Flood Susceptibility Mapping in Punjab, Pakistan: A Hybrid Approach Integrating Remote Sensing and Analytical Hierarchy Process

Abstract

Flood events pose significant risks to infrastructure and populations worldwide, particularly in Punjab, Pakistan, where critical infrastructure must remain operational during adverse conditions. This study aims to predict flood-prone areas in Punjab and assess the vulnerability of critical infrastructures within these zones. We developed a robust Flood Susceptibility Model (FSM) utilizing the Maximum Likelihood Classification (MLC) model and Analytical Hierarchy Process (AHP) incorporating 11 flood-influencing factors, including “Topographic Wetness Index (TWI), elevation, slope, precipitation (rain, snow, hail, sleet), rainfall, distance to rivers and roads, soil type, drainage density, Land Use/Land Cover (LULC), and the Normalized Difference Vegetation Index (NDVI)”. The model, trained on a dataset of 850 training points, 70% for training and 30% for validation, achieved a high accuracy (AUC = 90%), highlighting the effectiveness of the chosen approach. The Flood Susceptibility Map (FSM) classified high- and very high-risk zones collectively covering approximately 61.77% of the study area, underscoring significant flood vulnerability across Punjab. The Sentinel-1A data with Vertical-Horizontal (VH) polarization was employed to delineate flood extents in the heavily impacted cities of Dera Ghazi Khan and Rajanpur. This study underscores the value of integrating Multi-Criteria Decision Analysis (MCDA), remote sensing, and Geographic Information Systems (GIS) for generating detailed flood susceptibility maps that are potentially applicable to other global flood-prone regions.

1. Introduction

Floods are the most frequent and destructive of all natural catastrophes globally, making them one of the most significant hydro-meteorological hazards. They cause massive economic losses yearly and affect millions [1]. There are four main types of floods: urban floods, coastal floods, river floods, and flash floods [2,3]. Flash floods are characterized by a rapid rise and fall, typically with little or no warning, and are usually caused by heavy rainfall over a small area. These events often include pluvial flooding, which occurs before runoff enters a watercourse, and fluvial flooding, when a watercourse’s capacity is quickly exceeded [4]. Flash floods can develop rapidly, often due to heavy rain or melting snow, especially in steep areas where water rushes downhill quickly. Human activities, such as urbanization and deforestation, combined with the effects of climate change, exacerbate the consequences of flooding. The expansion of urban areas and climate change have led to more frequent and intense floods. This problem is particularly severe in Mediterranean countries, where flash floods are common, and global warming is expected to worsen these floods, leading to even more significant damage [5,6,7,8,9]. To mitigate the impacts of flash floods, it is essential to forecast and identify flood-prone regions [10,11]. Flood susceptibility refers to the likelihood of an area experiencing flooding based solely on physical and environmental factors such as TWI, LULC, and proximity to water bodies. This concept does not consider flood frequency, intensity, or potential impacts but focuses on identifying areas naturally prone to flooding [12]. In contrast, flood hazard assessments account for the likelihood and severity of floods, incorporating historical data and modeling to predict flood intensity and frequency. This distinction influences methodology: while Flood Susceptibility Mapping (FSM) relies on geographic and environmental data, flood hazard assessments require dynamic modeling and flood frequency analysis to inform detailed risk management strategies [13].

Due to its ability to process large volumes of spatial data and visually represent the results, GIS has greatly expanded research in flood susceptibility. Data-driven approaches, which include statistical and machine learning models, aim to link Flood Conditioning Factors (FCFs) with previously flooded areas [14]. Several popular statistical methods are used to analyze flood-related data, including the “Frequency Ratio (FR), Statistical Index (SI), Weight of Evidence (WoE), Index of Entropy (IoE), and Evidentiary Belief Function (EBF)” [15,16]. Many researchers also use machine learning models to predict flood likelihood. Two of the most widely used models are Random Forest (RF) and Support Vector Machine (SVM) [8,17,18,19,20]. Other commonly used models in flood research include “K-Nearest Neighbors (KNNs), Decision Trees (DTs), LightGBM, and Extreme Gradient Boosting (XGBoost)” [21,22,23]. Given the complexity of flood prediction and modeling limitations, many researchers have turned to hybrid models that combine the above methods [24,25]. For example, four hybrid models combining WoE and FR with SVM have been used to map flood sensitivity, while others have combined SI with benchmark SVM and RF [26].

Additionally, researchers are exploring the use of Deep Learning (DL) methods [27,28], including Convolutional Neural Networks (CNNs), both individually and as part of stacking models [29], to improve flood prediction accuracy. These models require tuning multiple parameters to minimize errors and maximize performance [30,31]. Hybridized models like XGBoost and RF, optimized using metaheuristic methods, address these challenges and improve overall model performance [32]. On the other hand, knowledge-driven approaches, such as MCDA, rely on decision-maker expertise to select and balance criteria factors to choose the optimal option. These approaches offer advantages over other models regarding interpretability, simplicity, and applicability in regions lacking sufficient data. However, they also have notable disadvantages, including subjectivity and the lack of a consistent guideline for ranking variables [14,33]. MCDA techniques in GIS have demonstrated relatively good performance in mapping flood vulnerability. A recent review [34] found that these methods are among the most widely used for studying flood risks. Among the various approaches to flood risk analysis, one of the most common is the AHP [35,36,37,38,39]. According to [40], AHP, combined with GIS, was used to spatially map flood vulnerability in a specific region of Tunisia and assess the relative weights of contributing factors. However, one key disadvantage of this method is the subjectivity involved in assigning expert weights, which is a limitation that needs to be addressed.

One study in India [41] used a specific version of the AHP, the Fuzzy Analytical Hierarchy Process (FAHP), to identify areas at risk of flooding and compared its performance with the regular AHP method. The FAHP approach outperformed other Multi-Criteria Decision-Making (MCDM) methods overall. Another study in Iran [42] combined AHP with two other standard risk assessment methods, VIKOR and TOPSIS, to create detailed flood risk maps in areas with limited data. In China, researchers [43] used the Ordered Weighted Averaging (OWA) method to generate various flood risk maps, considering both optimistic and pessimistic perspectives. The study also compared three different MCDM methods, EDAS, VIKOR, and TOPSIS, for determining flood risk [3]. The findings revealed that VIKOR and TOPSIS performed better than EDAS, with a strong correlation between the results of TOPSIS and EDAS. Table 1 provides an overview of works in this field, along with the relevant considerations using MCDA techniques. The abbreviations used in Table 1 can be found in Abbreviations.

Pakistan is highly vulnerable to natural disasters [65]. The country faces a variety of natural hazards, including droughts, landslides, earthquakes, and floods. Flooding, in particular, has become a significant and urgent issue, causing severe damage to human lives and livelihoods [66]. The devastating August 2022 flood in Pakistan [67], just before a severe heatwave in May, disproportionately affected the country’s southern regions. Affected about one-third of Pakistan, the fifth most populous nation in the world, the large flood left around 32 million people homeless and sadly claimed 1,486 lives, including 530 children [68]. The flood is expected to have inflicted economic losses of more than USD 30 billion. Apart from the immediate devastation, the extensive damage to agricultural areas raises questions about food shortages; meanwhile, the conditions in makeshift shelters enhance the possibility of disease transmission [69]. Research on the primary causes of the catastrophic August 2022 flood remains limited. Several factors contributed to this disaster, including daily average recorded rainfall, accelerated glacier melt contributing additional water, and the development of an intense low-pressure system, exacerbated by the extreme heat experienced from May to June [70].

