, geology plays a significant role in determining the flood-susceptible area. In this study, four types of geological structures were identified (Fig. 3m), among them Chhotanagpur gneissic complex is the most dominant structure.

The geomorphology of any area controls the various geomorphic events, among them flash floods are very sensitive events. To make proper FFSM, geomorphology helps significantly because several geomorphic features have their influences on flood occurrence. The current study identified five geomorphic areas in general (Fig. 3n); pediment pediplain complex is the dominant one in this region.

Soil texture has a great impact on flood events which carries the major flood vulnerability indication, because it has a strong impact on holding water, infiltration rate, and subsurface flow formation. The surface runoff and intensity of flood levels are significantly influenced by the soil composition (Cosby et al. 1984). Different soil textures and hydraulic properties have different effects on runoff formation (Lovat et al. 2019). In this study, five types of soil texture (Fig. 3o) are present which have different effects on flood occurrence.

LULC has direct and indirect control on infiltration rate, surface runoff, and evapotranspiration of an area (Bui et al. 2018; Roy et al. 2020); this emerges as a broadly accepted flash flood-indicating parameter in recent times. For example, high vegetation cover increases infiltration rate and reduces runoff, decreasing the probability of flood events, whereas bare land and urbanized area are highly vulnerable to flood (Ngo et al. 2021). In recent times, most of the flood events occur due to the encroachment toward the river channel and changes in land use and land cover pattern in the riparian area. Several studies give much more importance to LULC in case of flood events. LULC change is the significant reason for flash flood occurrence in this study area (Fig. 3p); in this study, LULC map shows that the southern portion of the study area characterized a significant built-up area along the river channel that may trigger flash flood occurrence.

Multicollinearity assessment

Several flood causative factors were used to predict flash flood-susceptible areas. Multicollinearity test has been used to minimize the probable error in modeling associated with variables. If two or more variables are highly correlated with each other than the model, it decreases the accuracy of the output result (Saha et al. 2021c). Multicollinearity (MC) helps identify those factors and characterize a linear dependency between those factors (Arabameri et al. 2018; Saha et al. 2021b). Usually, MC assessment is made with variance inflation factor (VIF) and tolerance techniques (TLT). Various studies (Khosravi et al. 2019; Band et al. 2020b; Malik et al. 2020) show that if VIF value > 10 and TLT value < 0.10, there is a multicollinearity issue. For getting better result in FFSM, VIF values should be less than 5. This MC is determined by the following equation:

$${\text{TLT}} = 1 - r^{2} ,$$
(5)
$${\text{VIF}} = \frac{1}{{{\text{TLT}}}} .$$
(6)

Models used in flash flood-susceptibility assessment

Till now, several methods had been used to get an accurate result in identifying flood-susceptible areas by various researchers. In the present time, ML has become an essential approach to make a better result because of its high accuracy and precision level with large dataset. In this study, three important ML approaches, such as support vector regression (SVR), the ensemble of support vector regression with particle swarm optimization (SVR–PSO), and grasshopper optimization algorithm (SVR–GOA), have been used to estimate the exact flash flood-susceptible area.

Support vector regression (SVR)

The SVR modeling approach is rooted in statistical learning or Vapnik–Chervonenkis (VC) theory (Awad and Khanna 2015), and at the beginning it was used to solve the pattern recognition problem. In 1999, Vapnik (Vapnik 1999) promoted the SVM method to deal with function fitting problems which form the support vector regression method (Rahman and Hazim 1996). This supervised ML algorithm is characterized by the use of sparse solution, kernels, and VC control of the margin and number of support vectors (Drucker et al. 1997; Awad and Khanna 2015). SVR algorithm helps to develop the structure and control complex functions within a system (Saha et al. 2021a). Maximization of nominal margin through regression task analysis is the significant benefit of the SVR model (Li et al. 2010). It also gives us the flexibility to describe how much error is tolerable in our model and will find the hyperplane to fit the data (Sharp 2020). In the case of a complex dataset, the SVR model is mostly used and solves this dataset by developing several curved margins (Kalantar et al. 2018). In these ML algorithms, the structural risk minimization norm (SRM) plays a very significant role in identifying the relationship between the input and output variables (Saha et al. 2021a). Thus, it is necessary to calculate SRM in an SVR model and this can be calculated using the following equations.

