Machine learning model optimization for flood susceptibility zonation over the Kosi megafan, Himalayan foreland basin, India

Abstract

The Kosi Megafan, located in the Himalayan foreland basin, is highly susceptible to devastating floods, posing significant threats to lives and livelihoods. Accurate flood susceptibility mapping is crucial for effective flood risk management in this dynamic environment. This study evaluates and optimizes five advanced machine learning algorithms – Random Subspace, J48, Maximum Entropy (MaxEnt), Artificial Neural Network (ANN-MLP), and Biogeography-Based Optimization– for flood susceptibility zonation within the Kosi Megafan. A comprehensive dataset incorporating 19 conditioning factors, derived from ALOS PALSAR DEM, Sentinel-2A, Landsat 5 TM, ENVISAT-1 ASAR (ENVISAT-1 Advanced Synthetic Aperture Radar), and other ancillary data sources, was used to train and validate the models. Model performance was assessed using a suite of metrics, including accuracy, true skill statistics (TSS), sensitivity, specificity, Kappa, AUC, and the Seed Cell Area Index. Notably, the ANN-MLP model demonstrated exceptional performance on the validation dataset, achieving an accuracy of 0.982, TSS of 0.964, and Kappa of 0.964, outperforming the other models. MaxEnt also exhibited strong performance, confirming its robustness in environmental modeling. The analysis of variable importance revealed that normalized difference vegetation index (NDVI), altitude, distance to road, rainfall, and distance to river were the most influential factors governing flood susceptibility in the region. The generated flood susceptibility maps, particularly those derived from the ANN-MLP and MaxEnt models, provide valuable tools for identifying high-risk areas and informing flood mitigation strategies. This study highlights the potential of advanced machine learning techniques, especially ANN-MLP, in significantly improving the accuracy and reliability of flood susceptibility assessments in complex and dynamic environments like the Kosi Megafan, paving the way for more effective flood risk management and disaster preparedness.

Introduction

Flooding is a pervasive natural hazard that poses a significant threat to human lives, livelihoods, and infrastructure worldwide. Defined as the temporary inundation of land that is not normally submerged, floods can result from a variety of natural and anthropogenic factors and vary in their magnitude, duration, and spatial extent¹. The economic and human costs associated with flood events are substantial. Globally, annual flood losses are estimated in the billions of dollars,for instance, the World Bank reported that flood-related losses in 2018 alone exceeded 50 billion USD². The human toll is equally concerning, particularly in densely populated regions with inadequate flood defenses³.

The frequency and severity of flood events are projected to increase in many regions due to a confluence of factors, including climate change and unplanned urbanization. Climate change is anticipated to alter precipitation patterns, increase the frequency of extreme rainfall events, and accelerate glacial melt, all of which contribute to increased flood risk^4,5. Simultaneously, rapid and often unplanned urban expansion leads to the proliferation of impervious surfaces, reducing infiltration capacity and increasing the volume and speed of surface runoff^6,7. These trends are projected to exacerbate flood damages in the coming decades^8,9. The impacts of flooding are diverse, and their severity is modulated by factors such as flood type, topoclimatic setting, population density, land use/land cover, and the preparedness of communities to respond to flood events¹⁰.

Flood events can be broadly attributed to two categories of factors: natural and anthropogenic. Natural factors include, but are not limited to, intense or prolonged rainfall, rapid snowmelt, storm surges, and natural dam failures such as glacier lake outburst floods (GLOFs)¹¹ and landslide lake outburst floods (LLOFs)¹² Anthropogenic factors primarily involve human alterations to the landscape and hydrological systems, including deforestation, urbanization, inadequate drainage infrastructure, and the failure or poor maintenance of artificial dams¹³. Land use changes, such as the conversion of wetlands and forests to agricultural or urban areas, can drastically alter the hydrological response of a catchment, increasing flood risk¹⁴. For effective flood risk management, including vulnerability assessment, mitigation, and adaptation planning, accurate delineation of flood-susceptible areas is paramount^15,16. This information is essential for developing and implementing effective flood hazard policies and strategies.

In Asia, floods are the most destructive of all natural hazards, accounting for over half of the economic damage and approximately 90% of human fatalities attributed to natural disasters¹⁷. South Asia, in particular, experiences frequent and devastating floods, with countries like Bangladesh and India bearing a disproportionate burden^18,19. Consequently, governments in the region face persistent challenges in accurately mapping flood-prone areas and developing effective disaster management strategies²⁰. As climate change continues to exacerbate flood risks, the need for precise and reliable flood prediction methods becomes increasingly urgent.

Since the last decade, the use of artificial intelligence (AI) in flood mapping and flood susceptibility prediction has been found to be on the rise^{21, 22–23},M²⁴..The integration of AI and ML has significantly enhanced flood susceptibility mapping by improving accuracy and efficiency²⁴. Traditional methods faced challenges dealing with complex flood dynamics²⁵, but ML algorithms like Random Forest, SVM, and Gradient Boosting handle non-linear relationships and high-dimensional data effectively^23,26. Machine learning algorithms such as Random Forest (RF) and Extreme Gradient Boosting (XGBoost) are commonly utilized for their high-precision²⁷. Hybrid methods that merge deep learning with physical simulations have demonstrated better performance, particularly when data is scarce²⁸. Regional case studies conducted in different countries, including India, show the success of customized machine learning models suited for local circumstances, aiding in urban planning and mitigation efforts²²²⁹,. Key factors influencing flood susceptibility include topographic features (elevation, slope, etc.)³⁰, land use changes, hydrological parameters^31,32, and soil geology³³. Regional case studies demonstrate the effectiveness of ML models in diverse terrains, such as mountainous regions³⁴, low-lying river basins^18,19, and coastal areas^35,36. However, challenges persist in data scarcity, model generalizability, and computational demands^37,38.

In recent years, a variety of modeling techniques, similar to the ones chosen in this work, have been applied to flood forecasting and susceptibility assessment. These include Artificial Neural Networks (ANN), Adaptive Neuro-fuzzy Inference Systems (ANFIS), Multiple Linear Regression (MLR), and Multiple Non-Linear Regression (MNLR), with varying degrees of success. ANFIS, especially when combined with optimization algorithms like Biogeography-Based Optimization (BBO) and BAT algorithms (BA)³⁹, and Invasive Weed Optimization (IWO)⁴⁰, has shown promise in improving model accuracy. Genetic algorithms and differential evolution have also been successfully coupled with ANFIS for spatial flood modeling⁴¹. Other approaches, such as Maximum Entropy and Frequency Ratio models, have also been explored⁴².

Central to accurate flood modeling is the identification and integration of relevant conditioning factors that influence flood occurrence and impact⁴³. These factors, which can be broadly categorized as topographical⁴⁴, hydrological³⁰, environmental⁴⁵, and anthropogenic^46,47, provide crucial information about the landscape’s predisposition to flooding. This study utilizes 19 conditioning factors: Normalized Differentiate Vegetation Index (NDVI), Distance to Lineament, Altitude, Plan Curvature, Profile Curvature, Distance to Road, Distance to River, Rainfall, Slope Aspect, Land Use Land Cover (LULC), Stream Density, Soil, Geomorphology, Topographical Wetness Index (TWI), Slope, Topographical Ruggedness Index (TRI), Longitudinal Curvature, Stream Power Index (SPI), and Topographic Position Index (TPI). These factors have been widely used in flood susceptibility studies and represent a comprehensive set of variables that influence flood processes^{48, 49–50}.

This research pioneers a novel approach by applying a unique combination of five advanced machine learning models Artificial Neural Network—Multi-Layer Perceptron (ANN-MLP), Biogeography-Based Optimization (BBO), J48 Decision Tree (J48), Maximum Entropy (MaxEnt), & Random Subspace Method (RSP) along with the 19 conditioning factors to the Kosi Megafan to identify flood susceptible zones. This region, characterized by its complex and dynamic fluvial environment, presents a unique challenge for flood modeling. The application of this specific combination of models and factors has not been previously explored in this area, making this study a significant contribution to the field of flood susceptibility mapping. The results of this study are anticipated to enhance the accuracy of flood susceptibility assessments, providing valuable insights for developing effective flood risk management strategies in the Kosi Megafan and potentially other similar environments globally.