The MCDA model is widely recognized and extensively used in flood risk assessment, with the AHP being one of the most commonly employed empirical methods [71]. AHP identifies optimal solutions for specific issues by applying a weighted assessment procedure based on pairwise comparisons of each parameter. When combined with remote sensing and GIS [72], this approach has proven effective in flood analysis and mapping flood-prone regions. GIS integrated with AHP offers a consistent, efficient, and precise method suitable for various applications. However, the reliance of the AHP method on expert judgment to determine the weight values of indicators introduces cognitive limitations and subjectivity [73]. To ensure the reliability of the AHP results, it is essential to verify that the weights assigned to different factors are consistent. It is done by calculating the consistency ratio and ensuring that it remains below 10%, which helps reduce bias and enhances the trustworthiness of the results. This process is crucial for generating accurate flood maps [74].

Area mapping of flood-prone regions requires the integration of multiple datasets, including hydrological data, geomorphological information, rainfall, river flow, and topographic features derived from Digital Elevation Models (DEMs). These essential datasets, typically generated through remote sensing methods, are analyzed using GIS to create comprehensive flood-prone region maps [75]. Key factors in flood risk assessment for the proposed site include TWI, elevation, slope, precipitation, rainfall, distance to rivers and roads, soil type, drainage density, LULC, and NDVI. An extensive review of current research and relevant studies has clearly defined these criteria and their relative importance [76,77,78]. The planned study will produce a detailed flood risk map for Punjab Province, Pakistan, aiming to understand the flooding risks in this area better. The research will assess the likelihood of flooding, the area’s vulnerability, and the potential impact by utilizing maps, water flow data, landform characteristics, and climate data. Modern mapping techniques and decision-making tools will provide valuable insights for key stakeholders, such as government officials and disaster relief organizations. Ultimately, this research will improve flood management strategies, help mitigate potential damage, and protect communities. The primary objectives of this research are as follows:

• Use Landsat 8 images and ArcMap to analyze environmental factors like elevation and slope.

• Examine the Sentinel-1 GRD product with VH polarization to assess flood extent in Dera Ghazi Khan and Rajanpur.

• Apply GIS-AHP multi-criteria analysis to evaluate 11 factors, including TWI, slope, rainfall, distance from roads and rivers, drainage density, and LULC, to rank these factors based on their importance in flood risk mapping.

• After learning insights from the training dataset, create a detailed flood susceptibility map using the machine learning algorithm. The flood susceptibility mapping process also considered ranking variables obtained through AHP.

2. Materials and Methods

2.1. Study Area

Punjab Province in Pakistan (see Figure 1) has a climate that varies from semi-arid to arid, with average temperatures ranging from a high of 29 °C to 31 °C to a low of 16 °C to 18 °C [79,80]. It is a subtropical region with five major rivers flowing through it and boasts the largest population in Pakistan, with about 127 million people [81]. The monsoon season, which lasts from June to September, brings heavy rainfall. In 2022, the province saw more rain than usual, about 70% higher than the average [82]. We chose South Punjab as our study area because it is especially prone to flooding and has suffered repeated floods in recent years [83,84]. These floods have caused severe problems, including damage to infrastructure, loss of life and livelihoods, food shortages, and public health issues [85]. South Punjab was also most recently struck by a significant flood between June and October 2022 [82].

Our research zeroes in on two specific districts in Punjab: Dera Ghazi Khan (DGK) and Rajanpur (see Figure 2). These districts lie within areas prone to significant flooding. DGK nestles between the Indus River and the Koh-e-Suleman mountain range, bordering Baluchistan Province. It is home to around 2.8 million people, spread across three sub-districts called tehsils: Kot Chutta, DGK, and Koh Suleman. The district covers a vast area of 11,922 km² [86]. The main crops grown here are sugarcane, rice, wheat, and cotton [87].

Rajanpur District is situated on the western bank of the Indus River and spans an area of 12,318 km² [86]. About 2 million people live in Rajanpur, which is divided into three tehsils: Rojhan, Jampur, and Rajanpur. The district’s primary crops are wheat, cotton, and sugarcane [88].

2.2. Dataset Description

This study utilized GEE to efficiently collect, preprocess, and analyze large remote sensing datasets. The GEE platform’s ability to process extensive datasets without large-scale data downloads provided a significant advantage. A total of 850 randomly selected training points within the study area were used, with 70% allocated for model training and 30% reserved for validation [89].

For the imagery data, Landsat-8 of the Punjab province was obtained using GEE’s image collection capabilities. GEE’s ability to quickly extract and analyze vast datasets without downloading large amounts of data enabled the use of various filter criteria, such as cloud masking and date selection, ensuring the accuracy and quality of the imagery [90]. The Sentinel-1A Level-1 Ground Range Detected (GRD) scenes were processed using GEE to support flood susceptibility mapping. The analysis focused on VH polarization, which is sensitive to surface roughness changes and is affected by flooding. Ascending and descending orbits were used to achieve full spatial coverage. Images from February 2022 (pre-flood) and June–July 2022 (post-flood) were filtered and clipped to the region of interest. These images were then mosaicked to create pre- and post-flood views. Speckle filtering was applied to enhance image clarity, and backscatter increases were analyzed to identify flooded areas. Finally, the total flooded area was calculated and mapped to illustrate the extent of the flooding.

This study utilized a hybrid approach, combining remote sensing data from the Google Earth Engine (GEE) platform, the AHP for evaluating the importance of various factors, and the MLC algorithm for flood susceptibility mapping. The sequence of steps followed in this study is illustrated in Figure 3.

2.3. Impactful Factors Selection

FSM relies on the user’s ability to select the most relevant and valuable elements, as these choices directly impact the accuracy of the model’s predictions. The predictive variables used in FSM remain incomplete. Based on a literature review, we chose 11 impactful variables for this study area [88,91,92,93,94,95,96]. These variables are TWI, elevation, slope, precipitation, rainfall, distance to rivers and roads, soil type, drainage density, LULC, and NDVI.

TWI: The TWI is a key indicator for assessing flash-flood risk in watershed areas [97]. It accounts for the region’s flatness and hydrological conditions [98], reflecting the relationship between geomorphology and drainage. According to Cao et al. [99], the TWI is calculated using the Equation (1):

(1)$TWI=Ln(B/\mathit{Tan}\mu )$

where $B$ is the watershed area, and $\mu$ is the slope gradient. In Punjab Province, TWI values were calculated using DEM in ArcGIS 10.8, ranging from −16.4 to 14.8 (see Table 2).

Elevation: Elevation significantly affects flood sensitivity [100]. Lower places are more likely to flood because of their location as river confluence spots [101]. This work generates a digital elevation map of Punjab Province from GEE utilizing Shuttle Radar Topography Mission (SRTM) data. Table 2 shows the variation of elevation within the research area from 68 to 2260 m.

Slope: Slope angle is an essential component affecting surface runoff in hydrological studies and a necessary topographic layer [102]. Emphasizing the requirement of models that include low flows, as demonstrated in flow authority models [103], Barker et al. [104] observed a stable link between slope and surface flow rate. Using ASTER-GDEM data in ArcGIS 10.8, Punjab Province’s slope map was produced with slope angles ranging from 0° to 37.9° (see Table 2).

