ABSTRACT

The number of natural disasters is increasing in different parts of the world due to the eccentricity of the weather. These natural disasters have made the daily lives of people very miserable. Flood organization in floodplain regions is much higher than in other natural disasters, and due to a lack of proper flood control plans and identification of appropriate flood areas, local people are easily exposed to flood disasters. In India, various parts of the Bhagirathi-Hooghly River basin are prone to heavy rains and loss of carrying capacity due to overflowing of the riverbanks, causing severe floods, which increase the amount of social, financial and socio-economic damage to the people. Due to the need for a specific flood control and planning system, the region experiences flood every year. Through this article and identification of the flood-susceptible regions of the Bhagirathi basin, flood-vulnerable and risk areas have also been identified separately for disaster assessment and flood protection measures. Based on 12 flood inventory conditioning parameters, a susceptibility analysis is performed through bivariate, multivariate, and machine learning models. Parametric vulnerability indices develop by susceptibility, exposure, and resilience on a block-wise small scale to assess socio-economic damage due to floods. Based on that, the spatial distribution of flood risk has been developed by amalgamating the pixel-based flood susceptibility obtained by raster normalization and the flood vulnerability generated by the block-based spatial distribution using the ArcGIS interface. The results obtained from these observations will help policymakers develop holistic, sustainable development through flood prevention and control plans by considering the local environment and climate at the micro-scale of the block level.

1 INTRODUCTION

Floods are also known as standard and terrible natural disasters among various natural disasters like earthquakes, landslides, tsunamis, droughts, riverbank erosion, and volcanic eruptions (Das 2019, 2020; Termeh et al. 2018). About one-third of the total natural disasters are affected by floods, and severe floods occur in almost all countries of the world, especially in riverine plains (Das 2020; Adhikari et al. 2010). The financial, social, and socio-economic aspects of local people are severely affected by flood, as well as loss of properties and lives, which is very common (Parsian et al. 2021; Mehravar et al. 2023). In floodplain areas, due to the presence of necessary living facilities, the population has increased, which in turn has increased the severity of floods through encroachment on the natural flow of rivers, changes in land use, and the destruction of natural habitats along the riverbanks. Also, due to a reduction in the river's carrying capacity because of sedimentation and excessive rainfall during the monsoon because of climate change, the natural water level of the river rises, and floods the banks of the river (Wang et al. 2021; Sinha and Ghosh 2012; Avand and Moradi 2021). According to statistics, 75% of the total floods in the world are deadly flash floods, and the rest are riverine and coastal floods (Malik et al. 2020). According to the WHO, from 1998 to 2017, more than 2 billion people were affected by floods, with about 82% of people living in floodplains losing their lives and causing financial losses of about US$96 billion (Alfieri et al. 2017; Khosravi et al. 2019). An increase in population density and urban structure in the floodplain, uncontrolled and unscientific construction along the riverbanks, increase in urban encroachment and urbanization, decrease in natural navigability of the river, and uncontrolled rainfall make the flood situation chronic and complicated (https://www.who.int/health-topics/floods#tab=tab_1). According to the Aqueduct Global Flood Analyzer, an average of 21 million people worldwide are affected by floods every year. This number will reach 54 million in 2030 due to economic and social development and continued climate change (https://www.wri.org/data/aqueduct-global-flood-analyzer).

Also, according to this organization, the current and future GDPs of these countries are being affected by floods (Botzen et al. 2019). Of the 164 flood-prone countries worldwide, 15 countries account for 80% of the population directly affected by floods, and among these countries in Southeast Asia are Bangladesh, India (with an average of 4.8 million affected people per year and $14.3 billion in total GDP loss) and China's position is at the top (Svetlana et al. 2015; Taguchi et al. 2022; Zhang et al. 2022). In India's Ganga-Brahmaputra floodplain region (West Bengal, Assam, and Bihar), the amount of flood disasters is very high due to excessive population density, uncontrolled and unscientific construction along the banks of the river, urban encroachment, and gradual decrease in navigability of the river (Mohapatra and Singh 2003; Ramachandran et al. 2019; Thattai et al. 2017). Coastal and riverine floods in Kerala (Vijaykumar et al. 2021), Andhra Pradesh (Kantamaneni et al. 2019), Orissa (Hazra 2022), Gujarat (Waghwala and Agnihotri 2019), Maharashtra (Pathak et al. 2020) and flash floods in Himalayan foothills along the Terai-Duars region (Prokop et al. 2020), Uttarakhand (Dash and Punia 2019), and Himachal Pradesh (Bisht et al. 2018) have been observed in India on a seasonal basis, https://ffs.india-water.gov.in/. According to the Indian Policy Commission 2021–2026, 49,815 Mha of India's total land area is flood-prone, and an average of 7.17 Mha area has flooded every year (of which 3.94 Mha area is considered agriculture) (Baky et al. 2020; Dandapat and Panda 2017). Notable and severe flood-prone floods in India include Mumbai (2005), Gujarat (2015, 2017), Uttarakhand (2013, 2021), Assam (2016, 2020, 2022), Kerala (2018), and West Bengal (2000, 2015, 2017).

Uncontrolled rainfall due to climate change is responsible for floods, but urban construction and encroachment due to population along the riverbanks dramatically increase the severity of floods (Rahman et al. 2019; Vignesh et al. 2021). Policymakers and strategists have adopted vital flood risk management measures to prevent the socioeconomic losses of people due to floods (Naulin et al. 2013). The main tasks of this plan are to identify flood-prone areas within a particular catchment, build models for specific mitigation strategies, map flood-prone and vulnerable regions, and assess future flood risk (Dottori et al. 2018; Chan et al. 2022). Therefore, the current study of floods has shifted from ancient flood protection to flood risk management, mainly divided into flood risk assessment and mitigation. The main objective of flood risk assessment is to identify areas prone to flooding. Flood susceptibility mapping is widely used for flood management, planning, and risk assessment (Mishra and Sinha 2020; Motevalli and Vafakhah 2016). This mapping, based on spatial and temporal data, helps the local administration and government identify any region's flood potential with predictable locations. Three flood measurement methods are used to assess the flood situation (Bentivoglio et al. 2022): susceptibility, inundation, and hazard. Susceptibility is measured based on the MCDA method (Akay 2021), inundation is based on remote sensing (Lin et al. 2016), and hazard calculation is based on the numerical method (Dottori et al. 2021). Sometimes there is scouring for bridges over the river, and the resulting sediments are deposited in the river channel as sandbars, reducing the carrying capacity of the river. In this situation, the possibility of flooding during monsoons becomes very high (Pandey et al. 2021; Guguloth et al. 2024).

Geographical Information Systems (GIS) and Remote Sensing (RS) methods make it easy to determine flood susceptibility areas (Vojtek et al. 2021). Flood susceptibility is determined based on the relative probability of flood, depending on the extent and duration of the previous flood. As the amount of flood organization is much higher in the plains and floodplain areas, methods and statistics on flood vulnerability, risk analysis, and mapping are essential to analyze the flood susceptible character of those areas (Wang et al. 2021).

The multi-criteria decision analysis-based AHP model is popular for determining flood susceptibility mapping as a multi-criteria decision analysis model (Hammami et al. 2019; Souissi et al. 2020). The most common statistical models can be divided into multivariate and bivariate statistics based on reliable results. The bivariate statistical approach assesses the correlation between flood control parameters and past flood organizations, like Frequency Ratio (FR) (Ghosh et al. 2022), Information Value (IV) (Moazzam et al. 2020), Certainly Factor (CF) (Cao et al. 2020), Weights of Evidence (WOE) (Shafapour Tehrany et al. 2017), and Shannon Entropy (SE) (Wubalem et al. 2021; Aronica et al. 2002). The multivariate statistical approach assesses the correlation between independent and dependent variables important to flood organization (Das 2019). Logistic Regression (LR) and Discriminant Analysis (Choubin et al. 2019), used for flood susceptibility modeling, are notable examples of multivariate statistical approaches that help to reveal flood susceptibility through reliable results.

Hydraulic engineering centre-river analysis system (HEC-RAS) (Namara et al. 2022) and soil water assessment tool (SWAT) (Boithias et al. 2017) models are also used as hydrological models for determining flood vulnerability and risk based on rainfall-runoff system. Researchers and scientists are currently developing different models based on machine learning (ML) to overcome the multiple limitations of the above models. As a branch of artificial intelligence, the ML method enhances the performance of any model, and much of the data within that model can be easily analyzed in one place (Mosavi et al. 2018). Currently, the combined nature of the ML algorithm with GIS in determining flood susceptibility makes it easier to quickly and accurately analyze the nature of inundation in large basins. ML-based models can accurately measure the nature and severity of other natural disasters, including flood susceptibility (Bui et al. 2020; Rahman et al. 2019; Samantaray et al. 2021). Popular ML models for determining flood susceptibility in an area are Artificial Neural Network (ANN) (Pham et al. 2020), Adaptive Neuro-fuzzy Inference System (ANFIS), Decision Tree (DT) (Khosravi et al. 2018), Support Vector Machine (SVM) (Costache et al. 2021) Random Forest (RF) (Chen et al. 2021), and Extreme Gradient Boosting (XGBoost) (Ni et al. 2020; Arabameri et al. 2019). These methods provide an accurate idea of the future flooding of a region. However, with remote sensing and GIS development, flood susceptibility is determined by generating large-scale hydrological data and time series of a large area. Determining flood susceptibility is done using GEE, eliminating the mathematical complexity through processing large amounts of data (Mehravar et al. 2021).

Although naturally occurring, floods cause more social and socio-economic damage to people and become a significant obstacle in a country's financial GDP, and other social and political areas. At present, the amount of flooding is continuously increasing in different countries of the world due to global warming (Deroliya et al. 2022). Advanced statistical methods are needed to assist in flood risk management for measuring various aspects of social and socio-economic losses. For that reason, the flood vulnerability index (FVI) is widely used as an indicator-based decision-making system, biased from different statistical methods (Balica et al. 2009; Balica and Wright 2010). The FVI index is used by many policymakers for decision-making in flood risk management and assessing the collateral effects of floods in both parametric and non-parametric ways. Due to many factors, the FVI index provides a pattern of different levels of flood vulnerability in a region (Mavhura et al. 2017; Nasiri et al. 2019). The FVI index informs the public and policymakers about climate vagaries so that they can implement any necessary adaptation measures and strengthen the resilience of flood-prone communities. The FVI index helps to identify specific elements of flood organization in a region, which decision-makers can use to determine the extent of potential damage and act in long-term flood management. The FVI index mainly depends on indicators like exposure, susceptibility, and resilience (De Bruijn 2004; Barroca et al. 2006). There is no alternative to the FVI index in flood-prone areas for taking early warning and identifying the exact location through spatial distribution mapping. Flood susceptibility mapping identifies spatial prohibition of flood-prone places, but the vulnerability is measured through FVI distribution mapping and vice versa, which helps to validate flood susceptibility mapping (Sullivan and Meigh 2005; Penning-Rowsell et al 2005; Smith 2013).

The Indo-Gangetic floodplain region of India is recognized as the most flood-prone, and 60% of India's total river flow is in this region. At present, floods are organized due to the vagaries of the summer monsoon and result in social and socio-economic damage through heavy loss of human life, property, livestock, and agriculture. As a significant downstream tributary of the Ganga, the floodplains carried by the Bhagirathi River in southern West Bengal play a substantial role in developing agriculture and industry, and in the socio-economic development of the people of West Bengal (Rudra 2010; Rudra 2014; Bhattacharjee and Behera 2018; Das et al. 2022). The flood plains are densely populated, with all the amenities of life. By observing the floods over the last few decades, it is seen that 40% to 75% of the area has been flooded, and due to this flood, about 20 lakh people have suffered financially and socially. As the carrying capacity of the Bhagirathi River continues to decrease with increasing urban encroachment due to overcrowding, the region is prone to flood disasters (Mohanty et al. 2020; Mainuddin and Kirby 2021). Therefore, as a part of flood control management, there is a need for accurate flood susceptibility mapping to identify flood-prone areas and flood vulnerability assessment is needed for precise analysis of socio-economic disasters.

Since the Bhagirathi River is the main river of West Bengal, our primary goal in this article is to create an accurate and precise flood susceptibility map of the Bhagirathi basin by reviewing different bivariate, multivariate, and machine learning algorithms (Mainuddin and Kirby 2021; Islam et al. 2022) Also, identifying the flood-prone areas through this susceptibility mapping and highlighting the flood risk areas through the accurate assessment of socio-economic vulnerability and disaster will help the common people and policymakers formulate the correct policies required for flood risk management.