$$y = k\left( z \right) = v\emptyset \left( z \right) + c,$$
(7)

in which input data and the resultant value are shown by \(z = \left( {z_{1} ,z_{2} , \ldots z_{n} } \right)\) and \(y_{b} \in R^{l}\), respectively. In addition to this, \(v \in R^{l}\) represents the weightage factor, \(c \in R^{l}\) represents the constant number of the mathematical function, and \(l\) represents the data size in the respective model. \(\emptyset \left( z \right)\) represents the irregular function for map of the input dataset. To define \(v\) and \(c\), the following equation can be used and developed based on the SRM principles:

$${\text{Minimize}}:\left[ {\frac{1}{2}||v||^{2} + P\mathop \sum \limits_{b = 1}^{1} (\zeta_{b} + \zeta_{b}^{*} )} \right],$$
$${\text{Subject}} {\text{to}}:\left\{ {\begin{array}{*{20}c} {y_{b} - \left( {v\emptyset \left( {z_{b} } \right) + c_{b} } \right) \le \varepsilon + \zeta_{b} } \\ {\left( {v\emptyset \left( {z_{b} } \right) + c_{b} } \right) - y_{b} \le \varepsilon + \zeta_{b}^{*} } \\ {\zeta_{b} ,\zeta_{b}^{*} \ge 0} \\ \end{array} } \right. ,$$
(8)

where the penalty factor is represented by \(P\), \(\zeta_{b} ,\zeta_{b}^{*}\) indicates loose variables, and \(\varepsilon\) represents the optimized performance of the model. The Lagrangian function was used to solve the optimization problem:

$$L(v,c,\zeta_{b} ,\zeta_{{_{b} }}^{*} ,\beta_{b} ,\beta_{{_{b} }}^{*} ,\delta_{b} ,\delta_{{_{b} }}^{*} ) = \frac{1}{2}\left| {\left| {\left| v \right|^{2} } \right.} \right. + P\sum\limits_{b = 1}^{l} {\left( {\zeta_{b} + \zeta_{{_{b} }}^{*} - \sum\limits_{b = 1}^{l} {\beta_{b} \left( {\zeta_{b} + \varepsilon - y_{b} + v\emptyset \left( {z_{b} z} \right) + c} \right) - \sum\limits_{b}^{l} {\beta_{{_{b} }}^{*} \left( {\zeta_{{_{b} }}^{*} + \varepsilon + y_{b} - v\emptyset \left( {z_{b} z} \right) - c} \right) - \sum\limits_{b = 1}^{l} {\left( {\delta_{b} \zeta_{b} + \zeta_{{_{b} }}^{*} \delta_{{_{b} }}^{*} } \right)} } } } \right)} ,$$
(9)

in which the Lagrangian multipliers are represented by \(\delta_{b} ,\delta_{b}^{*}\),\(\beta_{b} and \beta_{b}^{*}\).

Subsequently, SVR can be calculated by:

$$K\left( z \right) = \mathop \sum \limits_{b = 1}^{l} (\beta_{b} - \beta_{b}^{*} )m\left( {z,z_{b} } \right) + c,$$
(10)

where the kernel function is expressed through \(m\left( {z,z_{b} } \right) = \langle \phi \left( z \right),{ }\phi \left( {zb} \right)\rangle\).

