Introduction

According to statistics provided by the United Nations, among the natural disasters, floods and storms have brought the most casualties and losses to human societies. Between 2000 and 2008, nearly 99 million people worldwide have been affected by flooding (Opolot 2013). The flooding trend in recent years suggests that most of Iran’s regions are exposed to destructive floods. In addition to financial and psychological damage, floods cause soil erosion and nutrient loss. The continuation of this situation entails irreparable damage to water and soil resources. In the current situation, it is expected that the socio-economic and environmental consequences of floods will be felt more than ever in the context of urbanization, increasing deforestation, and sustainability of rainfall because of climate change in the various regions. Therefore, operation prevention are essential and necessary (Alvarado-Aguilar et al. 2012; Billa et al. 2006; Dang et al. 2011; Huang et al. 2008). One of these measures is to provide a flood map that is necessary in integrated management for sustainable development (Rahmati et al. 2016b).

Lee et al. (2012) found the accuracy of the frequency ratio (FR) model with area under the curve (AUC) of receiver operating characteristics (ROC) of 91.5% for preparing flood susceptibility mapping (FSM) in Busan, South Korea. Tehrany et al. (2013) and Tehrany et al. (2014) provided FSM for Kuala Terengganu County in Malaysia using two sets of decision-making methods, a combination of FR and logistic regression (ensemble model), support vector machine (SVM), and weight-of-evidence (WOE). They found that the accuracy of decision trees, the ensemble model, SVM, and WOE models were 87%, 90%, 95.67%, and 96.48%, respectively. Youssef et al. (2016b) prepared FSM for Jeddah County in Saudi Arabia using FR and logistic regression (LR). They found that the accuracy of FR and LR models was 89.6% and 91.3%, respectively. Rahmati et al. (2016b) prepared FSM in Golestan Province, Iran, using FR and WOE models. According to the results, these two models had the same and reasonable efficiency for identifying FSM. Khosravi et al. (2016) prepared FSM with four different models: FR, WOE, analytical hierarchy process (AHP), and FR-AHP for Haraz Watershed, Iran. They found that the accuracy of FR, WOE, AHP, and FR-AHP models were 96.55%, 96.95%, 94.99%, and 84.69%, respectively. Rahmati et al. (2016c) evaluated the accurate and reliable performance of AHP technique in potential flood hazard zones identification by comparing with the results of HEC-RAS hydraulic model in some part of the Bashar River downstream of Yasooj city in Iran. Mojaddadi et al. (2017) evaluated the ensemble method of FR and SVM with a radial basis function kernel in FSM for Damansara River catchment in Malaysia. Based on the results, the accuracy of FR-SVM model was 78.9%. Haghizadeh et al. (2017) and Siahkamari et al. (2018) applied the Shannon’s entropy, FR, and maximum entropy models for FSM in the Madarsoo Watershed, Golestan Province, Iran. Based on the results, the accuracy of Shannon’s entropy, FR, and maximum entropy models was 73.5, 74.3, and 92.6%, respectively. Shafizadeh-Moghadam et al. (2018) compared eight models in FSM for Haraz Watershed, Iran. Based on the results, the highest and lowest accuracy values were reported for boosted regression trees model with 0.975% and generalized linear model with 0.642%, respectively. Darabi et al. (2019) applied the genetic algorithm rule-set production (GARP) and quick unbiased efficient statistical tree (QUEST) models to produce FSM in Sari city, Iran. Based on the results, the accuracy of GARP and QUEST models was 93.5 and 89.2%, respectively. Falah et al. (2019) evaluated an artificial neural network (ANN) model with the the accuracy of 92.0% in FSM for Emam-Ali township in Mashhad city, Iran. Chen et al. (2019a) applied the machine learning-based reduced error pruning trees (REPTree) with bagging (Bag-REPTree) and random subspace (RS-REPTree) ensemble models in FSM for Quannan County, China. Based on the results, the highest accuracy value was reported for RS-REPTree model with 0.907%. Costache and Tien Bui (2019) compared six ensemble models by combining the FR and WOE on the one hand, with ANN, rotation forest (RF), and classification and regression trees (CART) in FSM for Putna River Watershed, Romania. Based on the results, all six ensemble models indicated a high flood prediction performance from 86.8 to 93.9%. Khosravi et al. (2019) compared three mlti-criteria decision-making (MCDM) analysis techniques (VIKOR, TOPSIS, and SAW) along with two machine learning methods (naive bayes trees (NBT) and naive bayes (NB)) in FSM for the Ningdu Watershed, China. Based on the results, all models indicated a high flood prediction capability (> 95%). Mind'je et al. (2019) evaluated the logistic regression model with the accuracy of 79.8% in FSM for Rwanda, Africa.

