Flood susceptibility mapping using support vector regression and hyper‐parameter optimization

Floods are both complex and destructive, and in most parts of the world cause injury, death, loss of agricultural land, and social disruption. Flood susceptibility (FS) maps are used by land‐use managers and land owners to identify areas that are at risk from flooding and to plan accordingly. This study uses machine learning ensembles to produce objective and reliable FS maps for the Haraz watershed in northern Iran. Specifically, we test the ability of the support vector regression (SVR), together with linear kernel (LK), base classifier (BC), and hyper‐parameter optimization (HPO), to identify flood‐prone areas in this watershed. We prepared a map of 201 past floods to predict future floods. Of the 201 flood events, 151 (75%) were used for modeling and 50 (25%) were used for validation. Based on the relevant literature and our field survey of the study area, 10 effective factors were selected and prepared for flood zoning. The results show that three of the 10 factors are most important for predicting flood‐sensitive areas, specifically and in order of importance, slope, distance to the river and river. Additionally, the SVR‐HPO model, with area under the curve values of 0.986 and 0.951 for the training and testing phases, outperformed the other two tested models.


| INTRODUCTION
Natural disasters cause damage and loss of life on a large scale (Tehrany, Pradhan, & Jebur, 2014).Reducing the risk they pose to society is a daunting global task that requires the efforts of physical and social scientists, economists, policy makers, and political leaders (Barati, 2018).Iran is a country exposed to a wide range of natural hazards, including large earthquakes, drought, and floods.It thus has a strong interest in strategies that reduce the damage from disasters (Bui et al., 2019).
Although Iran is a semi-arid country, it has experienced devastating floods in past centuries, and the frequency of such events in the future is expected to increase as climate changes (Modarres, Sarhadi, & Burn, 2016;Mohammadi, Darabi, Mirchooli, Bakhshaee, & Haghighi, 2021).Damage and loss of life from floods in Iran have been exacerbated by poor management of floodplains, land-use changes, loss of forest, overgrazing, and construction of inefficient hydraulic structures (Hooshyaripor, Faraji-Ashkavar, Koohyian, Tang, & Noori, 2020;Tang, 2020).
More broadly, the destructive consequences of floods can be significantly reduced by better management of floodplains.One tool that makes this possible is accurate flood susceptibility (FS) maps (Fenicia et al., 2014;Tehrany et al., 2014).Traditional forms of flood analysis and zoning based on one-dimensional rainfall-runoff models are expensive and commonly fail to capture the spatial complexity of floods (Fenicia et al., 2014).Instead, researchers are increasingly turning to spatial datadriven, machine-learning methods to create accurate FS maps (Hong et al., 2020).Tehrany et al. (2014), for example, used the weight of evidence model (WoE) with bivariate statistical analysis to determine the importance of factors that affect flooding.They entered these factors into the support vector machine (SVM) model to evaluate the correlation between each factor and the spatial occurrence of flooding.Finally, they tested the performance of their ensemble WoE-SVM method using the area under the curve (AUC), which provides measures of predictability and success.In another study, Tehrany, Pradhan, and Jebur (2015) used SVM and the frequency ratio (FR) method to assess spatial FS.Finally, they compared the performance of their ensemble model with that of another benchmark machine-learning algorithm (decision tree, DT).The FR and SVM methods return high prediction rates that exceeded those of the DT model.Termeh, Razavi, Pourghasemi, and Keesstra (2018) created flood risk maps for Jahrom city, Iran, by combining compatible neural-fuzzy inference systems (ANFIS) with a variety of metaheuristic algorithms, including ant colony optimization (ACO), genetic algorithm (GA), and particle swarm optimization (PSO).Based on AUC values, the ANFIS-PSO ensemble model had the highest accuracy, although FR, ANFIS-ACO, ANFIS-GA and ANFIS-PSO performed nearly as well.Shirzadi et al. (2020) developed a new group learning method (GA-BN-NN) that combines Bayesian belief network, extreme learning machine and backpropagation models using GA optimizes.Finally, Saha et al. (2021) recently evaluated the performance of FS in the Koiya River basin, India.They combined superpipes (HP) and support for vector regression (SVR) machinelearning algorithms and showed that the combined approach had higher sensitivity, specificity, and accuracy than the HP and SVR algorithms alone.
Our paper builds on the aforementioned body of research by creating and testing FS maps for the Haraz watershed in northern Iran.We chose the Haraz watershed for study because numerous devastating floods have occurred there during the past century, and the likelihood of similar disasters in the future is high.
Our objectives in this paper are two-fold.First, we strive to further develop high-power SVM ensemble machine-learning methods for use in spatial natural hazard assessments.Second, we aim to produce maps that provide accurate flood forecasts in the Haraz watershed.Researchers in other fields of study have used the hyperparameter optimization (HPO) method that we employ in this paper with SVM (Ahmad, Mourshed, & Rezgui, 2018;Meng et al., 2016;Wang, Zheng, Yoon, & Ko, 2018).It is noted that the main purpose of current research is combination of HPO method and support vector regression (SVR) with increasing the accuracy of FS mapping that have not been used previously.The structure of the paper is as follows.Section 2 describes the study area and discusses the factors used to evaluate flood susceptibility.Also, our method is summarized in several subsections in Section 2. The results and discussion are then presented in Section 3. We conclude the paper with a summary of our findings are then presented in Section 4.