2 MATERIALS AND METHODS

2.1 Study area

The Bhagirathi River flows through West Bengal, India, and is a major tributary of the Ganges. It is separated from the Ganges near the Mithipur block of Murshidabad district (24°29'4.13"N/ 88°3'47.54"E) and flows towards the confluence with the Rupnarayan River near Gadiara, Howrah (22°13'10.64"N/ 88°2'56.52"E), encompassing Kolkata (Ghosh and Sarkar 2020). Tributaries like the Ajay and Mayurakhhi from the Chhotanagpur Plateau have accumulated much sediment and deposited it in the Bhagirathi River. Also, the lack of scientific dredging and continuous urban encroachment has dramatically reduced the river's navigability. Geologically, this area is in the Rarh region, the lower part of the moribund deltaic part of the Bengal basin. It is composed of recent deposits of the Pleistocene period (Ghosh and Kar 2018; Paul et al. 2019). Initially, the area is covered with sandy clay and sand along the river's course. Fine silt, sandy loam, and loamy soil have been found in the flat portion of the plain (Figure 1). Although the Bhagirathi River is the main river in this basin, the river's course bifurcates by tributaries, such as the Bansloi, Mayurakkhi, Babla, Ajay, Khari, and Kunti from the west, and the Jalangi and Churni rivers from the east. In Tribeni, the river has branched into the decaying Saraswati River over the past few years. The total catchment area, including the main river and tributaries, is 7,076 km².

Figure 1 Location map of study area.

The hydrodynamic condition here differs significantly from other regions, as the whole study area belongs to floodplain morphology. Lateral bank line movement is observed through the meandering river flow, resulting in a riverbank erosion problem. In addition to meandering, floodplain features like wetlands, ox-bow lakes, and shoal formations (Sanyal and Lu 2005, 2006; Chakraborty and Mukhopadhyay 2019) also continuously change the hydrodynamic behaviour of the river. Due to the shallow slope of the area (maximum 2° to 4°), rainwater very quickly falls into the river as runoff after rainfall. Due to the tropical monsoon climate, the region has 110 to 124 rainy days per year, and the average annual rainfall is between 1,400 and 1,800 mm.

This portion of southern West Bengal consists of 9 districts, 75 blocks, and several mouzas. Some of these blocks are prone to river erosion, and some areas are prone to floods. Due to some areas’ embankments, the height is higher than the natural plain. However, the water accumulates during the monsoon in the low-lying areas next to the embankment, opposite the river. Most of the blocks on the riverbanks are prone to floods, but only if submergence is some distance away. Since the outlet of the Bhagirathi basin compresses like a funnel enclosing the urban area at the bottom, the runoff causes problems by accumulating sediment in the middle of the river as sandbars (Mukherjee et al. 2009; Bandyopadhyay et al. 2014; Bandyopadhyay et al. 2016; Sutradhar and Mondal 2023). As a result, a reduction of navigability, and heavy rains in the upstream region increase the water level, resulting in floods. Although the Bhagirathi River originates as a tributary of the Ganges, its water flow depends on the Farakka Barrage and the Indo-Bangladesh Water Treaty, reducing its flow of water day by day. The unscientific construction of jetties and rampant sand mining from the riverbed increases the possibility of flood vulnerability in this region.

2.2 Flood Inventory Map

The Bhagirathi basin has experienced terrible floods. In 2000, 2003, 2004, 2005, 2006, 2011, 2013, 2016, and 2020, the region was severely damaged by floods. Past flood events are a significant indicator of flood susceptibility development. If the watershed's climatic, geomorphological, and hydrological conditions remain the same in the future, then the possibility of an equal consequence will be highlighted through the Flood Inventory Map. A Flood Inventory Map has been derived from the Flood Extent Map using GEE, as well as a different flood layer acquired from the Bhuban website (Figure 2). The flood pixels were assigned a value of 1, and non-flood pixels were assigned as 0. The value of flood determining factors was extracted from these pixels and analyzed by R Statistical Software (3.2.3). This study used the Google Earth engine to indicate 346 flood points and 150 non-flood points. These points were divided into a 70:30 ratio as training and testing points for model studies in flood hazard susceptibility mapping. 

Figure 2 Flood inventory map of Bhagirathi-Hooghly basin.

2.3 Flood susceptibility factor

Based on several pieces of literature on flood susceptibility and the availability of data in this region, the study included 12 factors (Table 1) which affect soil erosion (Tehrany et al. 2018; Mind'je et al. 2019).

Table 1 Description of flood affecting factors.

Parameter	Variable type	Source	GIS type	Resolution
Elevation	independent	https://earthexplorer.usgs.gov/	grid	30×30
Slope	independent	Derived from DEM using ARC Toolbox	grid	30×30
Drainage density	independent	https://www.hydrosheds.org/products/hydrorivers Drainage Density has been made using the river data in ArcGIS interface through using and line density tool	grid	30×30
Distance from river	independent	https://www.hydrosheds.org/products/hydrorivers Distance from river has been made using the river data in ArcGIS interface through using Euclidian Distance	grid	30×30
TWI	independent	Derived from DEM using following formula:	grid	30×30
Curvature	independent	Derived from DEM	grid	30x30
NDWI	independent	Derived from satellite image using following formula (Landsat 8):	grid	30×30
Roughness	independent	Derived from DEM using following formula	grid	30×30
Rainfall	independent	https://www.pypi.org/project/imdlib/ Average annual rainfall for 35 years from 1985 to 2020	grid	30×30
NDVI	independent	Derived from satellite image using following formula (Landsat 8):	grid	30×30
SOIL	independent	https://www.fao.org/soils-portal/data-hub/soil-maps-and-databases/faounesco-soil-map-of-the-world/en/	vector	30×30
LULC	independent	Derived from Sentinel-2B, processed in ArcGIS with supervised classification.	grid	10x10

Elevation

Elevation is one of the factors in determining flood susceptibility. Elevation refers to the range of the highest and lowest points of a particular region. Elevation affects the geological features and vegetation characteristics of that area (Shahabi et al. 2020). Elevation plays a significant role in determining the direction of overflow of a place, transportability, and the depth of the flood (Botzen et al. 2013; Chowdhuri et al. 2020). The elevation range in the region is 1–93 m (Figure 3a).

Figure 3(a-l) Flood susceptibility factors and their spatial distribution in the Bhagirathi basin.

Slope

Slope is an important factor in the study of flood hazards. Surface runoff, infiltration processes, and other hydrological activities are specifically determined by the slope of the region (Youssef et al. 2011). The slope of an area is determined by the elevation contour. Surface runoff is very high in areas with steep slopes, and vertical percolation is low, which multiplies the flood wave velocity by increasing the rate of soil erosion (Chen et al. 2015). In this area, the slope is determined by the degree and the slope range between 3.82°–44.54° (Figure 3b). However, in about 75% of the land, the slope is less than 5°.

TWI

Surface water and runoff depend on a region's topography wetness index (TWI) value (Figure 3e). TWI generally determines the topography control over a region's hydrological processes. When the TWI value is low (Naito and Cairns 2011), the surface runoff increases with the probability of flooding. The value of TWI varies between 3.52–24.47 (Figure 3c).

Curvature

Curvature describes the nature and allocation of the land surface. The nature of the runoff over the land and the soil's water-holding capacity is determined through its curvature. The probability of flooding in a region is inversely proportional to the curvature of that region. Therefore, the flatter the area, the greater the chance of flooding. About 85% of the Bhagirathi basin is flat land, so there is a high chance of flooding (Figure 3d).

Roughness

Roughness is one of the essential parameters in flood hazard mapping (Figure 3g). A smooth surface leads to a more rapidly rising flood wave, while peak discharge can be significantly lower on rough surfaces. Since the study area is in a floodplain region, the roughness is much less, ranging from 0.11–0.88 (Figure 3e).

Soil

Different soils differ in nature, composition, characteristics, infiltration capacity, and as a result water holding capacity varies. The amount of surface runoff is determined by the amount of water that will percolate over the water holding capacity of the soil. When the infiltration rate is low, the surface runoff increases, which increases the chances of flooding (Figure 3f). If the rainfall is more than the percolation rate in an area, excess water flows through the downslope of the region and causes flooding.

LULC

LULC affects a region's runoff, evaporation, and evapotranspiration. The type and nature of land use in a particular area determines the flow dynamics of water and the effective management of water resources (Bai et al. 2015) (Figure 3g). Changes in the LULC over time play a crucial role in determining flood events. Floods are inversely proportional to the areas covered by vegetation, but in fallow lands, impervious areas have increased surface runoff and flooding due to reduced water absorption. As land in the rural sector is mostly flat land, the region is easily susceptible to flooding (Mahmoud and Gan 2018).

Average rainfall

The average yearly rainfall in this region is about 1,500 mm (Figure 3h). In most areas, excessive rainfall is one of the causes of floods. If there is more than normal rainfall in an area, the infiltration capacity of the soil decreases after the excess water flows through the runoff. As a result, the river is unable to carry that excess water, causing flooding. This study measured the average annual rainfall for 35 years from 1985 to 2020.

Distance from river

The distance from the river is essential in calculating regional flood susceptibility. It is measured by the ring of radial buffer at intervals of 500 m from the river up to 3,946 m. The river's proximity multiplies the risk of flooding in an area (Figure 3i). The area near the river is much more vulnerable than distant areas (Choubin et al. 2019).

Drainage density

Drainage density is an essential physical parameter in a drainage basin. It refers to a ratio between the total length of the channel in a particular basin area and the basin area. Drainage density is decisive in determining flood occurrence (Srivastava and Bhattacharya 2006). Severe flood-prone areas are mostly connected to a higher percentage of drainage density. Though the study area lies in the floodplain region, the drainage density is greater, ranging from 1.12–9.02 km/km² (Figure 3j).

NDWI

Waterlogging areas of the river are quickly identified from satellite images through NDWI (Otsu 1975; Xu 2006). In ArcGIS 10.4.1, a different shape file generates consisting of the riverbank lines from each image through polyline in another year, separating the floodplain area from the riverbed (Figure 3k).

NDVI

NDVI is a dimensionless index that assesses the vegetation cover in a catchment area and the impact of flood events on the vegetation (Shrestha et al. 2013; Powell et al. 2014) (Figure 3l). NDVI values range from -1 to 1. There is a reciprocal relationship between the value of NDVI with a flood. The higher the NDVI, the lower the risk of flooding and vice versa. The NDVI rate is calculated by a raster calculator in ArcGIS. In this study, the NDVI value varied between -0.25 to 0.51, evaluating minor vegetation-prone areas as flood-affected.

3 METHODOLOGY

3.1 Flood susceptibility analysis

At first, we performed a multi-collinearity test using an SPSS statistical package to comprehend the relationship among the conditioning variables. When independent variables in a regression model correlate, multicollinearity develops. It is challenging to fit the model and comprehend the results when the correlation between the variables is too strong. All components are tested for multicollinearity using the tolerance (TOL) and variance inflation factor (VIF). VIF and TOL coefficients must be less than 10.0 and 0.01, respectively. It was noticed that no multi-collinearity issues are associated between the 14 variables; therefore, all 14 conditioning factors were used as an input for FSM. The flood susceptibility map generated from several bivariate models such as FR, LR, and ensemble machine learning techniques such as KNN, XGM, and SVM, which are divided into five classes of probability from very low (0) to very high (1) classes. Classification techniques like natural break, equal interval, quantile, standard deviation, etc., are available for reclassification of the flood susceptibility model in ArcGIS. The equal interval technique places each value of every class at equal spacing. Its main disadvantage is that it cannot carry all the pixels. The various literature of flood susceptibility studies shows that the quantile and natural break method is used in most places. Quantile is a popular technique that provides much better performance.

Multivariate susceptibility analysis with LR

The LR method estimates the regression basis flood susceptibility (Hosmer et al. 2013). It is the equivalent of multilinear regression, and it is considered the best-fitted model for assessing the correlation between independent and dependent variables in flood hazard mapping (Shafapour Tehrany et al. 2017; Das and Lepcha 2019). It depicts the possibility of flood events over the occurrence. This model analyzed the probability of flooding by considering independent and dependent variables. This variable can be continuous and discrete. In this case, the presence and absence of flood potential is expressed through binary digits. The analysis of flood susceptibility by LR is valid only if the dependent variable is binary (Fustos et al. 2017). 0% refers to the probability of non-flood, and 100% means the high chances of flood occurrence.