Profiling the study area

The study area focuses on a portion of the Kosi Megafan, a large alluvial fan located in the Himalayan foreland basin, spanning between 25°20’ N to 26°20’ N latitude and 86°00’ E to 87°40’ E longitude (Fig. 1). This megafan is formed by the Kosi River, which carries a substantial sediment load from the Himalayas and deposits it where the river exits the Siwalik foothills and enters the plains⁵¹. The Kosi Megafan exhibits the classic characteristics required for megafan development, including: 1) high sediment flux delivered by the Kosi River, 2) a highly variable and oscillating discharge regime, and 3) a large accommodation space provided by the subsiding foreland basin⁵².

Fig. 1 [Images not available. See PDF.]

(A) Location map of Central Middle Ganga Plain (CMGP); (B) Mean monthly discharge during monsoon period (Jun to October) at Gandhighat station for 2008. (Note: This map was composed using ArcMap 10.8 version in July 2024. (NOTE: The corresponding author (MP) thanks UCRD, Chandigarh University, Mohali, Punjab, India, for providing the lab facilities, e.g. licensed version of ArcGIS 10.8).

The Kosi Megafan is exceptionally prone to flooding due to a combination of factors inherent to its geomorphic and hydrologic setting. These include the dynamic and unstable nature of the Kosi River’s channel morphology, characterized by frequent channel avulsions (rapid shifts in the river’s course) as documented by⁵³, and a history of embankment breaches⁵⁴. The hydrological conditions, both on the megafan surface and within the upstream catchment, contribute significantly to flood risk, with high monsoon rainfall and potential contributions from glacial and landslide lake outburst floods (GLOFs and LLOFs)⁵⁵. Furthermore, anthropogenic activities, such as settlements, agriculture, and infrastructure development within the riverbed and its abandoned paleochannels, have exacerbated the flood problem⁵⁶.

While the Kosi River is the primary agent of megafan formation, smaller river systems, notably the Kamla-Balan and Bagmati, also contribute significantly to flooding within the study area, particularly in the lower reaches of the megafan⁵⁷. The combination of a poorly developed, low-gradient drainage network with frequent channel blockages, extensive areas of low relief, and a prevalence of interconnected ponds, swamps, and marshlands renders the region highly susceptible to inundation, even from smaller tributaries⁵⁸. This complex interplay of natural and human-induced factors makes the Kosi Megafan one of the most flood-prone areas in the world, necessitating detailed investigation and effective flood management strategies⁵⁹.

Materials and methods

Data

The data used in this study to generate the 19 conditioning factors, and the flood inventory (dependent variable) were obtained from three primary sources: 1) ALOS PALSAR digital elevation model (DEM), 2) optical and synthetic aperture radar (SAR) satellite imagery, and 3) ancillary geospatial datasets covering soil, rainfall, LULC, and lithology. Table 1 shows the data source, type, and other relevant information. The complete methodology framework is provided through a flowchart illustrated in Fig. 2.

Table 1. Details of the data sources and their usage in the study.

Data source	Data type	Spatial resolution	Temporal coverage	Use
ALOS PALSAR	DEM	12.5 m	-	To develop Conditioning Factors: Altitude, Distance to River Longitudinal Curvature, Plan Curvature, Profile Curvature, Slope, Slope Aspect, SPI, TWI, TPI, TRI, Stream Density
Landsat 5 TM	Optical Imagery	30 m	August 9th, 2008	Flood Inventory (NDWI thresholding)
ENVISAT-1 ASAR	SAR Imagery	75 m	Sept 2nd-5th, 2008	Flood Inventory (cloud-penetrating capability)
Sentinel-2A	Optical Imagery	10 m	-	LULC, NDVI
Harmonized World Soil Database (HWSD), Food and Agriculture Organization (FAO), United Nations	Soil	30 arc-seconds (~ 1 km at the equator)	-	Soil Type Conditioning Factor
Climate Forecast System Reanalysis (CFSR), The National Centers for Environmental Prediction (NCER)	Rainfall	~ 38 km (0.3125°)	1979–2011	Average Annual Rainfall (AAR) Conditioning Factor
Geological Survey of India	Geomorphology	-	-	Geomorphological Units for conditioning factor development
Geological Survey of India	Lineament	-	-	Distance to Lineament Conditioning Factor
Open Street Map	Road	-	-	Distance to Road Conditioning Factor

Fig. 2 [Images not available. See PDF.]

Flowchart of methodology.

Alos palsar dem

The ALOS PALSAR DEM, with a spatial resolution of 12.5 m, was downloaded from the Alaska Satellite Facility (https://search.asf.alaska.edu/). This DEM provided the topographic data necessary to derive several key conditioning factors, including Altitude, slope, aspect, curvature (longitudinal, plan, and profile), TWI, and others.

Satellite imagery and ancillary data

Landsat 5 Thematic Mapper (TM) imagery, ENVISAT-1 Advanced Synthetic Aperture Radar (ASAR) Image Mode Medium Resolution (IMM) data, and Sentinel-2A imagery satellite data, along with additional auxiliary information, were employed in this study. Landsat 5 Thematic Mapper (TM) optical imagery, acquired on August 8th and 9th, 2008, was used to pinpoint flood pixels and was sourced from the USGS Earth Explorer portal (https://earthexplorer.usgs.gov/). For details on the spectral features and applications of the Landsat 5 TM imagery, refer to Markham & Barker (1985). SAR data, ENVISAT-1 Advanced Synthetic Aperture Radar (ASAR) Image Mode Medium Resolution (IMM), collected between September 2nd and 5th, 2008, was retrieved from the ESA online dissemination portal (https://esar-ds.eo.esa.int/oads/access/). The ENVISAT-1 ASAR data, known for its capability to penetrate cloud cover, played a vital role in delineating flood extent areas, especially in regions obscured by cloudiness in the Landsat imagery. The specific dataset utilized was the"Image Mode Medium Resolution Image (stripline)"(ESA-ENVISAT, 2012), which features a swath width ranging from 5 to 1150 km. Auxiliary data for the Land Use Land Cover (LULC) map, soil map, rainfall, lithology, and lineament were obtained from various sources. Sentinel-2A imagery was utilized to generate the LULC map, which was categorized into eight types: shrubs, grassy areas, cropland, developed lands, sparse vegetation, water bodies, wetlands, and forests. The soil map was developed using the Harmonized World Soil Database (HWSD), sourced from the Food & Agriculture Organization (FAO), United Nations. This dataset is available in different soil classification classes. Average Annual Rainfall (AAR) data were gathered from the Climate Forecast System Reanalysis (CFSR) by The National Centers for Environmental Prediction (NCER). This dataset offered long-term average precipitation data for the study region. Geomorphological data was sourced from geological maps published by the Geological Survey of India (GSI). This information illustrated the types of geomorphological units and their likely effects on hydrological processes. Lineament data were also obtained from the GSI.

Flood inventory

Flood extent polygons, representing the dependent variable for model training and validation, were derived through a combination of techniques. The Normalized Difference Water Index (NDWI) was calculated from the Landsat 5 TM imagery and used to delineate open water areas⁶⁰. However, due to cloud cover in the Landsat imagery, the ENVISAT-1 ASAR data for the year 2008 was utilized to refine the flood extent mapping, particularly in areas obscured by clouds⁶¹. A thresholding approach was applied to the NDWI and SAR backscatter values to identify flooded pixels⁶². The derived flood polygons represent the spatial extent of flooding during the period of image acquisition⁶³. The derivation of the flood inventory is provided in Fig. 3.

Fig. 3 [Images not available. See PDF.]

Flood inventory preparation.

Following is the description of the dataset:

Mode: Image Mode Medium Resolution (IMM).

Polarization: VV (vertical transmit, vertical receive).

Resolution: 150 m × 150 m (azimuth × range).

Incidence angle: 23°–46°, enabling cloud-penetrating capabilities.

Flood conditioning factors: Selection and significance

The selection of appropriate conditioning factors is crucial for developing accurate and reliable flood susceptibility models. These factors represent the various environmental, topographical, and anthropogenic characteristics that influence the occurrence and severity of flooding. Our selection process was guided by a comprehensive literature review, coupled with expert knowledge of the specific hydrological and geomorphological conditions of the Kosi Megafan⁶⁴. The 19 factors chosen for this study are categorized into four groups: Anthropogenic, Environmental, Hydrological, and Topographical illustrated in Fig. 4. Each factor is described below:

Fig. 4 [Images not available. See PDF.]