| Study area
The Haraz watershed is located on the north slope of the central Alborz Mountains in Mazandaran Province, Iran.The watershed has an area of 4014 km 2 and is located between 35 45 0 and 36 22' N latitude, and 50 43 0 and 52 45 0 E longitude.It includes the highest mountain in Iran (Damavand Mountain, 5595 m above sea level, asl) (Figure 1).The lowest elevation in the catchment is 328 m asl.The watershed is hilly to mountainous and has a humid temperate to seasonally cold climate that is characteristic of Caspian coastal areas (Shahabi et al., 2020).Average annual precipitation is about 723 mm, and most rainfall occurs in winter and October (Chapi et al., 2017).October is typically the wettest month of the year, with an average of 160 mm of rain.The minimum winter temperature is À25 C, and the summer maximum is about +36.5 C (Chapi et al., 2017).The study area is mountainous, so that the slopes of 0-6 include only 5% of the basin.Land cover includes forest, groves, pasture land, barren land, and residential areas.Pasture land constitutes about 92% of the watershed.Devastating floods caused by heavy rainfall and changes in land use have occurred in recent decades (Bui et al., 2018).

| Flood conditioning factors
Flood indicators were chosen based on characteristics of the study area, the scale of the study, and data availability (Bui et al., 2016).Based on previous studies, expert opinion, and field observations, we selected 10 flood conditioning factors to develop FS models (Khosravi et al., 2018).Three of the 10 factors are topographic (slope, elevation, curvature); 5 are hydrological (rainfall, stream power index [SPI], topographic wetness index [TWI], distance to river, river density); 2 are land cover (land use, normalized difference vegetation index); and 1 is geological (Figures 2 and 3).Elevation, slope angle, curvature, TWI, SPI, distance to river, and drainage density were extracted from the ASTER Global DEM (https:// gdex.cr.usgs.gov/gdex)with 30 Â 30 m spatial raster resolution.Rainfall was mapped using a simple Kriging method of 20 years  of meteorological data and geology layer was originally produced by the Iran Geological Survey Department, from the Mazandaran Regional Water Organization with a scale of 1:100000.Land use was defined using the Neural Network Algorithm and supervised classification in Environment for Visualizing Images (ENVI 5.1) software by Landsat 8 (ETM + ) satellite images.Then all the layers converted to a raster resolution of 30 m for raster analysis.