(1)

Where:

P

=

probability of flood occurrence ranging from 0 to 1.

(2)

Where:

X1…Xn	=	each flood influencing factor,
n	=	total no. of input factors, and
Bi	=	coefficient estimate from sample data.

This study used R Studio software to perform a logistic regression analysis. LR results show that drainage density, distance from the river, elevation, slope, and TWI are important factors in flood susceptibility modeling as their significant value is less than 0.5. Other factors are statistically insignificant in the case of model building as their value is more than 0.5.

Bivariate susceptibility analysis with FR

FR is a popular, well-accepted, quantitative flood hazard inventory mapping methodology. Several studies have used the FR technique to map flood susceptibility (Tehrany et al. 2014; Samanta et al. 2018; Rahmati et al. 2016). Estimating past flood records is necessary to predict future flooding in a region. FR is a bivariate statistical method that builds a quantitative correlation between the frequency of flooding and the factors influencing the flood.

(3)

FSI refers to the flood susceptibility index, and FR assigns the frequency rank of each conditioning factor. FR refers to the ratio of flood-prone areas to the whole study area. It refers to the probability of flood and non-flood zone subject to a given attribute (Lee and Talib 2005).

(4)

Where:

E	=	flood event of each factor,
F	=	total no. of flood events,
M	=	number of pixels of each class of any aspect, and
L	=	actual number of pixels of the study area.

The value of FR refers to the correlation between the occurrence of a flood and the conditioning factors influencing it. The FR method examines the role of subdivisions of each flood-forming element, comparing the proportion of the amount of flood organization with the specific area of a region. The FR model is developed by examining the contribution to flood organization according to the subdivision of each flood organizing component (Table 2).

Table 2 Calculation of Frequency Ratio.

Parameter	Class	Range	Flood Point (FP)	% of FP	Area (pixels)	% of area	FR	Nornalized Frequency Ratio (FRn)
Elevation	1	0 – 11	184	53.179	1,731,889	22.353	2.3791	1
	2	18 – 11	118	34.104	2,477,767	31.979	1.0664	0.4483
	3	18 – 29	20	5.78	1,269,987	16.391	0.3527	0.1482
	4	29 – 41	20	5.78	1,180,023	15.23	0.3795	0.1595
	5	41 – 93	4	1.156	1,088,393	14.047	0.0823	0.0346
			346		7,748,059
Slope	1	0 – 1.05	232	67.052	3,500,040	45.173	1.4843	1
	2	1.06 – 2.79	80	23.121	2,611,460	33.705	0.686	0.4622
	3	2.8 – 5.24	25	7.225	1,195,709	15.432	0.4682	0.3154
	4	5.25 – 9.61	9	2.601	384,511	4.963	0.5241	0.3531
	5	9.62 – 44.54	0	0	56,339	0.727	0	0
			346		7,748,059
Curvature	1	Concave	47	13.584	1,332,961	17.204	0.7896	0.6727
	2	Plain	266	76.879	5,074,746	65.497	1.1738	1
	3	Convex	33	9.538	1,340,351	17.299	0.5513	0.4697
			346		7,748,058
Roughness	1	0.11 – 0.24	228	65.896	2,240,234	29.013	2.2713	1
	2	0.25 – 0.36	51	14.74	1,872,029	24.244	0.608	0.2677
	3	0.37 – 0.46	33	9.538	1,703,443	22.061	0.4323	0.1903
	4	0.47 – 0.58	20	5.78	1,408,672	18.243	0.3168	0.1395
	5	0.59 – 0.89	14	4.046	497,222	6.439	0.6284	0.2767
			346		7,721,600
TWI	1	3.52 – 7.46	77	22.254	2,932,058	37.842	0.5881	0.2943
	2	7.47 – 9.68	65	18.786	1,927,777	24.881	0.755	0.3779
	3	9.69 – 12.06	79	22.832	1,479,972	19.101	1.1953	0.5982
	4	12.07 – 14.94	103	29.769	1,154,371	14.899	1.9981	1
	5	14.95 – 24.47	22	6.358	253,880	3.277	1.9405	0.9712
			346		7,748,058
DD	1	0.42 – 0.85	108	31.214	2,207,506	28.491	1.0956	0.9739
	2	0.86 – 1.84	124	35.838	2,468,300	31.857	1.125	1
	3	1.85 – 3	85	24.566	1,967,202	25.39	0.9676	0.8601
	4	3.01 – 4.63	20	5.78	854,340	11.027	0.5242	0.466
	5	4.64 – 9.01	9	2.601	250,710	3.236	0.8039	0.7146
			346		7,748,058
DR	1	0 – 500	116	33.526	2,105,315	27.172	1.2338	1
	2	500 – 1,000	98	28.324	2,048,637	26.441	1.0712	0.8682
	3	1,000 – 1,500	69	19.942	1,776,489	22.928	0.8698	0.7049
	4	1,500 – 3,000	47	13.584	1,297,282	16.743	0.8113	0.6575
	5	>3,000	16	4.624	520,335	6.716	0.6886	0.5581
			346		7,748,058
Rainfall	1	1,231.92 – 1,319.73	152	43.931	1,722,239	22.228	1.9764	1
	2	1,319.74 – 1,405.54	69	19.942	2,136,512	27.575	0.7232	0.3659
	3	1,405.55 – 1,513.3	22	6.358	1,417,008	18.289	0.3477	0.1759
	4	1,513.31 – 1,613.08	53	15.318	1,369,001	17.669	0.8669	0.4387
	5	1,613.09 – 1,740.79	50	14.451	1,103,298	14.24	1.0148	0.5135
			346		7,748,058
Soil	1	Jc50-2a	4	1.156	214	0.327	3.5314	1
	2	Lo49-2a	11	3.179	6167	9.434	0.337	0.0954
	3	Gc9-3a	40	11.561	6772	10.359	1.116	0.316
	4	Lo48-2a	137	39.595	12,948	19.807	1.999	0.5661
	5	Je71-2a	57	16.474	18,846	28.83	0.5714	0.1618
	6	Be80-2a	81	23.41	16,639	25.454	0.9197	0.2604
	7	Ge52-3a	16	4.624	3,784	5.789	0.7989	0.2262
			346		65,370
LULC	1	Waterbody	14	4.046	260,234	3.362	1.2035	1
	2	Vegetation	28	8.092	1,011,887	13.073	0.619	0.5144
	3	Agriculture	169	48.844	2,754,844	35.591	1.3724	1.1403
	4	Agriculture barren	72	20.809	2,338,185	30.208	0.6889	0.5724
	5	Build up	63	18.208	1,375,078	17.765	1.0249	0.8516
			346		7,740,228
NDVI	1	-0.26	8	2.312	232,500	2.965	0.7797	0.5996
	2	0.02 – 0.13	58	16.763	1,210,992	15.446	1.0853	0.8345
	3	0.14 – 0.2	85	24.566	2,424,512	30.924	0.7944	0.6109
	4	0.21 – 0.26	109	31.503	2,473,710	31.552	0.9985	0.7678
	5	0.27 – 0.51	86	24.855	1,498,512	19.113	1.3004	1
			346		7,840,226
NDWI	1	-0.5	16	4.624	887,534	11.32	0.4085	0.2935
	2	-0.05	65	18.786	1,412,383	18.015	1.0428	0.7493
	3	0.05 – 0.1	80	23.121	1,861,142	23.738	0.974	0.6998
	4	0.11 – 0.16	88	25.434	2,099,892	26.784	0.9496	0.6823
	5	0.17 – 0.41	97	28.035	1,579,276	20.143	1.3918	1
			346		7,840,227

Susceptibility analysis with SVM

SVM is a popular data mining machine learning method invented by Vapnik (2013) based on a set of linear indicator regressions applied for function determination. It is also known as the Maximum Margin Method, which provides higher performance and better results with limited data points (Tehrany et al. 2019; Meliho et al. 2022). The SVM model uses kernel mathematical functions for data transformation.

(5)

Where:

K (Xi Yi)	=	kernel function,
n	=	total number of training samples used in SVM model,
Xi	=	i-th training sample,
Yi	=	class label (+1 or -1 in binary classification) corresponding to the i-th training sample,
ai	=	weight or coefficient associated with the i-th training sample, and
b	=	bias (intercept) in the SVM decision function.

Hyperplane generates through the training dataset while converting from the actual SVM dataset to a high dimensional feature space. SVM returns 0 and 1 as the output; 0 means no flood, and 1 means maximum flood value.

Susceptibility analysis with RF

RF is a series of different and unique decision trees giving different results. RF is the integration of these decisions (Breiman 2001). RF provides better results than the decision tree (Rahman et al. 2019). If the RF is based on a decision tree, its influence will be overfitted to the data because it will be equivalent to a single DT.

(6)

Where:

I	=	the procedure and refers to the averaging value of all parameters,
H(X)	=	final predicted class label for input X produced by the RF,
avk	=	average over k trees in RF,
k	=	number of decision trees in RF, and
	=	sum of indicator functions counting how many trees predict class Y.

As the number of trees increases, the generalization of the error tends to converge. Thus, the RF model overcame the overfitting tendency (Pourghasemi and Kerle 2016). The RF model begins with an increase in decision trees, but the trees do not use all the original data. Instead of using bootstrap samples containing 66% of the original data, this is called the bagging technique. If the number of DT has increased, then the RF converges to:

(7)

Where:

PE	=	overall misclassification probability of RF,
Pxy	=	joint probability over input space X, and true labels Y,
avk	=	average across all k trees in the forest, and
J	=	all possible incorrect class labels in a classification problem.

This study developed a flood susceptibility map through the RF model using R software's Random Forest package that provides binary output, from which the flood probability illustrates each grid cell.

Susceptibility analysis with KNN

As part of non-parametric supervised ML, KNN is used in regression analysis and problem classifiers. KNN determines the distance from one point to another along a specific space and calibrates it smoothly (Mishra et al. 2022; Xu et al. 2023). The basic premise of KNN is that if two points are located at the exact geographic coordinates, they will be close to each other and have the same characteristics. Based on the spatial allocation, this algorithm can easily express the probability of flooding. The success of KNN is attributed towards Euclidian Distance measures in the present article (Kaur et al. 2021).

(8)

Where:

X (X1…n) and Y (Y1…n)

=

distance between two points in n dimension.

Susceptibility analysis with XGBoost (XGB)

XGB is a fast, efficient machine-learning approach invented by Friedman in 2001. It is a combination of many prediction models, especially DT. This model mainly applies to classifier and regression versions (Kaur et al. 2021; Pourghasemi et al. 2017). It provides an integer value when dealing with classifier problems and gives real value in regression. This method is preferred by data scientists (Chen and Guestrin 2016) for its fast performance.

(9)

Where:

k	=	number of decision trees, and
fk	=	prediction of decision trees (k = 1,2,3…. n).

Model performance validation

The Area Under Curve (AUC) is widely used to evaluate overall performance (Yilmaz 2010; Hong et al. 2016). It is plotted in 2-D, showing specificity on the X-axis and sensitivity on the Y-axis. Its value ranges from 0.5 to 1, which indicates low performance to high performance, respectively (Yesilnacar and Topal 2005; Roy et al. 2020).

(10)

Where:

SAUC	=	area under curve,
Xk	=	1-specificity, and
Sk	=	1-sensitivity of ROC.

3.2 Validating FSI with socio-economic vulnerability assessment

Flooding in a flood-prone area results in social and economic damage to people and is measured mainly by the FVI. As mentioned, we identified the flood-prone areas through the FSI method but measured the vulnerability through the FVI method (De Bruijn 2004). Data has been collected from a survey of an average of 80 households from each flood affected mouza. Short-term and long-term flood control planning examines the parametric FVI index developed through the mutual amalgamation of social, financial, environmental, and natural factors. However, these components of FVI thoroughly link to exposure, susceptibility, and resilience (Smith 2013; Rudra 2010; Rudra 2014). When people, animals, and resources are affected by floods, it is measured through exposure; when it is affected by social aspects, it is measured through susceptibility. Again, if the place where there was a flood in the past is continuously affected by the current flood, then the measure of damage and the future potential is highlighted through resilience (Balica and Wright 2010).

