Enhancing Flash Flood Susceptibility Modeling in Arid Regions: Integrating Digital Soil Mapping and Machine Learning Algorithms

doi:10.21203/rs.3.rs-4919471/v1

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Enhancing Flash Flood Susceptibility Modeling in Arid Regions: Integrating Digital Soil Mapping and Machine Learning Algorithms

https://doi.org/10.21203/rs.3.rs-4919471/v1

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Flash floods in arid regions are among the most dangerous and destructive disasters worldwide, with their frequency increasing due to intensified climate change and anthropogenic activities. This study aims to identify susceptibility areas to flash floods in arid regions, characterized by high vulnerability, numerous complexities, and unknown mechanisms. 19-flash flood causative physiographic, climatic, geological, hydrological, and environmental parameters were considered. Using the Boruta wrapper-based feature selection algorithm, temperature, distance to the river, and elevation were identified as the most effective parameters. Four standalone and hybrid machine learning models (Random Forest (RF), Support Vector Regression (SVR), GLMnet, TreeBag, and Ensemble) were employed to model and determine flash flood susceptibility maps. Based on performance evaluation metrics (accuracy, precision, recall, and Areas Under Curve (AUC) indexes), the RF and Ensemble models exhibited the best performance with values of (0.94, 0.93), (0.97, 1), (0.92, 0.88), (0.94, 0.94), respectively. The findings highlighted the previously overlooked role of soil in flood susceptibility mapping studies, particularly in arid areas with high levels of silt and clay soils. This study introduced digital soil mapping for the first time in flood susceptibility studies, providing an effective approach for the spatial prediction of soil properties using easily accessible remote sensing data to generate soil maps in areas with limited available data. It emphasizes the importance of examining the role of soil in arid areas during flash flood modeling and recommends using Ensemble and RF models for their high flexibility in such studies.

Soil

Boruta wrapper-based

Ensemble Model

NDVI

Google Earth Engine

Semnan

Flash floods are among the most dangerous and deadly natural disasters worldwide, causing significant loss of life and economic damage annually (Wang and Vivoni 2022; Othman et al. 2023). Climate change, coupled with anthropogenic activities (Hooshyaripor et al. 2020), has intensified the frequency and severity of flash floods. Vulnerability and sensitivity to flash flooding vary across different regions worldwide. Despite prolonged droughts in arid and semi-arid areas, these regions are especially susceptible to flash floods due to high-intensity convective thunderstorms (Wang and Vivoni 2022). According to the 6th IPCC report, extreme rainfall events are increasing in the Middle East, leading to more frequent flash floods in the region (Hassan et al. 2022). Climate modeling predictions indicate that aridity has intensified in the Middle East (Bozorg-Haddad et al. 2020), with some areas experiencing a 40% increase compared to the reference period (1970–2000). This intensification of aridity is expected to lead to a higher frequency of extreme events such as droughts and out-of-season flash floods. The combination of prolonged droughts and heavy rainfall exacerbates the adverse effects of flash floods in these areas (Othman et al. 2023).

Flood susceptibility mapping (FSM) method is one of the most efficient and reliable approaches for identifying flood-sensitive areas (Mia et al. 2023; Liu et al. 2023; Kaya and Derin 2023), and it has been widely adopted and evaluated worldwide (Andaryani et al. 2021; Kalantar et al. 2021; Ghosh et al. 2022; Khaddari et al. 2023; Pradhan et al. 2023; Saravanan et al. 2023; Yang et al. 2023; Habibi et al. 2023; Seydi et al. 2023). In recent years, substantial efforts have been dedicated to refining and evolving the FSM approach, resulting in numerous research endeavors in this field. These studies can be categorized into two primary groups: (i) examining the role and contribution of various flood causative factors in flood formation (Al-Juaidi 2023; Riazi et al. 2023), and (ii) evaluation of different algorithms for modeling and zoning sensitive areas (Mehravar et al. 2023; Razavi-Termeh et al. 2023). Advances in science and artificial intelligence have brought increasing attention to deep learning and machine learning approaches for FSM (Tien Bui et al. 2020; Ahmadlou et al. 2021; Shahabi et al. 2021; Saha et al. 2022; Li and Hong 2023). These methods, known for their high flexibility in learning and generalization, are suitable for addressing complex phenomena with non-linear relationships (Mathew et al. 2021; Sheikh et al. 2023). However, machine learning and deep learning models still face challenges and limitations in FSM (Mia et al. 2023). Recent studies have shown that hybrid ensemble machine learning approaches can overcome these limitations, exhibiting superior performance compared to conventional and individual methods (Costache et al. 2020b, 2022; Gudiyangada Nachappa et al. 2020; Shirzadi et al. 2020; Prasad et al. 2022; Li and Hong 2023).

The fragile condition of soil in arid regions significantly contributes to flash floods. These areas have fragile ecosystems (Cui et al. 2019; Sheikh et al. 2020), poor soil quality, and sparse vegetation cover (McGwire et al. 2000; Fakhri et al. 2022), resulting from frequent droughts (Saadat et al. 2013; Sheikh et al. 2021) and sudden floods, soil erosion intensifying, and compromising soil permeability. Soil plays a crucial role in flood dynamics (Morgan 2005; Saco et al. 2021) in arid and semi-arid regions, regulating water infiltration and influencing runoff volume. The risk of flood hazards rises as soil infiltration capacity diminishes (Samanta et al. 2018). Sparse vegetation coverage and low soil moisture, exacerbated by severe aridity and low infiltration rates, lead to shallow soil with low organic matter, poor profile diversity, and loose structure (Verheye 2009). Given the significance of soil in flash floods, particularly in arid regions (Nabinejad and Schüttrumpf 2023) and the lack of comprehensive information, the preparation of accurate soil maps is imperative. However, global soil maps are often utilized in FSM research where local datasets are lacking (Komolafe et al. 2020; Ahmed et al. 2023; Penki et al. 2023). Considering the high cost and limited sampled data, digital soil mapping (DSM) technique emerges as a powerful and essential tool (Ma et al. 2019). In addition to providing accurate information, it is a cost-effective and detailed technique (van Zijl 2019). Conventional soil mapping techniques are often characterized by their time-consuming nature and high costs. In contrast, DSM, leveraging state-of-the-art technologies, facilitates streamlined data collection and processing, integrating diverse datasets such as satellite imagery, remote sensing, and on-site observations to enhance soil information depth and comprehensiveness (Ma et al. 2019; Arrouays et al. 2020).