Particle swarm optimization (PSO)

The PSO modeling approach developed by James Kennedy and Russel Eberhart in 1995 is based on the social behaviour of fish schooling or birds flocking (Kennedy and Eberhart 1995), which is a nature-inspired algorithm and used to find out the optimal solutions of nonlinear functions. This ML method was inspired by the collective/swarm motion of biological organisms (Kennedy and Eberhart 1995). The PSO model defines each optimization issue as a bird that searches particles or space (Rizeei et al. 2019). Generally, a class of unsystematic particles that is modified by PSO is used to explore the ideal answers by using interactive techniques (Cheng et al. 2018). This PSO is a simple, efficient, and also effective optimization algorithm that helps to solve multimodal, discontinuous, and non-convex problems (Alatas et al. 2009). Although this optimization method has experienced many changes since 1995, many researchers have developed a new version of it to understand the various aspects of the algorithm (Poli et al. 2007). In analogy, PSO is an evolutionary computation method that follows a stochastic optimization model based on swarm intelligence (Rana et al. 2011) and shows a set of solutions in a search space to achieve the best solution or position. The algorithm of PSO can be described in the following way. If dataset on a particle i uses d-dimensional representation, the location is \(Y_{i} = (y_{i1} ,y_{i2, \ldots ,} y_{id} )^{T}\), the respective speed is \(V = (v_{i1} ,v_{i2, \ldots , } v_{id} )^{T}\), and other vectors are alike, then,

$$v_{id}^{k + 1} = w*v_{id}^{k} + c_{1} *rand_{1}^{k} *\left( {pbest_{id}^{k} - x_{id}^{k} } \right) + c_{2} *rand_{2}^{k} *\left( {gbest_{id}^{k} - x_{id}^{k} } \right) ,$$
(11)
$$y_{id}^{k + 1} = y_{id}^{k} + v_{id}^{k + 1} ,$$
(12)

where \(v_{id}^{k}\) is particle i in the kth iteration of the d-dimensional speed; c1, c2 are the accelerating coefficients, with \(c_{1 }\) = \(c_{2}\) = 2; rand1, 2 is the random number between 0 and 1; \(x_{id}^{k}\) is particle i in the kth iteration of the d-dimension of the present location; \(pbest_{d}\) is the individual extreme point position where particle i is located in the d-dimensional; \(gbest_{d}\) is the overall situation extreme point position in which the total particle group is situated in the d-dimensional. W represents primary weight value of the inertia and the values ranging from 0 to 1.4. Here, the essential reduction can make by w for the number of iterative smaller, and in the march of time w linearly decreases.

Grasshopper optimization algorithm (GOA)

Optimization is the process of finding the best value for the variable to minimize and maximize an objective function of a particular problem. Based on objectives optimization, problems are classified into two, single objective and multi-objective optimization problems (Marler and Arora 2004). For this purpose, the mathematical optimization method has been used in many research works to make optimal results (Intriligator 2002; Dunning et al. 2017) but, in recent times, nature-inspired population-based algorithms, stochastic optimization approaches have become more popular (Yang 2010). Several nature-inspired multi-solution-based meta-heuristic algorithms such as genetic algorithms (GA) (Holland 1992), particle swarm optimization (PSO) (Kennedy and Eberhart 1995), and ant colony optimization (ACO) (Dorigo et al. 2006) have been used in different works in the past years. Among them, grasshopper optimization algorithms (GOA) are emerging as important meta-heuristic, multiple objective-based multi-solution approaches (Saremi et al. 2017). GOA is totally dependent on the swarm nature of grasshoppers, which gave the most accurate and competitive results than other nature-inspired optimization methods (Luo et al. 2018). This method has been applied in various fields due to its efficiency and simple implementation (Łukasik et al. 2017; El-Fergany 2017; Mirjalili et al. 2018a; Tharwat et al. 2018). The mathematical equations proposed for this model are as follows. In this model, the position of the i-th grasshopper is denoted as \(X_{i}\) and represented as:

$$X_{i} = S_{i} + G_{i} + A_{i} ,$$
(13)

where \(S_{i}\) indicates social interactions, \(G_{i}\) represents gravity force on the i-th grasshopper and \(A_{i}\) indicates wind advection (Mirjalili et al. 2018b).

