1 Introduction

Flood, one of the most predominant environmental calamities, is defined as a situation, where water level rise is due to huge precipitation and in this manner overflow of the excess water over the flood plain (Malik, Chandra Pal, et al., 2020; Malik, Pal, et al., 2020). A major portion of the global populations lives in the flood plain areas, and they indirectly or directly depend on the flood plain; thereby, encroachment of human, modification of river, loss of ecosystem and climate change can cause a great threat (WMO, 2018). According to the WMO (2018), storms and floods around the world have caused millions of death from 1970 to 2012.Torrential rainfall has been considered as the prime factor behind the occurrences of a flood (Malik et al., 2020; Malik, Pal, et al., 2020; Minh et al., 2018). Sudden morphological changes generally occur because of flood (Balen et al., 2010; Tu et al., 2016).

Flood is one of the key crises all over the world, which has caused over one million of deaths for the periods of 1970 to 2012 (WMO, 2018), and 109 million people were affected during 1995 to 2015 resulting in economic loss of 75 billion US$ in every year (Malik, Chandra Pal, et al., 2020; Malik, Pal, et al., 2020). It also affects the agriculture, natural ecosystem, cultural heritage, bridge, transporting network (Markantonis et al., 2013). Also, flood also transports the hazardous wastes in the modern days generated by several industries (Khosravi et al., 2019). Natural and anthropogenic reasons both are responsible behind the flood. But recent studies have indicated that the changes in climatic phenomenon have altered the nature and magnitude of the flood (Roy et al., 2020; Saha et al., 2021). Recent works have found that from the last few decades, human interventions to the natural system through urbanization, deforestation, riverside encroachment by human settlement result in progressively decreasing floodplain connectivity with river and increases in flood frequency with greater duration (Christensen & Christensen, 2003; Costache et al., 2021; Roy et al., 2020; Saha et al., 2021).

In case of Asia, near about 90% of damages were occurred by the flood (Smith, 2013), whereas tropical rivers of South Asia experience frequent flood event (Chowdhuri, Pal, & Chakrabortty, 2020a, 2020b; Mirza, 2011). In case of India, there is no exemption to this phenomena and thereby became the most horrible flood-affected nation following Bangladesh (Brammer, 2010). Central Water Commission of India (CWC) reported that every year 32 million population has been suffering from floods due to nearly 7.21 million hectors of land inundation (Kale, 2014). Along with this, the devastating flood of Mumbai (in 2005), Jammu and Kashmir (in September 2014), Uttarakhand (in June 2013) is one of the few examples of devastating floods in India. Previous studies have concluded that flood cannot be eliminated (Bandyopadhyay et al., 2016; Huang et al., 2008). Therefore, assessment of FS and its management is very much essential to understand the flood-affected areas to reduce flood damages by considering some proper suitable measurements (Hagen & Lu, 2011).

2 Literature Reviews

Geographic information system is recognized as very significant tool for data analysis and management (Falah et al., 2019; Rahmati et al., 2016). FS mapping is an important part of predicting and managing impending floods (Falah et al., 2019; Kourgialas & Karatzas, 2011). Several approaches have been applied to predict the FS of an area (Solomatine & Ostfeld, 2008), e.g., (Al-Juaidi et al., 2018) used LR model; (Souissi et al., 2020; Swain et al., 2020) used analytical hierarchy process in GIS platform; Haghizadeh et al. (2017) used Shannon’s entropy model; (Rahmati, Pourghasemi, et al., 2016; Tehrany et al., 2014) applied support vector machine and WoE; (Lee et al., 2017) used random forest and boosted regression trees; (Chowdhuri, Pal, & Chakrabortty, 2020a, 2020b) used evidential belief function; (Mukerji et al., 2009) applied neuro-fuzzy, neuro-GA and ANN models; and (Najafzadeh & Zahiri, 2015) and (Zahiri & Najafzadeh, 2018) used an adaptive learning network to estimate river discharge and floodplain modeling and many more. Apart from this, several hydrological models were also applied for flood inundation mapping (Costabile & Macchione, 2015; Malik & Pal, 2020a; Zheng et al. 2018). So, it can be said that numerous scholars have come out with their methods for FS mapping. Although lots of methods are available for FS mapping (Wheater et al., 1993), each method has its specific negative and positive aspect (Tehrany & Kumar, 2018). Thus, it became somewhat confusing to understand the top suitable and globally satisfactory methods for FS analysis (Tehrany & Kumar, 2018). Among several groups of FS mapping model, FL, MCDA, FR, decision trees (DT), LR, artificial neural network (ANN) and machine learning (ML) are the most popular models (Lee et al., 2017). The available popular methods are divided into four categories, e.g., quantitative, qualitative, hydrological and machine learning method (Arabameri, Karimi-Sangchini, et al., 2020; Arabameri, Saha, et al., 2020; Pradhan & Youssef, 2011; Rahmati, Pourghasemi, et al., 2016; Rahmati, Zeinivand, et al., 2016; Saha et al., 2021). Besides this, database requirement in hydrological model implementation, calibration and verification are not easily available in data scarcity area and for developing countries, these models are very complex in nature (Falah et al., 2019). Therefore, application of freely available datasets like digital elevation data, rainfall information and remotely sensed datasets in GIS environment has become more popular.

So, on the one hand, as we have mentioned earlier, FS mapping is very important to the government agencies, academicians, policymakers and people associated with the flood-affected areas, and on the other hand, several FS models are available to execute this. Therefore, the application of multiple FS models and their comparative assessment are very much significant to develop the FS maps. In this study, our main objective is to develop the FS maps based on MCDA, FL, FR and LR to assess the reliability of the particular models in forecasting the FS area.