Iran has faced increasingly severe flash floods, causing significant damage to infrastructure, the economy, and human lives. For instance, the 2019 flash floods incurred estimated damage of over 2.2 billion (USD), affecting around 2 million people and damaging approximately 12,000 km of roads (https://en.wikipedia.org/wiki/2019_Iran_floods). This study aims to accurately delineate flash flood susceptibility zones within the watersheds of Semnan province, Iran, and categorize the entire basin area based on flash flooding potential. To our knowledge, the combination of the DSM method with FSM approaches is novel. The development of ensemble ML models based on Random Forest (RF), Support Vector Regression (SVR), GLMnet, and TreeBag with Boruta wrapper-based feature selection is also innovative in flood susceptibility research. Another unique feature of this study is that the location of the basin in an arid mountainous area with gypsum and salty soils adds to its complexity, enhancing our knowledge of the flash flood phenomenon in similar areas lacking datasets and information. On the other hand, it is vital to enhance and improve methods for estimating areas prone to flash floods and detecting susceptibility regions in arid regions of the world, especially in developing countries. These regions are more susceptible to flash floods than developed countries due to poor infrastructure development, limited technological progress, and lower per capita income, resulting in higher risks and damages. The results of this study can play a crucial role in planning and mitigating flash floods in areas susceptible to future inundation. They can also assist local authorities in identifying sensitive regions, facilitating timely warnings and alerts from the responsible authority to manage the evacuation and relocation of individuals from vulnerable zones. This study aims to (1) identify flash flood inventory locations, (2) apply the DSM approach to generate soil maps to improve FSM accuracy, (3) detect effective flash flood influencing factors using Boruta wrapper-based algorithm feature selection, and (4) evaluate the performance of several machine learning methods, including RF, SVR, GLMnet, TreeBag, and Ensemble, to detect and classify susceptible flooded areas.

2.1 Study Area

The study region (Fig. 1) comprises the watersheds of Semnan province (WSP), located in the central desert of Iran, covering a total area of 96816 km². The study area extends geographically from 34^◦15' to 37^◦ 20' north latitudes and 51^◦ 50' to 57^◦03' east longitude. 60% and 30% of study areas are located in arid and semi-arid climates, respectively, and a small part of the area has a humid climate. The region exhibits drastic elevation variations, ranging from 3886 m in the narrow belt northern boundary to 649 m in the southern part of the province. Annual precipitation is 140 mm, varying between 70 to 420 mm, while the average temperature is 17 ⁰C, fluctuating between 14 to 25 ⁰C.

Semnan’s river networks primarily consist of ephemeral and seasonal flows from the southern slopes of the Alborz mountains, flowing into the central desert. Major rivers in the study region include Hable-Rud, Tash, Gol-Rodbar, and Ahmad-Abad, with Hable-Rud being the only permanent river in the area. The study region is prone to flash floods due to its location in the southern part of the Alborz mountains, severe topographic variations, extreme rainfall events, and environmental and soil conditions.

2.2 Methodology

Overview

The workflow of the study (Fig. 2) consists of four main sections: (i) creating flash flood inventory maps based on historical flash flood records; (ii) preparing spatial datasets of environmental covariates that affect flash floods, including hydrological, meteorological, topographical, and other environmental variables. Additionally, recognizing the importance of soil properties in flash flood regimes and generation processes, the DSM method was applied to create soil properties maps. Finally, all causative flash flood parameters were transformed to a 30×30 m resolution; (iii) analyzing the distribution of frequency, associations, and multi-collinearity of the flash flood influencing factors. The Variance Inflation Factor (VIF) and Tolerance indexes were employed to assess multi-collinearity, and Boruta wrapper-based algorithms were used for feature selection, and (iv) using a modeling approach to generate flash flood susceptibility maps. Stand-alone TreeBag, SVR, RF, GLMnet, and Ensemble algorithms were applied. The performances of the models were evaluated using statistical evaluation criteria.

2.3 Datasets

To generate a flash flood susceptibility map and predict flash floods, two groups of datasets were used. The first group consists of flash flood inventory data illustrating historical flash floods, while the second group comprises the causative factors of this hazard.

2.3.1 Flash Flood Inventory Map

In arid regions, the monitoring network is weak due to persistent dry seasons and the presence of an ephemeral stream network, resulting in limited available flash flood data. However, in this study, we pinpointed the locations of historical flash floods by collecting data from official and media reports, conducting field surveys, and obtaining information from the Ministry of Energy and the Ministry of Agriculture of Iran. This dataset includes a total of 245 points, comprising both flood and non-flood occurrences (Fig. 1).

2.3.2 Flood Conditioning Factors

In arid regions, geo-environmental factors and their interactions significantly impact flash flood events. Identifying these factors can enhance predictions and susceptibility mapping of flash floods. In the current study, we investigated 19 flood-influencing factors (e.g., meteorological, hydrological, topographical, plant cover, geological, and soil parameters) for flash flood susceptibility analysis (see Table 1). All environmental covariates were converted to 30 m pixel size resolution. The maps of these 19 flood-influencing factors are illustrated in Figs. 3 to 6. Detailed descriptions of each flood causative factor can be found in the Supplementary Materials (A1).