Precipitation: Precipitation is the primary driver of river floods, with heavy rainfall causing flooding when streams can no longer handle the excess water. Since runoff is directly linked to precipitation, higher rainfall leads to increased runoff and, consequently, higher flood risk [105]. This study used annual precipitation data from rainfall stations within and near the study area to ensure spatial dataset consistency. Precipitation was calculated using CHIRPS Daily Data. The mapped precipitation values in the study area range from 1.57 to 27.4 mm (see Table 2).

Rainfall: Several studies have suggested a connection between precipitation levels and flooding in a region [106]. However, the amount of rainfall required to trigger flooding remains unclear [107]. Despite this uncertainty, it is generally believed that rainfall plays a significant role in flood occurrence across various ecological conditions [108]. In this study, rainfall data was calculated using CHIRPS Daily Data. The rainfall values in the study area range from 208 to 1850 mm (see Table 2).

Distance From Rivers: Flood events typically occur in regions influenced by the stream network [109], with areas closer to streams experiencing more frequent flooding than those farther away. These proximity zones are particularly vulnerable to flooding [110]. This study calculated the distance from rivers using topographical maps and the Distance Tools in ArcGIS 10.8, ranging from 0.000916 to 10,000 m (see Table 2).

Distance From Road: Road construction can contribute to flooding in areas where it was previously uncommon, especially when roads are built over ancient watercourses, leading to increased flood frequency. It can also block transportation routes between cities or villages. The distance from roads, a key factor influencing flooding, was measured using the Euclidean distance tool in ArcGIS 10.8, with values ranging from 0.000947 to 5000 m (see Table 2).

Drainage Density: Higher flow density in the upper levels of stream networks is more strongly linked with flooding than runoff [110]. Consequently, drainage density frequently directly relates to flood danger. This work computed Punjab Province’s drainage density using ArcGIS 10.8 and the river line map. Derived from the flow lattice map, the drainage density map spans 0 to 378.4 m/km (see Table 2).

Soil Type: Soil type significantly impacts drainage due to specific soil characteristics such as texture, porosity, and structure [111]. Topographic factors often influence these soil features. In Punjab Province, soil characteristics are classified into 11 qualitative categories, such as Jc/Zo, Rc/Xk/Xh, and others (see Table 2).

LULC: The LULC pattern and any changes to them all affect the flood periodicity in a given area. LULC is very important in determining hydrological reactions. Reneau et al. [112] showed how changes in these patterns could increase flood danger. This research categorized the five LULC layers produced from Landsat 8 data: water, other vegetation, agricultural land, settlements, and sand/charland (see Table 2).

NDVI: The NDVI shows soil conditions and vegetative development, therefore affecting precipitation absorption and runoff across the terrain. Landsat 8 OLI data were the first high-resolution data fused to create a 30 m resolution thematic NDVI map pixel-by-pixel. Table 2 shows that the NDVI values in the study region span from −0.416 to 0.679.

Although initial evaluations considered social resilience indicators like GDP, water conservancy projects, and medical services, these factors were ultimately excluded from the final model [113]. Each selected factor was processed in a GIS environment and converted into $30 \mathrm{m}\times 30 \mathrm{m}$ raster grids for analysis using the AHP method. Table 2 outlines the critical factors impacting model accuracy in mapping flood susceptibility across Punjab Province.

Table 2

Detail of impactful factors for flood susceptibility.

Factor	Description	Data Source/Method	Range
TWI	$TWI=Ln\left(B/Tan\mu \right),$$\mathrm{where} B$ represents the upslope area (m2), and μ the slope gradient in degrees; high TWI areas are more prone to flooding due to water accumulation [114].	It is calculated using DEM data in ArcGIS 10.8.	−16.4 to 14.8
Elevation	Low-elevation areas are more susceptible as water flows down a gradient and accumulates in these regions, raising flood potential [115].	DEM derived from Shuttle Radar Topography Mission (SRTM) data.	68 to 2260
Slope	Steeper slopes facilitate rapid runoff, reducing water infiltration and increasing flood risk in lower elevations [116].	Derived from ASTER-GDEM with ArcGIS 10.8.	0° to 37.9°
Precipitation (rain, snow, hail, sleet),	Excessive rainfall can lead to river and stream overflow, particularly in flood-prone topographies with low absorption rates [117].	CHIRPS Daily: Climate Hazards Center InfraRed Precipitation with Station.	1.57 to 27.4 mm
Rainfall	More significant rainfall correlates directly with flood risk, especially in regions with poor drainage or low vegetation cover [118].	CHIRPS Daily: Climate Hazards Center InfraRed Precipitation with Station.	208 to 1850 mm
Distance from Rivers	Distance to river networks increases flood susceptibility as water levels rise, especially in low-lying adjacent areas [119].	It was calculated using ArcGIS 10.8 Distance Tools and topographical maps.	0.000916 to 10,000 m
Distance from Roads	Roads near water bodies can obstruct natural flow, elevating flood frequency and severity, especially when drainage systems are inadequate [120].	Calculated using Euclidean distance in ArcGIS 10.8 Spatial Analyst Tool.	0.000947 to 5000 m
Drainage Density	High drainage density (stream length per unit area) predicts higher flood susceptibility in upper stream areas as water accumulates [121].	It was analyzed using river line maps in ArcGIS 10.8.	0 to 378.4 m/km
Soil Type	Soil properties, including porosity and drainage capacity, influence water retention and runoff, impacting flood risk based on soil type [122].	Represented with 11 categories for Punjab Province in ArcGIS 10.8.	Qualitative categories (e.g., Jc/Zo, Rc/Xk/Xh, etc.)
LULC	Different land uses impact flood risk, with water bodies, wetlands, and agricultural lands generally more prone to flooding [123].	Created using Landsat 8 data in ArcGIS 10.8.	Qualitative categories (e.g., Water, Sand/Charland, etc.)
NDVI	Measures vegetation density affecting water infiltration and runoff; areas with lower vegetation cover have a higher flood risk due to limited water absorption capacity [124].	High-resolution pixel-level fusion using Landsat 8 OLI for NDVI mapping with 30 m resolution.	−0.416 to 0.679

Multicollinearity in Impactful Factors

Previous research has demonstrated the importance of determining the degree of collinearity between independent variables before beginning the modeling process [125,126]. Multicollinearity can diminish a model’s accuracy and make a technique unstable [127]. The Tolerance Index (TOL) and the Variance Inflation Index (VIF) can detect multicollinearity [128]. A VIF score greater than 5 and a tolerance less than 0.1 indicate multicollinearity between the independent variables [129]. Table 3 presents the evaluation metrics for the multicollinearity test among the 11 factors.

By applying these evaluation metrics, we can ensure the reliability and stability of the FSM model, address multicollinearity, and enhance the overall predictive power of the selected impactful factors.

2.4. Analytical Hierarchy Process (AHP) for Factors Ranking

In order to determine how 11 variables affected flood susceptibility mapping, this research used Saaty’s AHP [131]. Pairwise comparisons are at the heart of AHP, an approach that uses expert judgment to create priority scales for rating alternatives [132]. In conjunction with AHP-MCDA techniques, GIS has recently become popular in evaluating different physical flood conditioning and vulnerability elements. In order to map potential hazards using AHP, several researchers have focused on different physical flood conditions and vulnerability characteristics, including TWI, slope, elevation, LULC, drainage density, and soil type [10,133,134,135,136,137,138,139]. Following the four-step process described in [140], this study consists of the following: (i) making a decision hierarchy; (ii) ranking the factors and sub-factors that have an impact; (iii) considering available options and assigning weights to each attribute; and (iv) checking that subjective judgments are consistent. According to [131], this procedure mathematically entails assigning a score between 1 and 9 to each element.