3 Materials and Methods

Reliable FS map and its accuracy relied on the scale and convenience of the information as well on the models which have been applied to generate this map (Chapi et al., 2017; Mind’je, 2019a). Therefore, based on the previous studies, LULC map, soil map, geological map, rainfall and DEM have been considered (Table 1) to predict the FS. All the FS parameters have been divided following the natural breaks method offered by ArcGIS software for further analysis. Four models, such as FL, MCDA, FR and LR models, have been applied to address the FS map. Therefore, the applied models were categories into two major approaches, i.e., heuristic and statistical model. The heuristic model is the model in which rank-based weights are assigned according to its importance in that particular event, for example FL, MCDA and FR models, whereas statistical models are those, where based on the statistical analysis weights are being given as in case of LR model. Assessments of these methods and its validation have been determined through statistical measures to predict best suitable models. Detailed flowcharts are given in Fig. 1 to show the steps and procedure of this study to develop the FS maps of a study area.

Table 1 Detail list of data applied for the present study and its sources
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Fig. 1
figure 1

Methodological framework of the study showing detailed process of flood susceptibility mapping and its validation processes

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3.1 Study Area

The Dwarkeswar River basin (DRB) of the West Bengal has been selected as the study area, and it is located within the Bengal basin. According to the RMSI report on India Flood Risk, Gangetic plain and West Bengal were under the extreme flood risk zone (RMSI, 2015). According to the Disaster Risk Index of States and Flood Hazard Index, in both cases, West Bengal stands second in India (Thakur and Chauhan, 2018). West Bengal is primarily an agrarian state with high population density in the low-lying alluvial region; this flood problem has become jeopardized. Irrigation and Waterways Department (IWD) of Govt. of West Bengal (Irrigation and Waterways Directorate Govt. of West Bengal, 2016) in their several reports has stated that 42 percent area of the state is prone to flood, whereas (Kale, 2003a, 2003b) argued that approximately twenty million (55.8%) of the region is susceptible to flood. (Kadam & Sen, 2012) and (Chapman & Rudra, 2007) concluded that during the September 2000 flood (Table 2), twenty million people were affected. Although several measures were taken by the Government to prevent the floods, still every year the lower part of the east-flowing rivers of the western part of the West Bengal has been suffering from floods (Malik & Pal, 2020a). So, in this DRB enormous loss of economy, agriculture, biotic habitat and social stability has been observed by the floods and its surrounding regions historically (Table 2).

Table 2 Historical account of floods and its affected area of West Bengal
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Dwarkeswar River is identified as Dhalkishore (SOI, 1978). It is one of the major rivers in the Bengal basin. The river basin is located within 87°47′58ʺE to 86°31′08ʺE longitude and 23°40′25ʺN to 23°32′00ʺN latitude (Fig. 2), covered an area of 4356.6 sq. km. It originates near Tilboni hill of Chhotonagpur Plateau in Puruliya district (O’Malley, 1995). After originating from Panjoniya or locally named as Dungru, tributaries like BekoNala, Berai, Arkasha, Dangra Nala, Kumari Nala, Shankari, Futuari Nala, Dudhbhaiya Nala, etc., discharge its water in Dwarkeswar River. Near Ghatal town, Dwarkeswar River meets with Shilabati River and finally forms the Rupnarayan River (O’Malley, 1995). The elevation of the Dwarkeswar River ranges between 438 and 10 m (Fig. 2) with monotonous rolling topography and scattered residual hills of hard rock sometimes devoid of vegetation.

Fig. 2
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Location map of the study area showing administrative location, drainage network and distribution of elevation

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The lower part of the study area is sufferers from repeated flooding. I&W Dept. has stated that poor drainage condition is responsible for such frequent flood. Three river gauge stations have been found along this river, among which one gauge station is placed near Bankura Town, which is located in the upper part of the river basin. The previous records from 1978 to present have been indicated that river flow height crossed the EDL six times near the Arambag station. Apart from this, the nature of river flow is flashy.

Having a subtropical nature of climate, the study area is a dry region. The river dries up in the hot and cold periods. Geologically, the higher part of this region consists of Chhotonagpur Granite Gneiss Complex which belongs to the Proterozoic age. The central part of this river basin is associated with the Cainozoic Laterite. Holocene Sediment is found in the lower part of the river basin (GSI 1999). The spatial pattern of this river basin is elongated in nature (Fig. 2). Maximum length and width of the drainage basin are 159.84 km and 40.80 km, respectively. The total extent of the main trunk stream is 228.65 km. Bifurcation ratio of the river basin always exceeds 3 (Table 3); thereby, it is very much prone to flood (Strahler, 1957).

Table 3 Drainage basin and network properties of the Dwarkeswar River
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3.2 Flood inventory mapping

Historical documentation of flood-prone areas is known as flood inventory (FI) data, which is generally prepared based on previous records (Pourghasemi & Beheshtirad, 2015). FI map is very much useful to predict the future flood (Rahmati, Pourghasemi, et al., 2016; Rahmati, Zeinivand, et al., 2016). However, its reliability markedly relies on the spatial and temporal extent of flood record. In this study, FI map has been prepared applying 1400 (700 each for non-flood and flood) points from the study area extracted from Dartmouth Flood Observatory (DFO) and IWD, Govt. of West Bengal for the period of 2000–2018. Flood points have been validated through field survey. Entire dataset was divided into 70/30 ratio, in which 70% of the dataset has been selected randomly to run the model and remaining part has been used invalidation (Fig. 1).