Table 1

The properties of flash flood causative factors
Category	Causative Factor	Description	Ranges (in the study region)	Source	Dataset	Spatial Resolution
Topographic Parameters	TWI	Topographic Wetness Index (TWI), proposed by Beven and Kirkby (1979), is directly related to flooding because it indicates the potential of wetness and flow accumulation in a basin (Riazi et al. 2023).	3.58 to 14.14	DEM	ASTER	30 m × 30 m
	Slope	The steepness of the terrain surface makes flat regions more likely to flood. Slope plays a crucial role in flood dynamics and distribution (Riazi et al. 2023).	0 to 68.60	DEM	ASTER	30 m × 30 m
	Aspect	The direction of the slope controls the direction of runoff flow and slope stability (Al-Juaidi 2023; Luu et al. 2023).	….	DEM	ASTER	30 m × 30 m
	Elevation	Elevation above sea level affects flood vulnerability, with lower elevation areas being more prone to flooding. There is an inverse relationship between flood events and altitude (Khaddari et al. 2023).	648.92 to 3885.77	DEM	ASTER	30 m × 30 m
	Curvature	Slope gradient changes in a particular direction are classified into three classes: flat, convex, and concave (Seydi et al. 2023).	…	DEM	ASTER	30 m × 30 m
	Plan Curvature	The slope direction changes across a surface. A positive curvature value indicates a convex slope gradient in the upward direction, while a negative curvature value indicates a concave slope gradient (Al-Juaidi 2023).	-3.49 to 3.55	DEM	ASTER	30 m × 30 m
	Distance to River	The spatial distance between a particular point and a nearby river affects flood vulnerability, with areas closer to rivers being more susceptible to flooding.	0 to 39160 m	DEM	ASTER	30 m × 30 m
	Catchment Area	The watershed or drainage basin area has a strong association with flash flooding (Yin et al. 2023).		DEM	ASTER	30 m × 30 m
Meteorological Parameters	Rainfall	Total annual rainfall and the daily rainfall data from ERA-5 Land were examined for the period 2001–2020. Quantile Mapping (QM) (Katiraie-Boroujerdy et al. 2020; Enayati et al. 2021) was used to minimize biases in grid-based datasets compared to observations.	70.59 to 420.53	ERA-5 Land / Rainfall gauging	Annual series	9 km × 9 km
Meteorological Parameters	Temperature	Mean annual temperature data from ERA5-Land for 2001–2020 were selected. A bias-correction method (Mao et al. 2015; Ji et al. 2020) was implemented to minimize biases and enhance the accuracy of grid-based datasets.	8.66 to 22.83	ERA-5 Land / Temperature gauging	Annual series	9 km × 9 km
Hydrological Parameters	SPI	Stream Power Index (SPI), proposed by (Moore et al. 1991), has a direct relationship with flooding.	0 to 2813528	DEM	ASTER	30 m × 30 m
	STI	Sediment Transport Index (STI) measures	0 to 9026	DEM	ASTER	30 m × 30 m
	Flow accumulation	The aggregated flow of water over a landscape toward a particular location, which is directly related to flooding.	900 to 12525800	DEM	ASTER	30 m × 30 m
	MRVBF	Multi-resolution Index of Valley Bottom Flatness proposed by (Gallant and Dowling 2003),detects valley bottoms by employing a slope classification limited to convergent areas, which are more likely to contain water compared to simply low areas (Huang et al. 2014; Mueller et al. 2016).	0 to 8.99	DEM	ASTER	30 m × 30 m
Geological Parameters	Geology	Geological features maps show that various lithology units exhibit varying levels of permeability and susceptibility to flooding (Lee et al. 2012; Choubin et al. 2019; Costache et al. 2020c).	…	National Geoscience Database of Iran	…	1:100,000
Geological Parameters	LULC	Land use and land cover maps show that most hydrological processes are affected by different LULC uses. LULC categories include broadleaf forests, shrublands, grasslands, croplands, urban areas, sparse vegetation, Juniper forests, permanent water bodies, herbacious wetlands, haloxylon, salty land, and gardens.	…	European Space Agency (ESA) WorldCover	Sentinel-1 and Sentinel-2 data	10 m × 10 m
Vegetation Parameter	NDVI	Normalized Difference Vegetation Index (NDVI) shows an inverse association between vegetation coverage and flooding.	0.01 to 1	Landsat satellite (OLI)	Monthly series	30 m × 30 m
Soil Parameters	CN	Curve Number (CN) indicates the potential for runoff, with higher values suggesting a greater potential for runoff.	45 to 100	LULC and Soil map	…	30 m × 30 m
Soil Parameters	Infiltration	Saturated hydraulic conductivity (K_s) delineates the velocity of water flow and characterizes the intrinsic capacity of soil to transmit water within saturated zones (Gootman et al. 2020). Due to inadequate information and scarce sampling in arid and semi-arid regions, the DSM was used to create soil maps.	0.03 to 2.58	Sand, Silt, Clay, soil organic matter maps	…	30 m × 30 m

2.4 Statistical Methods

2.4.1 DSM

DSM, extended by McBratney et al. (2003), is a framework that uses various spatial modeling techniques and methods to predict and map soil properties. This method has evolved from conventional soil mapping and classification to developing and populating spatial soil information systems (Ma et al. 2019). The basic concept in DSM is SCORPAN model (McBratney et al. 2003).

$$S\,=\,f(s,\,c,\,o,\,r,\,p,\,a,\,n)\,+\,e$$

where the variables soil (s), climate (c), organisms (o), relief (r), parent materials (p), age (a), and geographical position (n) determine the soil attribute to be predicted (S), and the variable e represents the error.

DSM aims to overcome the limitations of traditional soil survey methods by providing more detailed and accurate soil data (Ma et al. 2019; Wadoux et al. 2020). To achieve this, the association between soil properties and environmental covariates such as topography, vegetation cover, and climate is recognized for estimating soil properties at unsampled locations through a predictive function (Cheshmberah et al. 2022). According to the literature, the models and methods employed in DSM include geostatistics (Malone et al. 2016; Hilal et al. 2023), machine learning (Wadoux et al. 2020; Khaledian and Miller 2020), regression models (Vaysse and Lagacherie 2017; Lamichhane et al. 2019), Pedotransfer Functions (PTFs) (Bouma 1989; McBratney et al. 2002), Soil-Landscape Models (Wolski et al. 2017), remote sensing (Yang et al. 2020; Fathololoumi et al. 2020), data fusion, and expert knowledge. Each approach is chosen based on specific objectives, available data, and the characteristics of the study area. In this study, first the associations among the environmental covariates and soil properties were identified. Terrain parameters calculated from DEM and remotely sensed images were two main sources of environmental covariates in this study. Then, the RF model was applied to create the soil maps in unsampled regions. Supplementary Materials (A1) contain the soil properties and maps.

2.4.2 Feature optimization process

Boruta wrapper-based algorithm Feature Selection

Boruta is a feature selection algorithm developed as a wrapper-based approach based on a random forest classification (Amiri et al. 2019; Habibi et al. 2023). The Boruta algorithm functions by comparing the importance of each feature against that of randomly generated shadow features. A shadow attribute is created for each attribute, and its value is estimated by shuffling original attribute values across objects (Kursa and Rudnicki 2010). Subsequently, the shadow features are evaluated to identify the maximum Z-score (MZS). Any feature that scores better than MZS is assigned a hit. Features with importance scores significantly lower than MZS (Z-scores < MZS) are considered irrelevant and rejected. Conversely, features with importance scores significantly higher than MZS (Z-scores > MZS) are considered relevant and confirmed (Szul et al. 2021).