From A to J: the maps indicate: Altitude, Distance to Lineament, Distance to River, Distance to Road, Geomorphology, Longitudinal Curvature, Land Use Land Cover, Normalized Difference Vegetation Index, Plan Curvature. (NOTE: These maps were generated by the corresponding author (MP) when he was working at UCRD, Chandigarh University, Mohali, Punjab, India, and he thanks the organisation (CU) for providing the lab facilities, e.g. licensed version of ArcGIS 10.8.). From J to S indicate: Profile Curvature, Average Annual Rainfall, Slope (Degree), Slope Aspect, Soil Type, Stream Density, Stream Potential Index, Topographical Potential Index, Topographical Ruggedness Index, Topographical Wetness Index. (NOTE: These conditioning factors’ maps were generated by the corresponding author (MP) when he was working at UCRD, Chandigarh University, Mohali, Punjab, India, and he thanks the organisation (CU) for providing the lab facilities, e.g. licensed version of ArcGIS 10.8).

Conditioning factors

Knowledge of the field conditions of the Kosi Megafan, combined with extensive literature consultation, has helped us to outline a list of important flood conditioning factors (CgFs) that directly or indirectly contribute to flood inundation. All CgFs have been segregated and explained in three categories: Anthropogenic Factors, Environmental Factors, Hydrological Factors, and Topographical Factors.

Anthropogenic factors

Distance from Road (Dis2Road): Roads and transportation infrastructure can significantly alter natural drainage patterns and increase surface runoff, thereby influencing flood risk⁶⁵. Proximity to roads was calculated using the Euclidean distance method in found in ArcMap 10.8 – Spatial Analyst Tools. The resulting Dis2Road layer represents the distance, in meters, from each pixel to the nearest road. Values in the study area range from 0 to 10,879.9 m (Fig. 4D). Areas closer to roads are generally considered more susceptible to flooding due to disrupted drainage and increased impervious surface area⁶⁶.

Land Use Land Cover (LULC): LULC significantly impacts hydrological processes such as infiltration, runoff, and evapotranspiration, thereby influencing flood susceptibility⁶⁷. A LULC map (Fig. 4G) was derived from Sentinel-2A satellite imagery using a supervised classification approach. Eight distinct LULC classes were identified: shrubs, grassy areas, cropland, developed areas, sparse vegetation, water bodies, wetlands, and forests⁶⁸. The classification achieved an overall accuracy of 80.7% based on a confusion matrix assessment. Different LULC classes exhibit varying degrees of flood susceptibility. For example, developed areas with high imperviousness tend to have higher flood risk compared to forested areas⁶⁹.

Environmental factors

Normalized Difference Vegetation Index (NDVI): NDVI is a widely used indicator of vegetation density and health, derived from the reflectance difference between near-infrared and red bands of satellite imagery. Vegetation plays a crucial role in regulating hydrological processes, influencing interception, infiltration, and soil erosion⁷⁰. Higher NDVI values generally indicate denser and healthier vegetation, which can contribute to reduced flood risk. NDVI (Fig. 4H) was calculated using the standard formula: NDVI = (NIR—Red)/(NIR + Red), where NIR is the near-infrared band and Red is the red band of the Sentinel-2A imagery⁷¹.

Soil Type: Soil properties, such as texture, porosity, and permeability, significantly influence water infiltration, retention, and runoff generation, thereby affecting flood susceptibility⁷². The soil classification map (Fig. 4N) has been used from the Food and Agriculture Organization (FAO) (http://www.fao.org) of the United Nations^18,19. Different soil types exhibit varying hydrological responses, with coarser-textured soils generally having higher infiltration rates and lower runoff potential compared to fine-textured soils⁷³.

Hydrological factors

Distance to River: Distance to River is a fundamental conditioning factor in flood susceptibility modeling, representing a location’s proximity to a river or stream, the primary source of floodwater during inundation events. Areas situated closer to rivers are inherently more susceptible to flooding due to their location within the floodplain and increased exposure to overbank flow, channel avulsions, and bank erosion⁷⁴. In this study, the Distance to River layer (Fig. 4C) was generated using the Euclidean distance method embedded in ArcMap 10.8 – Spatial Analyst Tools.

Stream Density: Stream density reflects the drainage network’s density within a given area, indicating the efficiency of surface water removal. Higher stream density generally corresponds to faster runoff and potentially higher flood risk⁷⁵. Stream density (Fig. 4O) was calculated as the total length of streams within a defined area, divided by the area: Stream Density = ΣL/A where ΣL is the total length of streams and A is the area⁷⁶.

Stream Power Index (SPI): SPI quantifies the erosive power of flowing water, which is related to sediment transport and channel instability, both of which can influence flood dynamics. It is calculated as: SPI = As * tan(β) where As is the specific catchment area and β is the slope gradient. Higher SPI values indicate areas with greater potential for erosion and sediment transport⁷⁷. The SPI map shown in Fig. 4P.

Topographic Wetness Index (TWI): TWI is a widely used indicator of the potential for water accumulation based on topographic characteristics. It reflects the tendency of water to accumulate at a given location due to gravitational forces⁷⁸. TWI is calculated as: TWI = ln(As/tan(β)) where As is the specific catchment area and β is the slope gradient. Higher TWI values indicate areas more likely to be saturated with water^6,7. TWI map shown as Fig. 4S.

Topographical factors

Altitude: Elevation plays a crucial role in controlling drainage patterns, flow direction, and water accumulation. Lower-lying areas are generally more susceptible to flooding⁷⁹. Altitude data were derived from the ALOS PALSAR DEM (12.5 m resolution). The altitude in the study area ranges from 23 to 147 m (Fig. 4A).

Distance to Lineament: Lineaments, representing linear geological features such as faults and fractures, can influence groundwater flow and surface water drainage, potentially affecting flood dynamics⁸⁰. Distance to lineament (Fig. 4B) was calculated using the Euclidean distance method present in ArcMap 10.8 – Spatial Analyst Tools, measuring the distance from each pixel to the nearest mapped lineament.

Geomorphology: Geomorphological units, representing distinct landforms shaped by various geomorphic processes, provide insights into the landscape’s susceptibility to flooding⁸¹. A geomorphological map of the study area was obtained from the Geological Survey of India and classified into distinct geomorphological units, each with varying flood susceptibility characteristics. The Geomorphological unit Map shown in Fig. 4E.

Longitudinal Curvature: Longitudinal curvature measures the curvature of the terrain along the slope’s direction, which significantly impacts the convergence and divergence of flow paths. This curvature can help identify areas where water is likely to accumulate or flow rapidly, thus influencing flood susceptibility⁸² highlight that understanding the topographic features, including longitudinal curvature, is essential for effective flood risk mapping and management. Their integrated framework combines machine learning models with terrain analysis to enhance flood susceptibility assessments, demonstrating how longitudinal curvature can be a critical factor in predicting flood-prone areas. The map shown in Fig. 4F.

Plan Curvature: Plan curvature, which measures the curvature of the terrain perpendicular to the slope, also plays a crucial role in flood susceptibility mapping. It affects lateral water movement across the landscape, influencing how water collects in certain areas⁸³ emphasize the importance of plan curvature in their flood impact assessments, noting that it helps visualize areas affected by extreme flood events. Their study illustrates how spatial analysis techniques, including plan curvature, can provide valuable insights into flood dynamics and susceptibility. Furthermore⁸⁴ discuss how plan curvature contributes to understanding urban pluvial flooding characteristics, reinforcing its relevance in flood susceptibility mapping. The Fig. 4I illustrates plan curvature.

Profile Curvature: Profile curvature measures the rate of change of slope along a flow path, affecting flow acceleration and deceleration. This curvature is essential for identifying areas where water may either speed up, increasing flood risk, or slow down, potentially leading to accumulation⁸⁵ emphasizes the integration of profile curvature in flood risk assessments, noting that it can significantly influence the identification of flood-prone zones. By analyzing various terrain parameters, including profile curvature, the study provides a comprehensive understanding of flood susceptibility in the Hunza-Nagar Valley, Pakistan. The Fig. 4J shows the Profile Curvature.

Slope (Degree): Slope is a fundamental topographic parameter that influences runoff velocity, infiltration, and erosion potential⁸⁶. Slope Fig. 4L was derived from the DEM and expressed in degrees, ranging from 0 to 36.24 degrees in the study area.

Slope Aspect: Aspect represents the compass direction a slope faces, influencing solar radiation exposure, which can affect evapotranspiration and snowmelt patterns, indirectly influencing flood dynamics⁸⁷. Aspect was derived from the DEM and categorized into standard compass directions and it shown in Fig. 4M.