The above-mentioned equation may discuss about the movements of the grasshopper, and the social interactions of the grasshopper may be discussed as:

$$S_{i} = \mathop \sum \limits_{{\begin{array}{*{20}c} {j = 1} \\ {j \ne {\mathbf{i}}} \\ \end{array} }}^{N} s\left( {d_{ij} } \right)\widehat{{d_{ij} }},$$
(14)

where \(d_{ij}\) represents the distance between the i-th and j-th grasshopper, and \(s\) is the function that describes the strength of social forces and is represented as:

$$s \left( r \right) = fe^{{\frac{ - r}{l}}} - e^{ - r} ,$$
(15)

where \(f\) represents the intensity of attraction and \(l\) is attractive length scale. The details about the algorithms of GOA can be found in Mirjalili et al. (2018b) and Arora and Anand (2019a).

As previously mentioned, all the methods have some drawbacks and shortcomings, which gave some biasness in the produced result. According to Zhang and Hong (2019), such algorithms have numerous disadvantages such as trapping at local optima and low population density which makes premature convergence. In the case of large and noisy datasets, SVR modeling approach will be underperformed. The PSO model easily falls into local optimum in high-dimensional space and also has a low convergence rate. GOA modeling approach also faced problems such as slow convergence and trapping in local optima (Luo et al. 2018). To eliminate the biases and overcome the shortcomings, in this research work, two ensemble methods such as SVR–PSO and SVR–GOA have been used along with SVR modeling approach.

Validation of the models

Any scientific study entirely depends on appropriate validation techniques; without it, the produced result does not apply in reality (Saha et al. 2021a). In this study, six important statistical techniques, such as specificity, sensitivity, positive predictive value (PPV), negative predictive value (NPV), kappa coefficient, and receiver operating characteristics curve (ROC)–AUC, kappa coefficient analysis with one graphical validation technique namely Taylor diagram (Taylor 2001), have been used to validate the predictive result of the aforementioned models and asses the multiple aspects of models’ performances. The number of pixels was used in the accuracy assessment of flood and non-flood areas. The four statistical parameters such as true positive (TP), true negative (TN), false negative (FN), and false positive (FP) have been used to calculate the validation techniques. The accuracy of the aforementioned models depends on these validation technique values: if the values were higher, then the models gave better results and vice versa (Khosravi et al. 2019). The above mentioned statistical parameters used in this study were calculated through the following equations

$${\text{Specificity}} = \frac{{{\text{TN}}}}{{{\text{FP}} + {\text{TN}}}},$$
(16)
$${\text{Sensitivity}} = \frac{{{\text{TP}}}}{{{\text{TP}} + {\text{FN}}}},$$
(17)
$${\text{PPV}} = \frac{{{\text{TP}}}}{{{\text{FP}} + {\text{TP}}}},$$
(18)
$${\text{NPV}} = \frac{{{\text{TN}}}}{{{\text{TN}} + {\text{FN}}}}.$$
(19)

ROC–AUC analysis was used to validate the models, which is a widely accepted technique. ROC analysis was completed by plotting on the X axis Y axis which are popularly known as sensitivity and specificity. It helps to assess the predictive ability of models which is a well-established technique for this type of estimation. The range from 0.5 to 1 represents the poor performance to excellent performance of the models. This ROC–AUC technique was calculated by the following equation:

$${\text{AUC}} = \mathop \sum \limits_{k = 1}^{n} \left( {X_{k + 1} - X_{k} } \right)(S_{k + 1} - S_{k} - S_{k} /2),$$
(20)

where area under curve is represented by AUC, and sensitivity and specificity are represented by \(S_{k}\) and \(X_{k}\), respectively.

In this study, kappa coefficient statistical techniques were also used to determine the validity of the produced result; the kappa statistic value helps to identify the difference between the observed phenomenon in the present and the predicted results by the adopted modeling approaches (Viera and Garrett 2005). The kappa coefficient was calculated by the following equation (Carletta 1996):

$$k = \frac{{P_{o} - P_{e} }}{{1 - P_{e} }} ,$$
(21)

where kappa coefficient is represented by k, the observed samples by \(P_{o}\) and the predicted result by \(P_{e}\).