Therefore, the methods used to investigate and map flood susceptibility in recent years were including FR, multivariate statistical analyzes, WOE, MCDM, LR, and decision tree. In recent years, advanced methods in FSM, data mining have been considered as a useful tool such as ANN (Falah et al. 2019; Costache and Tien Bui 2019), SVM (Tehrany et al. 2014; Mojaddadi et al. 2017), adaptive neuro-fuzzy inference system (ANFIS) with grid partitioning method and metaheuristic optimization algorithms (Razavi Termeh et al. 2018; Tien Bui et al. 2018), and random forest model (RF) (Rahmati and Pourghasemi 2017). ANFIS has showed good results in modeling non-linear processes. ANFIS has adjusted the characteristics of the system according to training data and metadata according to the required accuracy. ANFIS generates FIS by two methods (grid partitioning and subtractive clustering methods) (Vafakhah and Kahneh 2016). RF is a new supervised classification method in modeling process. RF method have been used in various studies such as forest fire, landslide susceptibility mapping (Pachauri et al. 1998; Cevik and Topal 2003; Sidle and Ochiai 2006; Pradhan et al. 2011; Catani et al. 2013; Pourghasemi and Kerle 2016; Youssef et al. 2016a; Chen et al., 2018a, b, c, 2019b, d), ecological studies, and groundwater potential mapping (Rahmati et al. 2015; Naghibi et al. 2016; Chen et al. 2019c). Therefore, new ensemble models should be further investigated.

Given the negative effects of floods, the identification of flood-prone areas is essential. Therefore, due to the aforementioned issues and the lack of information and data of appropriate quality in most watersheds, ANFIS with subtractive clustering method and RF models are used due to the good accuracy in the preparation of FSM and a groundwater potential mapping, as well as landslide susceptibility mapping. In addition, there have been no studies, which compare the ANFIS and RF differences and apply the ANFIS with subtractive clustering method in the preparation of FSM. In the present study, the effectiveness of these two models was investigated in the preparation of the FSM in the Gilan Province, Iran.

Materials and methods

General characteristics of the study area and database

The present study was conducted in the Gilan Province with an area of 14,100 km2 between the northern latitudes of 36° 34′ 00″ to 38° 27′ 00″ and eastern longitudes of 48° 34′ 00″ to 48° 36′ 00″ at the southern margin of the Caspian Sea. The Gilan Province is limited to the Caspian Sea from the north, to the Alborz Mountains from the south, to Mazandaran Province from the east, and to Ardabil Province from northwest (Fig. 1). The mean above sea level varies from − 128 m in coastal areas to 2700 m in mountainous areas. The Caspian strip is considered a temperate and humid region, under the influence of the northern Siberian air masses and the western air masses of the Mediterranean and the Atlantic.

Fig. 1
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Location of the study area

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Also, the Alborz Mountain, like a barrier, prevents the outflow of moist air masses and floods to the central parts of Iran, causing significant atmospheric precipitation in northern provinces. In addition to rangeland cover, the Gilan Province is often covered with broad-and-hardwood forests.

After collecting spatial information of flood events using flood database, flood inventory map including 220 flood locations (Fig. 2) was prepared. Also, the geological map of the region at the scale of 1:100,000 from the Geological Survey and Mineral Explorations of Iran (GSI) and topographic map at 1:50,000 scale from the Iran National Cartographic Center were obtained. Land use map was prepared using Landsat 8 OLI images (27 Jun 2016).