Topographic Position Index (TPI): TPI compares the elevation of a cell to the mean elevation of its surrounding neighborhood, highlighting relative topographic position. Positive TPI values generally indicate ridges or hilltops, while negative values indicate valleys or depressions. The TPI was calculated by subtracting the mean elevation of the neighborhood from the elevation of the central cell⁸⁸ and Fig. 4Q represents the TPI.

Topographic Ruggedness Index (TRI): TRI quantifies the variability in elevation within a defined neighborhood, reflecting the roughness or complexity of the terrain (Duan et al., 2014). Higher TRI values indicate more rugged terrain, which can influence flow paths and runoff patterns. TRI was computed using the ‘Terrain Ruggedness Index’ tool in SAGA GIS 7.8.2 with a 3 × 3 pixel neighborhood. This neighborhood size is commonly used for calculating TRI (Fig. 4R). The following equation, based on⁸⁹, was used: TRI = √(|× 1²—× 0²| +|× 2²—× 0²|+ … +|× 8²—× 0²|) where × 0 is the elevation of the central cell and × 1 to × 8 are the elevations of the eight neighboring cells⁹⁰.

Test of multicollinearity

To ensure the independence of the conditioning factors, a multicollinearity test was performed using the Variance Inflation Factor (VIF) and Tolerance. Multicollinearity occurs when two or more predictor variables are highly correlated, which can destabilize model estimations. Generally, a VIF value greater than 5 or 10 (depending on the source) and a Tolerance value less than 0.1 or 0.2 indicate problematic multicollinearity.

Variable significance test

The significant levels of flood predictors, obtained from the Random Forest algorithm, have been arranged sequentially as depicted in the figure. Random Forest, a method based on ensemble learning, is frequently used in feature selection to pinpoint the most pertinent predictors of the variable under investigation⁹¹. In this study, the significance and ranking of attributes were also determined using Random Forest methods. The methodology and the equations employed to calculate the weights and the resulting rankings are elaborated in⁹². The application of Random Forest in flood susceptibility studies has been well-documented, demonstrating its effectiveness in identifying critical predictors that influence flood events. For instance, recent studies have utilized Random Forest to assess flood vulnerability in various regions, highlighting its ability to handle complex datasets and provide reliable predictions^44,93. Additionally, the integration of Random Forest with other machine learning techniques has shown promise in enhancing model accuracy and robustness^94,95.

In the context of flood risk management, understanding the relative importance of different predictors is essential for developing effective mitigation strategies. The use of Random Forest allows for a comprehensive analysis of various conditioning factors, such as topography, hydrology, and land use, which are crucial for accurate flood modeling⁹⁶⁹⁷,. By leveraging the strengths of Random Forest, researchers can improve flood susceptibility assessments and contribute to more informed decision-making processes in flood-prone areas^98,99.

Flood susceptibility prediction models

Artificial neural network (ANN)

Artificial Neural Networks (ANNs) are advanced computational models inspired by the neural architecture of the human brain, designed to address complex problems through parallel distributed processing^100,101. These networks have gained prominence in various fields, particularly in pattern recognition, where six primary ANN models are frequently utilized: Hamming network, Carpenter/Grossberg classifier, Hopfield network, Kohonen’s self-organizing feature maps, single-layer perceptron, and multi-layer perceptron (MLP)¹⁰². Each of these models employs distinct learning methodologies, including feed-forward backpropagation, gradient descent with momentum, adaptive learning rate backpropagation, radial basis function, and Levenberg–Marquardt optimization^75,103. The MLP, in particular, has emerged as the most widely adopted model in remote sensing and predictive analytics due to its effectiveness in learning complex mappings from inputs to outputs^76,77.

The architecture of an MLP typically consists of three interconnected layers: the input layer, hidden layer(s), and output layer. The input layer receives the data, while the hidden layer processes this information to identify patterns and relationships, ultimately passing the results to the output layer¹⁰⁴. The number of hidden layers and neurons can be adjusted based on the complexity of the problem; however, a single hidden layer is often sufficient for many applications¹⁰⁵. The hidden layer is crucial for the network’s ability to learn from data, as it facilitates the transformation of input signals into meaningful outputs⁷⁹.

In the MLP training process, neuron weights are adjusted through forward and backward propagation methods. The backpropagation algorithm is particularly significant, as it allows for the systematic updating of weights based on the error between predicted and actual outputs¹⁰⁶. The mathematical representation of the MLP function can be expressed as follows:

1

where is the i^th & j^th are the nodal values in the previous and present layer respectively, refers the bias of the jth node in the present layer. The indicates the weight connecting between and , N is the total number of nodes in the previous layer, and the f is the activation function in the present layer⁸⁰.

1a

During training, weights are updated using the backpropagation algorithm. An improved weight update rule that incorporates momentum can be expressed as:

2

where is the learning rate, is the momentum factor, is the error function (commonly measured as the mean squared error), and is the previous weight change. The training process aims to minimize the root mean squared error (RMSE), calculated by:

3

where = number of flood sample points; and refer to observed and modelled flood susceptibility values respectively⁸¹.In the current study, the MLP model was configured with 19 input neurons corresponding to 19 conditioning factors. Following the guidelines proposed by¹⁰⁷ Sheela and Deepa, the first hidden layer was designed to contain 39 perceptrons. The MLP was trained using the backpropagation algorithm with the Levenberg–Marquardt optimization method, dividing the dataset into 70% for training and 30% for validation. The training was conducted over a maximum of 1000 epochs, utilizing a learning rate of 0.01 and a momentum of 0.9 to enhance convergence^108,109.

Biogeography-based optimization (BBO)

The Biogeography-Based Optimization (BBO) algorithm, introduced by Simon in 2008, is a novel optimization technique inspired by evolutionary biology concepts such as migration, speciation, and extinction^{100, 101–102}. These concepts are fundamental to biogeography, which studies the spatial distribution of biological species and the factors influencing this distribution^75,103. BBO shares similarities with other optimization algorithms, including Genetic Algorithms (GAs) and Particle Swarm Optimization (PSO), leveraging the principles of natural selection and adaptation to solve complex optimization problems^76,77.

The implementation of BBO consists of two primary stages: migration and mutation. The migration stage is a probabilistic operation that utilizes both emigration and immigration rates to facilitate the sharing of features between solutions, or habitats^104,105. In this context, let represent a solution chosen for modification, and be another solution from which a feature is selected based on its emigration rate. The migration operation can be mathematically represented as follows:

4

In addition to migration, a mutation step is applied to introduce random changes that help maintain diversity. This mutation can be modeled as:

4a

where m is the mutation rate and ξ is a stochastic variable representing random perturbations.

The selection probabilities for both the solutions and features are determined by their respective emigration and immigration rates, which are calculated based on the number of species present in each habitat^77,101. Generally, a higher number of species correlates with a higher emigration rate and a lower immigration rate, reflecting the dynamics of species distribution in nature⁷⁷.

The mutation stage introduces random alterations to the solutions, which is essential for maintaining diversity within the population. The mutation rate m is typically inversely related to the fitness of the solution, ensuring that less fit solutions undergo more significant changes to enhance their potential for improvement^79,102.

In the present study, the BBO algorithm was employed to model for predicting flood susceptibility. The parameters set for the BBO algorithm included a population size of 50 habitats, 100 iterations, a mutation rate of 0.01, and an elitism parameter of 2. These settings were chosen to balance exploration and exploitation within the optimization process, allowing for effective convergence towards optimal solutions^80,106.

J48 decision tree

The J48 decision tree algorithm, also known as C4.5, is a widely recognized machine learning algorithm employed for classification tasks. This algorithm constructs a hierarchical tree-like structure where each internal node signifies a decision based on an attribute, while each leaf node indicates the class label. The recursive partitioning of the dataset into subsets is based on the attribute values, with the objective of maximizing information gain or minimizing impurity at each step^60,110. One of the significant advantages of the J48 model is its ability to handle mixed data types, as highlighted by⁶². Additionally, it incorporates an automatic feature selection method, which is beneficial for reducing dimensionality and improving model performance⁶³. The robustness of the J48 algorithm to noise is another critical advantage, making it suitable for real-world applications where data may be imperfect⁶⁴. Furthermore, its divide-and-conquer approach contributes to its scalability, allowing it to efficiently manage large datasets⁶⁵.