Results

Multicollinearity assessment

It has been proved that MC assessment is necessary to make any susceptibility modeling. It decreases the causative bias, which helps to improve the accuracy of the study. In this study, MC assessment was adopted to identify the suitable factors for FFSM. In this assessment, 16 causative parameters were selected and the MC test was assessed using VIF and TLT statistical techniques. The outcome of this test showed that TLT value ranged from 0.37 to 0.77, whereas VIF value from 1.29 to 2.66. This test implies that the present research work is within permissible limit and there is no MC issue. The highest and lowest VIF values were found in slope (2.66) and SPI (1.29), respectively. In the same way, the highest and lowest TLT value found in SPI (0.77) and slope (0.37), respectively (Table 1).

Table 1 Variance inflation factor (VIF) and tolerance of flood causative factors
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Flash flood-susceptibility assessment

In this study, SVR, and its ensemble of SVR–PSO and SVR–GOA models were used to assess the flash flood-susceptible area. All three models classified the river basin area into five zones, those are very low, low, moderate, high, and very high, to better understand spatial variation of flood-susceptible areas (Table 2).

Table 2 Spatial coverage of three models in study area
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In the flash flood-susceptible map prepared by the SVR model (Fig. 4a), the areal coverage of very high and high zone was approximately 46.23 \(km^{2}\) (12.67%) and 36.23 \(km^{2}\) (9.93%), which were mainly located in the middle to southern portion along the river. This flood significantly impacted the people in the riparian area who lived in close proximity to the river channel. The rest of the area is under moderate, low and very low flood-prone regions and the spatial coverage was approximately 37.43 \(km^{2}\)(10.26%), 153.36 \(km^{2}\)(42.03%) and 91.62 \(km^{2}\)(25.11%), respectively.

Fig. 4
figure 4

Flash flood-susceptibility mapping by using ML algorithms; a support vector regression SVR, b ensemble of SVR–PSO, c ensemble of SVR–GOA

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In the ensemble of the SVR–PSO model (Fig. 4b), the very high and high susceptible areas are situated in the middle to the southern stretch of the river channel, which is mostly adjacent to the river channel. The spatial coverage of very high and high zones was approximately 47.21 \(km^{2}\)(12.94%) and 28.79 \(km^{2}\)(7.89%), respectively, of the river basin. On the other hand, most of the area contains a low susceptible zone, which is mostly situated in the northern portion of the river basin. Spatial coverage of moderate, low, and the very low zone was approximately 27.69 \(km^{2}\)(7.59%), 164.97 \(km^{2}\)(45.21%) and 96.22 \(km^{2}\)(26.37%), respectively, of the basin.

In the SVR–GOA model (Fig. 4c), the spatial coverage of the very high and high zones is 40.10 \(km^{2}\)(10.99%) and 25.94 \(km^{2}\)(7.11%), respectively. This model showed that a very high amount of area was under a very low flood-susceptible zone, about approximately 258.38 \(km^{2}\)(70.81%), and the rest of the area was under low and moderate zones. The spatial coverage was approximately 19.26 \(km^{2}\)(5.28%) and 21.20 \(km^{2}\)(5.81%), respectively. These results imply that the occurrence of flash flood susceptibility in the downstream region of the northeast portion (near to the river) of the study region is more probable than in the upstream part of the northwest portion.