The Z-score is defined as:

$$Z - score\,\,=\,\frac{{MDA}}{{SD}}$$

that MDA refers to Mean Decrease Accuracy, and SD is the Standard Deviation of accuracy losses. For more details on the Boruta algorithm, you can refer to (Kursa and Rudnicki 2010; Masrur Ahmed et al. 2021).

2.4.3 Multi-collinearity Test

In multiple regression models, multi-collinearity is a statistical phenomenon characterized by strong associations between two or more independent variables (Daoud 2017; Al-Juaidi 2023). The Variance Inflation Factor (VIF) (Wang et al. 2020; Towfiqul Islam et al. 2021; Habibi et al. 2023) and Tolerance (TOL) (Everitt and Howell 2005; Yaseen et al. 2022) are commonly employed to gauge multi-collinearity between the ith independent variable and other in a regression model. Values of VIF > 10 and TOL < 0.1 indicate a likely multi-collinearity problem in the variables (Khosravi et al. 2018; Liu et al. 2021; Luu et al. 2023). VIF and TOL are estimated using the following equation (Band et al. 2020; Pourghasemi et al. 2021):

$$VIF\,=\,\frac{1}{{1\, - \,R_{i}^{2}}}\,=\,\frac{1}{{TOL}}$$

In this study according to VIF and TOL values, multi-collinearity test is conducted on 19 flood causative factors.

2.4.4 Modeling

- Machine Learning (ML) Methods

Machine learning proves to be a powerful tool for predicting natural hazards (Hasan et al. 2023; Riazi et al. 2023) due to its numerous advantages, such as the rapid identification of trends and patterns, automation of recurring tasks, handling of complicated multidimensional variables (Razavi-Termeh et al. 2023), and data noise. Additionally, it enhances forecast accuracy and reduces measurement errors (Luu et al. 2023). The accuracy and reliability of predicted maps have led to the integration of machine learning (ML) methods in FSM (Hasan et al. 2023; Yang et al. 2023; Riazi et al. 2023; Seydi et al. 2023). In this study, various ML methods, including RF, SVR, TreeBag, GLMnet, as well as an ensemble model, were employed.

Table 2

the details of the ML models
Model	Description
RF	The RF algorithm is an ensemble ML method used for regression, data classification, and unsupervised learning, as proposed by Breiman (2001). Key advantages of the RF algorithm include its capability to handle large datasets with associated conditional variables, thereby increasing prediction accuracy. Being a nonparametric method, it can be applied to various types of data without concern about outliers, noise, or over-fitting. Moreover, RF assesses the built-in variable importance by comparing it to the prediction results through the random permutation of the variables (Zhao et al. 2018).
SVR	SVR is a type of Support Vector Machine (SVM) (Cortes and Vapnik 1995) introduced by (Drucker et al., 1997). SVR employs a symmetrical loss function in its training, serving as a supervised-learning technique, and penalizing both high and low misestimates equally (Awad and Khanna 2015). Unlike other models, SVR minimizes the observed training error and includes a regularization term. This combination improves the model’s generalization ability (Castelli et al. 2020). Additionally, the convexity of the fitness function and its constraints ensures the absence of local minima in the error surface, adding to the attractiveness of SVR (Smola and Schölkopf 2004; Awad and Khanna 2015).
TreeBag	The TreeBag model (Breiman 1996), also known as bootstrap aggregation, is an ensemble model that utilizes bagging techniques and combines decision tree classifiers to enhance classification and regression tasks. This methodology effectively leverages diverse training sets to mitigate errors and improve overall predictive performance (Chan and Paelinckx 2008; Eloudi et al. 2023).
GLMnet	Friedman et al., (2010) introduced the Lasso and elastic-net generalized linear model (GLMnet). The GLMnet model is an optimization algorithm that minimizes the objective function to optimize each parameter using cyclical coordinate descent. it employs an iterative optimization approach for each parameter of the model, utilizing cyclical coordinate descent, and the optimization process continues until convergence is achieved. For further information, refer to (Guo et al. 2021).
Ensemble	The ensemble method has garnered more attention in modeling ML algorithms due to its flexibility, accuracy, and ability to analyze datasets with both linear and non-linear data types (Riazi et al. 2023; Razavi-Termeh et al. 2023). The ensemble model exploits the wisdom of the crowd (Baker and Ellison 2008; Acito 2023) to create more accurate forecasts by combining predictions from numerous models. Other advantages of ensemble models include increased forecast accuracy, prevention of over-fitting, and management of complicated variable associations (Choubin et al. 2019; Hosseini et al. 2020). In the present study, an averaging ensemble model was utilized.

2.4.5 Accuracy Analysis

Several model assessment indices have been applied to validate the accuracy of the ML models. To evaluate the performance of the models, various statistical metrics, including Accuracy, Precision, Recall, and AUC, have been employed (Table 3). Higher values of these metrics are indicative of better accuracy.

Table 3

the details of the accuracy indices
Index	Description	Formula
Accuracy	The number of correctly categorized points from the confusion matrix is presented based on a metric (McGrath and Gohl 2022; Yaseen et al. 2022; Arabameri et al. 2022; Kumar et al. 2023)	$\frac{{True\,Positives\,+\,True\,Negatives\,}}{{True\,Positives\,+\,True\,Negatives\,\,+\,False\,Positives\,+\,False\,Negatives\,}}$ (4)
Precision	The ratio of true positives to all positive results (Onan 2015; McGrath and Gohl 2022; Yaseen et al. 2022; Karakas et al. 2023; Kumar et al. 2023)	$\frac{{True\,Positives}}{{True\,Positives\,+\,False\,Positives}}$ (5)
Recall	The ratio of true positives to true positives and false negatives (Onan 2015; McGrath and Gohl 2022; Yaseen et al. 2022; Karakas et al. 2023; Kumar et al. 2023)	$\frac{{True\,Positives}}{{True\,Positives\,+\,False\,Negatives}}$ (6)
AUC	(Area Under the Curve) (Jaafari et al. 2019; Saha and Bhattacharya 2021; Al-Juaidi 2023; Yang et al. 2023)	$\frac{{\sum {True\,Positive\,+\,\sum {True\,Negative} } }}{{P\,+\,N}}$ (7) Where P and N denote the presence and absence of flood, respectively

Where True Positive and False Positive indicate the number of correctly predicted flood points in the flood class and non-flood class, respectively. True Negative and False Negative represent the number of correctly predicted non-flood points in the non-flood class and flood class, respectively (Khosravi et al. 2018).