Fig. 2
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Map of flood locations in the study area

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Methodology

In this study, eleven effective factors including slope angle, aspect, plan curvature, profile curvature, altitude, distance from rivers, drainage density, geology, land use, topographic wetness index (TWI) (Eq. 1) (Beven and Kirkby 1979), and stream power index (SPI) (Eq. 2) (Moore et al. 1991) were used to prepare FSM. Since there are a significant negative correlation between elevation and rainfall in the study area (Fig. 3), we used altitude in this study to avoid collinearity.

Fig. 3
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Altitude map of the study

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Raster grid maps with 30 m × 30 m resolution were then derived for all effective factors. The various stages of the research are presented in Fig. 4.

$$ TWI=\ln \left(\frac{\alpha }{\tan \beta}\right) $$
(1)
$$ SPI={A}_s\tan\ \beta $$
(2)
Fig. 4
figure 4

Flow chart of research method

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where α is the total upslope catchment area draining downward from a point with a slope angle of β and As is the specific area (local upslope area draining through a certain point per unit contour length) of a basin (m2/m).

Frequency ratio method

After producing and categorizing each of the effective factors in the research, the layers were overlaid with flood inventory map, so that the number of floods in each class could be attributed to different factors. In the next step, the FR coefficients of each class/category were determined through Eq. 3.

$$ \mathrm{FR}=\frac{\mathrm{Percent}\ \mathrm{of}\ \mathrm{flooded}\ \mathrm{pixcels}\ \mathrm{in}\ \mathrm{each}\ \mathrm{class}}{\mathrm{Percent}\ \mathrm{of}\ \mathrm{each}\ \mathrm{factor}\ \mathrm{class}\ \mathrm{pixcels}} $$
(3)

Adaptive neuro-fuzzy inference system

There are two methods of grid partitioning and subtractive clustering to generate FIS. In subtractive clustering, the input data is divided into several groups by the size of the impact radius. In this case, the number of linear and non-linear factors has significantly decreased, which facilitates the process of network training. In this research, subtractive clustering method was used to investigate the effect of FIS generation on the performance of ANFIS model. Data standardization (Erdirencelebi and Yalpir 2011; Kisi et al. 2013; Sidle and Ochiai 2006; Vafakhah 2012) was carried out as follows:

$$ {X}_{\mathrm{Standardized}}=\frac{X_{\mathrm{i}}-{X}_{\mathrm{min}}}{X_{\mathrm{max}}-{X}_{\mathrm{min}}} $$
(4)

where XStandardized is the standardized value, Xi is the original value, and Xmin and Xmax are, respectively, the minimum and maximum value.

After data standardization and determining the input variables, the data were divided into two parts: training and testing datasets. Optimal replications and range of influence were determined in the model using hybrid optimization method. The range of influence was changed from 0.4 to 0.8 with steps of 0.01, and the optimal range of influence was determined.

Random forest model

To implement this model, firstly, a large number of decision trees were determined on the basis of trial and error. Then, all the trees were combined together for prediction (Cutler et al. 2007). For implementation of RF model, R software and “randomForest” package was used (Naghibi and Pourghasemi 2015; Pourghasemi and Kerle 2016; Rahmati et al. 2016a; Youssef et al. 2016a). When predictor variables and target variables were identified, RF begins with the emergence of a decision tree. This tree does not use all the available data for the tree, and, instead uses the bootstrap sample, which only contains 66% of the original data, which is referred to as the bagging technique (Breiman 2001).

Evaluation of the performance of the models

In this research, 70% and 30% of the flood locations were used for calibration and validation and performance evaluation of the models, respectively. Then, using the receiver operating characteristics (ROC) curve, the accuracy of the flood susceptibility map was determined (Pourghasemi et al. 2012). The area under the ROC curve represents the predicted value of the system by describing its ability to accurately estimate events (flood occurrence) and non-occurrence of the event (absence of flood). Using the ROC curve, the accuracy of the model was estimated quantitatively. The most ideal model is the model with the highest the area under the curve (AUC) and AUC values vary from − 1 to 0.5. If the model cannot estimate the flood event better than the probable viewpoint, that is, AUC is less than 0.5, and then the model used does not have usability for prediction. AUC and the estimation are classified as 0.5–0.6 weak, 0.6–0.7 moderate, 0.7–0.8 good, 0.8–0.9 very good, and 0.9–1 excellent (Rahmati et al. 2015).