3.3 Flood susceptibility factors

Here, 14 flood causative factors have been incorporated on the basis of earlier works (Table 4 and Fig. 3) incorporating TWI, NDVI, elevation, aspect, slope, PlC, DD, PrC, distance from river, rainfall, LULC, SPI, geology and soil. Selected factors are very significant for assessing and delineating of FS regions of any area.

Table 4 Multi-collinearity test of flood conditioning factors
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Fig. 3
figure 3figure 3

Flood susceptibility factors and its spatial variation in the study area such as a elevation, b aspect, c distance from river, d drainage density, e NDVI, f stream power index, g wetness index, h rainfall, i plan curvature, j profile curvature, k slope, l geology, m soil and n land use and land cover

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3.3.1 Elevation

Elevation has been considered as an important aspect in FS assessment. Also, lower altitude is generally associated with flood-prone areas (Roy et al. 2020). The relationship between FS and elevation is inversely related to the elevation (Malik, Chandra Pal, et al., 2020; Malik, Pal, et al., 2020), thereby indicating that areas associated with very low altitude may experience a severer flood. So, it is the most important variable to estimate FS. Here, the elevation map was created from SRTM data with 30 m spatial resolution (Fig. 3a).

3.3.2 Aspect

Aspect is an major attribute to predict the FS (Mind’je et al., 2019; Tang et al., 2020; Tehrany et al., 2015). It is the maximum slope direction (Choubin et al., 2019). The aspect map of the study area was generated from the DEM in Arc GIS software (Fig. 3b).

3.3.3 Distance from the river

It is a vital parameter to determine the FS (Choubin et al., 2019). Due to excessive and storm rainfall in a drainage basin, channel flow increases and when it crosses the limits of the channel capacity, it turns into flood. Therefore, nearer to the river, FS is more and away from the river, FS decreases. It has been estimated in the ArcGIS software from the extracted drainage network of DEM and topographical maps (Fig. 3c).

3.3.4 Drainage density

It is defined as the length of drainage per unit area (Horton, 1932). In a drainage basin, concentrated flow occurred after rainfall and subsequently, when the channel flow crosses the limits of channel capacity, its excess water overflows in the adjacent area and creates a flood. Therefore, it is one of the key aspects in the assessment of the FS of any area (Arabameri, Karimi-Sangchini, et al., 2020; Arabameri, Saha, et al., 2020). Topographical maps from the Survey of India in association with DEM (Fig. 3d) were used to demark stream network. After that, DD has been computed by the line density tool available in the ArcGIS.

3.3.5 Estimation of Normalized Difference Vegetation Index (NDVI)

NDVI is an index of vegetation status, which indicates the phenomenological nature of the vegetation. This index can help to identify the FS area (Kumar & Acharya, 2016; Paul et al., 2019). NDVI was calculated from the Landsat8 OLI/TIRS Eq. (1) (Fig. 3e).

$${\text{NDVI}} = \frac{{\left( {{\text{NIR}} - {\text{RED}}} \right)}}{{\left( {{\text{NIR}} + {\text{RED}}} \right)}}$$
(1)

where NIR represents near infrared band (Band no 5 for Landsat8 OLI/TIRS) and RED indicates band no 4 for Landsat8.

Nature of vegetation changes in response to variations in geomorphology, and thereby, the flood plain vegetation is different from other kinds of vegetation. In this way, it is very much helpful to predict the FS area.

3.3.6 Stream Power Index

Stream power index or SPI represents the intensity of the surface runoff and potentiality of erosion (Termeh et al. 2018). High amount of SPI indicates the greater ability of surface runoff, and low amount of SPI denotes the poorer surface runoff. Thus, substantial rainfall may lead to the flood in the low SPI area. In this study, it was calculated in the ArcGIS platform applying SRTM DEM using Eq. (2) (Fig. 3f).

$${\text{SPI}} = A_{s} \times \tan \beta$$
(2)

where SPI represents stream power index; specific basin area (in m2) represented by \(A_{s}\) and \(\beta\) represents the slope (in degree). It was applied by several researchers to estimate the FS (Saha et al., 2021).

3.3.7 Topographic Wetness Index

Topographic wetness index or TWI is an important factor which was previously applied by several scholars to predict the FS of an area (Costache et al., 2021; Saha et al., 2021). Areal dispersal and saturation of surface runoff are strongly controlled by this TWI. In this research work, the TWI was computed in the GIS platform from the DEM following the given Eq. (3) (Fig. 3g).

$${\text{TWI}} = \ln \left( {\frac{{A_{s} }}{{\tan \left( {{\text{slope}}} \right)}}} \right)$$
(3)

where \(A_{s}\) represents the specific catchment area (m2m−1) and the slope has been measured in degree. Preceding research works display that FS and TWI are related positively to each other (Saha et al., 2021). Thus, this indicator is very good to determine the proneness of the flood.

3.3.8 Rainfall (mm)

Rainfall is the greatest significant parameter for FS mapping (Costache et al., 2021; P. Roy et al., 2020; Saha et al., 2021). The upper part of the study area is characterized by semiarid climate and very small rainfall, while the lower and middle part is associated with a monsoon climate. Monthly rainfall data for all the selected stations from IMD were collected for the period of 2000–2018 and interpolated in the ArcGIS environment to extract the basin rainfall (Fig. 3h). Several previous studies strongly argued that positive relationships exist between rainfall and flood (Bandyopadhyay et al., 2016; Chowdhuri & Chakrabortty, 2020a, 2020b; Das et al., 2018). So huge rainfall is strongly associated with a greater probability of flood occurrence, and in opposite situation, it is devoid of flood occurrence.