3.1 Preprocessing of flash flood influencing factors

3.1.1 Multi-collinearity analysis

Table 4 indicates the results of VIF and TOL for 19-influencing factors. A VIF score > 10 and TOL < 0.1 indicate a significant multi-collinearity problem (Costache et al. 2020a). Multicollinearity among the flash flood influencing factors can lead to increased standard errors in the regression models. Based on Table 4, elevation and aspect have the highest and lowest VIF values, as 8.88 and 1.06, respectively. Overall, all the factors exhibit negligible multi-collinearity. So, all influencing factors can be considered independent variables and were used in flash flood susceptibility modelling.

Table 4

The results of the multi-collinearity association between flood-influencing factors
Variables	Tolerance	VIF
Aspect	0.94	1.06
Catchment Area	0.20	5.06
Flow Accumulation	0.65	1.54
Elevation	0.11	8.88
MRVBF	0.37	2.71
Plan Curvature/ Curvature	0.76	1.32
Slope	0.21	4.70
TWI	0.21	4.70
SPI	0.24	4.14
STI	0.43	2.34
Infiltration	0.39	2.53
Distance to River	0.70	1.43
Geology	0.88	1.14
LULC	0.62	1.61
CN	0.52	1.91
NDVI	0.48	2.07
Rainfall	0.12	8.41
Temperature	0.12	8.08

3.1.2 Correlation Matrix

The correlation matrix (Fig. 7) illuminated the interconnections among key influencing flash flood factors. Temperature exhibited a robust negative correlation with both rainfall (-0.88) and elevation (-0.86). A notable positive correlation was recognized between SPI and catchment area (0.84). Slope and TWI displayed a substantial negative correlation (-0.83), while positive correlations were observed between slope and both the STI (0.62) and elevation (0.60). MRVBF showed a negative correlation with elevation (-0.58) and slope (-0.54), along with a positive correlation with temperature (0.53). The results revealed that NDVI had both a positive association with rainfall (0.66) and a negative association with temperature (-0.64). However, the correlation matrix indicated that significant relationships were not recognized for the geology, plan-curvature, distance to river, aspect, and flow accumulation parameters.

3.2 Distribution of flash flood event frequency based on their causative factors

The influencing flash flood factors were divided based on natural break, and flash flood records were identified within each subclass. By dividing the number of flash flood records in each subclass by the total number of flood records in the region studied, the relative frequency was obtained. Figure 8, presents the outcomes of the flash flood frequency analysis and their corresponding causative factors. Considering the annual mean temperature range (8 to 22°C) in Semnan province, 50% of floods occurred at temperatures between 14 and 20°C, while the lowest number of floods was recorded in the highest temperature class. The results indicated that temperatures below 14°C contribute to 25% of the flash flood frequency, particularly in the northern belt mountain region. Conversely, temperatures exceeding 18°C also accounted for 25% of the flash flood frequency. It is noteworthy that these areas include desert regions with limited datasets and knowledge.

Over 75% of flash flood events occur in areas with a total rainfall less than 180 mm per year. Interestingly, locations with higher rainfall values (> 200 mm per year) exhibit the lowest flash flood frequency (only 25% of the total occurrences). The maximum frequency was detected at approximately 150 mm per year, while the minimum frequency of flash floods was identified in the highest rainfall class (Fig. 8). This area, characterized by high elevation, generates runoff, leading to water flow accumulation in regions with slower angle slopes and lower altitudes. A peak in flash flood frequency (75%) was observed in areas with an NDVI below 0.25. As the NDVI value increases, there is a corresponding decrease in recorded flash flood frequency. These findings suggest that the maximum flash flood frequency was observed in locations with NDVI ranges between 0.05 and 0.15, representing over 40% of all observed events. Lower values of the STI were associated with the highest probability of flooding, with 50% of flood events occurring within the STI range of < 13. In contrast, only 25% of flash flood events were observed where STI values exceeded 40.

The slope class of 0–4 demonstrated the highest incidence of flash floods, constituting 75%, whereas flash floods were found to be infrequent on steep slopes. The SPI values indicated that lower values were associated with a higher frequency of flash floods compared to other ranges. SPI values less than 355 accounted for half of the total flood frequency, while only 25% of flash flood frequency occurred in SPI values exceeding approximately 3500.

Variation in elevation indicated that lower elevations are associated with a higher probability of flash flood frequency, with 75% of the total occurrences observed at elevations below 1600 m. In contrast, flood frequency diminished in high-elevation areas. According to the TWI, areas with higher potential wetness are susceptible to a greater frequency of flash floods. TWI values range from 3.6 to 14, and in regions where TWI is less than 8, only 25% of flash flood occurrences were recorded (Fig. 8). The peak frequencies of flash floods were identified within the TWI range of 8 to 9.5, constituting 50% of the total frequency.

In the studied region, the CN ranged from 45 to 100, and the results highlighted that the maximum flood frequency is associated with CN values between 80 and 90. Notably, half of the flood events occurred when CN values exceeded 85. Considering the distance to rivers factor, approximately 60% of flash flood events took place within a distance of less than 1 km from rivers. By increasing distance to rivers, the frequency of flash flood events decreases (Fig. 8). In addition, MRVBF varied from 0 to 9 in the study region. A significant finding demonstrated that 75% of flash flood events were observed when MRVBF was less than 3.4. Similarly, as MRVBF increased, the frequency of floods decreased.

3.3 Selection of flood-influencing factors based on the Boruta wrapper-based algorithm

To enhance the performance of ML models, the Boruta feature selection was applied (Table. 5 and Fig. 9). The MZS was considered a threshold, and the mean importance of each feature through all iterations was compared with the MZS. The results of the Boruta algorithm showed that all 19-flash flood-influencing factors were confirmed and had effects on flash floods; with CN recognized as a tentative feature. Based on Table. 5 and Fig. 9, the following features showed the maximum importance: temperature (26.51), distance to river (23.71), elevation (16.46), TWI (16.33), MRVBF (14.16), curvature (14.04), and NDVI (13.49). In contrast, CN, plan curvature, aspect, and infiltration showed the minimum importance, with their importance measure estimated at 4.27, 4.81, 4.81, and 4.81, respectively.