| Hydrological factors
Rainfall can be a significant factor in flooding (Cao et al., 2017).The probability of flooding increases as the rainfall increases (Shahabi et al., 2021).Precipitation maps were generated using mean annual precipitation data acquired from 18 meteorological stations for the period 1991-2011.Different interpolation methods were used to prepare the rainfall map.The map was made the simple Kriging method and has five categories:   3e).Most areas impacted by floods are located close to rivers.Therefore, distance to river is an important factor in mapping flood-prone areas in a watershed (Butler & Pidgeon, 2011;Fern andez & Lutz, 2010).In this research, distance to rivers was defined from topographic maps of the watershed.River distances were set using buffers in the ArcGIS10.5environment, and six distance classes were established using the natural break method: 0-50, 50-100, 100-150, 150-200, À200-250, and > 250 m (Figure 3g).
River density is another important variable used to map FS (Vojtek & Vojtekov a, 2019) The stream network in this study was extracted from the DEM using the Arc-Hydrology extension in ArcGIS 10.5, and drainage density was calculated using the linear function in the software.The river density map in this study has six classes that were defined using the natural break method: 0-0.34, 0.34-0.62, 0.62-0.85, 0.85-1.09, 1.09-1.36, and 1.36-2.09km/km 2 (Figure 3h).
SPI is an important hydrological factor that provides a measure of the intensity and erosive power of runoff on slopes (Bui et al., 2016).SPI values were calculated as follows, based on Moore and Wilson (1992): where A s is the specific watershed area (m 2 ) and β is the local slope gradient (in degrees).The SPI map has six classes (Figure 3i).
The TWI provides a measure of water accumulation in a catchment and thus can be used to identify areas where soils approach saturation (Beven, 2011).TWI values were calculated as follows, based on Beven and Kirkby (1979): The TWI map created for this study has six categories (Figure 3j).
Dense vegetation typically reduces the severity of flooding.The normalized difference vegetation index (NDVI) is an image-derived metric that serves as a proxy for vegetation density (Tehrany, Pradhan, & Jebur, 2013).NDVI is calculated by measuring reflections in the red and near-infrared (NIR) part of the electromagnetic spectrum, as follows (Tucker & Sellers, 1986): where Red and NIR are spectral reflectance in the red and NIR regions, respectively.NDVI ranges from 1 and À 1, and the map created for this study has six classes (Figure 3k).

| Geological factor
Permable soils and areas with highly soluble rocks such as limestone have low drainage densities (Srivastava, Bansod, & Khare, 2021).Therefore, bedrock Geology and soils affect rainfall infiltration and thus surface runoff (Stefanidis & Stathis, 2013).Geological data were extracted from a 1:100,000-scale geological map provided by the National Geological Survey of Iran.Data were checked by in the field and by airphoto interpretation.

| Support vector regression
SVM is a machine-learning method introduced by Cortes and Vapnik (1995).SVM can be used for two purposes, classification and regression.Support vector classification (SVC) is used for classification, and SVR is used for regression (Sugimoto, Yokoyama, Fujita, & Fukuyama, 2006).SVR, is a model that fits a curve with a margin of ε to the data, in such a way that the least error occurs in the test data.The reader is referred to Huang, Wei, and Zhou (2022), Isazadeh, Biazar, and Ashrafzadeh (2017), Jha and Hayashi (2014), Moazenzadeh, Mohammadi, Shamshirband, and Chau (2018), Pai and Hong (2007) and Smola and Schölkopf (2004) for details on SVR.
Adjusting hyper-parameters is superior to using default parameters in machine-learning algorithms.Hyperparameters can be optimized manually by testing all possible values (Wicaksono & Supianto, 2018), although doing so is a time-consuming and laborious task.Alternatively, optimized hyper-parameters can be selected automatically using the Classification Learner app.This app uses an optimization scheme that minimizes model classification error and returns a model with the optimized hyper-parameters.Following optimization, one can use the resulting model in the same way as one would with any other trained model.HPO with the Classification Learner app is done in four steps: 1. Choose a model type and decide which hyperparameters to optimize.2. Specify how the optimization will be performed (optional).3. Train the model.4. Evaluate the trained model.