3.3.9 Plan Curvature

It is important factor in detecting the FS (Lee et al., 2012; Paul et al., 2019), and it represents vertical to the slope bearing. A negative value indicates the concave profile, whereas zero denotes the flats surface and positive value represents the convex profile. It influences the runoff, and thereby, it will provide fruitful insight into the FS prediction. It has been generated from DEM using ArcGIS platform (Fig. 3i).

3.3.10 Profile Curvature

The curvature of terrain in the slope direction is called profile curvature. This can determine significant control over the surface runoff. In this way, it will provide a significant indication of FS assessment (Arabameri et al. 2019). Profile curvature has been computed in the ArcGIS environment using Arc tool from the DEM (Fig. 3j). Profile curvature is also similar to the plan curvature in terms of nature of profile and its representing value (Fig. 3j).

3.3.11 Slope

Slope determines the nature and strength of water stagnation and water percolation (Rahmati, Pourghasemi, et al., 2016; Rahmati, Zeinivand, et al., 2016). It is also negatively related to the flood. Heavy rainfall on the surface with extremely low slope is accompanied with very low surface runoff velocity, water inundation and thereby floods (Rahmati, Pourghasemi, et al., 2016). Besides the same situation with moderate-to-high slopes subjected to a higher rate of runoff and thereby less vulnerable to flood, slope map was prepared from the 30 m SRTM DEM data in the ArcGIS software (Fig. 3k).

3.3.12 Geology

A varying geological character of a river and its basin can determine the nature of infiltration, channel properties and runoff generation (Miller et al., 1990) and thereby can indicate the FS of a river basin (Sahana & Patel, 2019). Earlier research works have also discussed the significance of the geological factor in the assessment of FS of an area (Table 4) (Khosravi et al., 2019; Lee et al., 2017; Malik & Pal, 2021). Consequently, the geological aspect was incorporated to formulate the FS map of the DRB. This datum from GSI was collected, and nine geological components were identified (Fig. 3l).

3.3.13 Soil

It is another flood contributing factor. Surface runoff properties and thereby flood peak are determined by infiltration rate of soil (Chen et al. 2020). Apart from this, types of soil are also influenced by the floods and its deposits. So, soil type carries a significant indication for FS. Past literature also indicates that soil is an important aspect in the FS mapping (Ganguly et al., 2008; P. Roy et al., 2020; Saha et al., 2021) (Table 4). Soil maps of all corresponding districts were collected from NBSS&LUP. Eight types of soil are observed in the Dwarkeswar River (Fig. 3m).

3.3.14 Land Use and Land Cover (LULC)

Evapotranspiration, infiltration and runoff are generally influenced by the LULC of an area (Kadam & Sen, 2012; Kumar & Acharya, 2016; Rahmati, Pourghasemi, et al., 2016; Rahmati, Zeinivand, et al., 2016). So, it directly or indirectly influences the FS of an area. Literature review on FS parameters (Table 4) indicates that most of the scholars have incorporated LULC to predict FS in their studies. In this study, LULC map was collected using Bhuban’s Geospatial Gateway from Indian Space and Research Organization (ISRO) (Table 1). Five categories of LULC were considered, such as agriculture, bare ground, settlement, water body and vegetation (Fig. 3n).

3.4 Multi-collinearity Test

Multi-collinearity test has been used in this study to eliminate the related factors from the model to reduce the possible chance of error, where the tolerance and variance inflation factor (VIF) act as an important part to identify the inaccuracy. The tolerance and VIF have been calculated in the following given formulas 4 and 5.

$${\text{Tolerance}} = 1 - r^{2}$$
(4)
$${\text{VIF}} = 1/{\text{Tolerance}}$$
(5)

where tolerance level < 0.1 and VIF results > 10 represent multi-collinearity issue (Khosravi et al., 2019). In this study, less than 5 VIF value has been considered to judge the parameters for FS modeling.

3.5 Flood susceptibility mapping

Several popular FS models exist (Dottori et al., 2018). But considering data availability and suitable of approaches, four popular models such as FZ, MCDA, LR and FR have been used for FS analysis. A detailed description of these models has been described below.

3.5.1 Multi-criteria Decision Analysis (MCDA)

It was prepared by Saaty in 1977. MCDA is one of the most popular methods of heuristic analysis (Malik et al., 2019). Pairwise comparisons were done to reach some logical conclusion (Fernández & Lutz, 2010). Pairwise disintegration, amalgamation and comparison of priorities are the basic principle behind this model (Malik et al., 2019). Several research works following this model have been done to estimate FS (Rahmati, Pourghasemi, et al., 2016; Rahmati, Zeinivand, et al., 2016). It was used in a numerous perspectives to achieve the required goal, for example, gully erosion vulnerability, groundwater valuation (Chakrabortty et al., 2018), gold assessment (Madani, 2011), landslide susceptibility (Ma et al., 2019; Yilmaz, 2010), flood vulnerability (Dano et al., 2019; Nachappa et al., 2020) and so on. In the case of developing nations and the area which is lacking of adequate information, this model is very much helpful. Consistency ratio (CR) is very important to evaluate the factors (Ergu et al., 2011), which provide the decision to be accepted only if the CR =  > 0.10. It was computed using the given Eq. (6):

$${\text{CR}} = {\text{CI}}/{\text{RI}}$$
(6)

Here, RI is the random index and CI denotes consistency index which were derived from the number of parameters (n). CI is calculated using Eq. (7).

$$CI = \left( {\lambda \max - n} \right)/\left( {n - 1} \right)$$
(7)