Table 5

The results of the Boruta variable importance (IMP. is the importance measure calculated through several iterations)
Variable	Mean. IMP.	Median. IMP.	Min. IMP.	Max. IMP.	Decision	Ranked
Aspect	4.81	4.86	2.41	7.00	Confirmed	16
Catchment Area	11.26	11.24	9.52	12.92	Confirmed	9
Flow Accumulation	9.78	9.62	8.80	11.09	Confirmed	11
Elevation	16.46	16.49	14.88	18.42	Confirmed	3
MRVBF	14.16	14.14	12.81	15.33	Confirmed	5
Plan Curvature	4.81	4.89	1.96	6.83	Confirmed	16
Curvature	14.04	14.01	12.28	16.14	Confirmed	6
Slope	10.33	10.32	9.19	11.63	Confirmed	10
TWI	16.33	16.35	14.32	17.95	Confirmed	4
SPI	8.51	8.49	7.12	10.06	Confirmed	12
STI	7.25	7.23	5.57	9.23	Confirmed	14
Infiltration	4.81	4.78	3.62	6.63	Confirmed	16
Distance to River	23.71	23.64	21.23	25.84	Confirmed	2
Geology	6.59	6.67	4.95	8.08	Confirmed	15
LULC	7.32	7.26	6.17	8.88	Confirmed	13
CN	4.27	4.14	2.55	6.03	Confirmed	17
NDVI	12.85	12.75	11.14	14.33	Confirmed	7
Rainfall	12.41	12.49	10.80	13.82	Confirmed	8
Temperature	26.51	26.38	24.21	29.09	Confirmed	1

3.4 Model construction and validation

The four standalone and hybrid ML models (RF, SVR, GLMnet, TreeBag, and Ensemble) were employed to generate flash flood susceptibility maps in the examined region. The flash flood inventory map (Fig. 1) played a pivotal role in training and testing these ML models. Initially, a binary scale was applied to classify points as flooded or non-flooded, with 1 and 0 denoting flooding and non-flooding locations, respectively. For model training and testing, a 70:30 ratio approach was adopted. The flash flood inventory map was divided into two segments, with 70% assigned to the training dataset and the remaining 30% to the testing dataset. Given the problem of binary nature in the susceptibility classification, non-flood locations were considered for dataset generation. In the subsequent step, optimal parameter values for each machine learning model (RF, SVR, GLMnet, TreeBag, and Ensemble) were determined. It is essential to underscore that the selection of the best hyperparameter configuration directly impacts the performance of ML models (Yang and Shami 2020). Consequently, the hyperparameter tuning process was conducted before the actual training of the models.

In the subsequent phase, we generated flash flood susceptibility maps utilizing machine learning models (Fig. 10). The maps were created with 30 × 30-m cells. The natural break classification approach was used to categorize each prediction map. The resulting risk maps were then classified into four distinct categories: low, moderate, high, and very high susceptibility.

According to Fig. 10, the southern part of the WSP exhibited the lowest susceptibility to flash flooding, while the highest risk was identified in the northern half of the study region across all predicted models. Both the SVR and TreeBag models displayed a tendency to overestimate the very high class (20 and 21% of the total area, respectively). The GLMnet model, on the other hand, underestimated the very high class and overestimated the moderated class (9 and 27% of the total area, respectively). The results of the RF and Ensemble models were nearly identical.

The percentage coverage of each susceptibility class of flash flood maps based on the ML models is illustrated in Fig. 11. According to Fig. 11, the TreeBag, SVR, RF, GLMnet, and Ensemble models indicate that about 21, 20, 12, 9, and 17% of the total area fall within the very high susceptibility class, respectively. The area with high susceptibility class covers approximately 10, 15, 16, 18, and 14% of the total area based on the TreeBag, SVR, RF, GLMnet, and Ensemble models, respectively.

The performance of each model was assessed using evaluation criteria such as accuracy, precision, recall, and AUC indexes. The results of the evaluation for the ML models are presented in Fig. 12. Based on these findings, all considered models exhibited acceptable performance, with the average values of accuracy, precision, recall, and AUC index across all classification models estimated at 0.88, 0.93, 0.84, and 0.88, respectively. Upon closer examination of Fig. 12, it is evident that among all prediction models, the GLMnet model displayed the weakest performance, with corresponding values of 0.73, 0.87, 0.62, and 0.75 for accuracy, precision, recall, and AUC, respectively. In summary, the evaluations of the models’ accuracy showed that the RF and Ensemble models exhibited superior performance in the flash flood susceptibility modeling.

4.1 The relationship between the recorded flash flood events and their causative factors

According to Fig. 4, the lowest flash flood frequency (25%) is recorded in regions with annual rainfall of more than 200 mm (200–460 mm), located on the northern border of WSP. This corresponds to the maximum rainfall class. Although an increasing probability of flooding with higher rainfall is expected, the main limiting factors are the high elevation and steep slope in these parts. In addition, other factors such as the small size of their area (only 2% of the basin), favorable vegetation cover with broad-leaf and Juniperus forests (with NDVI values estimated at 0.6, the maximum in the basin), and high permeability have also been effective. These results are consistent with those of Das et al. (2018), Band et al. (2020), and Hosseini et al. (2020), who indicated that higher altitude regions are less susceptible to flash flooding, while lower altitude areas are more prone to flooding during flash flood events. Band et al. (2020) indicated a negative correlation between flash flood occurrence and vegetation density. Consequently, areas with more vegetation density experienced lower runoff compared to those lacking vegetation cover in Markazi Province, Iran. Similarly, Hosseini et al. (2020) detected the importance of NDVI in controlling and infiltration runoff in the Gorganroud River Basin, Iran. The vegetation cover plays a crucial role in enhancing soil properties such as infiltration capacity, water absorption, and reducing erosion. In arid regions, degraded lands and extended gypsum soils often lead to sparse and scattered vegetation cover, increasing the risk of flash floods. Razavi-Termeh et al. (2023) highlighted that NDVI significantly impacts flood occurrences, with vegetation-covered surfaces helping to prevent flooding.