| Linear kernel
The linear kernel (LK) was first proposed by Campbell, Sturim, Reynolds, and Solomonoff (2006).The backup vector machine uses the LK function to transfer data to a higher dimension space (Samadzadegan & Ferdosi, 2011).The equation for the LK function is: If we define the training points in SVR as [x i :y i ] and the input vector as R n x i and the class value as y i À1:1 f g:i ¼ 1:, …,i, decision rules are defined by an optimal plane in which they divide the binary classification into the following relation: where Y is the output of the relation, y i is the value of the instance sample class x i , and the parameters a i and b determine the page supercharger.K x i :x j À Á is a LK function.

| Analysis of spatial correlation SWARA
SWARA is a method for determining weight values, which has an important role in multi-criteria decision-making applications.SWARA ranks the most important criterion first and the least important one last.In the use of the SWARA method, expert opinion plays an important role in prioritizing criteria and calculating weights.For this reason, SWARA is considered a specialist method (Keršuliene, Zavadskas, & Turskis, 2010).The two main steps are as follows (Stanujkic, Karabasevic, & Zavadskas, 2015): 1. Experts determine models and criteria, and then prioritize the criteria according to their importance by arranging them in descending order.2. All criteria are weighted.
Based on previous research and expert knowledge, criteria ranking is determined as follows: The expert estimates the relative importance of the second criterion, j, by considering and relating it to the previous criterion (j À 1).The expert then proceeds iteratively in this manner to the final criterion.The importance relativity of the mean value, S j is calculated as follows (Keršuliene et al., 2010): where n is the number of experts, A i is the ranks of the experts for each factor, and j is the number of the factors.
The coefficient K j is determined as follows: The recalculated weight Q j is: The relative weights of the evaluation criteria are expressed as follows: where W j represents the relative weight of the criterion j th , and m shows the total number of criteria.

| Factor selection using the One-R technique
One R (short for "One Rule") is an exact classification algorithm that generates a rule for each predictor in the data, then selects the rule with the least error as the "one rule" (Nguyen et al., 2020).In this study, ORAE (One Rule Attribute Evaluation), an effective filter selection method (Nhu et al., 2020), was used to choose factors.
The ORAE method defines a unique rule for each element in the training data set using statistical correlations between an output variable and a set of selected input factors (Yildirim, 2015).In this study, ORAE independently classifies all factors based on their importance in solving flood prediction problems.

| Statistical metrics
SVR-HPO model results were evaluated using quantitative criteria such as sensitivity, specificity, and accuracy.A 2 Â 2 contingency table was created based on the training and validation flood modeling data that includes all possible outcomes of TP, FP, FN and TN.True positive (TP) is the number of pixels that are correctly classified as a flood event.False positive (FP) is the number of pixels that are incorrectly classified as a flood event.True negative (TN) is defined as the number of pixels correctly classified as non-flood, whereas false negative (FN) is defined as the number of incorrect pixels as non-flood (Althuwaynee, Pradhan, Park, & Lee, 2014).The sensitivity, specificity, and accuracy calculations are formulated as follows:

| ROC curve
Receiver operating curve (ROC) is a graphical representation of the detection ability of a binary classification measurement system.This curve is considered one of the efficiency evaluation tools, which can be used to examine concepts such as sensitivity and specificity of a test.The ROC was used to determine the accuracy of the FS maps (Falah et al., 2019;Naghibi, Ahmadi, & Daneshi, 2017).

| Parameter tuning and hyperparameter optimization fit
Successful use of SVR is always challenging as it requires that parameters related to model architecture be determined.In general, the performance and accuracy of SVR depend on the choice of two parameters (ϵ and C) and core functions.Parameter ϵ determines the deviation of the regression solution from the training data in the input space.However, the set limit is not strict, because observations that are exceeded are also "tolerated" (i.e.included in the regression process), as long as they are within the deviation range specified by the box C constraint.In this study, optimizations were performed with three hyper-parameters (box constraint, kernel scale, and epsilon) using the "fitrsvm" function in MATLAB.The fitrsvm method uses kernel functions to map predictor data (Rajput & Kaulwar, 2019).Table 1 shows the optimized SVR hyper-parameters, and Figure 4 shows the objective results in the training phase (min observed objective) and testing phase (estimated min objective) using hyperparameters optimization.class (6.9-11.5)has the highest SWARA value (0.08) and the lowest TWI class (1.9-3.9) has the lowest value (0.00).In terms of river density, the highest probability of flooding (0.37) is associated with classes 2.67-3.66 and 3.66-7.3,and the lowest probability (0.01) is linked to class 0.401-1.17counterintuitive, it is explained by the fact that flooding is only common at low elevations where slopes are lower and the drainage network is denser.