In this study, the evaluation matrix was simplified to a square matrix $A$ of size $n\times n$, where each element $aij$ $(i,j=\mathrm{1,2},...,n)$ represents the weight ratio of a criterion, as shown in Equation (2). For the flood susceptibility mapping in this research, 11 criteria were considered, resulting in a $11\times 11$ matrix.

(2)$\mathrm{Let} C=\left(Cj\right|j=\mathrm{1,2},......,n) \mathrm{is} \mathrm{a} \mathrm{set} \mathrm{of} \mathrm{criteria}.$

All pairwise comparisons were considered legitimate after determining the priority vector and its weights for each component, with the condition that the Consistency Ratio (CR) was within the allowed range of inconsistency, which has been set at 5.8–10.00%. The AHP allows for a 10% margin of variation at most. Then, we used Equation (3) to get CR.

(3)$CR={\displaystyle \frac{CI}{RI}}$

A comparison was made between the Random Consistency Index (RI) and the Consistency Index (CI). Using the average of the priority vector $\left(\lambda \right)$ and the total number of components $\left(n\right)$, the CI is calculated as a first step using Equation (4). Table 4 describes the parameters used to build the priority vector, which defines the relative weights allocated to each layer.

(4)$CI={\displaystyle \frac{\lambda \mathit{max}-n}{n-1}}$

As seen in Table 4, impactful factors were categorized to allocate weights. The AHP was selected as part of a multi-criteria decision-making process to find its importance and rank it based on multiple factors. All possible criteria were compared in a pair at the first stage of the AHP. The results of these comparison matrices are shown in Figure 4, where non-diagonal values indicate the relative relevance of the factors when compared. A component compared to itself is represented by the diagonal values, which are set to one.

2.5. Maximum Likelihood Classification Model

The MLC model uses Bayesian classification principles. Bayesian classification represents classes as $C_i$ where $i=1,...,N$. If $N$ represents the number of classes and the measurement vector v determines the class of a given pixel, Equation (5) defines the conditional probabilities:

(5)$P\left(C_i\right|v),i=1...N$

If a full set of conditional probabilities, $P\left(C_i\right|v)$, for a pixel is available, we can assign the class using the decision rule see Equation (6):

(6)$v\in C_{i}ifP\left(C_i\right|v)>P(C_j\left|v\right)\mathrm{for} \mathrm{all} j\ne i.$

Equation (7) assigns the pixel with measurement vector v to the class $C_i$ if $P\left(C_i\right|v)$ holds the highest probability among all classes. The set of class conditional probabilities $P\left(C_i|v\right)$ describes the likelihood of a pixel at position v belonging to each class $C_i$. Labeled training data for each class provides estimates for these probabilities.

We can then estimate $P\left(C_i\right|v)$ using Bayes theorem as follows:

(7)$P\left(C_i|v\right)={\displaystyle \frac{P\left(v|C_i\right)P\left(C_i\right)}{P\left(v\right)}}$

where $P\left(C_i\right|v)$ is the prior probability of class $C_i$, and $P\left(v\right)$ is the probability of the measurement vector $v$ in the entire dataset. The probability $P\left(v\right)$ is given by Equation (8):

(8)$P\left(V\right)=\sum {\displaystyle \frac{N}{i=1}}P(v|C_i\left)P\right(C_i)$

Substituting Equation (7) into Equation (6), we get Equation (9):

(9)$v\in C_i if P\left(v|C_i\right)P\left(C_i\right)>P\left(v|C_j\right)P\left(C_j\right) for all j\ne i.$

This approach is valid as long as $P\left(C_i\right|v)$ is known from the training data. We assumed that $P\left(C_i\right|v)$ follows a multivariate normal distribution, standard in classification problems like the MLC method. We used statistical tests for normality, such as the Shapiro-Wilk test, which was applied to the dataset features to validate this assumption. Additionally, we visually inspected the data using Q-Q plots to assess whether the data conforms to a normal distribution. If we found deviations, we made the necessary transformations or adjustments to meet the assumption. Equation (10) gives the multivariate Gaussian distribution function for $N$ dimensions.

(10)$P(v|C_i)=(2\pi {)}^{-{\displaystyle \frac{N}{2}}}{\left|Y_i\right|}^{-{\displaystyle \frac{1}{2}}}\mathit{exp}[-{\displaystyle \frac{1}{2}}(v-Z_i{)}^T]{Y_i}^{-1}(v-Z_i)$

where $Z_i$ and $Y_i$ are the mean vector and covariance matrix of the data in class $C_i$, respectively.

2.6. Training Dataset

The training dataset was created using input data from each conditioning factor, with each instance labeled according to its corresponding flood susceptibility class, as defined by the decision criteria in Table 4. The importance and ranking of each factor were determined using the AHP method. This dataset was the foundation for the model to learn the relationships between the factors and flood susceptibility. The MLC then used the dataset to generate the flood susceptibility map of the study area.

Flood Susceptibility Mapping

Using statistical probability-based methods, the MLC model was crucial in accurately classifying flood-prone areas. By incorporating MLC, the precision in categorizing flood-prone zones. Classification of the flood susceptibility zones was based on a robust data-driven approach. The analysis achieved a more precise flood susceptibility classification by employing MLC (machine learning algorithm) in conjunction with the AHP-derived weights or ranking of variables. Five different possible flood zones were considered while making the flood susceptibility map (see Figure 5). Using ArcGIS 10.8, the area of each flood-potential zone was calculated using km² and percentages. Furthermore, the basin-level flood-susceptibility map was superimposed on the district-level shapefile of the basin to ascertain the proportion of land occupied by each district in the five flood-potential zones and to rank them accordingly. The use of the MLC algorithm efficiently classifies the flood risk areas. It helps verify the distribution of flood susceptibility across different regions, providing decision-makers with a reliable tool for effective flood risk management.

2.7. Modelling Validation

Generally speaking, there are accepted methods for verifying models. These tests include the prediction rate curve, the robustness technique (RT), the success rate curve, Cohen’s Kappa (CK), and the fitting performance measure (FPM) [141]. The models in this paper were validated using the ROC curve (see Table 3). The FSM was evaluated using one-third of flood locations that were unutilized for model training. The ROC curve shows the model with the most significant area under the curve (AUC). The estimate of the flood rate is obtained via the prediction curve. Thus, a necessary result and output of a model is the effectiveness of flood vulnerability mapping [142]. Moreover, we have validated the model by matching their outputs to ground truth data or actual observed facts. While the remainder of the entire sample points were utilized as test data, seventy percent (n = 595) of them were randomly created as training data. Consequently, the capacity of the model to predict and validate [143,144] was assessed using the AUC method. Equation (11) helped one to plot the real positive rate on the y-axis against the false positive rate on the x-axis and ascertain the result. This study confirmed the model using AUC.