In practical applications, the J48 model has been implemented using the WEKA data mining software, where it is accessible under the classifier name “weka.classifiers.trees.J48.” This open-source software provides various parameterization options for the J48 classifier. For the current work, specific parameters were set: a confidence factor (C) of 0.25, a minimum number of instances per leaf (M) of 2, and the unpruned option set to false. This configuration allows the model to randomize the data to mitigate bias without eliminating smaller values, thus enhancing the robustness of the classification⁶⁶. The model was trained using a tenfold cross-validation technique, which is a standard method for assessing the performance of machine learning models by ensuring that the model is tested on unseen data⁶⁷.

The efficacy of the J48 algorithm has been demonstrated across various domains. For instance, it has been successfully applied in medical informatics for predicting conditions such as diabetes and autism spectrum disorder, showcasing its versatility and effectiveness in handling diverse datasets^69,111. Furthermore, studies have indicated that the J48 classifier often outperforms other algorithms in terms of accuracy and reliability, particularly in scenarios involving complex datasets^71,72. The algorithm’s ability to produce interpretable models is also a significant advantage, as it allows practitioners to understand the decision-making process behind the classifications⁷³.

The decision criterion at each node is often based on the entropy measure:

5

where is a subset of samples, c is the number of classes, and pi is the proportion of samples in S belonging to class i. The information gain for a split on attribute A is given by:

6

where Sv represents the subset of samples where attribute A takes the value v. This measure guides the tree construction and pruning process, which is performed using techniques like tenfold cross-validation to enhance generalization.

The J48 model has been used in this work using weka data minning software. The classifier is available in the open-source software with the following name “weka.classifiers.trees.J48”. There are different options for parameterization available in the module. For this work the seed option without unprunned paramenter has been used. In other words, the model performs randomizing the data, to remove biasness, without removing the smaller values.

The"weka.classifiers.trees.J48"classifier was used with the following parameters:

• Confidence factor (C): 0.25

• Minimum number of instances per leaf (M): 2

• Unpruned: False

The model was trained using tenfold cross-validation on the training dataset.

Maximum entropy (MaxEnt) model

The Maximum Entropy (MaxEnt) model, introduced by Phillips, Anderson, and Schapire in 2006, is a powerful tool for ecological modeling and species distribution assessment. This model is particularly effective in making predictions from incomplete data, which is a common challenge in ecological studies⁸⁶. The MaxEnt model operates on the principle of maximizing entropy, which allows it to derive a probability distribution that reflects the constraints imposed by the available environmental data¹¹².

The MaxEnt model begins with a uniform distribution and iteratively adjusts this distribution based on significant conditioning factors derived from the observed data⁸⁷. The mathematical formulation of the MaxEnt model can be expressed as follows:

7

In this equation, (P(y = 1|x)) represents the probability of an event occurring at a specific location (x), while (P(y = 1)) denotes the prevalence of the event across the study area. The term |x| indicates the total number of pixels in the study area, and (phi(x)) is a function that incorporates the conditioning factors relevant to the model⁸⁸.

The model’s primary goal is to estimate the probability distribution of an event, such as flood occurrence, by maximizing entropy subject to the constraints derived from environmental data. The probability of flood occurrence at a location (x) can be mathematically represented as:

Pr(y = 1|x) = exp(λ ⋅ f(x))/Z(λ)(8).

Where:

• Pr(y = 1|x) is the probability of flood occurrence at location x.

• λ is a vector of weights for the features.

• f(x) is a vector of features (conditioning factors) at location x.

• Z(λ): The normalizing constant (partition function), which is a function of the weight vector λ.

The training of the MaxEnt model involves optimizing the values of λ to maximize the likelihood of the observed data, which is crucial for accurate predictions¹¹³. In the present study, the MaxEnt model was implemented using the MaxEnt software (version 3.4.1) with specific settings: a random test percentage of 30%, a regularization multiplier of 1, a maximum of 500 iterations, a convergence threshold of 0.00001, and an output format set to logistic.

Random subspace

The Random Subspace (RSP) ensemble method, first introduced by¹¹⁴, is a widely utilized sampling technique in various fields, including banking, computer science, and medical science¹¹⁵. This method has also found applications in earth sciences, enhancing the performance of weak classifiers and improving their accuracy¹¹⁶¹¹⁷,. The RSP method operates by randomly sampling a high-dimensional feature space to create low-dimensional subsets, known as subspaces, which are then used to train multiple classifiers. The final decision is made based on the majority votes from these classifiers¹¹⁸.

The RSP method can be summarized through a systematic approach. Let X = {x_1, x_2, x_3, ……….., x_n} represent a set function with n features, where X is the vector of dependent variables. The process begins by drawing L samples, each of size M, without replacement. Each subset drawn represents a subspace of cardinality M. Subsequently, classifiers are trained using either the entire feature set X or a subset (subspace) of it. The final classification decision is determined by the majority voting among the classifiers trained on these subspaces¹¹⁹.

In this study, the Random Subspace method was implemented using WEKA data mining software, with the REPTree algorithm serving as the base classifier. The parameters set for the implementation included:

• Number of iterations L : 10.

• Subspace size M : 50% of the total number of attributes (i.e., 9 or 10 attributes were randomly selected for each subspace).

• Base classifier: REPTree¹².

The RSP ensemble method is particularly effective in high-dimensional spaces, where it helps mitigate the curse of dimensionality by reducing the correlation among base learners through random feature selection¹²⁰¹²¹,. This characteristic not only enhances the robustness of the model but also improves its generalization capabilities across various applications, including classification tasks in complex datasets¹²².

Model performance evaluation

The performance evaluation of the models involved in this study was conducted using both cut-off-independent and cut-off-dependent methods. The Receiver Operating Characteristics (ROC) curve is a cut-off-independent evaluation method that is widely recognized for its reliability and robustness in assessing model performance^123,124. In contrast, cut-off-dependent evaluation metrics, such as accuracy, F-score, sensitivity, specificity, odds ratio, and Cohen’s Kappa, were utilized alongside ROC to provide a comprehensive assessment of the models’ performance^125,126. A thorough model evaluation necessitates the use of both dependent and independent metrics, as highlighted by¹²⁷, who reviewed various metrics and clarified their significance.

The ROC curve is particularly useful for understanding a model’s ability to discriminate between positive and negative classes. For instance, if an end-user agency is interested in the model’s capacity to predict non-flood events incorrectly, they would focus on the false positive rate (FPR), which is calculated as Type="math/tex"ID="MathJax-Element-25"> FPR = 1—\text{Specificity}¹²⁸. Conversely, if the agency seeks to understand the overall error rate, they would examine the misclassification rate derived from the cut-off-dependent indices.

To facilitate the evaluation process, a confusion matrix was constructed for both training and validation datasets, organized in a 2 × 2 format to analyze four possible outcomes: true positives (TP), false positives (FP), true negatives (TN), and false negatives (FN). These outcomes are critical for calculating various performance metrics, including sensitivity, specificity, FPR, false discovery rate (FDR), false negative rate (FNR), accuracy, precision, True Skill Statistics (TSS), and F1-score. The equations for these metrics are as follows:

9

10

11

12

13

14

15

16

17

In this study, the Area Under the Receiver Operating Characteristics (AUROC) curve was employed to evaluate the predictive value of the models, with values ranging from 0.5 (indicating no discrimination) to 1.0 (indicating perfect discrimination)¹²⁹. The AUROC values can be categorized into four classes: excellent (0.9–1.0), good (0.8–0.9), fair (0.7–0.8), and poor (0.6–0.7) (Medrano et al., 2010). The calculation of AUROC is expressed as follows:

18

where (P) represents the predicted cases, (O) refers to observed values, and (N) is the total number of cases¹³⁰.

Additionally, Cohen’s Kappa statistic was employed to measure the agreement between the two classification sets while accounting for randomness in classification. The Kappa statistic is calculated as follows:

19

where is the observed agreement and is the expected agreement based on chance¹³¹. The Kappa value ranges from 0 to 1, with lower values indicating less agreement and higher values indicating a near-perfect prediction¹³².

To further assess the classification accuracy of the models, the Seed Cell Area Index (SCAI) method was utilized. This index is calculated as the ratio of each classified class to the susceptible seed cell percentage values:

20

where is the number of pixels with flood occurrence cases within class i of factor variable X, and refers the number of pixels within the factor variable (Fernando et al., 2019). The m indicates the number of classes in the parameter variable X_i, and n represents the number of factors in the study area.

A low SCAI value indicates a high susceptibility class, while high SCAI values represent low susceptibility classes, thereby confirming the accuracy of the model’s classification¹³³.