(11)

To extract information about the vulnerability components in order of importance, we perform psychometric monitoring through the UNESCO questionnaire (www.unesco-ihe-fvi.org) on 75 blocks on a scale from 5 (high) to 1 (low). Then the information obtained was expressed as spatial distribution through ArcGIS in choropleth, based on 20 factors from 4 components. In the case of the Bhagirathi River basin, FVI components are analyzed by exposure, susceptibility, and resilience factors. The spatial distribution of the FVI index is produced by Jenks's natural breaks algorithm in the ArcGIS interface.

Social component

Through the social component, the abilities, skills, knowledge, values, and beliefs of individuals, communities, and groups discuss with the help of a specific index and scale. Besides, the evaluation of social equality in health, housing, and education performs through this element. Human health, housing, education levels etc., belong to the social component (Balica et al. 2009; Balica and Wright 2010).

(12)

Where:

FVISOCIAL	=	Flood Vulnerability Index for the social component,
PFA	=	total population living in flood affected area,
CM	=	percentage of dependent population to total population,
PE	=	population with access to early warning systems,
AP	=	awareness and preparedness level,
WS	=	income level, and
ER	=	education ratio.

Economic component

Economic factors measure the financial loss and wealth of a flood-affected area. However, even if there is urban economic development in flood-prone areas along the riverbanks, the probability of flooding increases proportionally. High life expectancy, flood insurance, urban planning etc., belong to this element (Balica et al. 2009; Balica and Wright 2010).

(13)

Where:

FVIECONOMIC	=	Vulnerability Index for the economic component,
HDI	=	Human Development Index (measures overall socio-economic development: life expectancy, education, income),
Ineq	=	Gini coefficient depicting wealth disparity,
AmInv	=	annual investment in flood resilience (quantifies proactive spending on infrastructure (e.g., levees, drainage, reducing vulnerability), and
InsCov	=	flood insurance coverage (determines the percentage of households/businesses with insurance).

Environmental component

All the factors that evolved due to flooding and human-induced cause and affected the environment categorize under the environmental component of vulnerability assessment. Factors such as urbanization, industrialization, and human encroachment affect the ecology (Balica et al. 2009; Balica and Wright 2010).

(14)

Where:

FVIENVIRONMENT	=	Flood Vulnerability Index through the environment component,
Rainfall	=	Precipitation Intensity/Frequency (measures extreme rainfall events that directly trigger flooding),
DA	=	agricultural land use,
NR	=	natural retention capacity to assess ecosystems’ innate ability to mitigate floods (e.g., wetlands, mangroves),
EV	=	Ecosystem Vulnerability Index (evaluates ecological fragility, e.g., species diversity loss, soil degradation), and
LU	=	land use change rate to monitor urbanization.

Physical component

When various natural and artificial environmental elements affect flooding, they are part of the physical component. Physical components include elements such as topography, heavy rainfall, evaporation rate, flood return periods, proximity to rivers, river discharge, etc. (Balica et al. 2009; Balica and Wright 2010).

(15)

Where:

FVIPHYSICAL	=	Flood Vulnerability Index using the physical component,
T	=	Topographic Vulnerability Index which quantifies terrain susceptibility (e.g., low-lying areas, slope steepness),
DHR	=	Heavy Rainfall Duration/Frequency to measure extreme precipitation events,
RD	=	River Discharge Capacity to assess a river's ability to handle water volume,
FO	=	Flood Occurrence Frequency to track historical flood recurrence rates,
D_SC	=	Drainage System Efficiency Coefficient to evaluate artificial drainage infrastructure (e.g., canals, pumps).

Based on this exposure, susceptibility and flood resilience will be used to measure combined social, financial, environmental, and natural factors, which are considered to be vulnerability components. The entire FVI methodology depends on the mutual agreement of these two (Balica et al. 2009; Balica and Wright 2010).

(16)

4 RESULTS AND ANALYSIS

4.1 Results of Multicollinearity Test

This study tests the multicollinearity of 12 factors affecting flooding based on the quality of VIF and TOL (Equations 13 and 14). VIF values range from 1.028 to 2.681, categorized under the highest and lowest VIF associated with distance from the river and average rainfall, respectively. In the case of TOL, the range is between 0.373 and 0.973. The highest and lowest values of TOL are observed in the average rainfall and distance from the river (Table 3). No multicollinearity problem exists among the 12 factors mentioned above in demarcating the flood susceptibility zone. This study uses Pearson's correlation to assess the linear correlation of each pair of conditioning factors. The results show that the value does not exceed 0.7, which confirms that all the elements are free from multicollinearity, and there is no influencing factor among the 12 factors. If there is a high correlation value between any two factors, the analysis performs repetition by deleting one of the factors from the dataset (Figure 4).

Table 3 Multicollinearity on susceptibility indicator.

Susceptibility Parameter	Collinearity Test
	TOL	VIF
Elevation	0.854	1.301
Slope	0.786	1.272
Drainage density	0.383	2.612
Distance from river	0.373	2.681
TWI	0.717	1.396
NDWI	0.679	1.473
Roughness	0.964	1.038
Average rainfall	0.973	1.028
Curvature	0.754	1.32
NDVI	0.667	1.500
Soil	0.702	1.347
LULC	0.697	1.968

Figure 4 Pearson correlation coefficient for flood affecting factors.

Application of LR on flood susceptibility

The multivariate statistical LR model performed over the Bhagirathi basin and the middle, south-eastern, southern, and south-western portion has been found more susceptible to flood (Figure 5a). The upper part of the basin shows low-to-moderate susceptibility compared to the lower basin's high susceptibility section. Generally, flat alluvial plains and river proximity are the main reasons for increasing flood susceptibility. According to the LR model, the Sagardighi, Nabagram, and Berhampre blocks of the Murshidabad district, the Krishnanagar I and II, Ranaghat I, Santipur, and Nabadwip blocks of the Nadia district, the Balagarh block of the Hooghly district, the Amdanga, Habra II, and Barrackpore I blocks of North 24 Parganas, and the Amta 1 and Udaynarayanpur blocks of the Howrah district are the most susceptible to flood. The AUC value for the LR model is 0.816 (Figure 6).

Figure 5(a-f) Flood susceptibility mapping by using: (a) LR, (b) FR, (c) SVM, (d) RF, (e) KNN, and (f) XGB.

Figure 6 Susceptibility model validation with sensitivity and specificity by the AUC curve.

Application of FR on flood susceptibility

The FR model has applied the bivariate statistical analysis over this basin, and the middle, south-eastern, south-western, and north-western portions of the basin are more susceptible to flood. A few slices of the upper basin show lower to moderate susceptibility, and the rest, except the western portion, show higher susceptibility. Distance from the river, elevation, drainage density, and NDVI are the main factors responsible for increasing susceptibility by the FR model (Figure 5b). The Suti I and II, Sagardighi, Bhagabangola II, Kandi, Nabagram, Berhampre blocks of Murshidabad district; Purbasthali I and II, Kalna I blocks of the East Bardhhaman district; Naklashipara, Kaliganj, Krishnanagar I and II, Ranaghat I, Santipur, Nabadwip blocks of Nadia district; Balagarh, Chinsurah-Magra, Jangipara, Serampore-Uttarpara blocks of Hooghly district; Amdanga, Habra II, Barrackpore I blocks of North 24 Parganas; and the Amta 1 and Udaynarayanpur, blocks of Howrah district, are most susceptible to flood according to the FR model. The AUC value for the LR model is 0.913 (Figure 6).

Application of ML algorithm on flood susceptibility

SVM, RF, KNN, and XGB were applied over the Bhagirathi basin to prove flood susceptibility under a machine learning algorithm (Figure 5c-f). Each model differs from the others through susceptibility generation. The performance of the RF model appeared to be better than others (Table 4).

Table 4 Summary of blocks affected by flood obtained from SVM, RF, KNN, and XGB.

Model	Susceptible District	Susceptible Blocks	AUC Value
SVM	Murshidabad	Sagardighi, Beldanga I and II	0.819 (Figure 6)
	Nadia	Krishnanagar I and II, Ranaghat I and II, Nabadwip
	East Bardhhaman	Purbasthali I and II, Kalna I and II
	Hooghly	Chinsurah-magra, Jangipara, Serampore-Uttarpara
	North 24 parganas	Amdanga, Barrackpore I
	Howrah	Amta 1, Domjur, Sankrail, Panchla
RF	Murshidabad	Sagardighi, Nabagram, Kandi, Berhanpore, Bharatpur II	0.975 (Figure 6)
	Nadia	Kaliganj, Nakashipara, Krishnanagar I and II, Ranaghat I
	East Bardhhaman	Purbasthali I and II, Kalna I and II, Katwa II
	Hooghly	Balagarh, Chinsurah-magra, Jangipara, Serampore-Uttarpara
	North 24 parganas	Amdnaga, Habra II, Barrackpore I,
	Howrah	Udaynarayanpur, Amta I, Uluberiia I, Shyamnagar I
	South 24 parganas	Budge Budge II, Falta
KNN	Nadia	Kaliganj, Nabadwip, Krishnanagar I and II, Ranaghat I	0.942 (Figure 6)
	East Bardhhaman	Purbasthali I and II, Katwa II, Katwa I
	Hooghly	Balagarh, Chinsurah-magra, Jangipara, Serampore-Uttarpara
	North 24 parganas	Amdnaga, Habra II, Barrackpore I
	Howrah	Udaynarayanpur, Amta I, Uluberiia I, Shyamnagar I, Sankrail, Panchla, Domjur
	South 24 parganas	Budge Budge II, Falta
XGB	Murshidabad	Sagardighi, Suti II, Berhampore	0.869 (Figure 6)
	Nadia	Kaliganj, Nakashipara, Krishnanagar I, Nabadwip
	East Bardhhaman	Purbasthali I, Katwa II
	Hooghly	Balagarh,
	North 24 parganas	Amdnaga, Habra II
	Howrah	Udaynarayanpur, Amta I, Shyamnagar I
	South 24 parganas	Budge Budge II, Falta

Performance evaluation of flood susceptibility model

Six individual models' accuracy, quality, and predictability were calibrated and implemented for the flood susceptibility map. First, it is necessary to verify the validity and prediction of these four indexes based on actual and false-positive rates. All four models are validated based on their predictive ability. Success rates perform using training datasets (350 points), which depend on flood locations in 70% of the region. The prediction accuracy depends on the rest of the data set not used in training (150 points) and guided the flood situation in 30% of the region. The AUROC was used to evaluate the performance of each model. All the AUROC obtained from the individual model piling into a single frame for visual interpretation. Furthermore, the fact that the AUROC value is close to 1 indicates that the model is reliable. The results reveal that the best performance among all the individual models belongs to RF (0.975) followed by KNN (0.942), FR (0.913), XGB (0.869), SVM (0.819), and LR (0.816), respectively (Figure 7).

4.3 Application of FVI on socio-economic vulnerability

The psychometric socio-economic vulnerability analysis of flood-prone zones is presented using the FVI index on UNESCO’s questionnaire. The social, economic, environmental, and physical components are distributed spatially through household survey data after arranging it in a choropleth manner in the ArcGIS interface. Each part is reclassified into five classes: very low, low, moderate, high, and very high.

The social component is analyzed based on the population in flood-prone areas, the number of people who have past flood experiences, the rate of child mortality, the presence of awareness programs and warning systems, and the percentage of asphalted roads in the selected river basins. The social component values range between 0.09–0.93 (Figure 7a). In a block-wise view, Kandi of the Murshidabad district (0.91), and Nabadwip and Krishnanagar II of the Nadia district (0.93 and 0.91) are severely affected by the social component. Twenty-two point 6% and 14.5% of the areas of the basin have the lowest and highest social component-related vulnerability.

Figure 7(a-e) Spatial distribution of flood vulnerability indices by using (a) social, (b) economic, (c) environmental, (d) physical components, and (e) flood vulnerability.

The economic component is mainly diagnosed by HDI, wealth inequality, economic recovery, and investment amount. The value of the economic component ranges between 0.07–0.95 (Figure 7b). Among the 75 blocks of the selected river basin, Purbasthali II of Bardhhaman district (0.95), and Nabadwip and Kaliganj in the Nadia district (0.95 and 0.91) are severely disastrous in terms of the economic component: 13.3% and 15.9% of the basin have the lowest and highest economic component-related vulnerability.