Model validation

All of the models used in this study needed to be validated. The validation was done using the AUC value from the ROC curve and various statistical indices such as specificity, sensitivity, PPV, NPV, kappa coefficient and one graphical model including Taylor diagram. As mentioned, all the models play a significant role in analyzing and determining the accuracy of the adopted model’s result. In this present study, validation is necessary because all the data collected from different sources were remotely sensed, so there was some possibility of error. Here, all the predicted results of different models were obtained using training and validating datasets. In this present research, AUC analysis of the aforesaid ML models is presented in Fig. 5a, b. Based on the result, it was clear that all the models had high accuracy, but the SVR–GOA model was the most suitable modeling approach among other models for this research work because of its AUC values, which were 0.951 and 0.938 for training and validation, respectively, followed by SVR–PSO (training 0.948, validating 0.924) and SVR (training 0.911, validating 0.901) Apart from ROC, all the statistical indices showed (Table 3) that SVR–GOA modeling approach has high predictive capacity in FFSM. The kappa value of SVR–GOA (training = 0.82 and validation = 0.79) also state that this ensemble approach is the most optimal, followed by SVR–PSO and standalone PSO. From the Taylor diagram, we can easily determine the efficiency of all the predictive models and, from this, it is established that the SVR–GAO model is most optimal than SVR single alone model and ensemble of SVR and PSO (Fig. 6). The effect plots are probability plots that demonstrate the outcomes of a variable or relationship. It is essential to be using them to categorize significant results. The spots that appear to be outliers are the true critical influences, not those that fall within the conventional probability plot line. The probability plot clearly shows that the SVR–GAO is the most optimum model when evaluating the likelihood ratio (Fig. 7). Additionally, the RMSE variation graph is also presented in Fig. 8 based on individual learning algorithms, i.e., SVR, SVR–PSO and SVR–GOA.

Fig. 5
figure 5

Model validation by ROC curve analysis; a training dataset, b validating dataset

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Table 3 Predicting capability of three models by six adopted statistical techniques
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Fig. 6
figure 6

graphical representation of Taylor diagram of all the applied models

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Fig. 7
figure 7

Probability plot of SVR a, SVR–PSO b, and SVR–GOA c model

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Fig. 8
figure 8

Graphical representation of RMSE of three applied learning models. a SVR, b SVR–PSO, c SVR–GOA

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Factor importance analysis

All the adopted models have their principle to estimate the importance of each causative factor. In the present study, all predicted models were used to estimate the variable importance in FFSM. In the SVR model, the most significant variables in forecasting flash flood susceptibility were rainfall (100), altitude (86.22), geomorphology (63.39), slope (52.21), NDWI (41.49), and TWI (32.45), while in PSO modeling the controlling factors for FFSM were rainfall (100), NDWI (44.83), geology (34.11), altitude (31.67), NDVI (29.61), and slope (28.09). In the case of the GOA model, the most important variables were rainfall (100), altitude (74.69), slope (55.99), geomorphology (41.11), NDWI (39.68), and distance from the river (32.48). Besides these variables, other variables adopted in this study by all predicting models have their moderate to low importance (Table 4).

Table 4 Factors importance analysis
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Discussion

Flash floods are one of the most dangerous and complex natural disasters due to their short time occurrence, high-speed water runoff, and huge sediment transportation that can result in sudden destruction in properties as well as human lives. However, its complete prevention is impossible. Because of this, it is critical to develop flood prediction and mitigation strategies to save lives and reduce the socioeconomic impacts of flood events, which pose several challenges to the local authorities. Several attempts have been done by different researchers to develop a proper mitigation strategy; among them, FFSM is one of the crucial flood mitigation strategies by which flood-prone areas can be easily identified and proper structural and non-structural procedures can be adopted to minimize the effects of flooding. Several methods and modeling approaches have been used to identify flood areas, but it is also a crucial task to find out the appropriate methods that have more liability and predictivity. The prime objective of our study was to explore the suitability of employing ensemble models (SVR–PSO and SVR–GOA) in flash flood-susceptibility mapping. A significant number of studies have performed spatial modeling using ensemble models (Al-Abadi 2018; Arora and Anand 2019b; Band et al. 2020b; Roy et al. 2020; Pham et al. 2021a; Towfiqul Islam et al. 2021). In the recent era, ML algorithms and artificial intelligence have attracted substantial interest, especially for evaluating environmental hazards, because of their high predictive accuracy and ability to work with large datasets which are less expensive (Band et al. 2020b; Fu et al. 2020). All these methods have given optimal results based on appropriate flood affecting factors in a particular region. Although substantial improvement has been made in FFSM, undoubtedly, advancement is required to improve flash flood-susceptibility mapping performance. These ML algorithms have comparable model accuracy with several methods to model flood likelihood and differentiate the relationship between environmental effect and flood incidence (Goetz et al. 2015). A thorough investigation of this differentiation is essential to choose a suitable algorithm for a specific field of research (Bazai et al. 2020). Wu et al. (2019) and Xiong et al. (2019) have used SVR as a powerful ML technique to identify flash flood areas in China and obtained prominent results. Sahoo et al. (2021) also used an ensemble of ANFIS–GOA modeling approaches to predict the flood in the Mahanadi River basin and found notable outcomes. In predicting effective drought index, Malik et al. (2021) employed SVR–PSO algorithms where they got significant results in prediction.