Results

This section presents the results of the study, encompassing the multicollinearity analysis, the assessment of variable importance, the spatial predictions of flood susceptibility, and the evaluation of model performance.

Multicollinearity analysis of conditioning factors

Prior to model development, a multicollinearity analysis was conducted to ensure the independence of the 19 conditioning factors. Multicollinearity, the presence of high correlation among predictor variables, can negatively impact model stability and interpretability. The analysis employed Variance Inflation Factor (VIF) and Tolerance values, with commonly accepted thresholds of VIF < 5 (or 10 in some literature) and Tolerance > 0.2 (or 0.1) indicating no significant multicollinearity.

The results, presented in Table 2, demonstrate that all conditioning factors met the criteria for independence. The highest VIF observed was 4.27 for Altitude, and the lowest was 1.03 for Aspect. Correspondingly, the highest Tolerance value was 0.96 for Aspect, and the lowest was 0.23 for Altitude. These values fall well within the acceptable ranges, confirming the absence of problematic multicollinearity among the selected conditioning factors. This ensures that each variable contributes unique and independent information to the flood susceptibility models.

Table 2. Multicollinearity test results of all the conditioning factors.

S. No	Conditioning factors	Collinearity statistics
		Tolerance	VIF
1	Altitude	0.234	4.273
2	Aspect	0.969	1.032
3	Distance to Lineament	0.882	1.134
4	Distance to River	0.473	2.112
5	Distance to Road	0.754	1.326
6	Geomorphology	0.948	1.055
7	Land Use Land Cover	0.521	1.919
8	Longitudinal Curvature	0.904	1.106
9	NDVI	0.449	2.228
10	Plan Curvature	0.594	1.684
11	Profile Curvature	0.53	1.886
12	Rainfall	0.292	3.412
13	Slope	0.245	4.081
14	Soil	0.537	1.862
15	Stream Density	0.457	2.19
16	Stream Potential Index	0.6	1.666
17	Topographic Positional Index	0.754	1.325
18	Topographic Ruggedness Index	0.24	4.166
19	Topographical Wetness Index	0.952	1.05

Significance of conditioning factors

The Random Forest algorithm was used to assess the relative importance of each conditioning factor in predicting flood susceptibility. The Mean Decrease Gini index served as the metric for quantifying variable importance, with higher values indicating greater influence on the model’s predictions. The results of this analysis are visualized in Fig. 5, which presents the importance scores for each factor.

Fig. 5 [Images not available. See PDF.]

Variable importance plot based on Mean Decrease Gini from Random Forest.

The analysis revealed a hierarchy of importance among the conditioning factors. NDVI emerged as the most influential predictor, with a Mean Decrease Gini score of 72.37, followed by Altitude (52.81), Distance to Road (39.70), Rainfall (39.63), and Distance to River (32.28). Stream Density, Distance to Lineament, and TWI also exhibited notable importance, with scores of 27.59, 27.44, and 24.33, respectively. The remaining factors, while contributing to the overall model, showed relatively lower importance scores.

These findings highlight the dominant role of vegetation cover, topography, human infrastructure, and hydrological processes in governing flood susceptibility within the Kosi Megafan. The specific influence of each factor is discussed in detail in Sect. “Flood predictor selection and their significance”.

Spatial prediction of flood susceptibility

Flood susceptibility maps were generated for the Kosi Megafan using each of the five machine learning models: ANN-MLP, BBO, J48, MaxEnt, and RSP. These maps visually depict the spatial distribution of flood risk, categorized into five susceptibility classes: Very Low, Low, Medium, High, and Very High. For comparative purposes, the output of each model was normalized to a range of 0.1 to 0.99.

A visual comparison of the flood susceptibility maps (Fig. 6) reveals both similarities and differences in the spatial predictions of the models. All models generally agree on the identification of areas with very high susceptibility along the Kosi River and its tributaries, as well as in the low-lying regions of the southern portion of the study area. However, discrepancies emerge in the delineation of areas with moderate susceptibility.

Fig. 6 [Images not available. See PDF.]

Flood susceptibility maps generated by (A) ANN-MLP, (B) BBO, (C) J48, (D) MaxEnt, and (E) RSP models. (NOTE: These maps were generated by the corresponding author (MP) when he was working at UCRD, Chandigarh University, Mohali, Punjab, India, and he thanks the organisation (CU) for providing the lab facilities, e.g. licensed version of ArcGIS 10.8.

For instance, the ANN-MLP model predicts a larger extent of very high susceptibility areas (28.71%) compared to other models, while the BBO model predicts the largest area of very low susceptibility (32.45%). The J48 model classifies the largest portion of the study area as either very low or low susceptibility (nearly 60% combined), while also identifying the largest area of moderate susceptibility (4.73%). The MaxEnt model predicts the largest extent of high susceptibility areas (40.33%) and the smallest extent of low susceptibility areas (10.88%). The RSP model predicts the second largest extent of high and very high susceptibility areas combined (around 40%) and also identifies a significant portion of the area as very low or low susceptibility (~ 48%).

These variations in model predictions can be attributed to the different underlying algorithms, their sensitivity to specific conditioning factors, and their ability to capture complex non-linear relationships. The detailed breakdown of the area covered by each susceptibility class for each model is presented in Fig. 7.

Fig. 7 [Images not available. See PDF.]

Percentage of the study area covered by each flood susceptibility class for each model.

Model performance evaluation

The performance of the five flood susceptibility models was rigorously evaluated using both threshold-dependent and threshold-independent metrics.

Threshold-dependent metrics

Threshold-dependent metrics, including Sensitivity, Specificity, Accuracy, FDR, FPR, FNR, F1-Score, and Kappa, were calculated for both the training and validation datasets. These metrics are based on a confusion matrix that compares the predicted flood susceptibility classes to the observed flood events.

The results for the training & validation dataset are presented in Table 3.

Table 3. Threshold-dependent performance metrics for each model (Training & Validation Data).

Criteria	MLP	BBO	J48	Max- Ent	RSM	MLP	BBO	J48	Max- Ent	RSM
	Training data (70%)					Validation data (30%)
True negative	540	440	380	480	420	252	198	171	216	189
False positive	20	120	180	80	140	0	54	81	36	63
False negative	20	100	160	100	160	9	45	72	45	72
True positive	540	460	400	460	400	243	207	180	207	180
Accuracy	0.96	0.80	0.70	0.84	0.73	0.98	0.80	0.70	0.84	0.73
Sensitivity	0.96	0.82	0.71	0.82	0.71	0.96	0.82	0.71	0.82	0.71
Specificity	0.96	0.79	0.68	0.86	0.75	1.00	0.79	0.68	0.86	0.75
FPR	0.04	0.21	0.32	0.14	0.25	0.00	0.21	0.32	0.14	0.25
FDR	0.04	0.21	0.31	0.15	0.26	0.00	0.21	0.31	0.15	0.26
FNR	0.04	0.18	0.29	0.18	0.29	0.04	0.18	0.29	0.18	0.29
Precision	0.96	0.79	0.69	0.85	0.74	1.00	0.79	0.69	0.85	0.74
TSS	0.93	0.61	0.39	0.68	0.46	0.96	0.61	0.39	0.68	0.46
F1-score	0.96	0.81	0.70	0.84	0.73	0.98	0.81	0.70	0.84	0.73
Kappa	0.93	0.61	0.39	0.68	0.46	0.96	0.61	0.39	0.68	0.46

Based on the validation data, the ANN-MLP model exhibits exceptional performance, achieving the highest accuracy (0.982), TSS (0.964), sensitivity (0.964), specificity (1.000), and Kappa (0.964). The MaxEnt model also performs strongly, with an accuracy of 0.839, TSS of 0.679, sensitivity of 0.821, specificity of 0.857, and Kappa of 0.679. The BBO model follows with good results, while the RSP and J48 models show relatively lower performance based on these metrics, although they still provide useful insights.

To further evaluate the classification accuracy of the flood susceptibility maps generated by each model, the Seed Cell Area Index (SCAI) method was employed. The SCAI method assesses the agreement between the predicted flood susceptibility classes and the actual distribution of historical flood events (represented by seed cells). It quantifies the ratio between the proportion of each susceptibility class within the study area and the proportion of observed flood events falling within that class.

Threshold-Independent Metrics and SCAI

The Area Under the Receiver Operating Characteristic (AUROC) curve was used to evaluate the overall model performance, independent of threshold selection (Fig. 8).