In contrast, the maximum flash flood frequency (75%) was identified in areas with 70–180 mm annual rainfall, covering approximately 90% of the basin area. These regions are characterized by a slower angle slope and lower altitudes compared to the northern belt of WSP. Runoff naturally flows from higher to lower elevations, increasing the likelihood of flash floods in flat regions (Hosseini et al. 2020). The slope of the terrain significantly affects water and runoff patterns. The results indicated that flash floods occur more frequently in areas with lower angle slopes than in those with higher angle slopes (Band et al. 2020). As a result, slope is considered one of the most influential variables in many studies of flash floods due to its substantial impact on surface runoff (Tehrany et al. 2015; Razavi Termeh et al. 2018; Band et al. 2020). Due to the arid climate, aridity-type soils, and limited precipitation, these parts exhibit weak vegetation cover, a characteristic of the arid regions. The poor pastures and bare lands, dominated by grasslands and scattered shrub-lands, have resulted in the lowest NDVI values in the WSP (less than 0.25). On the other hand, soil limitations such as shallow soil depth and the presence of gypsum and salt have reduced permeability in this part of the basin, resulting in higher CN values (more than 80). Because of differences in infiltration, texture, and structure, soil type and soil depth influence drainage processes (Hosseini et al. 2020).

4.2 Identification of the effective causative factors

The Boruta wrapper-based algorithm (Table. 5 and Fig. 9) identified temperature, distance to the river, and elevation as the most influential factors contributing to flash flood events in the WSP, respectively. While the literature extensively covers flood sensitivity studies, the role of temperature as an influencing flood factor has received limited attention (McGrath and Gohl 2022). Ceppi et al. (2012) highlighted the significance of temperature in precipitation type and maximum discharge events, emphasizing its role in snow dynamics. In one study, the land surface temperature was applied to flood susceptibility mapping by Madhuri et al. (2021) for GHMC in India. McGrath and Gohl (2022) underlined the significant role of temperature in spring flooding, attributing it to temperature rise, snowmelt, and heavy rainfall in Canada (McGrath and Gohl 2022). Furthermore, Rehman et al. (2022) demonstrated the importance of temperature changes in identifying very high and high flood susceptibility regions in the Bhagirathi sub-basin of India, emphasizing its influence on the Indian monsoon season. Despite being relatively neglected in flood susceptibility analysis, our results underscored the critical control role of temperature in rainfall within the study region. The correlation matrix results (Fig. 7) showed a strong association between temperature and rainfall (-0.88) in the WSP. In addition, the contribution of temperature to evapotranspiration and soil moisture cannot be disregarded, especially in arid regions. Distance to the river was ranked as 2nd most important parameter. Near the rivers, flash floods were more frequent and severe. Essentially, the distance from the river determined the extent and magnitude of the flash flood (Band et al. 2020). Flooding often originates in riverbeds and spreads to surrounding areas (Razavi-Termeh et al. 2023). According to Fig. 8, the maximum flash flood frequency occurred within a distance less than 1 km from river networks. Consistent with previous studies, distance to the river emerged as the most influential parameter in flood susceptibility modeling in the Haraz watershed, Iran (Shafizadeh-Moghadam et al. 2018) and in the Khiyav-Chai basin, Iran (Choubin et al. 2019). In the coastal region of Bangladesh, (Hasan et al. 2023) also identified the distance to the river as a crucial feature in flash flood susceptibility maps.

Elevation, the 3rd most important parameter, plays a pivotal role in flash flood causation (Razavi-Termeh et al. 2023). This parameter can influence the natural flow of runoff. High-elevation areas tend to be safe from flash flooding, whereas low-elevation areas are vulnerable to flooding during flash floods. Due to low slope and proximity to rivers, low-elevation areas are often affected by flash floods because they are close to the riverbank (Band et al. 2020). Elevation is considered one of the factors that affect flooding by many researchers and has been confirmed to be more sensitive to flooding in low-altitude areas (Chapi et al. 2017; Tehrany et al. 2019; Band et al. 2020; Razavi-Termeh et al. 2023). Moreover, it must be considered that the rainfall, vegetation density, and soil properties are controlled by elevation (Das 2018). In the Gorganrood watershed, Razavi-Termeh et.al. (2023) identified elevation as the most influential factor among 12-influencing factors for identifying flood-prone areas.

4.3 Analysis of the susceptibility flash flood map

To model flash flood potential in the study region, four stand-alone and hybrid ML models (RF, SVR, GLMnet, TreeBag, and Ensemble) were employed. The evaluated criteria, as depicted in Fig. 12, revealed that Ensemble and RF models exhibited the best performance. This aligns with previous studies that also reported the satisfactory performance of the RF model (Zhao et al. 2018; Band et al. 2020; Hosseini et al. 2020; Mahdizadeh Gharakhanlou and Perez 2022).

RF is an ensemble machine learning model that can ability investigate large datasets by factor contribution analysis (Zhao et al. 2018). It has been widely applied in natural hazard modeling (Avila-Aceves et al. 2023) and is highly suited for flood susceptibility mapping, due to its capability to address complex challenges involving multiple variables and nonlinearity (Zhao et al. 2018). Its capacity to handle an extensive array of continuous and discrete variables is one of the RF algorithm's strengths (Razavi-Termeh et al. 2023). A review of studies confirms the effectiveness of the RF model in flood susceptibility modeling

(Vafakhah et al. 2020;Abedi et al. 2022; Hasan et al. 2023).

Considering the strengths and weaknesses inherent in each model, coupled with the absence of universal consensus on a single model and the differences in results from one model to another, combined methods from several single models have recently been developed in flood susceptibility research. Ensemble forecasting models, by aggregating multiple models, can reduce uncertainty, improve generalizability, and stability, and reduce sensitive models in flood susceptibility analysis (Shafizadeh-Moghadam et al. 2018). Numerous studies have identified the remarkable performance of ensemble models in flood susceptibility analysis (Arabameri et al. 2020; Towfiqul Islam et al. 2021; Yang et al. 2023; Aydin and Iban 2023; Özdemir et al. 2023; Yaseen et al. 2022; Islam et al. 2023).

4.4 Strengths and Limitations

The main strengths and capacities of this study include: (i) investigating of flash flood mechanism in a mountainous arid region with complicated and challenging conditions, (ii) considering 19 environmental factors influencing flash floods, (iii) innovatively using of the DSM approach, marking a pioneering effort in flood susceptibility mapping, specifically in creating accurate soil parameter maps, (iv) applying bias-corrected data to estimate rainfall and temperature, (v) utilizing remote sensing dataset series to extract parameters, (vi) applying the Boruta wrapper algorithm for feature selection, (vii) using four stand-alone and hybrid ensemble ML models to flash flood susceptibility mapping.