The Bhagirathi basin's environmental component depends on the average yearly rainfall and evaporation rate, the percentage of forested area and degraded land, and the portion of the natural reservation in the river basin. The value of the environmental component ranges between 0.11–0.97 (Figure 7c). Purbasthali II and Kalna I of the Bardhhaman district (0.97 and 0.89), and the Berhampore block of Murshidabad district (0.89) are endangered due to environmental conditions caused by rapid urbanization: 23.3% and 38.4% of the basin have the lowest and highest environmental component-related vulnerability.

The physical component of this river basin performs through the average slope, maximum river discharge, frequency of flood, number of heavy rainfall days and dam storage capacity. The value of the physical component ranges between 0.09–0.94 (Figure 7d). Krishnanagar I of Nadia district (0.94), Nabagram of Murshidabad district (0.93) and Nabadwip of Nadia district (0.92) are affected heavily by the physical component effect: 25.2% and 27.7% of the basin have the lowest and highest physical component-related vulnerability, respectively.

The social, economic, environmental, and physical components amalgamate to determine the flood vulnerability indices (Figure 7e). The amount of vulnerability is highest in the Nabadwip block of Nadia district (0.93), Kandi block of Murshidabad district (0.91), and Purbasthali II block of East Burdwan district (0.88):  16.1% and 34.7% of the basin have the lowest and highest total flood vulnerability.

4.4 Flood risk assessment

We have developed the spatial distribution of flood risk through the amalgamation of the pixel-based flood susceptibility obtained by raster normalization and the flood vulnerability generated by the block-based spatial distribution obtained from the Jenks natural breaks algorithm in the ArcGIS interface. The FVI spatial distribution converts to raster normalization for preparing a risk map. This flood risk mapping is done based on pixel values through raster normalization. According to this risk map (Figure 8), the Kandi and Sagardighi blocks of Murshidabad district, Kaliganj, Nakashipara, Nabadwip, Krishnanagar II, Ranaghat I block of Nadia district, and Purvasthali II block of East Burdwan district identify as the most flood risk areas. The probability will increase rapidly in those places, and the policymakers need to complete specific flood risk reduction assessments soon for the sake of local people.

Figure 8 Block-wise spatial distribution of flood risk map.

5 DISCUSSION

A flood is a natural disaster that is difficult to prevent. As a result of floods, financial, social and socio-economic losses affect common people. However, flood disasters are gradually increasing due to extreme weather conditions and growing population pressure on the river. Most of the Bhagirathi basin, in southern West Bengal, has been flood-prone for the past few decades; flood-prone areas are identified by measuring socio-economic vulnerability for flood control measures. Through multivariate (LR), bivariate (FR), and ML algorithms (SVM, RF, KNN, XGB), the flood-prone areas were identified, and the spatial distribution of flood susceptibility was measured. Flood susceptibility maps were prepared based on raster normalization by combining R and ArcGIS interfaces based on regional disparity using 12 parameters. According to 6 different models, the Bhagirathi basin's middle, southwest, and southeast portions are the most flood-prone areas. The rate of flooding in the lower basin is much higher than in the upper part of the Bhagirathi basin. However, measuring multicollinearity among the 12 parameters shows that distance from the river, elevation, drainage density, and slope are responsible for flooding in this region.

Therefore, the settlements along the river's east and west banks have been the most affected by this flood. As the AUC value of the RF model is highest among the six different models, we have prioritized this model in terms of the spatial distribution of flood susceptibility of the Bhagirathi basin. However, the measurement of socio-economic vulnerability is very different from susceptibility. The socio-economic vulnerability of the regions presents in the form of choropleth through block-based spatial distribution with the help of UNESCO's questionnaire and household survey data. But according to Balica's FVI index, we have evaluated the FVI with only river basin parameters. According to the social aspect, if the number of people living along the river increases, there is no flood awareness and warning system, and there are few paved roads for post-flood rescue operations, the flood disaster will continue to increase. According to HDI, if financial inequality or the rich-poor gap is high in a region, and if financial provision and recovery in the post-flood period are low, the impact of floods is more significant. Environmentally, flood vulnerability highly depends on average annual precipitation, evaporation, and the amount of forest cover.

Regarding the physical environment, the elevation of a region, slope, river discharge, and maximum total annual rainfall play a role in flood organization. According to Jenks's natural breaks algorithm, the FVI index for vulnerability is classified into five scales from very low to very high. According to the FVI of the Bhagirathi basin, based on 20 parameters conducted by Baliica, 17.3% and 34.2% of the entire basin area have high and very high vulnerability. Kandi, Baharampur, and Nabagram block of Murshidabad; Nadiar Nabadwip, Krishnanagar I & II, Kaliganj Block; East Burdwan's Purvasthali II and Kalna I blocks are known as the most vulnerable areas. Next, to identify flood-prone areas, we amalgamated the spatial distribution of susceptibility and vulnerability to create a flood risk map based on raster normalization. According to the spatial distribution of flood risk, the Kandi and Sagardighi blocks of Murshidabad district, Kaliganj, Nakashipara, Nabadwip, Krishnanagar II, Ranaghat I block of Nadia district, and Purvasthali II block of East Burdwan district are the most flood-prone areas. As the size of the Bhagirathi basin is large, this flood risk map can help policymakers and common people take necessary decisions for flood control by identifying specific areas.

The Bhagirathi, formed in the lower basin of the main river Ganges, is recognized as one of the main tributaries of the Ganges. Generally, the probability of flooding along the floodplain near the confluence zone is much higher than in the upper part of any river basin. The flood risk map of the Bhagirathi basin expresses that the flood risk areas reside along the upper and middle parts of the basin. We have reviewed this issue from both susceptibility and vulnerability aspects and presented the right reasons with arguments. The Kandi and Sagardighi blocks of Murshidabad district, Kaliganj, Nakashipara, Nabadwip, Krishnanagar II, Ranaghat I blocks of Nadia district, and the Purbasthali II block of East Burdwan district identify as the highest flood risk areas in the Bhagirathi basin. Based on the 12 susceptible parameters, the above regions presented the lowest values, significantly increasing the probability of flooding. For example, these regions are in very flat and downwardly sloped areas (< 50). Areas within 500 m of the river have a higher TWI (>20) and lower roughness (<0.20). Apart from Nabadwip, urban development in the remaining blocks is much lower. Also, drainage density (>8), high vegetation water content (>0.30), and sparse vegetation (>0.30) in these vulnerable blocks are much higher than in other areas, which increases susceptibility and risk.

However, these flood-risk-prone blocks are densely populated. Apart from Kandi, Kaliganj, Nakashipara, and East II block, urbanization and industrialization are very high. Regarding the HDI index, Murshidabad district (0.46) is far behind the other three districts. Kandi and Sagardighi blocks have a high population but need more education, road construction, social awareness, and proper hygiene, significantly increasing flood vulnerability and risk. Although Nadia (0.57) and East Burdwan (0.64) have excellent HDI indices, the blocks there need more social, education, and health awareness. Kaliganj, Nakashipara, and Purbasthali II blocks are less financially sound than most of the affected rural areas. Despite the rapid urbanization in Nabadwip, Krishnanagar II and Ranaghat I blocks, the number of human settlements along the riverbanks due to population and livelihood is high, significantly increasing the vulnerability. The number of forested areas in all blocks is considerably lower, and the residents of the blocks have been affected by floods many times in the last decade. However, weather extremes in the last decade due to global warming have increased the risk of flooding in these areas.

6 CONCLUSION AND RECOMMENDATIONS

It is necessary to know the layout of the flood-prone regions to plan flood control measures. Then, by examining the social, financial, and socio-economic damage caused by floods to the local stakeholders of the area, it is necessary to highlight the direction of the flood risk trend in the region. This article highlights all three points to help formulate any flood control policy. The study takes a unique approach by identifying flood-prone areas, estimating the extent of human disaster there, and predicting future flood risk through machine learning algorithms. Through this article, the spatial distribution of flood susceptibility, vulnerability, and risk has been shown by reviewing and monitoring the flood situation of the Bhagirathi basin in West Bengal, through which the policymakers can adopt planned and scientific flood control management. Through a review of previous articles, 12 flood conditioning or susceptibility factors are analyzed using spatial distribution. The multicollinearity analysis of the flood conditioning factors shows that the distance from the river, drainage density, and elevation played an essential role in flood organization. According to flood inventory, bivariate, multivariate, and machine learning susceptible models were created with the help of 70% flood points, and the remaining 30% non-flood points were validated using AUC. According to AUC, the RF model is more acceptable than the LR, FR, SVM, KNN, and XGB models in determining the flood susceptibility of the Bhagirathi basin. A block-wise questionnaire-based flood vulnerability assessment has managed the socio-economic crisis resulting from flood organization. According to this FVI index, Navadwip, Kandi, and Purvasthali II blocks are recognized as the highest flood vulnerability areas in the Bhagirathi basin. Finally, the spatial distribution of flood risk is replicated with the help of raster normalization by combining the spatial distribution of susceptibility and vulnerability. Through these three assessments, the Bhagirathi basin's middle, southeast, and southwest parts are considered the most flood-prone areas. Also, the Kandi and Sagardighi blocks of Murshidabad district, Kaliganj, Nakashipara, Nabadwip, Krishnanagar II, Ranaghat I blocks of the Nadia district, and the Purbasthali II block of the East Burdwan district identify as flood-prone areas under this basin.

Based on this spatial distribution, policymakers will quickly adopt flood control management in the Bhagirathi basin. As the discussion is block-based, flood control measures must be implemented as a part of the small-scale development. However, this article includes several things that may improve flood control measures for future and realistic study. Currently, the use of SAR imagery is widespread and successfully validates the flood inundation system. Also, using few flood and non-flood points and not making a proper flood early warning system is one of the areas for improvement of these models. However, with the help of the HEC-RAS 1D/2D coupled model, flood inundation through bank breaching, and the relationship of the HEC-RAS simulation with other hydrological models can be highlighted.