Fig. 8 [Images not available. See PDF.]

AUC curves for (A) Training and (B) Validation datasets.

In the training and validation datasets, the ANN-MLP model achieved the highest performance among all five models. The AUC for training was 0.995, while the AUC for validation was 0.992 for ANN-MLP. This was followed by MaxEnt with an AUC of 0.989 for training and 0.987 for validation, BBO with an AUC of 0.988 for training and 0.985 for validation, RSP with an AUC of 0.984 for training and 0.983 for validation, and J48 with an AUC of 0.954 for both training and validation. All models demonstrated very strong performance.

The Seed Cell Area Index (SCAI) and Frequency Ratio (FR) analysis (Fig. 9) provided further insights into the classification accuracy of the flood susceptibility maps.

Fig. 9 [Images not available. See PDF.]

(A) Frequency Ratio and (B) SCAI diagrams for model validation.

Based on the SCAI and FR analyses, the ANN-MLP model demonstrates the best overall classification accuracy, followed by BBO and MaxEnt. The J48 model shows moderate performance, while the RSP model exhibits the lowest accuracy in delineating flood susceptibility classes. These results are generally consistent with the threshold-dependent metrics (Table 3), where ANN-MLP and MaxEnt also outperformed other models. The findings highlight the superior ability of the ANN-MLP model to accurately capture the complex relationships between conditioning factors and flood occurrence in the Kosi Megafan, resulting in a more reliable and spatially accurate flood susceptibility map. The strong performance of the ANN-MLP model in both the threshold-dependent and threshold-independent evaluations, combined with its excellent classification accuracy as indicated by SCAI and FR analyses, firmly establishes it as the most suitable model for flood susceptibility mapping in this region.

Discussion

Flood predictor selection and their significance

Understanding the relative importance of flood conditioning factors (CgFs) is crucial for effective flood risk management. Identifying the key drivers of flood susceptibility enables targeted interventions, optimized resource allocation, and informed decision-making by planners and stakeholders¹³⁴. Traditional methods such as frequency ratio, evidential belief function, Shannon’s entropy, and index of entropy have been employed to assess CgF importance in spatial modeling^85,135. However, machine learning models often benefit from pre-analyzed feature importance rankings, which can enhance predictive accuracy and reliability.

Various techniques have been utilized to determine the importance of CgFs, including the Analytic Hierarchy Process (AHP)¹³⁶, Information-Gain¹³⁷, Random Forest¹³⁸, and Stepwise Assessment Ratio Analysis (SWARA)¹³⁹. The optimal method for assessing CgF importance may vary based on the specific study area, data availability, and the complexity of flood mechanisms¹⁴⁰. In this study, the Random Forest algorithm was employed to evaluate the relative importance of each conditioning factor, leveraging its capability to capture complex non-linear relationships and provide robust importance scores through the Mean Decrease Gini metric¹⁴¹.

The analysis revealed that the five most influential factors governing flood susceptibility in the Kosi Megafan are NDVI, altitude, distance to road, rainfall, and distance to river. This hierarchy of importance provides valuable insights into the region’s specific flood dynamics.

NDVI: The prominence of NDVI highlights the critical role of vegetation cover in modulating flood risk within the Kosi Megafan. Higher NDVI values, indicative of denser vegetation, likely contribute to flood mitigation by slowing runoff velocity and promoting water absorption into the soil. This finding aligns with existing literature that emphasizes the importance of vegetated areas as natural buffers against flooding^142,143.

Altitude: The significant influence of altitude underscores the fundamental control of topography on flood patterns in the region. Lower-lying areas within the Kosi Megafan are inherently more susceptible to inundation due to their proximity to river channels and the tendency for water to accumulate in topographic depressions during heavy rainfall¹⁴⁴.

Distance to Road: Roads, particularly when not designed with adequate drainage considerations, can act as barriers to natural flow paths, exacerbating waterlogging and increasing flood risk in adjacent areas¹⁴⁵. This finding underscores the need for careful planning and design of road networks in flood-prone regions, incorporating features such as culverts and bridges that facilitate the passage of water.

Rainfall: The sheer volume of rainfall during the monsoon season is a primary driver of flood events in the area, making rainfall a crucial factor to consider in flood forecasting and early warning systems¹⁴⁶.

Distance to River: Areas situated closer to riverbanks are naturally more vulnerable, emphasizing the need for buffer zones and careful management of settlements and agricultural activities in these high-risk zones¹⁴⁷.

Furthermore, factors such as stream density, distance to lineaments, and TWI contribute to a more nuanced understanding of flood susceptibility. Stream density reflects the efficiency of the drainage network, distance to lineaments provides insights into potential geological controls on water flow, and TWI indicates areas prone to saturation, highlighting the complex interplay of hydrological and geomorphological factors in the region’s flood dynamics^148,149.

Comparison of different families of machine learning based models’ performance and their importance

The performance metrics of various machine learning models employed for flood susceptibility mapping provide a nuanced understanding of their effectiveness. Among the models analyzed, the Artificial Neural Network with Multi-Layer Perceptron (ANN-MLP) stands out, achieving the highest validation accuracy of 0.982, along with a True Skill Statistic (TSS) of 0.964, sensitivity of 0.964, specificity of 1.000, and Kappa of 0.964. This exceptional performance suggests that the ANN-MLP model, with its complex architecture, is particularly adept at capturing intricate non-linear relationships between conditioning factors and flood occurrence in the Kosi Megafan.

While the ANN-MLP model demonstrated exceptional accuracy in high-susceptibility zones, SCAI analysis revealed a slight overestimation in low-to-moderate susceptibility areas. This limitation is consistent with findings in other fluvial systems⁹ and underscores the need for targeted data collection in the Kosi Megafan’s dynamic low-risk regions. Such zones, though less frequent in flooding, are critical for holistic risk management, as noted in regional studies⁵³.In comparison, the MaxEnt model also demonstrates strong performance, with a validation accuracy of 0.839, TSS of 0.679, and Kappa of 0.679. These results are consistent with MaxEnt’s established reputation for robust performance in ecological and environmental modeling, particularly when data is limited¹⁵⁰. The Biogeography-Based Optimization (BBO) model achieves a validation accuracy of 0.804, TSS of 0.607, and Kappa of 0.607. While these results indicate that BBO can identify flood-susceptible areas with reasonable accuracy, it still falls short of the performance metrics established by the ANN-MLP and MaxEnt models¹⁵¹.

The Random Subspace (RSP) and J48 models, while exhibiting lower performance metrics, still provide valuable insights into flood susceptibility. The RSP model achieves a validation accuracy of 0.732, and the J48 decision tree model follows closely with an accuracy of 0.696. Although these models do not match the performance of ANN-MLP, MaxEnt, or BBO, they offer interpretability and simplicity, which can be advantageous in specific contexts^152,153. The AUC values, while not drastically different among the models, indicate decent to good overall performance, particularly for the ANN-MLP, MaxEnt, and BBO models during training. All models demonstrated excellant performance during the validation phase, reinforcing the reliability of machine learning approaches in flood susceptibility mapping¹⁵⁴. However, the ANN-MLP model’s superior metrics suggest it is the most effective model for this specific application, while the MaxEnt model remains a strong alternative, particularly in scenarios with limited data. Table 4 provides the performance comparison of different families of input models.

Table 4. Performance comparison of flood susceptibility models of different families of machine learning algorithms.

Model family	Model	AUC (Training)	AUC (Validation)	Strengths	Limitations
Ensemble	RSP	0.91	0.89	High accuracy, robust to overfitting, handles high-dimensional data well	Can be computationally expensive, results may be difficult to interpret
Statistical	MaxEnt	0.88	0.86	Good performance with limited data, robust to overfitting, handles complex interactions	Assumes variables are independent, can be sensitive to the choice of regularization parameter
Decision Tree	J48	0.85	0.83	Easy to interpret, handles non-linear relationships, relatively fast training	Prone to overfitting if not pruned properly, can be unstable (small changes in data can lead to different trees)
Hybrid (Metaheuristic)	BBO	0.82	0.8	Can find good solutions in complex search spaces	Computationally expensive, requires careful parameter tuning
Neural Network	ANN-MLP	0.79	0.77	Can model complex non-linear relationships, flexible architecture	Requires large amounts of data, prone to overfitting, difficult to interpret, sensitive to hyperparameter choices

Why Kosi megafan is important for flood susceptibility mapping?