| Factor selection
In this study, the One R method was used to investigate the influence of conditional factors on the occurrence of floods.The higher the value of Average Merit (AM), the stronger the factor influencing the flood model (Table 2).Calculating the AM using the One R method for each influencing factor showed that slope angle (AM = 0.57) and distance to river (AM = 0.53) are the most important factors controlling the FS.Historical data also show that floods in the studied area mostly occurred in low slopes and along rivers (Chapi et al., 2017).Other factors with AM ≠ 0 were also used in the FS modeling process.The results of other factors were ranked as river density (0.48), elevation (0.4), TWI (0.38), Geology (0.31), curvature (0.25), SPI (0.21), land use (0.03) and rainfall (0.02).These accord with Chapi et al. (2017).

| Development of flood susceptibility maps
After training and validating the SVR model with three ensembles (LK, BC, and HPO), the models were implemented and the outputs were obtained as weights (FS values).FS values were then grouped using the natural break, quantile, and geometric interval methods in ArcGIS (Kavzoglu, Sahin, & Colkesen, 2014;Quinlan, 1996).The natural break method groups similar values based on the inherent natural groupings of the data while maximizing differences between classes.
Because this method places clustered values in the same class, it is successful in mapping data that are not evenly F I G U R E 7 Flood susceptibility mapping using SVR-HPO.
distributed (Ayalew & Yamagishi, 2005).The quantile method, classifies data into a certain number of categories with an equal number of units in each category.
The geometrical interval method classifies a range of values and defines class breaks based on geometric series (Ajibade et al., 2021).
The method used to classify FS values depends on the histogram of the number of pixels (Meng et al., 2016;Pradhan, 2013).We prepared histograms of numbers of flood pixels for the five FS classes (VLS, LS, MS, HS, VHS) in order to select methods that yield the highest numbers of flood pixels in the high susceptibility (HS) and very high susceptibility (VHS) classes.We found that the natural break method best defines class boundaries on the FS maps obtained using the SVR-HPO, SVR-LK, and SVR-BC methods (Figure 6).We therefore applied boundaries defined by the natural break method on the FS maps.

| Preparation of flood susceptibility maps
Figures 7-9 show FS maps obtained with SVR and, respectively, HPO, LK, and BC.All maps show that the greatest risk of flooding occurs in the eastern, northern, and southern parts of the Haraz watershed.Most VHS areas are located along roads and waterways, and very low susceptibility (VLS) areas are at higher elevations, that indicating correct model results.

| Validation of flood susceptibility maps
Validation of the FS maps shows that SVR-HPO ensemble (AUC = 0.951) is slightly more accurate than the SVR-LK (0.949) and SVR-BC (0.949) models (Figure 10).All three ensemble models returned excellent AUC values.

| Experimental results and model comparisons
In Figure 11, we compare the performance of the SVR-HPO model with those of selected benchmark machinelearning models.Based on its sensitivity, specificity, and accuracy values of 96.40, the SVR-HPO model performs better than the reduced error pruning tree (REPTree), logistic model tree (LMT), Bayesian logistic regression (BLR), and logistic regression (LR) models.
Figure 12 shows the performance of the SVR-HPO model relative to standard machine-learning and optimization algorithms based on the area under the ROC curve.The SVR-HPO model with AUC values of 0.986 and 0.951 for the training and testing data outperformed the REPTree, BLR, LMT, LR, and several ANFIS (adaptive neuro-fuzzy inference system) ensemble models.