References

1. Adhikari, P., Y. Hong, K.R. Douglas, D.B. Kirschbaum, J. Gourley, R. Adler, and G. Robert Brakenridge. 2010. “A digitized global flood inventory (1998–2008): Compilation and preliminary results.” Natural Hazards 55, 405–422. https://doi.org/10.1007/s11069-010-9537-2
2. Ahmed, K.R., and S. Akter. 2017. “Analysis of landcover change in southwest Bengal delta due to floods by NDVI, NDWI and K-means cluster with Landsat multi-spectral surface reflectance satellite data.” Remote Sensing Applications: Society and Environment 8, 168–181. https://doi.org/10.1016/j.rsase.2017.08.010
3. Akay, H. 2021. “Flood hazards susceptibility mapping using statistical, fuzzy logic, and MCDM methods.” Soft Computing 25 (14): 9325–9346. https://doi.org/10.1007/s00500-021-05903-1
4. Alfieri, L., B. Bisselink, F. Dottori, G. Naumann, A. de Roo, P. Salamon, K. Wyser, and L. Feyen. 2017. “Global projections of river flood risk in a warmer world.” Earth's Future 5 (2): 171–182. https://doi.org/10.1002/2016EF000485
5. Arabameri, A., B. Pradhan, K. Rezaei, M. Sohrabi, and Z. Kalantari. 2019. “GIS-based landslide susceptibility mapping using numerical risk factor bivariate model and its ensemble with linear multivariate regression and boosted regression tree algorithms.” Journal of Mountain Science 1 (3) : 595–618. https://doi.org/10.1007/s11629-018-5168-y
6. Aronica, G., P.D. Bates, and M.S. Horritt. 2002. “Assessing the uncertainty in distributed model predictions using observed binary pattern information within GLUE.” Hydrological Processes 16 (10): 2001–2016. https://doi.org/10.1002/hyp.398
7. Avand, M., and H. Moradi. 2021. “Spatial modeling of flood probability using geo-environmental variables and machine learning models, case study: Tajan watershed, Iran.” Advances in Space Research 67 (10): 3169–3186. https://doi.org/10.1016/j.asr.2021.02.011
8. Bai, Y., M. Feng, H. Jiang, J. Wang, and Y. Liu. 2015. “Validation of land cover maps in China using a sampling-based labelling approach.” Remote Sensing 7 (8): 10,589–10,606. https://doi.org/10.3390/rs70810589
9. Baky, M.A.A., M. Islam, and S. Paul. 2020. “Flood hazard, vulnerability and risk assessment for different land use classes using a flow model.” Earth Systems and Environment 4, 225–244. https://doi.org/10.1007/s41748-019-00141-w
10. Balica, S.F., N. Douben, and N.G. Wright. 2009. “Flood vulnerability indices at varying spatial scales.” Water Science and Technology 60 (10): 2571–2580. https://doi.org/10.2166/wst.2009.183
11. Balica, S. and N.G. Wright. 2010. “Reducing the complexity of the flood vulnerability index.” Environmental Hazards 9 (4): 321–339. https://doi.org/10.3763/ehaz.2010.0043
12. Bandyopadhyay, S., P.K. Ghosh, N.C. Jana, and S. Sinha. 2016. “Probability of flooding and vulnerability assessment in the Ajay River, Eastern India: implications for mitigation.” Environmental Earth Sciences 75, 1–22. https://doi.org/10.1007/s12665-016-5297-y
13. Bandyopadhyay, S., N.S. Kar, S. Das, and J. Sen. 2014. “River systems and water resources of West Bengal: a review.” Geological Society of India (special publication) 3, 63–84.
14. Barroca, B., P. Bernardara, J.M. Mouchel, and G. Hubert. 2006. “Indicators for identification of urban flooding vulnerability.” Natural Hazards and Earth System Sciences 6 (4): 553–561. https://doi.org/10.5194/nhess-6-553-2006
15. Bentivoglio, R., E. Isufi, S.N. Jonkman, and R. Taormina. 2022. “Deep learning methods for flood mapping: a review of existing applications and future research directions.” Hydrology and Earth System Sciences 26 (16): 4345–4378. https://doi.org/10.5194/hess-26-4345-2022
16. Bhattacharjee, K., and B. Behera. 2018. “Determinants of household vulnerability and adaptation to floods: Empirical evidence from the Indian State of West Bengal.” International Journal of Disaster Risk Reduction 31, 758–769. https://doi.org/10.1016/j.ijdrr.2018.07.017
17. Bisht, S., S. Chaudhry, S. Sharma, and S. Soni. 2018. “Assessment of flash flood vulnerability zonation through Geospatial technique in high altitude Himalayan watershed, Himachal Pradesh India.” Remote Sensing Applications: Society and Environment 12, 35–47. https://doi.org/10.1016/j.rsase.2018.09.001
18. Boithias, L., S. Sauvage, A. Lenica, H. Roux, K.C. Abbaspour, K. Larnier, D. Dartus, and J.M. Sánchez-Pérez. 2017. “Simulating flash floods at hourly time-step using the SWAT model.” Water 9 (12): 929. https://doi.org/10.3390/w9120929
19. Botzen, W.J., J.C.J.H. Aerts, and J.C.J.M. Van den Bergh. 2013. “Individual preferences for reducing flood risk to near zero through elevation.” Mitigation and Adaptation Strategies for Global Change 18, 229–244. https://doi.org/10.1007/s11027-012-9359-5
20. Botzen, W.W., O. Deschenes, and M. Sanders. 2019. “The economic impacts of natural disasters: A review of models and empirical studies.” Review of Environmental Economics and Policy.
21. Breiman, L. 2001. “Random forests.” Machine Learning 45, 5–32.
22. Bui, D.T., N.D. Hoang, F. Martínez-Álvarez, P.T.T. Ngo, P.V. Hoa, T.D. Pham, P. Samui, and R. Costache. 2020. “A novel deep learning neural network approach for predicting flash flood susceptibility: A case study at a high frequency tropical storm area.” Science of the Total Environment 701, 134,413. https://doi.org/10.1016/j.scitotenv.2019.134413
23. Cao, Y., H. Jia, J. Xiong, W. Cheng, K. Li, Q. Pang, and Z. Yong. 2020. “Flash flood susceptibility assessment based on geodetector, certainty factor, and logistic regression analyses in Fujian Province, China.” ISPRS International Journal of Geo-Information 9 (12): 748. https://doi.org/10.3390/ijgi9120748
24. Chakraborty, S., and S. Mukhopadhyay. 2019. “Assessing flood risk using analytical hierarchy process (AHP) and geographical information system (GIS): application in Coochbehar district of West Bengal, India.” Natural Hazards 99, 247–274. https://doi.org/10.1007/s11069-019-03737-7
25. Chan, S.W., S.K. Abid, N. Sulaiman, U. Nazir, and K. Azam. 2022. “A systematic review of the flood vulnerability using geographic information system.” Heliyon 8 (3). https://doi.org/10.1007/s11069-019-03737-7
26. Chen, S., C. Gu, C. Lin, K. Zhang, and Y. Zhu. 2021. “Multi-kernel optimized relevance vector machine for probabilistic prediction of concrete dam displacement.” Engineering with Computers 37 (3): 1943–1959. https://doi.org/10.1007/s00366-019-00924-9
27. Chen, T. and C. Guestrin. 2016. “XGBoost: A scalable tree boosting system.” In Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining 785-794. https://doi.org/10.1145/2939672.2939785
28. Chen, Y., R. Liu, D. Barrett, L. Gao, M. Zhou, L. Renzullo, and I. Emelyanova. 2015. “A spatial assessment framework for evaluating flood risk under extreme climates.” Science of the Total Environment 538, 512–523. https://doi.org/10.1016/j.scitotenv.2015.08.094
29. Choubin, B., E. Moradi, M. Golshan, J. Adamowski, F. Sajedi-Hosseini, and A. Mosavi. 2019. “An ensemble prediction of flood susceptibility using multivariate discriminant analysis, classification and regression trees, and support vector machines.” Science of the Total Environment 651, 2087–2096. https://doi.org/10.1016/j.scitotenv.2018.10.064
30. Chowdhuri, I., S.C. Pal, and R. Chakrabortty. 2020. “Flood susceptibility mapping by ensemble evidential belief function and binomial logistic regression model on river basin of eastern India.” Advances in Space Research 65 (5): 1466–1489. https://doi.org/10.1016/j.asr.2019.12.003
31. Costache, R., A. Arabameri, I. Elkhrachy, O. Ghorbanzadeh, and Q.B. Pham. 2021. “Detection of areas prone to flood risk using state-of-the-art machine learning models.” Geomatics Natural Hazards and Risk 12 (1): 1488–1507. https://doi.org/10.1080/19475705.2021.1920480
32. Dandapat, K., and G.K. Panda. 2017. “Flood vulnerability analysis and risk assessment using analytical hierarchy process.” Modeling Earth Systems and Environment 3, 1627–1646. https://doi.org/10.1007/s40808-017-0388-7
33. Das, G., and K. Lepcha. 2019. “Application of logistic regression (LR) and frequency ratio (FR) models for landslide susceptibility mapping in Relli Khola river basin of Darjeeling Himalaya, India.” SN Applied Sciences 1, 1–22. https://doi.org/10.1007/s42452-019-1499-8
34. Das, S. 2019. “Geospatial mapping of flood susceptibility and hydro-geomorphic response to the floods in Ulhas basin, India.” Remote Sensing Applications: Society and Environment 14, 60–74. https://doi.org/10.1016/j.rsase.2019.02.006
35. Das, S. 2020. “Flood susceptibility mapping of the Western Ghat coastal belt using multi-source geospatial data and analytical hierarchy process (AHP).” Remote Sensing Applications: Society and Environment 20, 100,379. https://doi.org/10.1016/j.rsase.2020.100379
36. Das, S., A.N. Sheth, P. Bansal, J. Chuah, and R. Wasson. 2022. “A statistical comparison of flood-related economic damage in Indian states with reflections on policy implications.” International Journal of Disaster Risk Reduction, 72, 102,835. https://doi.org/10.1016/j.ijdrr.2022.102835
37. Dash, P. and M. Punia. 2019. “Governance and disaster: Analysis of land use policy with reference to Uttarakhand flood 2013, India.” International Journal of Disaster Risk Reduction 36, 101,090. https://doi.org/10.1016/j.ijdrr.2019.101090
38. De Bruijn, K.M. 2004. “Resilience indicators for flood risk management systems of lowland rivers.” International Journal of River Basin Management 2 (3): 199–210.
39. Deroliya, P., M. Ghosh, M.P. Mohanty, S. Ghosh, K.D. Rao, and S. Karmakar. 2022. “A novel flood risk mapping approach with machine learning considering geomorphic and socio-economic vulnerability dimensions.” Science of the Total Environment 851, 158,002. https://doi.org/10.1016/j.scitotenv.2022.158002
40. Dottori, F., L. Alfieri, A. Bianchi, J. Skoien, and P. Salamon. 2021. “A new dataset of river flood hazard maps for Europe and the Mediterranean Basin region.” Earth System Science Data Discussions 2021, 1–35. https://doi.org/10.5194/essd-14-1549-2022
41. Dottori, F., M.L.V. Martina, and R. Figueiredo. 2018. “A methodology for flood susceptibility and vulnerability analysis in complex flood scenarios.” Journal of Flood Risk Management 11, S632–S645. https://doi.org/10.1111/jfr3.12234
42. Fustos, I., R. Abarca‐del‐Rio, A. Ávila, and R. Orrego. 2017. “A simple logistic model to understand the occurrence of flood events into the Biobío River Basin in central Chile.” Journal of Flood Risk Management 10 (1): 17–29. https://doi.org/10.1111/jfr3.12131
43. Ghosh, A., and S.K. Kar. 2018. “Application of analytical hierarchy process (AHP) for flood risk assessment: A case study in Malda district of West Bengal, India.” Natural Hazards 94, 349–368. https://doi.org/10.1007/s11069-018-3392-y
44. Ghosh, A., M.B. Roy, and P.K. Roy. 2022. “Flood susceptibility mapping using the frequency ratio (FR) model in the Mahananda River Basin, West Bengal, India.” In: Islam, M.N., Amstel, A.V. (eds), India II: Climate Change Impacts, Mitigation and Adaptation in Developing Countries. Springer Climate. Springer, Cham. https://doi.org/10.1007/978-3-030-94395-0_3
45. Ghosh, B., and B. Sarkar. 2020. “Media and Risk: An Introduction.” In The Routledge Companion to Media and Risk, pp. 1-24. Routledge.
46. Guguloth, S., M. Pandey, and M. Pal. 2024. “Application of Hybrid AI Models for Accurate Prediction of Scour Depths under Submerged Circular Vertical Jet.” Journal of Hydrologic Engineering 29 (3): 04024010. https://doi.org/10.1061/JHYEFF.HEENG-6149
47. Hammami, S., L. Zouhri, D. Souissi, A. Souei, A. Zghibi, A. Marzougui, and M. Dlala. 2019. “Application of the GIS based multi-criteria decision analysis and analytical hierarchy process (AHP) in the flood susceptibility mapping (Tunisia).” Arabian Journal of Geosciences 12, 1–16. https://doi.org/10.1007/s12517-019-4754-9
48. Hazra, S., A. Ghosh, S. Ghosh, I. Pal, and T. Ghosh. 2022. “Assessing coastal vulnerability and governance in Mahanadi Delta, Odisha, India.” Progress in Disaster Science 14, 100,223. https://doi.org/10.1007/s12517-019-4754-9
49. Hong, H., H.R. Pourghasemi, and Z.S. Pourtaghi. 2016. “Landslide susceptibility assessment in Lianhua County (China): A comparison between a random forest data mining technique and bivariate and multivariate statistical models.” Geomorphology 259, 105–118. https://doi.org/10.1016/j.geomorph.2016.02.012
50. Hosmer Jr., D.W., S. Lemeshow, and R.X. Sturdivant. 2013. Applied Logistic Regression. John Wiley & Sons.
51. Islam, A., S. Ghosh, S.D. Barman, S. Nandy, and B. Sarkar. 2022. “Role of in-situ and ex-situ livelihood strategies for flood risk reduction: Evidence from the Mayurakshi River Basin, India.” International Journal of Disaster Risk Reduction 70, 102,775. https://doi.org/10.1016/j.ijdrr.2021.102775
52. Kantamaneni, K., N.N.V. Sudha Rani, L. Rice, K. Sur, M. Thayaparan, U. Kulatunga, R. Rege, et al. 2019. “A systematic review of coastal vulnerability assessment studies along Andhra Pradesh, India: A critical evaluation of data gathering, risk levels and mitigation strategies.” Water 11 (2): 393. https://doi.org/10.3390/w11020393
53. Kaur, R., C. Schaye, K. Thompson, D.C. Yee, R. Zilz, R.S. Sreenivas, and R.B. Sowers. 2021. “Machine learning and price-based load scheduling for an optimal IoT control in the smart and frugal home.” Energy and AI 3, 100,042. https://doi.org/10.1016/j.egyai.2020.100042
54. Khosravi, K., B.T. Pham, K. Chapi, A. Shirzadi, H. Shahabi, I. Revhaug, I. Prakash, and D.T. Bui. 2018. “A comparative assessment of decision trees algorithms for flash flood susceptibility modeling at Haraz watershed, northern Iran.” Science of the Total Environment 627, 744–755. https://doi.org/10.1016/j.scitotenv.2018.01.266
55. Khosravi, K., H. Shahabi, B.T. Pham, J. Adamowski, A. Shirzadi, B. Pradhan, J. Dou, et al. 2019. “A comparative assessment of flood susceptibility modeling using multi-criteria decision-making analysis and machine learning methods.” Journal of Hydrology 573, 311–323. https://doi.org/10.1016/j.jhydrol.2019.03.073
56. Lee, S., and J.A. Talib. 2005. “Probabilistic landslide susceptibility and factor effect analysis.” Environmental Geology 47, 982–990. https://doi.org/10.1007/s00254-005-1228-z
57. Lin, L., L. Di, E.G. Yu, L. Kang, R. Shrestha, M.S. Rahman, J. Tang, et al. 2016. “A review of remote sensing in flood assessment.” In 2016 Fifth International Conference on Agro-Geoinformatics (Agro-Geoinformatics) 1–4. IEEE.
58. Mahmoud, S.H., and T.Y. Gan. 2018. “Urbanization and climate change implications in flood risk management: Developing an efficient decision support system for flood susceptibility mapping.” Science of the Total Environment 636, 152–167. https://doi.org/10.1016/j.scitotenv.2018.04.282
59. Mainuddin, M., and J.M. Kirby. 2021. “Impact of flood inundation and water management on water and salt balance of the polders and islands in the Ganges delta.” Ocean & Coastal Management 210, 105,740. https://doi.org/10.1016/j.ocecoaman.2021.105740
60. Malik, S., S.C. Pal, I. Chowdhuri, R. Chakrabortty, P. Roy, and B. Das. 2020. “Prediction of highly flood prone areas by GIS based heuristic and statistical model in a monsoon dominated region of Bengal Basin.” Remote Sensing Applications: Society and Environment 19, 100,343. https://doi.org/10.1016/j.rsase.2020.100343
61. Mavhura, E., B. Manyena, and A.E. Collins. 2017. “An approach for measuring social vulnerability in context: The case of flood hazards in Muzarabani district, Zimbabwe." Geoforum 86, 103–117. https://doi.org/10.1016/j.geoforum.2017.09.008
62. Mehravar, S., M. Amani, A. Moghimi, F.D. Javan, F. Samadzadegan, A. Ghorbanian, A. Stein, A. Mohammadzadeh, and S.M. Mirmazloumi. 2021. “Temperature-Vegetation-soil Moisture-Precipitation Drought Index (TVMPDI); 21-year drought monitoring in Iran using satellite imagery within Google Earth engine.” Advances in Space Research 68 (11): 4573-4593. https://doi.org/10.1016/j.geoforum.2017.09.008
63. Mehravar, S., S.V. Razavi-Termeh, A. Moghimi, B. Ranjgar, F. Foroughnia, and M. Amani. 2023. “Flood susceptibility mapping using multi-temporal SAR imagery and novel integration of nature-inspired algorithms into support vector regression.” Journal of Hydrology 617, 129,100. https://doi.org/10.1016/j.jhydrol.2023.129100
64. Meliho, M., A. Khattabi, Z. Driss, and C.A. Orlando. 2022. “Spatial prediction of flood-susceptible zones in the Ourika watershed of Morocco using machine learning algorithms.” Applied Computing and Informatics, Pre-print.