Here, \(\lambda \max\) represents the highest eigenvalue in the data matrix. Therefore, successful application of the MCDA model in association with GIS has been used to assess the FS of the study area. In a systematic manner, a priority matrix was prepared on the basis of pairwise comparison of the selected parameters and their subtheme keeping CR value to 0.045. After that, all the parameters had been incorporated in the weighted overlay tool in ArcGIS to assess the FS of the study area using the given formula 8.

$${\text{FSusing}} {\text{MCDA}} = \{ \left( {E_{{\text{w}}} \times E_{{{\text{wi}}}} } \right) + \left( {{\text{DI}}_{{\text{w}}} \times {\text{DI}}_{{{\text{wi}}}} } \right) + \left( {{\text{DR}}_{{\text{w}}} \times {\text{DR}}_{{{\text{wi}}}} } \right) + \left( {{\text{DD}}_{{\text{w}}} \times {\text{DD}}_{{{\text{wi}}}} } \right) + \left( {{\text{NDVI}} \times {\text{NDVI}}_{{{\text{wi}}}} } \right) + \left( {{\text{SPI}} \times {\text{SPI}}_{{{\text{wi}}}} } \right) + \left( {A_{{\text{w}}} \times A_{{{\text{wi}}}} } \right) + \left( {R_{{\text{w}}} \times R_{{{\text{wi}}}} } \right) + \left( {{\text{TWI}}_{{\text{w}}} \times {\text{TWI}}_{{{\text{wi}}}} } \right) + \left( {{\text{RR}}_{{\text{w}}} \times {\text{RR}}_{{{\text{wi}}}} } \right) + \left( {{\text{PlC}}_{{\text{w}}} \times {\text{PlC}}_{{{\text{wi}}}} } \right) + \left( {{\text{PrC}}_{{\text{w}}} \times {\text{PrC}}_{{{\text{wi}}}} } \right) + \left( {{\text{Sl}}_{{\text{w}}} \times {\text{Sl}}_{{{\text{wi}}}} } \right) + \left( {{\text{G}}_{{\text{w}}} \times {\text{G}}_{{{\text{wi}}}} } \right) + \left( {{\text{So}}_{{\text{w}}} \times {\text{So}}_{{{\text{wi}}}} } \right) + \left( {L_{{\text{w}}} \times L_{{{\text{wi}}}} } \right)$$
(8)

where FS—flood susceptibility, MCDA—multi-criteria decision analysis, DR—distance from the river—elevation, DI—dissection index, E—elevation, DD—drainage density, SPI—stream power index, NDVI—normalized differential vegetation index, R—rainfall, A—aspect, RR—relative relief, TWI—topographic wetness index, PrC—profile curvature, PlC—plan curvature, So—soil, Sl—slope, L—LULC, \({\text{w}}\) —weight of the theme and \({\text{wi}}\)—weight of the individual classes.

3.5.2 Fuzzy Logic

Fuzzy logic or FL is an additional popular model to determine the FS of any region (Pulvirenti et al., 2011). It was presented by (Zadeh, 1965) to processes difficult problems (Zimmermann, 1996) in a simple manner. It comprises of three main portions, for example, fuzzification, defuzzification and fuzzy inference (Nandalal & Ratnayake, 2011). Membership value of this model ranges from 0 to 1. If the set of the situation is affirmative, then the value will be 1; on the other hand, it is 0 for non-members. So, it is a quantitative form of belief for a particular variable. Determination of fuzzy membership is not bound by strict laws (Ray et al., 2007). In this study, normalized value for fuzzy membership has been obtained from analytical hierarchy processes following (Saaty, 1977) and it has been applied for fuzzy membership function to reduce the biases in the model and result. Fuzzy index map was generated applying 14 selected factors. Fuzzified index maps were generated applying if–then policy in the GIS environment. After that, computed fuzzy index maps were incorporated through given Eq. (9).

$$\mu_{{{\text{combination}}}} = {\text{MAX}}\left( {\mu_{A} , \mu_{B,} \mu_{C} , \mu_{A} \ldots } \right)$$
(9)

where A, B, C represent selected theme.

3.5.3 Frequency Ratio (FR)

The FR is a popular probability method usually used for prediction performance analysis (Saro Lee & Sambath, 2006). In a wider sense, the probability of an event to the probability of non-event phenomenon for selected variables has been estimated through FR method (Bonham-Carter, 1994). This approach is based on the experimental relationship among the occurrence of floods and flood-related several conditioning factors. This is because of revealing the inter-relationship between the flood points and various conditioning factors for a particular area. FR model has been used in various fields for a long time with optimal precision result such as in landslide (S. Pal & Chowdhuri, 2019), gully (Arabameri, Pradhan, & Lombardo, 2019a, 2019b), flood (Samanta et al., 2018), susceptibility analysis and more. The value of FR has been calculated based on the ratio between percentage of flood pixel and percentage of total area pixel of respective factor’s classes. If the value of FR is > 1 and < 1, then it means higher and lower correlation among the flood occurrences and factors classes, respectively (Mandal et al., 2018). Equation (10) was used to calculate FR.

$${\text{FR}} = \frac{{\left( {{\text{NF}}_{{{\text{pix}}}} /\mathop \sum \nolimits_{i = 1}^{n} {\text{NF}}_{{{\text{pix}}}} } \right) \times 100}}{{\left( {{\text{NC}}_{{{\text{pix}}}} /\mathop \sum \nolimits_{i = 1}^{n} {\text{NC}}_{{{\text{pix}}}} } \right) \times 100}}$$
(10)

where FR represents frequency ratio value, \({\text{NF}}_{{{\text{pix}}}}\) indicates number of flood pixel in a respective factor’s class, \(\sum\nolimits_{{i = 1}}^{n} {{\text{NF}}_{{{\text{pix}}}} }\) indicates summation of all flood pixels in the total area, \({\text{NC}}_{{{\text{pix}}}}\) indicates number of pixel of respective factor’s class, and \(\sum\nolimits_{{i = 1}}^{n} {{\text{NC}}_{{{\text{pix}}}} }\) indicates summation of all pixel class in the total area.