Several geological, hydrological, morphological, and topographical factors are responsible for flooding (Tehrany et al. 2015). However, only a few factors have a significant role in causing flood events in a particular region, so selecting relevant factors is essential in FFSM (Khosravi et al. 2019). For instance, Luu et al. (2021) used R model and found that land use is the most important factor, followed by geology and slope largely influencing flood occurrence in Vietnam. Khosravi et al. (2018) investigated various models and found that slope was the most crucial factor in flash flood-susceptibility mapping in Iran. In this study, the three adopted models showed that rainfall was the most influential factor in flooding in this region. High intensity of rainfall in a small duration provides a massive amount of water in the river channel, flowing from higher elevation to flat area located at the lower portion of this basin. In addition, LULC change also accelerates flood occurrence. The finding revealed that, in addition to rainfall, altitude, slope, and geomorphology were the most significant factors contributing to flash flood occurrence in the study basin.

Validation of the models mentioned above was attained by several statistical techniques such as receiving operating system (ROC) with AUC analysis, specificity, sensitivity, PPV, and NPV. The result of validation techniques reveals that the SVR–GOA model is the best approach compared to other models (SVR, SVR–PSO), which gave better result and high accuracy. This model has high predictive performance (AUC = 0.951 and 0.938, sensitivity = 0.99 and 0.91, Specificity = 0.97 and 0.87, PPV = 0.97 and 0.86, NPV = 0.99 and 0.91 in training and validation, respectively), followed by SVR–PSO and SVR model. This is verified by the fact that SVR–GOA needed less time for calculation, with less error. In contrast, the conventional SVR model, for instance, needs a higher memory, enormous dataset, and more time for computation (Kalantar et al. 2018). Besides, conventional statistical methods need huge time, enormous datasets, and more input variables unsuitable for data-limited regions, including developing countries like India. However, the SVR–GOA algorithm showed higher accuracy compared to the other two models. It is worth mentioning that there is no previous literature concerning SVR–GOA in the FFSM. It can be said that this algorithm performed well in our case study; thus, it can predict the flash flood susceptibility very well. The proposed model can also be adapted to other natural hazards to get higher accuracy. But all the data-driven models face the most significant challenging issue like overfitting, and to eliminate this issue various techniques are being examined. All the adopted validation measures showed that the SVR–GOA ensemble models have a slight difference in training and testing dataset compared to the other two models and it can significantly overcome the overfitting problems due to the integration of two different models. Therefore, this verified ensemble model (SVR–GOA) was ready for FFSM of the entire study area. Additionally, the ensemble approach of SVR–GWO is also used globally for prediction analysis in different fields. The landslide susceptibility studies using SVR–GWO in Icheon Township, South Korea, gave an AUC result of 83% (Panahi et al. 2020), and study on landslide susceptibility in western Serbia using SVR–GWO gave an AUC result of 0.733 (Balogun et al. 2021), whereas the ensemble of SVR–GOA in this study gave an AUC result of 93.8% in the validation stage. Therefore, SVR–GOA is the most optimal in this study as compared to the previous ensemble of SVR–GWO. Furthermore, multivariate adaptive regression spline (MARS) model used in flood studies have shown AUC value of 0.93 (Mosavi et al. 2020). The application of artificial neural network (ANN) in flood studies revealed that the AUC values were 94.6% (training) and 92.0% (validation), and gave good prediction analysis (Falah et al. 2019). As compared to the MARS model, SVR–GOA gives the best performance, but in comparison with ANN, SVR–GOA gives slightly low performance in this study.