Results and discussion

The present research aims to provide a FSM map using three models, namely FR, ANFIS, and RF models and to compare their performance together.

Effective flood factors

Slope angle

A digital elevation model (DEM) by 30-m spatial resolution in Arc/GIS environment was used to prepare the slope map of the study area. As can be seen from the Fig. 5, the slope map was divided into five classes by quantile classification method (Tehrany et al. 2015). As shown in Table 1, class 2.36–6.21 degrees has the highest FR, subsequently has the highest value (1.55), which has the most effectiveness on flooding, and class of 76.01–20.72 degrees has the lowest FR (0.53).

Fig. 5
figure 5figure 5figure 5

Maps of the flood-conditioning factors (eleven in all): a slope angle, b aspect, c plan curvature, d profile curvature, e altitude, f distance from rivers, g drainage density, h land use, i geology, j topographic wetness index (TWI), and k stream power index (SPI)

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Table 1 The frequency ratio of previous flood events and flood-risk parameters
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Aspect

The aspect due to evapotranspiration and precipitation direction has a great influence on hydrological processes and, as a result, affects weathering and vegetation processes, especially in arid areas (Sidle and Ochiai 2006). The aspect map was prepared in 9 classes of north, northeast, east, southeast, south, southwest, west, northwest, and flat directions (Fig. 5) (Rahmati et al. 2016b). As shown in Table 1, the southeastern direction with a FR of 1.53 has the most effect on flooding and southwest direction with a FR of 0.6 has the least effect on flood.

Plan curvature

The surface curvature (plan curvature) map can be used to describe the divergence and convergence of flows in the basins, trenches, and drainage network (Naghibi and Pourghasemi 2015). The surface curvature map was prepared based on Fig. 5 in three classes including, convex, flat, and concave (Rahmati et al. 2016b). The study of the surface curvature map indicated that flat surfaces with a FR of 1.14 has the greatest effect on flood; in contrast, convex and concave slopes with a FR of 0.91 have the same effect on flood (Table 1).

Profile curvature

The semicircular curvature indicates the ratio of slope gradients in the direction of maximum slope, which was prepared in three classes, namely, concave, flat, and convex (Fig. 5). The study of the profile curvature indicated that the flat surfaces with a FR of 1.59 have the greatest effect and concave slope with a FR of 0.82 has the least effect on flood in the study area (Table 1).

Altitude

Altitude can be considered as one of the effective factors in flood studies (Tehrany et al. 2015). It is almost impossible to absorb flood in highlands. Altitude class map were prepared using the quantile method into 5 categories less than 0, 0–280, 280–687, 687–1558, and more than 1558 m (Tehrany et al., 2013, 2014, 2015. As shown in Table 1, the class 0–280 m with a FR of 1.96 has the most effect and the class of more than 1558 m with a FR of 0.43 has the least effect on flood in the study area (Fig. 5).

Distance from rivers

Distance from rivers plays a significant role in the velocity and extent of flood (Glenn et al. 2012). Map of distance from river was prepared and classified into seven classes (Fig. 5) (Darabi et al. 2019). The distance of less than 500 m with a FR of 2.45 has a significant effect on flood in the study area. Also, the class of more than 3000 m has a FR of 0.36 (Table 1).

Drainage density

Drainage density map was prepared using stream lines in km/km2 and then classified into four different classes using quantile classification method (Rahmati et al. 2016b) (Fig. 5). As shown in Table 1, class of 13.34–17.49 with a FR of 1.15 has the highest effect and the class less than 1.36 has the least effect on flood in the study area.

Land use

Land use directly or indirectly affects some of the components of hydrological processes such as infiltration, evapotranspiration, and runoff generation (Rahmati et al. 2016b). In the post-processing part of results, after preparing error matrix, accuracy of classification results was done based on overall accuracy, kappa coefficient, producers accuracy, and user accuracy. As shown in Table 1, residential areas with a FR of 2.56 have a great influence on flood in the study area (Fig. 5).