(11)$AUC={\displaystyle \frac{\sum TP+\sum TN}{P+N}}$

P represents all floods; N represents all non-floods; and TP and TN provide the overall count of accurately detected pixels [145]. This research examined the performance and efficacy of the AHP techniques concerning the AUC. Furthermore, the AUC computation found the model’s success and prediction rate using training and test data. We have guaranteed that the model fairly represents real-world circumstances and increases its dependability for further flood risk assessments by calibrating and verifying it using observable data.

3. Results and Discussion

This section presents the results, including an FSM of Punjab province, an analysis of multicollinearity among variables, and the AHP-based ranking of variables. We also provide graphical presentations of the calculated values for each affected factor in the study area. Finally, we discuss the validation results of the FSM and analyze its implications for critical infrastructure.

3.1. Impactful Factors Mapping

Figure 6 illustrates the 11 critical factors that influencing the impactful factors flood susceptibility in Punjab, Pakistan. Each map represents a parameter processed using GIS tool ArcGIS 10.8 (Developer: Esri) with values classified into five categories based on their range and impact on flood susceptibility.

Impactful Factors Multicollinearity

In Table 5, the TWI, slope, rainfall, distance from roads and rivers, drainage density, and LULC are the most significant predictors, with Beta values of 0.124, −0.089, 0.102, −0.102, −0.240, −0.148, and −0.220, respectively. These validated values emphasize their dominant roles in shaping flood susceptibility, while other factors like elevation, precipitation, soil type, and the NDVI also contribute meaningfully but to a lesser extent. Low VIF values across factors indicate minimal multicollinearity, confirming the model’s robustness in evaluating flood risk.

3.2. Flood Susceptibility Map (FSM)

The FSM is developed by considering 11 crucial factors influencing flooding: the TWI, elevation, slope, precipitation, rainfall, distance to rivers and roads, soil type, drainage density, LULC, and the NDVI. Spatial layers representing each of these parameters are created using ArcGIS 10.8 software, enabling the visualization of how they are distributed across the study area (see Figure 7). Each parameter’s contribution to flood susceptibility is represented by weights derived from AHP, which indicates its importance in determining the frequency and intensity of floods. Green represents very low weights, red represents extremely high weights, while yellow and orange represent intermediate weights. This FSM derived from the machine learning approach MLC allows decision-makers to prioritize resource allocation and design effective flood management strategies, helping to identify the most vulnerable locations.

The MLC model plays a vital role in the creation of the FSM. This model effectively classifies spatial locations into susceptibility zones, ranging from very low to very high. The use of MLC in this study ensures that the classification of areas, based on the training on the values of 11 impactful factors, maximizes the accuracy of zone categorization and provides a more reliable flood susceptibility map. The MLC model analyzes the input data, including the 11 conditioning factors mentioned earlier, and assigns each area to a class based on the likelihood of occurrence, ensuring a comprehensive and data-driven flood risk assessment.

The 11 physical flood conditioning factors contribute varying degrees to the overall flood susceptibility map, with their relative importance ranked through the AHP, complemented by the machine learning model for classification. The factors TWI, elevation, slope, precipitation, rainfall, distance to rivers and roads, soil type, drainage density, LULC, and NDVI contribute 13%, 14%, 8%, 9%, 9%, 21%, 4%, 9%, 8%, 8%, and 6%, respectively. The map represents the aggregate impact of these factors, with weights assigned based on their relative influence through AHP. At the same time, the MLC model was used for classification and predicts flood susceptibility more accurately by learning from the data patterns. For instance, factors such as elevation and proximity to the river have significant impacts on flood occurrence and thus contribute substantially to the classification of flood susceptibility. The resulting map highlights five flood susceptibility zones, ranging from very low to extremely high risk. Areas classified as high or very high risk are typically closer to major water channels, reflecting their increased susceptibility to flooding. Consistent with other studies [146,147], the results show that the basin region is subject to different types of flood risk.

Using the MLC model, the FSM for Punjab, Pakistan, achieved an overall accuracy of 90%, demonstrating that the MLC method is highly reliable for flood susceptibility classification, with minimal misclassification between adjacent classes. The confusion matrix in Table 6 shows the model’s accuracy and suggests that minor improvements could further enhance its performance, potentially reducing overlaps in classifications. According to the FSM, a substantial part of Punjab is at high flood risk, with 61.77% of the area classified as high or very high susceptibility. It impacts critical infrastructures, including schools and health facilities. These findings align with recent flood damage reports affecting over 30,000 schools and 2000 health facilities across Pakistan, highlighting the urgent need for targeted flood management interventions in the most vulnerable areas (see Table 7).

Using Maximum Likelihood Classification not only adds credibility to the analysis by providing statistically sound classifications but also enhances the decision-making process for flood management. By maximizing classification accuracy, the MLC model ensures that areas prone to flooding are accurately identified, thereby supporting authorities in implementing targeted and effective flood mitigation measures.

3.2.1. Validation of the FSMs

The model has achieved an overall accuracy of 90.0%, indicating high reliability in classifying flood susceptibility across the study area. The diagonal dominance in the confusion matrix reflects the model’s effectiveness, with limited misclassifications primarily occurring between adjacent classes. While the model performs well overall, fine-tuning may reduce minor overlaps, especially between susceptibility classes with similar flood characteristics, such as Low and Very Low or High and Very High (see Table 6).

3.2.2. Validation Result Through Area Under Curve (AUC)

With an accuracy rating of 90%, Figure 8 reveals the machine learning categorization method. Several significant policy ramifications for food risk management follow from the machine learning-based food risk mapping technique. Furthermore, integrating machine learning-generated flood risk maps into spatial planning and development decision-making helps guide future development away from the most dangerous areas [148]. The machine learning method offers a strong, participative, geospatially explicit framework for evaluating and controlling food hazards that fit local resources and situations. Policymakers should use these realizations to create a fairer and more firm society. The obtained results show the food prediction model’s acceptance and fit.

3.3. Flood Susceptibility of Critical Infrastructures

The flood susceptibility assessment reveals that a substantial portion of Punjab, Pakistan, is at significant flood risk. The very high-risk class encompasses 4,067,198.59 hectares, representing 27.17% of Punjab’s area, while the high-risk category covers an even more considerable extent of 5,185,365.03 hectares, accounting for 34.6% of the region. Moderate susceptibility spans 3,563,629.11 hectares or 23.01% of Punjab, while the low-risk class includes 2,030,859.39 hectares, representing 10.17%. The smallest area, 122,312.13 hectares (5.05%), falls under the very low-risk category. High and very high-risk zones collectively cover approximately 61.77% of the study area, underscoring significant flood vulnerability across Punjab (see Table 7 and Figure 9). As per various reports, floods in Punjab damaged numerous schools and health facilities, aligning with the figures provided, such as 2000 health facilities and over 30,000 schools being affected across Pakistan, particularly in flood-prone zones [149].

Among the most catastrophic natural disasters, floods drastically damage companies, homes, infrastructure, and livelihoods, causing significant financial losses and social disturbance. The floods Pakistan experienced in 2022 highlight the significant consequences such tragedies might bring about for a nation. The floods seriously affect homes, agriculture, livestock, transportation, communications, and infrastructure and devastate businesses [150,151,152]. Table 8 outlines the specific damages in many different regions.

The flood damages have mainly affected these sectors and influenced housing as well. Considering their broad effects on lives and food security, the losses in the cattle and agricultural sectors are essential. Apart from significant social and humanitarian issues, the floods also caused financial losses [150,151,152]. Table 9 summarizes these more secondary impacts.