3.5.4 Logistic Regression

Logistic regression (LR) is universally accepted widespread numerical method to estimate the FS (Mind’je et al., 2019a; Shafapour Tehrany et al., 2019). LR method is very much useful for the analysis of multiple independent factors of an event (Chowdhuri, Pal, & Chakrabortty, 2020a, 2020b). Therefore, the LR method has been applied to assess the FS from the following given Eq. (11).

$${\text{FS}} = V_{0} + {\text{Elevation}} \times W_{1} + {\text{Slope}} \times W_{2} + {\text{Drainage density}} \times W_{3} + {\text{Aspect}} \times W_{4} + {\text{Plan curvature}} \times W_{5} + {\text{Profile}} {\text{curvature}} \times W_{6} + {\text{Distance}} {\text{from}} {\text{river}} \times W_{7} + {\text{NDVI}} \times W_{8} + {\text{SPI}} \times W_{9} + {\text{Rainfall}} \times W_{10} + {\text{TWI}} \times W_{11} + {\text{LULC}} + {\text{Soil}} + {\text{Geology}}$$
(11)

where y—dependent variables or FS;\(V_{0}\)—the intercept of the model; and \(W_{1} \ldots W_{n}\)—partial regression coefficients. In this study, 70% data were selected randomly to execute the model. In this, LR has been analyzed in the SPSS software and coefficients for individual themes of the LR have been derived and the possibility of incidence was calculated by the given calculation number 12 and concluding vulnerability for flood map has been obtained.

$$P = 1/(1 + e^{ - y} )$$
(12)

where e—linear amalgamation of reliant parameters; P—is the probability of occurrence.

3.5.5 Model validation

The model validation of models and maps is an important aspect to test the reliability of a model or models. In this regard, AUC and ROC are considered as one of the best indicators to assess the models (Band et al., 2020; Pal et al., 2020). Besides, it was widely used in Earth Science and geo-spatial modeling (Arabameri et al., 2020; Arabameri, Saha, et al., 2020; Chowdhuri et al. 2020a, 2020b). The quantification of successful events and non-successful event and plotting of sensitivity and 1-specificity on the abscissa and ordinates, respectively, are the key aspect of it (Pourghasemi & Rahmati, 2018). Here, four models have been selected to estimate the FS and thereby comparative analysis of the applied models applying the given formula 13

$${\text{AUC}} = \frac{{\sum {\text{TP}} + \sum {\text{TN}}}}{P + N}$$
(13)

where TN or true negative is the classified non-flood pixel; TP or true positive is the categorized flood pixel; P is the sum of flood points; and N is the sum of non-flood points.

The value of AUC between 0.5 and 1.0 is considered as the best-fitted model (Yesilnacar & Topal, 2005; Yilmaz, 2010). In this study, 30% data were not incorporated to run the model and were considered as points for validation.

4 Result and analysis

Flood susceptibility map using AHP, FL, KD and LR was computed individually, and the result is given below.

4.1 Multi-collinearity test

Here, after literature review, several flood causative factors have been selected and the numbers of factors have been decreased to fourteen once successful multi-collinearity tests with less than 5 VIF value (Table 4).

4.2 Analysis of flood susceptibility

FS applying MCDA, LR, FR and FL was computed individually, and the result is as follows.

4.2.1 FS using MCDA

MCDA has been applied in FS modeling for the study area. It was observed that the lower section of this river basin is extremely susceptible to flood, whereas the higher part of the basin shows extremely little to moderate FS. The FS map was classified into 5 categories, e.g., very high (> 0.32), high (0.27–0.32), medium (0.20–0.27), low (0.15–0.20),and very low (< 0.15) FS zone in a GIS platform. Regional exposure of the FS area and its percentage is given in Table 6. Table 6 and Fig. 4c indicate that a greater part of the basin area is associated with very high FS area (23.44%), whereas very low, low, moderate and high FS zone covers 12.37%, 18.92%, 22.99% and 22.28% area of the basin, respectively. The areas of outer margin of dissected plateau fringe area to flat alluvial plain with an elevation range from 42 to 7m are prone to high and very high FS.

Fig. 4
figure 4

Spatial variation of flood susceptibility mapping using FL (a), FR (b), MCDA (c) and LR (d)

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4.2.2 FS using FL

FS map applying FL was computed to understand the FS mapping of the study area (Fig. 4a). Downstream section of the DRB is related to the very high (> 0.32) FS area covering 17.29% of the basin (Table 6). This area is characterized by very gentle slope and low elevation (below 36 m.). Paddy cultivation is the major economic activity of this area. The value of high FS index of this model ranges from 0.27 to 0.32 covering 23.02% area of the basin area. Moderate FS index of this model for the Dwarkeswar River varies from 0.20 to 0.27 and covers 20.25% area of the study area (Table 6). Low FS class ranges from 0.14 to 0.20 covering 19.90% area of the study area, which mainly belongs to the plateau fringe area of the basin, and its elevation varies from 80 to 434 m. Besides, below 0.14 represents very low FS index and its spatial coverage is 19.54% of the basin area (Table 6).