65. Mind'je, R., L. Li, A.C. Amanambu, L. Nahayo, J.B. Nsengiyumva, A. Gasirabo, and M. Mindje. 2019. “Flood susceptibility modeling and hazard perception in Rwanda.” International Journal of Disaster Risk Reduction 38, 101,211. https://doi.org/10.1016/j.ijdrr.2019.101211
66. Mishra, B.P., D.K. Ghose, and D.P. Satapathy. 2022. “Geospatial modeling using hybrid machine learning approach for flood susceptibility.” Earth Science Informatics 15 (4): 2619–2636. https://doi.org/10.1007/s12145-022-00872-x
67. Mishra, K. and R. Sinha. 2020. “Flood risk assessment in the Kosi megafan using multi-criteria decision analysis: A hydro-geomorphic approach.” Geomorphology 350, 106,861. https://doi.org/10.1016/j.geomorph.2019.106861
68. Moazzam, M.F.U., B.G. Lee, A.U. Rahman, N. Farid, and G. Rahman. 2020. “Spatio-statistical analysis of flood susceptibility assessment using bivariate model in the floodplain of river Swat, District Charsadda, Pakistan.” Journal of Geoscience and Environment Protection 8 (05): 159.
69. Mohanty, M.P., S. Mudgil, and S. Karmakar. 2020. “Flood management in India: A focused review on the current status and future challenges.” International Journal of Disaster Risk Reduction 49, 101,660. https://doi.org/10.1016/j.ijdrr.2020.101660
70. Mohapatra, P.K., and R.D. Singh. 2003. “Flood Management in India.” Natural Hazards 28, 131–143. https://doi.org/10.1023/A:1021178000374
71. Mosavi, A., P. Ozturk, and K.W. Chau. 2018. “Flood prediction using machine learning models: Literature review.” Water 10 (11): 1536. https://doi.org/10.3390/w10111536
72. Motevalli, A., and M. Vafakhah. 2016. “Flood hazard mapping using synthesis hydraulic and geomorphic properties at watershed scale.” Stochastic Environmental Research and Risk Assessment 30, 1,889-1,900. https://doi.org/10.1007/s00477-016-1305-8
73. Mukherjee, A., A.E. Fryar, and W.A. Thomas. 2009. “Geologic, geomorphic and hydrologic framework and evolution of the Bengal basin, India and Bangladesh.” Journal of Asian Earth Sciences 34 (3): 227–244. https://doi.org/10.1016/j.jseaes.2008.05.011
74. Naito, A.T., and D.M. Cairns. 2011. “Relationships between Arctic shrub dynamics and topographically derived hydrologic characteristics.” Environmental Research Letters 6 (4): 045506. https://doi.org/10.1088/1748-9326/6/4/045506
75. Namara, W.G., T.A. Damisse, and F.G. Tufa. 2022. “Application of HEC-RAS and HEC-GeoRAS model for flood inundation mapping, the case of Awash bello flood plain, upper Awash River Basin, Oromiya Regional State, Ethiopia.” Modeling Earth Systems and Environment 8 (2): 1,449–1,460. https://doi.org/10.1007/s40808-021-01166-9
76. Nasiri, H., M.J.M. Yusof, T.A.M. Ali, and M.K.B. Hussein. 2019. “District flood vulnerability index: urban decision-making tool.” International Journal of Environmental Science and Technology 16, 2249–2258. https://doi.org/10.1007/s40808-021-01166-9
77. Naulin, J.P., O. Payrastre, and E. Gaume. 2013. “Spatially distributed flood forecasting in flash flood prone areas: Application to road network supervision in Southern France.” Journal of Hydrology 486, 88–99. https://doi.org/10.1016/j.jhydrol.2013.01.044
78. Ni, L., D. Wang, J. Wu, Y. Wang, Y. Tao, J. Zhang, and J. Liu. 2020. “Streamflow forecasting using extreme gradient boosting model coupled with Gaussian mixture model.” Journal of Hydrology 586, 124,901. https://doi.org/10.1016/j.jhydrol.2020.124901
79. Otsu, N. 1975. “A threshold selection method from gray-level histograms.” Automatica 11 (285–296): 23–27.
80. Pandey, M., M. Jamei, M. Karbasi, I. Ahmadianfar, and X. Chu. 2021. “Prediction of maximum scour depth near spur dikes in uniform bed sediment using stacked generalization ensemble tree-based frameworks.” Journal of Irrigation and Drainage Engineering 147 (11): 04021050.
81. Parsian, S., M. Amani, A. Moghimi, A. Ghorbanian, and S. Mahdavi. 2021. “Flood hazard mapping using fuzzy logic, analytical hierarchy process, and multi-source geospatial datasets.” Remote Sensing 13 (23): 4,761. https://doi.org/10.3390/rs13234761
82. Pathak, S., M. Liu, D. Jato-Espino, and C. Zevenbergen. 2020. “Social, economic and environmental assessment of urban sub-catchment flood risks using a multi-criteria approach: A case study in Mumbai City, India.” Journal of Hydrology 591, 125,216. https://doi.org/10.1016/j.jhydrol.2020.125216
83. Paul, G.C., S. Saha, and T.K. Hembram. 2019. “Application of the GIS-based probabilistic models for mapping the flood susceptibility in Bansloi sub-basin of Ganga-Bhagirathi River and their comparison.” Remote Sensing in Earth Systems Sciences 2, 120–146. https://doi.org/10.1007/s41976-019-00018-6
84. Penning-Rowsell, E., P. Floyd, D. Ramsbottom, and S. Surendran. 2005. “Estimating injury and loss of life in floods: a deterministic framework.” Natural Hazards 36, 43–64. https://doi.org/10.1007/s11069-004-4538-7
85. Pham, B.T., T.V. Phong, H.D. Nguyen, C. Qi, N. Al-Ansari, A. Amini, L.S. Ho, T.T. Tuyen, H.P.H. Yen, H.B. Ly, and I. Prakash. 2020. “A comparative study of kernel logistic regression, radial basis function classifier, multinomial naïve bayes, and logistic model tree for flash flood susceptibility mapping.” Water 12 (1): 239. https://doi.org/10.3390/w12010239
86. Pourghasemi, H.R. and N. Kerle. 2016. “Random forests and evidential belief function-based landslide susceptibility assessment in Western Mazandaran Province, Iran.” Environmental Earth Sciences 75, 1–17. https://doi.org/10.1007/s12665-015-4950-1
87. Pourghasemi, H.R., S. Yousefi, A. Kornejady, and A. Cerdà. 2017. “Performance assessment of individual and ensemble data-mining techniques for gully erosion modeling.” Science of the Total Environment 609, 764–775. https://doi.org/10.1016/j.scitotenv.2017.07.198
88. Powell, S.J., A. Jakeman, and B. Croke. 2014. “Can NDVI response indicate the effective flood extent in macrophyte dominated floodplain wetlands?” Ecological Indicators 45, 486–493. https://doi.org/10.1016/j.ecolind.2014.05.009
89. Prokop, P., Ł. Wiejaczka, S. Sarkar, T. Bryndal, A. Bucała-Hrabia, R. Kroczak, R. Soja, et al. 2020. “Morphological and sedimentological responses of small stream channels to extreme rainfall and land use in the Darjeeling Himalayas.” Catena 188, 104,444. https://doi.org/10.1016/j.catena.2019.104444
90. Rahman, M., C. Ningsheng, M.M. Islam, A. Dewan, J. Iqbal, R.M.A. Washakh, and T. Shufeng. 2019. “Flood susceptibility assessment in Bangladesh using machine learning and multi-criteria decision analysis.” Earth Systems and Environment 3, 585–601. https://doi.org/10.1007/s41748-019-00123-y
91. Rahmati, O., H.R. Pourghasemi, and H. Zeinivand. 2016. “Flood susceptibility mapping using frequency ratio and weights-of-evidence models in the Golastan Province, Iran.” Geocarto International 31 (1): 42–70. https://doi.org/10.1080/10106049.2015.1041559
92. Ramachandran, A., K. Palanivelu, B.V. Mudgal, A. Jeganathan, S. Guganesh, B. Abinaya, and A. Elangovan. 2019. “Climate change impact on fluvial flooding in the Indian sub-basin: A case study on the Adyar sub-basin.” PloS One 14 (5): e0216461. https://doi.org/10.1371/journal.pone.0216461
93. Roy, P., R. Chakrabortty, I. Chowdhuri, S. Malik, B. Das, and S.C. Pal. 2020. “Development of different machine learning ensemble classifier for gully erosion susceptibility in Gandheswari Watershed of West Bengal, India.” Machine Learning for Intelligent Decision Science, 1–26.
94. Rudra, K. 2010. “Dynamics of the Ganga in West Bengal, India (1764–2007): Implications for science–policy interaction.” Quaternary International 227 (2): 161–169. https://doi.org/10.1016/j.quaint.2009.10.043
95. Rudra, K. 2014. “Changing river courses in the western part of the Ganga–Brahmaputra delta.” Geomorphology 227, 87–100. https://doi.org/10.1016/j.geomorph.2014.05.013
96. Samanta, S., D.K. Pal, and B. Palsamanta. 2018. “Flood susceptibility analysis through remote sensing, GIS and frequency ratio model.” Applied Water Science 8 (2): 66. https://doi.org/10.1007/s13201-018-0710-1
97. Samantaray, S., A. Sahoo, and A. Agnihotri. 2021. “Assessment of flood frequency using statistical and hybrid neural network method: Mahanadi River Basin, India.” Journal of the Geological Society of India 97, 867–880. https://doi.org/10.1007/s12594-021-1785-0
98. Sanyal, J., and X.X. Lu. 2005. “Remote sensing and GIS‐based flood vulnerability assessment of human settlements: A case study of Gangetic West Bengal, India.” Hydrological Processes: An International Journal 19 (18): 3699-3716. https://doi.org/10.1002/hyp.5852
99. Sanyal, J., and X.X. Lu. 2006. “GIS‐based flood hazard mapping at different administrative scales: A case study in Gangetic West Bengal, India.” Singapore Journal of Tropical Geography 27 (2): 207–220. https://doi.org/10.1111/j.1467-9493.2006.00254.x
100. Shafapour Tehrany, M., F. Shabani, M. Neamah Jebur, H. Hong, W. Chen, and X. Xie. 2017. “GIS-based spatial prediction of flood prone areas using standalone frequency ratio, logistic regression, weight of evidence and their ensemble techniques.” Geomatics, Natural Hazards and Risk 8 (2): 1538–1561. https://doi.org/10.1080/19475705.2017.1362038
101. Shahabi, H., A. Shirzadi, K. Ghaderi, E. Omidvar, N. Al-Ansari, J.J. Clague, M. Geertsema, et al. 2020. “Flood detection and susceptibility mapping using Sentinel-1 remote sensing data and a machine learning approach: Hybrid intelligence of bagging ensemble based on k-nearest neighbor classifier.” Remote Sensing 12 (2): 266. https://doi.org/10.3390/rs12020266
102. Shrestha, R., L. Di, G. Yu, Y. Shao, L. Kang, and B. Zhang. 2013. “Detection of flood and its impact on crops using NDVI-Corn case.” In 2013 Second International Conference on Agro-Geoinformatics (Agro-Geoinformatics), 200–204. IEEE.
103. Sinha, R., and S. Ghosh. 2012. “Understanding dynamics of large rivers aided by satellite remote sensing: a case study from Lower Ganga plains, India.” Geocarto International 27 (3): 207–219. https://doi.org/10.1080/10106049.2011.620180
104. Smith, K. 2013. Environmental Hazards: Assessing Risk And Reducing Disaster. London: Routledge. https://doi.org/10.4324/9780203805305
105. Souissi, D., L. Zouhri, S. Hammami, M.H. Msaddek, A. Zghibi, and M. Dlala. 2020. “GIS-based MCDM–AHP modeling for flood susceptibility mapping of arid areas, southeastern Tunisia.” Geocarto International 35 (9): 991–1017. https://doi.org/10.1080/10106049.2019.1566405
106. Srivastava, P.K., and A.K. Bhattacharya. 2006. “Groundwater assessment through an integrated approach using remote sensing, GIS and resistivity techniques: A case study from a hard rock terrain.” International Journal of Remote Sensing 27 (20): 4599–4620. https://doi.org/10.1080/01431160600554983
107. Sullivan, C., and J. Meigh. 2005. “Targeting attention on local vulnerabilities using an integrated index approach: The example of the climate vulnerability index.” Water Science and Technology 51 (5): 69–78. https://doi.org/10.2166/wst.2005.0111
108. Sutradhar, S., and P. Mondal. 2023. “Prioritization of watersheds based on morphometric assessment in relation to flood management: A case study of Ajay River basin, Eastern India.” Watershed Ecology and the Environment 5, 1–11. https://doi.org/10.1016/j.wsee.2022.11.011
109. Svetlana, D., D. Radovan, and D. Ján. 2015. “The economic impact of floods and their importance in different regions of the world with emphasis on Europe.” Procedia Economics and Finance 34, 649–655. https://doi.org/10.1016/S2212-5671(15)01681-0
110. Taguchi, R., M. Tanoue, D. Yamazaki, and Y. Hirabayashi. 2022. “Global-scale assessment of economic losses caused by flood-related business interruption.” Water 14 (6): 967. https://doi.org/10.1016/S2212-5671(15)01681-0
111. Tehrany, M.S., S. Jones, and F. Shabani. 2019. “Identifying the essential flood conditioning factors for flood prone area mapping using machine learning techniques.” Catena 175, 174–192.
112. Tehrany, M.S., L. Kumar, M.N. Jebur, and F. Shabani. 2018. “Evaluating the application of the statistical index method in flood susceptibility mapping and its comparison with frequency ratio and logistic regression methods.” Geomatics, Natural Hazards and Risk 10, 1. https://doi.org/10.1080/19475705.2018.1506509
113. Tehrany, M.S., M.J. Lee, B. Pradhan, M.N. Jebur, and S. Lee. 2014. “Flood susceptibility mapping using integrated bivariate and multivariate statistical models.” Environmental Earth Sciences 72, 4001-4015. https://doi.org/10.1007/s12665-014-3289-3
114. Termeh, S.V.R., A. Kornejady, H.R. Pourghasemi, and S. Keesstra. 2018. “Flood susceptibility mapping using novel ensembles of adaptive neuro fuzzy inference system and metaheuristic algorithms.” Science of the Total Environment 615, 438–451. https://doi.org/10.1016/j.scitotenv.2017.09.262
115. Thattai, D.V., R. Sathyanathan, R. Dinesh, and L.H. Kumar. 2017. “Natural disaster management in India with focus on floods and cyclones.” In IOP Conference Series: Earth and Environmental Science 80 (1): 012054. IOP Publishing.
116. Vapnik, V. 2013. The Nature of Statistical Learning Theory. New York: Springer Science & Business Media. https://doi.org/10.1007/978-1-4757-3264-1
117. Vignesh, K.S., I. Anandakumar, R. Ranjan, and D. Borah. 2021. “Flood vulnerability assessment using an integrated approach of multi-criteria decision-making model and geospatial techniques.” Modeling Earth Systems and Environment 7, 767–781.
118. Vijaykumar, P., S. Abhilash, A.V. Sreenath, U.N. Athira, K. Mohanakumar, B.E. Mapes, B. Chakrapani, A.K. Sahai, T.N. Niyas, and O.P. Sreejith. 2021. “Kerala floods in consecutive years-Its association with mesoscale cloudburst and structural changes in monsoon clouds over the west coast of India.” Weather and Climate Extremes 33, 100,339. https://doi.org/10.1016/j.wace.2021.100339
119. Vojtek, M., J. Vojteková, R. Costache, Q.B. Pham, S. Lee, A. Arshad, S. Sahoo, et al. 2021. “Comparison of multi-criteria-analytical hierarchy process and machine learning-boosted tree models for regional flood susceptibility mapping: A case study from Slovakia.” Geomatics Natural Hazards and Risk 12 (1): 1153-1180. https://doi.org/10.1080/19475705.2021.1912835
120. Waghwala, R.K., and P.G. Agnihotri. 2019. “Flood risk assessment and resilience strategies for flood risk management: A case study of Surat City.” International Journal of Disaster Risk Reduction 40, 101,155. https://doi.org/10.1080/19475705.2021.1912835
121. Wang, Y., Z. Fang, H. Hong, R. Costache, and X. Tang. 2021. “Flood susceptibility mapping by integrating frequency ratio and index of entropy with multilayer perceptron and classification and regression tree.” Journal of Environmental Management 289, 112,449. https://doi.org/10.1080/19475705.2021.1912835
122. Wubalem, A., G. Tesfaw, Z. Dawit, B. Getahun, T. Mekuria, and M. Jothimani. 2021. “Comparison of statistical and analytical hierarchy process methods on flood susceptibility mapping: In a case study of the Lake Tana sub-basin in northwestern Ethiopia.” Open Geosciences 13 (1): 1668-1688. https://doi.org/10.1515/geo-2020-0329
123. Xu, H. 2006. “Modification of normalised difference water index (NDWI) to enhance open water features in remotely sensed imagery.” International Journal of Remote Sensing 27 (14): 3025–3033. https://doi.org/10.1080/01431160600589179
124. Xu, K., Z. Han, H. Xu, and L. Bin. 2023. “Rapid prediction model for urban floods based on a light gradient boosting machine approach and hydrological–hydraulic model.” International Journal of Disaster Risk Science 14 (1): 79–97. https://doi.org/10.1007/s13753-023-00465-2
125. Yesilnacar, E., and T.A.M.E.R. Topal. 2005. “Landslide susceptibility mapping: a comparison of logistic regression and neural networks methods in a medium scale study, Hendek region (Turkey).” Engineering Geology 79 (3–4): 251–266. https://doi.org/10.1016/j.enggeo.2005.02.002
126. Yilmaz, I. 2010. “Comparison of landslide susceptibility mapping methodologies for Koyulhisar, Turkey: Conditional probability, logistic regression, artificial neural networks, and support vector machine.” Environmental Earth Sciences 61, 821–836.
127. Youssef, A.M., B. Pradhan, and A.M. Hassan. 2011. “Flash flood risk estimation along the St. Katherine Road, southern Sinai, Egypt using GIS based morphometry and satellite imagery.” Environmental Earth Sciences 62 (3): 611–623. https://doi.org/10.1007/s12665-010-0551-1
128. Zhang, J., X. Liao, and W. Xu. 2022. “Mapping global risk of GDP loss to river floods.” In Atlas of Global Change Risk of Population and Economic Systems (pp. 203-210). Singapore: Springer Nature. https://doi.org/10.1007/978-981-16-6691-9_16