The 2022 floods in Pakistan impacted over 33 million people, resulting in the loss of approximately 1730 lives and displacing 8 million individuals. These devastating consequences have caused a significant rise in the national poverty rate, expected to increase by 3.7 to 4 percentage points, pushing an additional 8.4 to 9.1 million people below the poverty line. The country’s GDP has also declined around 2.2% for FY22, with total economic losses nearing USD 30 billion. The floods caused widespread destruction, including the destruction of 1.4 million homes. With 627,793 people in official displacement sites, the scale of damage has created immense humanitarian needs across the region [153] (see Figure 10).

3.4. Flood Extent Map of Dera Ghazi Khan and Rajanpur

To identify flood-affected areas within DGK and Rajanpur, we used GEE, a powerful tool for analyzing satellite data [154]. It allowed us to create detailed flood extent maps for the study area using Sentinel-1A satellite data [155]. We used a change detection technique, comparing satellite images taken before and after the flood, to pinpoint the areas affected by the flooding [156]. Figure 11 displays the final flood extent maps, with blue areas indicating the regions flooded in 2022 in both DGK and Rajanpur districts.

The map clearly and instantaneously depicts the flooded regions, which are usually colored blue. Planning and implementing disaster response and mitigating techniques depend on understanding the degree and scope of floods, so this visualization aids in that regard. The map highlights the flooded areas and helps pinpoint the vital facilities in danger, like schools and hospitals, for prioritizing emergency response initiatives. Local officials, legislators, and disaster management organizations would use the extended Dera Ghazi Khan and Rajanpur map. It helps them to decide wisely on long-term resilience planning of infrastructure, emergency evacuation strategies, and resource allocation. GEE and advanced remote sensing technologies guarantee precise, current, and trustworthy flood maps, improving the general efficacy of flood control plans in these sensitive areas.

3.5. Discussion

By combining GIS with the AHP multi-criteria decision analysis, this work has given a critical new understanding of flood vulnerability in Punjab, Pakistan. The results provide a basis for informed decision-making in flood risk management. They underline the complicated interaction of numerous flood-conditioning elements and their effect on the geographical distribution of flood risk.

In determining flood sensitivity in the study region, the research identified TWI, slope, rainfall, distance from roads and rivers, drainage density, and LULC as the most essential factors. It supports the findings of other studies [10,42,54], highlighting the importance of these elements for accurately assessing flood risk. With a weight of 21.0%, the AHP study identified distance from rivers as the most important factor in predicting flood susceptibility. The analysis found that proximity to roads, steeper slopes, and higher TWI values consistently indicate greater susceptibility to floods due to increased runoff and water accumulation. The flood susceptibility map revealed that lowlands near major rivers with relatively flat topography were most prone to flooding. In line with other studies, the analysis also showed that rainfall, drainage density, and LULC patterns significantly influence flood vulnerability [54,157]. It is consistent with earlier research [41,61], which stresses the importance of considering the geographical distribution of flood susceptibility zones when developing targeted flood-reduction strategies. The model demonstrated that areas with significant concentrations of built-up land and bare ground, likely to have lower infiltration rates and runoff, exhibited much higher vulnerability ratings. Although water features are essential to the region, they contribute to higher sensitivity ratings. This realization is crucial for land use planning and development strategies, as it underscores the need to consider the impact of land use changes on flood vulnerability

Given that NDVI plays a significant role in determining surface runoff and infiltration in vegetated areas, we acknowledge that its spatial disconnections, as seen in Figure 6, may affect the final flood susceptibility map. A finer classification of the NDVI could potentially mitigate this issue by offering a more nuanced view of vegetation density, thereby improving the model’s prediction accuracy in vegetated flood-prone areas.

The research also looked for no notable collinearity when examining multicollinearity among the chosen flood-influencing elements. It suggests that the selected elements were independent and helped determine the general flood sensitivity. Moreover, other criteria, such as the confusion matrix, confirmed the model’s correctness. The findings with a standard error of 0.029 revealed a high general accuracy of 90%, confirming the model’s resilience in forecasting flood susceptibility. The flood susceptibility map then revealed the vulnerability of critical infrastructure, exposing a high concentration of health facilities and schools in Punjab’s high and moderate flood-risk zones. This result significantly impacts disaster readiness and mitigation, as these organizations are essential for providing services during and after a flood.

Although the research effectively used AHP as an efficient MCDA technique, it suffered constraints on data availability, mainly historical flood records, which are vital for model validation. Common to numerous research [41,46], this restriction emphasizes the need to gather and merge more thorough data. This study underlined the importance of including higher-resolution data in the following research as it admitted limits regarding the spatial resolution of input data, especially for smaller-scale characteristics, which might have influenced the accuracy of the conclusions. It emphasized the inherent subjectivity of the AHP approach, which weights aspects using expert judgment. Applying consensus-based or fuzzy logic methods reduces this limitation [41].

Notwithstanding these constraints, the research emphasizes the efficiency of the AHP approach for flood susceptibility mapping in Punjab, Pakistan, especially in regions with restricted data access. The results provide local decision-makers with essential data that will help them prioritize mitigating activities, distribute resources wisely, and apply focused actions to reduce future floods’ effects. As advised in [46], future studies should further investigate the construction of hybrid models integrating the capabilities of several MCDA methodologies, machine learning, and statistical methods to increase the accuracy and dependability of flood susceptibility mapping. Providing more accurate and robust flood risk assessments depends partly on addressing the dynamic character of flood vulnerability by including factors like climate change, land use changes, and infrastructure development.

The knowledge acquired by this research is a significant step toward improved flood risk control in Punjab, Pakistan. The results of this study will provide an excellent basis for creating more thorough and efficient flood-reducing plans as research in this sector develops, therefore creating safer communities.

3.6. Limitations

Discussing the study limits is essential as it helps expose any flaws and restrictions in the research methodology. Acknowledging these constraints guarantees a fair and realistic knowledge of the extent and consequences of the investigation, thus improving the credibility of the results, helping interpret results more precisely, and leading the following research developments.

• Depending on many input data and maybe erroneous or lacking data gaps affecting predicted accuracy.

• The exclusion of future land use, climatic patterns, and infrastructure development from past and present data creates a temporal restriction that limits the accuracy of long-term flood risk assessment.

• Using MCDA entails simplifications and assumptions that introduce uncertainty, particularly in complicated relationships.

• Because Punjab Province’s geography is unique and calls for customizing and validation, results may not be precisely relevant to other areas.

• Assuming historical flood patterns stay constant, the assumption of stationarity ignores any changes in climate, land use, or other dynamic elements.

• Particularly for smaller-scale characteristics, limits in spatial resolution of input data might impact accuracy.

• Improved accuracy is possible by using high-resolution data to augment outputs.