4.2.3 FS using FR

FR is another significant model to predict the FS of an area. In this study, another FR model was used for FS of this basin (Fig. 4b). Spatial distribution of FS index was classified into 5 parts following natural break method, such as low (< 0.28), low (0.28–0.37), moderate (0.37–0.48), high (0.48–0.65) and very high (> 0.65) (Fig. 4b). It was observed that the maximum part of the basin area is falling in the low FS category which represents 24.27% area of the study area (Fig. 4b and Table 5 and 6). The downstream section of the DRB belongs to the very high FS area and shows 24.16% of the drainage area (Fig. 4b and Table 6). It is characterized by plain alluvial land, low elevation not more than 42m and intensive agriculture, whereas very low, moderate and high FS zone covers 7.02%, 22.99% and 21.55% area of the basin area, respectively (Table 6). This result indicates that elevation and its related aspects are the major factors behind the susceptibility of flood in this river basin.

Table 5 Flood conditioning layers, their classes and respective logistic regression coefficients
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Table 6 Results of MCDA, FR, FL and LR in the case of each factor
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4.2.4 FS using LR

The FS map also shows similar kinds of result compared to the earlier models. Negative weights of the different factors of the LR indicate negative relation with the occurrences of the flood, whereas positive coefficient plays a positive role in FS. It was observed that coefficients of variation of different floods inducing variables are different (Table 6). Principal coefficient values of flood inducing factors are plan curvature (18.547), elevation (19.078), TWI (15.394), water body (15.463), Sijua formation (15.952) and Chinsura formation (16.174), while modest flood-inducing variables are agriculture (7.184), fine–fine loamy soil (9.976), urban area (5.798), vegetation (5.625), fine loamy–coarse loamy (6.079), fine loamy–sandy (7.298) and fine loamy (5.493). Besides this, according to LR model, fine soil (3.115), fine loamy–coarse loamy (2.514), gravelly loam (1.342) built-up area (1.307), NDVI (1.167), profile curvature (1.643), drainage density (0.537), slope (0.495), distance from the river (0.271), barren land (0.023), aspect (− 0.001), rainfall (-0.01),SPI (− 0.443) and entire geological factors excluding Sijua and Chinsura formations display negative to an insignificant character in the determination of FS. Here, very high FS category is associated with extremely low spatial coverage of the basin area (15.02%) and its FS index level is above 0.808 (Fig. 4d). Similar to the preceding result, this zone of very high FS zone is characterized by extremely low altitude and its associated factors such as Sl, RR and DI. The index value of high FS area ranges from 0.808 to 0.56, and it has occupied 16.69% area of the basin. Moderate FS zone covers 16.80% area of the basin, and the FS index varies from 0.067to 0.56. Very low and low FS index varies from < 0.002 and 0.002 to 0.067 and covers 30.89% and 20.59% of the DRB correspondingly.

4.3 Accuracy assessment

Here, selected models were applied to understand the FS of this area. Therefore, evaluations of these models have been done to judge the suitable models for the FS. Accuracy assessment shows that the AUC value of LR, FL, MCDA and FR was 0.916, 0.893, 0.857 and 0.835, respectively. So, it is clear that LR regression has become the best suitable method for the FS analysis of the Dwarkeswar River (Fig. 5). Figure 6 shows some snaps of flood situation.

Fig. 5
figure 5

Model evaluation of MCDA, FR, FL and LR using sensitivity and specificity by AUC analysis indicating higher accuracy of LR

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Fig. 6
figure 6

Flood-affected area a near Girijatala, Hooghly; b near Mansukha, vast agricultural field submerged under flood August 2016; c near Arambag, a school was affected by flood water from Dwarkeswar River during the same time and d near Thakurani Chak, Hooghly, where road and surrounding areas submerged under flood water

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5 Discussion

Flood is a major environmental hazards, and it cannot be fully prohibited. It became more frequent with greater intensity with the growing population, human invasion and climate change. Therefore, it is very much important to understand and prepare FS map through which with a scientific assessment with proper precautions and required management policy can be formed for the respective area. In this study, FL, MCDA, LR and FR models were applied for the preparation of FS mapping of the Dwarkeswar River.

FS mapping can be defined as the area susceptible to flooding on the basis of selected responsible factors (Lin et al., 2019). However, numerous factors are accountable for the flood like relief, aspect, rainfall, drainage condition, geology, geomorphology, LULC and so on (Tehrany et al., 2015). Besides, all the factors may not be accommodating into a particular model; in addition, all the factors may not contribute to FS models. So, the selection of effective FS factors following proper and scientific method is one of the vital and primary works in this regard. In this study, on the basis of previous studies, suitable FS factors were taken into consideration. FS mapping of the study has been done applying selected models. Model verification was done using AUC, and it has been found that LR performed best compared to FL, FR and MCDA. Consequently, this study found that FS applying the LR model is more dependable compared to other MCDA methods (FL, FR and MCDA). This is quite evident that LR outperforms the other MCDA method (Fig. 5) as LR can analyze the multiple factors of an event in a statistically sound way, whereas MCDA only considered the weights given by human who is supposed to be always associated with some biases (Guitouni & Martel, 1998; Roy & Vanderpooten, 1996; Thokala et al., 2016). Besides this, MCDA is hugely depended on the accessibility of the data (Guitouni & Martel, 1998; Thokala et al., 2016). The study by (Chakraborty & Mukhopadhyay, 2019) in the Coochbehar district of West Bengal (Kanani-Sadat et al., 2019) in the Kurdistan Province of Iran and (Souissi et al., 2019) in the arid areas of southeast Tunisia found that MCDA model is very successful with an AUC value of 89.64%, 91.8% and 74.51%, respectively, whereas this study found that the accuracy level of the MCDA model was 86.9%. (Nandalal & Ratnayake, 2011) studied on the forest and agriculture dominated Kalu-Ganga catchment of Sri Lanka, stated that FL is more suitable with very good accuracy. But the findings of (Tehrany & Kumar, 2018) stated that LR performed better than the statistical models. Besides, LR was able to forecast FS 79.45% accurately. Similarly, studies by (Nandi et al., 2016) and (Pham et al., 2020) depict that LR was greatly fruitful to forecast FS effectively 78.9% and 76% correspondingly. It was observed that elevation, plane curvature, older alluvium (Sijua formation) and recent alluvium (Chinsura formation) were very much dominating in the prediction of FS and its coefficients are as follows 19.078, 18.547, 15.952and 16.174, respectively, whereas SPI (− 0.443), aspect (− 0.001), rainfall (− 0.01) are the minimum effective for FS. So, the rainfall coefficient is very low, because the rainfall over the FS is not effectively responsible, but rainfall in the middle and upper part is the key reason for the occurrences of floods in this area.