While this study had some advantages, it also faced some limitations. The location of parts of the central desert of Iran caused scarce information and knowledge about flash floods in the southern part of the study region. In addition, the study encountered limitations due to a severe lack of basic data, inadequate field surveys, low distribution of climatic and hydrometric stations, and a deficiency of soil information in the region, especially regarding gypsum and saline soils.

This research aimed to analyze flash flood phenomena in arid and semi-arid regions, which are challenged by limited datasets, inadequate network monitoring, and numerous unknown mechanisms. The studied region possesses intricate environmental attributes due to its unique geographical location. The northern boundary of the WSP exhibits the highest elevation and precipitation, owing to its proximity to the southern slope of the Alborz Mountain and its exposure to humid air masses. In contrast, the central and southern parts of the WSP experience lower altitude and precipitation due to their proximity to the central desert, the largest desert in Iran. Drastic topographical variations, characterized by a difference in elevation of 3000 m, result in significant changes in both precipitation and temperature. Specifically, as elevation decreases from the northern to the southern part of the basin, precipitation decreases while temperature increases. These factors collectively shape the ecological, soil, vegetation, and ultimately hydrological properties, influencing the region's dynamics and interactions.

In this study, four stand-alone and hybrid ML models, including RF, SVR, GLMnet, TreeBag, and Ensemble were applied to generate the flash flood susceptibility map in the WSP. The Boruta wrapper-based algorithm for feature selection was used to identify effective causative flash flood parameters. According to the Boruta algorithm results, temperature, distance to the river, and elevation were chosen as the most important parameters, while the CN had the least importance. The accuracy metrics indicated that all considered models exhibited acceptable performance, with Ensemble and RF demonstrating the highest accuracy, thus being selected as the optimal ML models for flash flood susceptibility mapping in the study area. The generated maps based on Ensemble and RF models highlighted maximum vulnerability in the northern half of the WSP, while the southern half displayed the minimum susceptibility to flash floods. However, this could not be confirmed with certainty due to the lack of ground observations. The southern half of the WSP remains largely unknown due to its proximity to the central desert of Iran, which makes human habitation and ground measurement and observation difficult.

This study pioneered the use of the advanced DSM method in FSM studies for generating accurate soil maps in arid regions facing data scarcity. Our results underscored the pivotal role of soil in the mechanisms of flash floods, particularly emphasizing the critical influence of salt and gypsum formations in the region. These formations, characterized by low permeability and high erosion potential, significantly impact the intensity and frequency of floods in dry areas. Therefore, it is suggested to pay more attention to the role of these formations in flood sensitivity studies. Additionally, the use of ensemble models is recommended for their flexibility and enhanced accuracy in flash flood susceptibility mapping, especially in arid regions.

CRediT authorship contribution statement

Zahra Sheikh: Conceptualization, Data curation, Methodology, Visualization, Writing original draft, Writing-reviewing & editing. Ali Asghar Zolfaghari: Conceptualization, Methodology, Validation, Data curation, Supervision, Investigation, Visualization, Writing-review and editing, Project manager. Maryam Raeesi: Conceptualization, Methodology, Data curation, Visualization, Writing-reviewing & editing, Writing-Original draft preparation. Azadeh Soltani: Conceptualization, Writing-reviewing.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Author Contribution

Zahra Sheikh, Ali Asghar Zolfaghari, and Maryam Raeesi have participated in data curation, methodology, visualization, writing original draft, reviewing & editing. All authors have conducted conceptualization and reviewed the manuscript.

Acknowledgments

We would like to gratefully acknowledge the support provided by National Elites Foundation and General Department of Natural Resources and Watershed Management of Semnan Province. This research was made possible through the generous grants from these two organizations.

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Enhancing Flash Flood Susceptibility Modeling in Arid Regions: Integrating Digital Soil Mapping and Machine Learning Algorithms

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Abstract

Figures

1. Introduction

2. Material and Methods

2.1 Study Area

2.2 Methodology

2.3 Datasets

2.3.1 Flash Flood Inventory Map

2.3.2 Flood Conditioning Factors

2.4 Statistical Methods

2.4.1 DSM

2.4.2 Feature optimization process

2.4.3 Multi-collinearity Test

2.4.4 Modeling

2.4.5 Accuracy Analysis

3. Results

3.1 Preprocessing of flash flood influencing factors

3.1.1 Multi-collinearity analysis

3.1.2 Correlation Matrix

3.2 Distribution of flash flood event frequency based on their causative factors

3.3 Selection of flood-influencing factors based on the Boruta wrapper-based algorithm

3.4 Model construction and validation

4. Discussion

4.1 The relationship between the recorded flash flood events and their causative factors

4.2 Identification of the effective causative factors

4.3 Analysis of the susceptibility flash flood map

4.4 Strengths and Limitations

5. Conclusion

Declarations

Declaration of competing interest

Author Contribution

Acknowledgments

References

Additional Declarations

Supplementary Files

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Index	Description	Formula
Accuracy	The number of correctly categorized points from the confusion matrix is presented based on a metric (McGrath and Gohl 2022; Yaseen et al. 2022; Arabameri et al. 2022; Kumar et al. 2023)	\(\frac{{True\,Positives\,+\,True\,Negatives\,}}{{True\,Positives\,+\,True\,Negatives\,\,+\,False\,Positives\,+\,False\,Negatives\,}}\) (4)
Precision	The ratio of true positives to all positive results (Onan 2015; McGrath and Gohl 2022; Yaseen et al. 2022; Karakas et al. 2023; Kumar et al. 2023)	\(\frac{{True\,Positives}}{{True\,Positives\,+\,False\,Positives}}\) (5)
Recall	The ratio of true positives to true positives and false negatives (Onan 2015; McGrath and Gohl 2022; Yaseen et al. 2022; Karakas et al. 2023; Kumar et al. 2023)	\(\frac{{True\,Positives}}{{True\,Positives\,+\,False\,Negatives}}\) (6)
AUC	(Area Under the Curve) (Jaafari et al. 2019; Saha and Bhattacharya 2021; Al-Juaidi 2023; Yang et al. 2023)	\(\frac{{\sum {True\,Positive\,+\,\sum {True\,Negative} } }}{{P\,+\,N}}\) (7) Where P and N denote the presence and absence of flood, respectively