4. Conclusions

This study produced a complete flood susceptibility map for Punjab, Pakistan, using a GIS-AHP method in concert with the MLC model. The research successfully found important flood-triggering elements, including the TWI, slope, rainfall, distance from roads and rivers, drainage density, and LULC, thereby illustrating their significant influence on flood risk. With a 90% accuracy, the model emphasizes the critical contribution of these elements in designating flood-prone regions and offers insightful analysis for efficient management and preparation of disasters. The study verified the lack of multicollinearity among the chosen flood-influencing elements, therefore confirming their contribution to flood sensitivity. The study of the vulnerability of key infrastructure revealed that many schools and health institutions are in high and moderate-risk flood zones, therefore stressing the great necessity of proactive steps to protect these vital services. Although the AHP approach’s inherent subjectivity and data availability restrictions are accepted, this research supports AHP’s value in flood susceptibility mapping, especially in areas with little data. Including the MLC model helps to improve the flood prediction capacity by providing a consistent structure for flood risk evaluation. The results provide a strong basis for educated decision-making in flood risk management, thereby allowing lawmakers and stakeholders to prioritize mitigating activities, maximize resource allocation, and carry out focused steps to lower the effects of the subsequent floods. Future studies should concentrate on improving the approach by including high-density data, investigating hybrid models, and addressing the dynamic character of flood susceptibility to build completer and more effective flood mitigating strategies, thereby promoting safer communities.

Author Contributions

Conceptualization, R.M.A.L. and J.H.; methodology, R.M.A.L.; software, R.M.A.L.; validation, R.M.A.L. and J.H.; formal analysis, R.M.A.L.; investigation, J.H.; resources, J.H.; data curation, R.M.A.L. and J.H.; writing original draft preparation, R.M.A.L.; writing review and editing, R.M.A.L. and J.H.; visualization, R.M.A.L.; supervision, J.H.; project administration, J.H.; funding acquisition, J.H. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data that support our research findings are available from the corresponding author on request. The data are not publicly available due to privacy.

Acknowledgments

We are very grateful to the anonymous reviewers for their constructive comments and thoughtful suggestions.

Conflicts of Interest

The authors declare no conflicts of interest.

Abbreviations

Abbreviation	Full Form
ANP	Analytical Network Process
DD	Drainage Density
DEMATEL	Decision-Making Trial and Evaluation Laboratory
EDAS	Evaluation-Based on Distance from Average Solution
DFR	Distance from the River
FANP	Fuzzy Analytical Network Process
MABAC	Multi-Attributive Border Approximation Area Comparison
MFI	Modified Fournier Index
mNDWI	Modified Normalized Difference Water Index
NDBI	Normalized Difference Built-Up Index
SAW	Simple Additive Weighting
SPI	Stream Power Index
STI	Sediment Transport Index
TPI	Topographic Position Index
TRI	Topographic Ruggedness Index
VIKOR	VIseKriterijumsko Kompromisno Rangiranje
TOPSIS	Technique for Order of Preference by Similarity to Ideal Solution
WRI	Water Ratio Index
WASPAS	Weighted Aggregated Sum Product Assessment
MOORA	Multi-Objective Optimization based on Ratio Analysis
CORPAS	Complexity-based Ranking for Path Selection
CODAS	Combinative Distance-based Assessment
ARAS	Additive Ratio Assessment

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. Study area and flood-affected areas in Punjab Province.

Figure 2. (a) Geographical map showcasing the Punjab province of Pakistan, (b) detailed district maps of Punjab, with particular emphasis on Dera Ghazi Khan and Rajanpur districts, highlighted for the focus of this study.

Figure 3. Flowchart of this research for Flood Susceptibility Mapping.

Figure 4. Normalized matrix of the parameters.

Figure 5. Relative importance of factors used in the flood susceptibility model.

Figure 6. Impactful factors for flood susceptibility mapping (a–k) representing TWI, elevation, slope, precipitation, rainfall, distance to rivers and roads, soil type, drainage density, LULC, and NDVI.

Figure 7. Final flood susceptibility map for Punjab Province, Pakistan.

Figure 8. Area under curve (AUC) for flood susceptibility.

Figure 9. Percentage of flood areas in Punjab.

Figure 10. Impact of the 2022 floods in Pakistan: estimated flood-affected people, damaged houses, and humanitarian needs.

Figure 11. Final flood extent map of (a) Dera Ghazi Khan and (b) Rajanpur district of Punjab, Pakistan.

Table 1

Comparative analysis of MCDA approaches for flood susceptibility mapping.

Paper Reference	MCDA Models	Flood Factors
[44]	AHP	Slope, flow accumulation, rainfall, LULC, elevation, DFR, and geology
[42]	TOPSIS, and VIKOR	Soil, aspect, NDVI, geology, DD, SPI, LULC, TWI, plan curvature, DFR, slope, and elevation
[40]	AHP	Groundwater level, DD, soil, rainfall, geology, LULC, slope, and elevation
[45]	VIKOR, TOPSIS, and SAW	Curvature, STI, SPI, soil, NDVI, rainfall, slope, TWI, LULC, elevation, DFR, and geology
[46]	DEMATEL-ANP	TRI, curve number, DD, STI, SPI, soil, NDVI, rainfall, slope, TWI, LULC, elevation, DFR, and geology
[47]	FAHP	Convergence index, TPI, plan curvature, soil, aspect, rainfall, slope, TWI, LULC, elevation, DFR, and geology
[48]	AHP	DD, rainfall, slope, TWI, slope, LULC, elevation, DFR, and geology
[49]	AHP and ANP	Distance to the road, SPI, aspect, NDVI, rainfall, slope, TWI, LULC, elevation, DFR, and geology
[50]	AHP	Flow accumulation, rainfall, geology, LULC, slope, and elevation
[51]	AHP	Flow accumulation, DD, stream order, soil, geology, LULC, slope, and elevation
[52]	AHP	Curve number, flow accumulation, DD, soil, slope, LULC, elevation, DFR, and geology
[53]	AHP, ANP, FAHP, and FANP	Runoff, SPI, soil, rainfall, TWI, slope, LULC, elevation, and distance to the river network
[54]	AHP	Flow accumulation, rainfall, DFR, LULC, drainage density, soil, slope, geology, and elevation
[43]	AHP, TOPSIS, and OWA	Curvature, SPI, soil, aspect, NDVI, rainfall, LULC, TWI, DFR, slope, and elevation
[55]	EDAS-AHP	Plan curvature, soil, aspect, rainfall, slope, TWI, LULC, elevation, DFR, and geology
[33]	TOPSIS, and VIKOR	Plan curvature, drainage density, SPI, soil, aspect, NDVI, slope, TWI, LULC, elevation, DFR, and geology
[56]	AHP, TOPSIS, and MABAC	DD, soil, rainfall, slope, LULC, elevation, DFR, and geology
[41]	AHP and FAHP	NDBI, WRI, DD, STI, SPI, soil, aspect, LULC, TWI, and slope
[57]	TOPSIS, VIKOR, EDAS, and WASPAS	Roughness, TRI, TPI, flow accumulation, curvature, DD, STI, SPI, soil, aspect, NDVI, rainfall, geology, LULC, TWI, DFR, slope, and elevation
[58]	AHP	River length, DD, rainfall, LULC, TWI, DFR, slope, and elevation
[59]	WASPAS, MOORA, CORPAS, CODAS, ARAS, EDAS, VIKOR, and TOPSIS	Geomorphology, curvature, DD, SPI, soil, rainfall, geology, LULC, TWI, DFR, slope, and elevation.
[3]	TOPSIS, VIKOR, and EDAS	mNDWI, rainfall deviation, MFI, lineament density, roughness, TPI, TRI, geomorphology, curvature, drainage density, STI, SPI, soil, aspect, NDVI, rainfall, geology, LULC, TWI, slope, and elevation.
[60]	AHP	Geomorphology, distance to road, DD, soil, aspect, rainfall, LULC, TWI, DFR, slope, and elevation
[61]	AHP, FAHP, and ANP	Flow accumulation, TPI, TRI, curvature, DD, STI, SPI, soil, rainfall, slope, TWI, LULC, elevation, DFR, and geology
[62]	AHP	Elevation, aspect, slope, roughness, curvature (profile and plan), flow accumulation, flow direction, drainage density, soil, geology, NDVI, NDMI, LULC, and rainfall, DFR, TWI, STI, and SPI
[63]	AHP	TWI, slope, LULC, NDVI, soil type, elevation, rainfall, drainage density, distance to rivers and roads
[64]	TOPSIS, VIKOR and EDAS	Elevation, Slope, DFR, DD, Aspect, Flow accumulation, Roughness, Curvature, TWI, TPI, SPI, Geomorphology and Lithology, DFR, LULC, and NDVI

Table 3

Evaluation metrics for multicollinearity test among 11 factors [130].