SUPPLEMENTARY DOCUMENTATION

Table S1 FVI indicators in river basin scale.

Flood Vulnerability	Exposure (before flood)	Definition	Unit	Susceptibility (during flood)	Definition	Unit	Resilience (after flood)	Definition	Unit
Social component	population in flood prone area (PFA )	number of people living in flood prone area	persons	past experience (PE )	number of people have past flood experience, in less than 10 years	persons	warning system (WS )	if yes, then 1, and if not, then 0	dimensionless
				awareness and preparedness (AP )	Range between 1 to 10	dimensionless	evacuation road (ER )	% of asphalted road	%
				child mortality (CM )	number of children less than 1 year old, died per 1000 live birth	dimensionless
Economic component	HDI	human development index	dimensionless	inequality (Ineq)	Gini coefficient wealth inequality between 0 and 1	dimensionless	amount of investment (AmInv)	Ratio of investment over the total GDP	€ / €
							economic recovery (ER )	Affected economy due to flood in large time scale	dimensionless
Environmental component	rainfall (RAINFALL)	average rainfall/year in a river basin	%	natural reservation (NR)	% of total natural reservation in a river basin	%
	degraded area (DA)	% of degraded area	%
	evaporation rate (EV)	yearly evaporation rate	m/year
	land use (LU)	% of forested area in river basin	%
Physical component	topography (T)	average slope of river basin	dimensionless				dam storage capacity (D_SC)	total volume of water stored in dam	m3
	number of days with heavy rainfall (DHR)	heavy rainfall (more than 100 mm/day)	mm/day
	river discharge (RD)	maximum discharge record in last 10 years	m3/s
	frequency of occurrence (FO)	years between floods	day

Table S2 Areal extent of component wise vulnerability in Bhagirathi basin.

FVI	Social		Economic		Environmental		Physical		Total vulnerability
	area (km2)	area (%)	area (km2)	area (%)	area (km2)	area (%)	area (km2)	area (%)	area (km2)	area (%)
Very low	1602.74	22.66	1029.83	14.56	1645.18	23.26	1780.98	25.18	1140.87	16.13
Low	1280.21	18.1	1962.76	27.75	901.10	12.74	1024.17	14.48	1612.64	22.8
Moderate	1327.60	18.77	1056.71	14.94	875.64	12.38	877.05	12.4	640.81	9.06
High	1830.49	25.88	1156.44	16.35	931.51	13.17	1425.92	20.16	1222.21	17.28
Very high	1031.95	14.59	1867.27	26.4	2719.57	38.45	1964.88	27.78	2456.45	34.73