Geology

Petrology can be considered as an important factor in hydrology and sedimentation field of drainage. A petrologic map was prepared based on geological eras in four classes of Cenozoic, Mesozoic, Paleozoic, and Proterozoic (Fig. 5). As shown in Table 1, Paleozoic rocks have the most impact and the Cenozoic rocks have the least impact on flood in the study area.

Topographic wetness index

TWI indicates the amount of flow accumulation in each area from a drainage basin and the trend of water to downward slope by the force of gravity. TWI map was prepared in four different classes using quantile classification (Fig. 5). As shown in Table 1, 11.5–21.52 class with a FR of 1.37 has the greatest impact, and the class of less than 9.25 with a the FR of 0.55 has the least impact on flood in the study area.

Stream power index

SWI shows the flow power in terms of erosion. SWI map was prepared in four different classes using quantile classification (Fig. 5). As shown in Table 1, the class that is more than 29,482.15 with a FR of 1.42 has the greatest impact and a class of 0–250 with a FR of 0.78 has the least impact on flooding.

Flood map results using frequency ratio model

After weighing each effective factor in flood, the weights were finally summed up in the ArcGIS environment and the final FSM was prepared and classified into four categories of low, moderate, high, and very high susceptibility (Fig. 6) using quantile method (Rahmati et al., 2015; Zabihi et al. 2015). Based on the results obtained (Table 2), 19.95% of the area measuring 2780.83km2 were placed with a high sensitivity to flood.

Fig. 6
figure 6

Flood susceptibility map using FR model

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Table 2 The number and percentage of floods in FSM using FR model
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FR was used to determine the correlation of between flood points and effective factors. The results of the significant relationship between flood locations and effective factors using FR were presented in Table 1. The ratio one shows a moderate relationship between the flood points and the effective factors (Pradhan et al. 2011). If the value of the ratio is greater than one, there is high correlation, and if less than one, there is low correlation between flood points and effective factors (Lee et al. 2012). For altitude, zero to 280 class with a FR of 1.96 and the class greater than 1558 with a FR of 0.43 had the highest and lowest effect on flooding in the study area, respectively. This is due to the fact that floods are often formed in low altitude areas, while flood formation is impossible in high altitude areas (Rahmati et al. 2016b). Investigating the relationship between distance from rivers and flood events showed that distance of less than 500 m with a FR of 2.45 had a significant effect on flooding in the study area. Also, the class distance between 500–1000 m had a FR of more than one, which indicated the wide coverage of alluvial flood in the Gilan Province (Tehrany et al. 2013). Also, the class of more than 3000 m from rivers with a FR of 0.34 had the lowest effect on flooding in the study area.