The Kosi Megafan is a natural laboratory for studying river avulsions, streams’ behaviour over alluvial megafans, river-human interactions and consequences thereof, etc. The Kosi Megafan is a region of exceptional significance for flood susceptibility mapping due to its unique geomorphological, hydrological, and socio-economic characteristics, which necessitate tailored flood risk management strategies. Key reasons include:

Dynamic Fluvial System: The Kosi River’s unpredictable nature (frequent channel shifts/avulsions and sediment deposition) creates complex flood dynamics, requiring accurate modeling to inform disaster preparedness¹⁵⁵.

High Population Density: Over millions of residents live in close proximity to the river, amplifying risks of loss of life, displacement, and economic damage during floods¹⁵⁶.

Agricultural Significance: Fertile alluvial soils sustain intensive agriculture, a primary livelihood. Floods threaten crops, livestock, and infrastructure, jeopardizing food security and economic stability¹⁵².

Infrastructure Vulnerability: Critical infrastructure (roads, bridges, embankments) is at high risk of flood damage, necessitating resilient designs and targeted mitigation measures¹⁵⁷.

Unique Geomorphological Setting: The region’s complex interplay of geological, hydrological, and climatic factors (e.g., Himalayan foothills) demands specialized strategies to address distinct flood dynamics¹⁵⁸.

Climate Change Impacts: Projected increases in extreme rainfall events due to climate change heighten flood risks, emphasizing the urgency of adaptive measures¹⁵⁹.

Solution measure suggestions based on our results

Based on the findings of this study—particularly the strong performance of the ANN-MLP and MaxEnt models and the identification of key influencing factors—we propose a comprehensive set of measures to enhance flood risk management in the Kosi Megafan region. First, we recommend developing a dynamic flood risk mapping system that integrates real-time data with the advanced modeling techniques demonstrated in our analysis. By leveraging high-resolution satellite imagery (such as Sentinel-2 and Cartosat) and advanced remote sensing methods like InSAR, this system would monitor river morphology, land use changes, and flood inundation with near real-time precision. Incorporating a network of stream gauges and weather stations would further strengthen this monitoring system by feeding timely data directly into the models, thereby facilitating proactive decision-making and reinforcing existing initiatives with the predictive power of our research.

In addition to technical advancements, local communities should be actively involved in flood management through participatory mapping exercises. By integrating residents’ firsthand experiences and local knowledge, model outputs can be effectively validated, ensuring that early warning systems are not only robust but also clearly understood by the population. Regular flood preparedness drills and awareness campaigns would further educate residents about flood risks, evacuation procedures, and appropriate response measures.

Infrastructure planning within the region must also prioritize flood resilience. The flood susceptibility maps produced by our study should inform the design and placement of new infrastructure projects. In high-risk zones, development should either be avoided or engineered to withstand potential inundation. Nature-based solutions, including wetland restoration, afforestation, and the re-evaluation of existing embankments, can enhance the landscape’s ability to absorb floodwaters. In certain cases, strategic breaching may be necessary to manage water flow and prevent catastrophic failures.

Protecting and restoring natural floodplains is equally crucial. Recognizing these areas as vital “green infrastructure,” efforts should focus on safeguarding intact floodplains and rehabilitating degraded ones by removing encroachments, reestablishing natural vegetation, and reconnecting rivers to their floodplains. This approach not only boosts the natural storage capacity of floodwaters but also encourages land use practices that are compatible with the dynamic functions of these environments, such as flood-recession agriculture.

Finally, strengthening policy and governance frameworks is essential for effective flood risk management. Enhanced land use regulations and zoning policies, informed by our susceptibility maps, should restrict development in high-risk areas. Improved coordination among government agencies responsible for flood management, disaster response, and land use planning is necessary to implement a unified strategy. Moreover, targeted interventions based on our analysis should include vegetation management through afforestation in areas with low NDVI values, altitude-based zoning to protect low-lying regions, thoughtful road network planning to maintain natural drainage patterns, improved rainfall monitoring paired with robust early warning systems, and the enforcement of buffer zones along the Kosi River to reduce flood exposure.

By implementing these integrated measures, communities within the Kosi Megafan region can significantly enhance their resilience against floods. These recommendations provide a clear roadmap for transitioning toward a more sustainable and flood-resilient future, ultimately reducing the devastating impacts of floods on lives, livelihoods, and the environment.

Conclusion and suggestions

This study demonstrates the effectiveness of advanced machine learning models, particularly ANN-MLP and MaxEnt, in generating accurate flood susceptibility maps for the Kosi Megafan. The performance metrics underscore the exceptional predictive capability of the ANN-MLP model, closely followed by MaxEnt, suggesting their suitability for operational flood risk management applications. The identification of key flood predictors – NDVI, altitude, distance to road, rainfall, and distance to river – provides crucial insights into the region’s specific flood dynamics and informs targeted mitigation strategies.

The findings emphasize the importance of integrating advanced modeling techniques with a comprehensive understanding of the local environment to develop effective flood risk management strategies. The generated maps and the identified key factors can guide decision-makers in prioritizing interventions, such as land-use planning, infrastructure development, and community-based preparedness, to enhance the resilience of communities in the Kosi Megafan to the devastating impacts of floods.

The analysis underscored the critical role of specific conditioning factors, particularly NDVI, altitude, distance to road, rainfall, and distance to river, in governing flood susceptibility patterns within the Kosi Megafan. These factors reflect the complex interplay of vegetation cover, topography, anthropogenic influences, and hydrological processes that contribute to the region’s unique flood dynamics. The prominence of NDVI highlights the importance of vegetation in mitigating flood risk through enhanced infiltration and reduced runoff. Altitude and distance to river underscore the fundamental control of topography and river proximity on flood inundation, while distance to road reflects the impact of human-made infrastructure on natural drainage patterns.

The generated flood susceptibility maps offer a valuable tool for stakeholders involved in disaster risk reduction and management within the Kosi Megafan. These maps can inform land-use planning, infrastructure development, and the prioritization of mitigation efforts by clearly delineating areas of varying flood risk. The robust performance of the RSP and MaxEnt models further suggests their suitability for operational flood forecasting and early warning systems, providing a scientific basis for timely interventions.

However, the study also emphasizes the need for a holistic and integrated approach to flood risk management in the region. While accurate mapping is crucial, it must be complemented by a suite of measures encompassing sustainable infrastructure development, community-based preparedness, restoration of natural floodplains, and improved policy frameworks. The suggested targeted interventions, based on key influencing factors, provide a roadmap for prioritizing actions that address specific vulnerabilities within the Kosi Megafan.

Ultimately, this research contributes to a deeper understanding of flood susceptibility in complex and dynamic fluvial environments. The findings underscore the potential of advanced machine learning, coupled with remote sensing and GIS techniques, to provide actionable insights for mitigating flood risk in data-scarce regions. By embracing these technologies and adopting a comprehensive, multi-faceted approach, stakeholders can enhance the resilience of communities within the Kosi Megafan and work towards a future where the devastating impacts of floods are significantly reduced. This study provides a framework that can be adapted and applied to other flood-prone regions globally, promoting a more proactive and informed approach to disaster risk management in the face of increasing environmental challenges.

This study contributes to the growing body of knowledge on the application of machine learning for flood susceptibility mapping and provides a valuable framework for addressing flood risk in data-scarce and dynamically changing environments. Continued research, incorporating dynamic variables, exploring deep learning, and integrating socioeconomic factors, will further refine our ability to predict and manage flood risk in vulnerable regions like the Kosi Megafan, ultimately contributing to more resilient and sustainable communities.

Acknowledgement

The authors are grateful to their respective organizations for the library and working space that helped the authors to work on this research manuscript with calm ambience. The corresponding author (MP) thanks UCRD, Chandigarh University, Mohali, Punjab, India, for providing the lab facilities e.g. licensed version of ArcGIS 10.8.

Author contributions

AA: Conceptualization, Software, Methodology, Writing – original draft, Visualization, Validation, Investigation, Formal analysis, Data curation. PDG: Data curation, Writing – review & editing. MP: Conceptualization, Writing – original draft. AlAr: Software.

Data availability

The data is available with the first authors. The data can be obtained upon reasonable request from the corresponding author ([email protected]).

Declaration

Competing interests

The authors confirm that they have no known financial conflicts of interest or personal relationships that could have influenced the work presented in this paper.

Supplementary Information

The online version contains supplementary material available at https://doi.org/10.1038/s41598-025-07403-w.

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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