Water-related information is very crucial to manage the water resource (Mohammadi et al., 2020; Mohammadi, Guan, et al., 2020; Mohammadi, Linh, et al., 2020). Several measures were proposed below in this section, which can be considered in flood management. For example, numerous anthropogenic activities alter the channel morphology of the river and are narrowing the channel capacities mostly after the independence (Malik & Pal, 2020b, 2020c, 2020d). It was observed that the alignment of the embankment is extremely close to the active channel (Malik & Pal, 2020c). Numerous palaeo-channels have been found in the lower part of the Dwarkeswar River as well. So, these palaeo-channels should be renovated to provide an extra channel to pass the excessive flow in the main channel as well as to provide an additional water holding capacity to the floodplain. As well as, human encroachment in the form of should be restricted particularly near the river and appropriate assessment should be done before building any type of engineering construction on the river. Along with this, the study area is only associated with three river gauge height recording stations, and thus, it is very essential to increase the number of river flow monitoring stations equipped with modern instruments. The future prediction of flood inundation area and duration can be estimated through real-time monitoring. This will also help in taking required actions before the flood, during the flood and after the flood to manage the entire flood situation more effectively. Based on the flood frequency analysis (Malik & Pal, 2021) and FS map, LULC of the study area can be planned to reduce the flood effects. For example, an area with very high flood risk should be devoid of permanent settlements, and therefore, rehabilitation of the people from the high-risk zone to the comparatively low-risk zone can be done. Besides this, the structure of the house should be made keeping the view of historical flood height records in mind. Digging of new ponds and small water tank and their renovations should be implemented all over the river basin to reduce the flash flow of the river (Malik & Pal, 2020a). Besides, afforestation of bare surface with aboriginal plant species may also be proved to be an important way to reduce the lag time (Malik & Pal, 2020a). Apart from this, the crops, animal and human lives should be secured by different insurance policies which can help them to survive after any natural hazard. In this case, the local administrative bodies can play a very crucial role by enlisting all the needy people.

The outcome of the current work will be very beneficial to assess the FS, and thus, it will provide the basic needs of the policymakers and planners to identify, manage and reduce the impact of the flood with effective strategies in the DRB. However, it may also be applicable to the similar part of the Bengal Basin and other areas of the world. It will also help the investigators to select appropriate methods to analyze the FS of any area. Besides this, it may also be helpful for several Government Organizations, NGOs and academicians. Lack of spatiotemporal variation of flooded and rainfall data was the major limitation of the study. Another limitation of this study is that the FS map is only able to show the spatial extension of the flood rather than a spatial variation of flood depth and its velocity. So, a future study on the flood depth and its velocity in combination with various established hydrological models can be done.

6 Conclusion

In this study, MCDA and LR such as FL, APH and FR methods have been applied to assess the FS mapping of the Dhalkishore or Dwarkeswar River. Sixteen topographic and flood causative factors have been selected based on the FI datasets from earlier research works, and spatial databases were generated in the GIS environment to build the models. Multi-collinearity test has been used, and less than 5 VIF value has been considered as a threshold limit to avoid the multi-collinearity issue. The collected flood inventory data points were classified into two sets. Seventy percentage of the data were used as a model data input, and the remaining thirty percentage of the data were used for validation purposes using AUC. The MCDA model shows that 12.37%, 18.92%, 22.99%, 22.28% and 23.44% area of the basin is under very low, low, moderate, high and very high FS correspondingly. The FL model indicates that 17.29%, 23.02%, 20.25%, 19.90% and 19.54% area of the basin is under the very high, high, moderate, low and very low category of FS. Also, the FR model represents 24.16%, 21.55%, 22.99%, 24.27% and 7.02% very high, high, moderate, low and very low FS. On the other hand, LR predicts that 30.89%, 20.59%, 16.80%, 16.69% and 15.02% area of the basin is susceptible to very low, low, moderate, high and very high flood probability. According to the AUC test results, the AUC values of the selected models such as FL, MCDA, FR and LR are 0.893, 0.857, 0.835 and 0.916, respectively. So, the LR is more reliable compared to the MCDA, FL and FR in FS analysis. FS map using LR shows that 15.02% and 16.69% areas of the river basin are under the very high and high susceptible zones, respectively, which are mainly placed at the lower portion of the basin characterized by flat alluvial surface. According to the LR model, the elevation is the most dominating flood-controlling factors. Besides, the TWI, plane curvature, water body and geology were playing a dominating role in the prediction of FS map with coefficient value of greater than 15. So, this map can help the policymakers to prepare sound planning to reduce flood damages and human deaths in future in this area as well as the rest of the world. Major limitations of this study are the lack of all historical flood records, limited non-flood points and flood point’s data were used along with this all the models were not able to predict the FS 100% as the nature is very dynamic.