Metric	Definition	Formula
True Negative Rate (TNR)	The actual negatives correctly classified	TNR = TN/(FP + TN)
True Positive Rate (TPR)	The actual positives correctly classified	TPR = TP/(TP + FN)
False Negative Rate (FNR)	The actual positives incorrectly classified	FNR = FN/(TP + FN)
False Positive Rate (FPR)	The actual negatives incorrectly classified	FPR = FP/(FP + TN)
Cohen’s Kappa	Measure of agreement between observed and predicted values	((C/D) − Chance)/(1 − Chance)
Chance	Probability of agreement occurring by chance	((E × B/D) + (F × A/D))/D
TSS (True Skill Statistics)	Overall accuracy for true positives and true negatives	TPR + TNR − 1
Accuracy	Overall, true results for true positives and true negatives	(TP + TN)/(TP + TN + FP + FN)

Where: TP: “TP: True Positive, TN: True Negative, FP: False Positive, FN: False Negative, A: TP + FN, B: FP + TN, C: TP + TN, D: TP + TN + FP + FN, E: TN + FN, F: TP + FP”.

Table 4

Decision criteria for labelling training dataset for the maximum likelihood classification algorithm.

Flood Causative Criteria	Unit	Decision Criteria	Susceptibility Class	Flood Susceptibility Class Representation in Numeric	Weight (%)
TWI	Level	−16.4–−11.3	Very low	1	13
		−11.2–−8.1	Low	2
		−8.09–−2.47	Moderate	3
		−2.46–3.52	High	4
		3.53–14.8	Very high	5
Elevation	m	68–165	Very high	5	14
		166–328	High	4
		329–620	Moderate	3
		621–1100	Low	2
		1110–2260	Very low	1
Slope	%	0–0.891	Very high	5	8
		0.892–3.86	High	4
		3.87–8.46	Moderate	3
		8.47–14.5	Low	2
		14.6–37.9	Very low	1
Precipitation(Rain, snow, hail, sleet)	mm	1.57–5.02	Very low	1	9
		5.03–7.86	Low	2
		7.87–11	Moderate	3
		11.1–16.1	High	4
		16.2–27.4	Very high	5
Rainfall	mm	208–369	Very low	1	9
		370–524	Low	2
		525–743	Moderate	3
		744–1050	High	4
		1060–1850	Very high	5
Distance from the river	km	0.000916–1290	Very high	5	21
		1300–2860	High	4
		2870–4820	Moderate	3
		1830–7180	Low	2
		7190–10,000	Very low	1
Distance from the road	km	0.000947–490	Very high	5	4
		491–1240	High	4
		1250–2240	Moderate	3
		2250–3470	Low	2
		3480–5000	Very low	1
Drainage density	m/km	0–89.7	Very low	1	9
		89.8–107.3	Low	2
		107.4–165.5	Moderate	3
		165.6–215.8	High	4
		215.8–378.4	Very high	5
Soil type	Class	Jc/Zo	Very high	5	8
		Rc/Xk/Xh	High	4
		Lo/Yh	Moderate	3
		Yk	Low	2
		I/Qc/Be	Very low	1
LULC	LULC Class	Water	Very high	5	8
		Sand/Charland	High	4
		Agriculture land	Moderate	3
		Settlement	Low	2
		Other vegetation	Very low	1
NDVI	Level	−0.416–0.112	Very high	5	6
		0.113–0.215	High	4
		0.216–0.318	Moderate	3
		0.319–0.413	Low	2
		0.414–0.679	Very low	1

Table 5

Impactful factors multicollinearity test.

Coefficient
Factors	UnstandardizedCoefficients		StandardizedCoefficients	T	Significant	CollinearityStatistics
	B	Standard Error	Beta			Tolerance	VIF
Constant	0.616	0.123		5.355	0.000
TWI	0.017	0.005	0.124	2.620	0.003	0.632	1.210
Elevation	−1.488 × 10−5	0.000	−0.002	−0.069	0.890	0.641	1.190
Slope	−0.005	0.002	−0.089	−1.913	0.045	0.590	1.423
Precipitation (rain, snow, hail, sleet),	0.037	0.034	0.041	1.068	0.214	0.875	1.054
Rainfall	0.000	0.000	0.102	2.425	0.012	0.727	1.190
Distance from Rivers	−1.314 × 10−4	0.000	−0.102	−2.590	0.007	0.850	1.037
Distance from Road	−2.587 × 10−4	0.000	−0.240	−4.714	0.000	0.635	1.100
Drainage Density	−0.075	0.020	−0.148	−2.847	0.000	0.897	1.015
Soil Type	0.005	0.006	0.033	0.800	0.400	0.712	1.135
LULC	−0.042	0.009	−0.220	−3.804	0.000	0.710	1.352
NDVI	0.001	0.002	0.026	0.621	0.490	0.680	1.135

Table 6

Accuracy and confusion matrix of flood susceptibility map.

Prediction	Low	Very Low	Moderate	High	Very High	Accuracy
Low	47	1	2	1	0	$\mathrm{Overall} \mathrm{Accuracy}={\displaystyle \frac{\left(Total Number of Correctly Classified Pixels \left(Diagonal\right)\right)}{\left(Total Number of Reference Pixels\right)}}\times 100$Overall accuracy = (230/255) × 100=90.0%
Very Low	2	44	2	1	2
Moderate	1	1	45	2	2
High	0	1	1	48	1
Very High	2	0	1	2	46

Table 7

Flood area in Punjab concerning susceptibility class.

Susceptibility Class	Area (Hectare)	Flood Area Percentage
Very Low	122,312.13	5.05%
Low	2,030,859.39	10.17%
Moderate	3,563,629.11	23.01%
High	5,185,365.03	34.60%
Very High	4,067,198.59	27.17%

Table 8

Economic impact of the 2022 floods in Pakistan by sector.

Sector	Damages (USD Billions)	Description
Housing	5.6	Significant damage to residential buildings and displacement of people
Agriculture and Livestock	3.7	Severe impacts on food security and agricultural production
Transport and Communications	3.3	Extensive damage to infrastructure affecting mobility and communications

Table 9

Additional impacts of the 2022 floods in Pakistan.

Category	Impact
Total Economic Losses	Over USD 30 billion
Affected Population	33 million people
Deaths	More than 1730 lives lost.
Displacement	8 million people
National Poverty Rate Increase	Increase by 3.7 to 4 percentage points
GDP Impact	Reduction by approximately 2.2% of FY22 GDP

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