| CONCLUSION REMARKS
Preparing an FS map is one of the first steps in managing flood hazards.This is particularly pertinent to the situation in northern Iran, where flooding is a frequent destructive occurrence.In this study, we used three ensemble methods that include SVR, LK, BC, and HPO to model FS in the Haraz watershed.We divided our flood dataset into two series: 75% of the data were used for training and 25% for testing.We further selected 10 conditioning factors for modeling: three topographic factors (slope, elevation, curvature); five hydrological factors (rainfall, distance to river, river density, SPI, TWI); a land cover factor (land use), and a geological factor.
In this study, the most widely used classification methods, including natural break, quintiles, and geometric distances, were applied to the data in ArcGIS software.The natural break method was deemed to be the most suitable based on percentages of flood pixels in the HS and VHS flood classes.FS maps were prepared SVR-LK, SVR-BC, and SVR-HPO ensembles.The maps show five FS classes (very low, low, medium, high, and very high susceptibility).The high and VHS classes are restricted to low-lying areas near the outlet of the watershed and in narrow strips bordering rivers and streams.The modeling results show that 25.35% of SVR-BC pixels are in the high and VHS classes; corresponding percentages for SVR-HPO and SVR-LK are 25.23% and 24.42%.The high and very high FS areas transition with increasing distance from rivers into the medium susceptibility class.The results show that 26.99% of SVR-BC pixels, 26.09% of SVR-HPO pixels, and 26.77% of SVR-LK pixels are in the medium susceptibility class.Low and very low FS areas include mountains and hilly slopes that are far from rivers and streams.The SVR-BC model placed 47.66% of pixels in these two classes.Corresponding values for SVR-HPO and SVR-LK are 48.67% and 48.82%.The AUC results show that the SVR-HPO model had better predictive power than the other models in both the training and testing stages, with values of 0.986 and 0.951, respectively.
We compared statistical evaluation metrics and AUC values obtained with the SVR-HPO model used in this study with comparable metrics obtained with some benchmark machine-learning models and optimization algorithms in previously published flood studies of the Haraz watershed.These comparisons show that SVR-HPO model is more accurate than other techniques.Finally, our favored ensemble model yields a value of 96.40 for sensitivity, specificity, and accuracy indices, which is higher than the same values obtained by the benchmark models LR, LMT, BLR, and REPTree.

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I G U R E 1 Haraz watershed and locations of training and validation sites.

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I G U R E 2 Flowchart of the modeling process used in this study.
Hyper-parameters optimization results.

3. 2 |Figure 5
Figure 5 summarizes spatial correlations between flood occurrences and conditioning factors.It shows that slope is inversely related to flooding probability and that the highest SWARA value (0.4) is associated with the

F
. The lowest distance to river class (0-50 m) has the highest SWARA value (0.59), and the most distant class (>700 m) has the lowest value (0).The Triassic geological time period are most closely associated with floods (0.31).In terms of land use, the highest values of SWARA (0.75) are associated with water bodies, followed by residential areas (0.15), gardens (0.06), forests (0.02), pastures (0.01), and arable and barren lands (0).Finally, floods are most closely associated (SWARA = 0.4) with the lowest rainfall class (188-333 mm).Although this result might seem T A B L E 2 Factor ranks obtained using the One R method.I G U R E 6 FS classes based on different classification methods including natural break, geometrical interval and equal interval: (a) support vector regression (SVR)-hyper-parameter optimization (HPO); (b) support vector regression (SVR)-linear kernel (LK); (c) support vector regression (SVR)-base classifier (BC).

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I G U R E 8 Flood susceptibility mapping using SVR-LK.

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I G U R E 9 Flood susceptibility mapping using SVR-BC.F I G U R E 1 0 Results of ROC curve technique to evaluate flood models; (a) success rate curve (training dataset), (b) prediction rate curve (validation dataset).

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Comparison of accuracy, specificity, and sensitivity of the SVR-HPO model and some benchmark machinelearning models for the testing dataset.Not reported in the literature.A: Tien Bui et al. [19] U R E 1 2 Comparison of the performance of the SVR-HPO model and some benchmark machine-learning models based on AUC values.