This study has several limitations. First, due to the lack of hydrodynamic information on flooding, there is a certain degree of uncertainty in the proposed method. Second, inconsistency in spatial resolution of DEM-derived causal factors may create uncertainties in the causal factors applied in the proposed way. Third, we only considered the fluvial flash flood in this research. Finally, non-flood points were randomly chosen in the study basin based on expert knowledge and previous flood records. It can generate a certain level of errors in the modeling process (Khosravi et al., 2018). Thus, future studies should focus on the model to choose reliable non-flood points to enhance the quality of the input datasets.

The result and findings of the present study would help the flood hazard managers and researchers determine the vulnerability of flooding and in deciding ways to control and reduce the effects of flood events. Our study indicated the factors influencing flash floods. It recommends that the proposed method, a robust tool, can efficiently evaluate flood susceptibility in other basins when geo-environmental features of a specific basin and model input variables, in which hydrodynamic information may be available, are considered. Furthermore, it suggests that researchers select a suitable model to assess the flash flood susceptibility of any region. It will be noted that these modeling approaches only identify the flood-prone areas, and do not give any information about the depth or velocity of the flood. So, in the future, hydraulic models will be used to determine the flood intensity in this region.

Conclusion

In recent decades, flash flood-susceptibility assessment has been a hot topic at the national and international levels. Human encroachment on river banks and climate change are two major issues that increase flash floods in a regional context. In this study, we propose three ML algorithms including SVR and coupled ensemble algorithms (SVR–PSO and SVR–GOA) to identify the flash flood-susceptibility region of the Gandheswari River basin in West Bengal, India. In this regard, 16 environmental and topographic flood causative factors were identified, and the models were run using an empirical and reasonable approach. The multicollinearity test is also used to reduce the linear dependency between variables and improve the accuracy of adopted models. For flood inventories, flood and non-flood points were identified and used for validation. The SVR-based factor importance analysis was adopted to choose and prioritize the 16 flood causal factors for the spatial modeling. The results of SVR-derived model indicated that rainfall (100), altitude (86.22), and slope (52.21) factors mainly affected flood incidence in the study basin. In this study, it was determined that the SVR–GOA model outperformed the other two models. The AUC values of the SVR–GOA model in training and validation are 0.951 and 0.938, respectively. The spatial coverage of high and very high flash flood-susceptible regions in this model are 25.94 \(km^{2}\)(7.11%) and 40.10 \(km^{2}\)(10.99%), respectively, and the rest of the area was under moderate, low and very low flood-prone regions which are mostly found at the lower course of river basin near Satighat and Pathakpara regions. The primary focus of several studies was the identification of an appropriate method for FFSM. Suitable preventive measures and risk management strategies are the prime focus of FFSM. In the recent era, unplanned policy practice regarding LULC and climatic variability increased the flood events at an alarming rate (Pham et al. 2021a). As a result of this research, it is clear that the SVR–GOA modeling approach can be used in any climatic region to determine the flash flood-susceptible zone. Overall, the proposed model is robust for flash flood-susceptibility analysis. The findings of this study can assist policymakers at the local and national levels in implementing a concrete strategy to reduce flood risk, thereby minimizing economic damage and loss of life in the study area, especially those inhabitants living near the river basin. Although the proposed approach performed very well in our case study, our study has some shortcomings. For instance, uncertainty analysis was not measured in the proposed method. Considering uncertainty with ensemble models coupled with deep learning and hydrodynamics methods should be investigated further to improve the preferences of the proposed model. Hence, risk management and flood reduction actions are indeed necessary at local administration level for preventing recurrent flood impacts on human livelihoods and regional economy. Therefore, the information regarding flood risk should be given to the inhabitants of flood-prone regions within proper time (Hegger et al. 2017). Thus, this FFSM is an extremely important tool in the reduction of human and economic losses by implementing proper management strategies and this can help the financial sector to distribute proper compensation to the flood-affected area and to enforce the appropriate regulation regarding land use.