In the case of land use, the analysis of the FR to residential areas was 2.56, which showed a strong relationship with flood and residential land use in the study area. The main reason for this is that residential areas are often covered with impenetrable surfaces such as asphalt causing flooding. This finding is consistent with those of other studies (Lee et al. 2012; Rahmati et al. 2016b; Tehrany et al. 2014, 2015) and suggests that other land uses should not be changed to residential land use in the study area and watershed areas. The FRs obtained for forest, pasture, and farming land uses were 0.91, 0.89, and 0.71, respectively. The lower FR of pasture to the forest can be attributed to their high height, which is consistent with Rahmati et al. (2016b) results. Due to the presence of tree cover, forest land use is able to stop flood and reduces runoff generation and has a much lower FR than agricultural land use. As a result, it has a lower impact on flooding in the study area than the agricultural and residential land uses. For geology factor, while the Paleozoic formation forms less than 2% of the study area, they have the greatest effect on flooding. The stones of Mesozoic and Paleozoic formations with a FR of more than one have the most effect on flooding and the stones of Cenozoic and Proterozoic areas with a FR of less than one had the least effect on flooding. This result is consistent with Khosravi et al. (2016) result. The integration of the geology and river maps of the study area showed that due to the small area of Paleozoic rocks, many rivers flow through it, and the protozoan rocks are mostly found in mountainous areas with low flood occurrence. The FR of drainage density factor for different classes of less than 1.36, 1.36–2.11, 2.11–34.13, and 34.13 to 49.17 km2 were 0.91, 0.93, 1.01, and 1.15, respectively. With increasing drainage density, the FR increases, which has been emphasized in various studies (Cevik and Topal 2003; Nagarajan et al. 2000; Pachauri et al. 1998). Once drainage density increases, penetration decreases and surface runoff increases. As a result, with increasing drainage density, the risk of flooding increases in the lower lands. The results showed that the FRs for the south, southeast, and northeastern directions were more than one and therefore, they had the most impact on flooding in the study area. For the other six directions, the FR was less than one and the direction to the southwest with a FR of 0.6 had the least impact on flooding. These results are different with the results of Rahmati et al. (2016b). The reason for this mismatch can be climatic, geomorphic, and geological differences in two study areas. Slope angel factor can be used as another indicator to prove the negative relationship between high altitude and flooding. The lowest FR was 0.53 for class of 20.72–76.01. The highest FR was obtained for class of 2.36–6.21. As can be seen from the Table 1, flooding occurred in areas with high slope, but in lower areas, it occurred more frequently. The study of plan curvature indicated that the highest FR was equal to 1.14 for smooth surfaces with the most impact on flooding. The reason for this can be proved by the natural properties of flooding, where flooding occurs more often in flat areas. Overall, according to Lee et al. (2012), Tehrany et al. (2014), (2015), and Rahmati et al. (2016b), the most susceptible areas to flooding were the areas with lowest elevation, minimum slope angle, flat area, and close to rivers. The lowest FR is related to convex ranges.

Also, the study of the profile curvature factor, such as plan curvature, showed that it had the most FR relative to the smooth surfaces, and the convex and concave ranges with the same FR had the least impact on flooding. A survey of TWI indicated that the highest FR was equal to 1.37 for the last class (11.52–21.5) and the lowest FR was equal to 0.55 for the first class (less than 25.9). The more the TWI values, the higher the flood volume; this is due to the conditions of soil saturation. The more saturated the soil, the greater the flooding.

In the case of the SPI, the class higher than 15.29482 with a FR of 42.1 and the class 0.250 with a FR of 0.78 had the highest and lowest impact on flooding, respectively. SPI shows the flow power in terms of erosion (Tehrany et al. 2015). As a result, the higher the flow power, the more flooding.

ANFIS

Data standardization results

FR were standardized for classes of each effective factor using Eq. (2). This equation indicates the standardization between two values of zero to one, which is presented in the last column of the Table 1.

Subtractive clustering results

After normalizing the weights obtained from the FR model, the map of each factor affecting flood, such as slope angle, aspect, altitude, distance from rivers, drainage density, geology, land use, plan curvature, profile curvature, TWI, and SPI in ArcGIS environment were prepared based on standardized weights.

In the subtractive clustering, with a change in the range of influence from 0.4 to 0.8, with steps of 0.01 in different repetitions, considering the lowest error in the testing stage, the optimal range of influence was determined 0.52 by trial and error.

Flood map results using ANFIS model

After determining the optimal range of influence and repetition, the ANFIS model was performed and then all the maps of the effective factors were normalized, and entered into Matlab 2014 software pixel-to-pixel. The ANFIS model was implemented and the weight of each pixel was obtained and finally a flood map was provided (Fig. 7), classified based on quantile method. By studying Table 3, it is obvious that the moderate class has the largest area percentage (34.45%), followed by high (26.57%), low (26.17%), and very high (12.81%) classes.

Fig. 7
figure 7

Flood susceptibility map using ANFIS model

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Table 3 The number and percentage of floods in FSM using ANFIS model
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Random forest model results

RF model is another decision tree technique in this study. As mentioned, for the implementation of this technique, the “randomForest” package was used in the R software. First, based on the error rate diagram, the random variables were determined using the caret packet, the optimal number of random variables for splitting each node was determined, and then with the help of this number of random variable, the error rate diagram was drawn in terms of the number of trees, and decision was made regarding the number of optimal trees. Accordingly, the final RF model with 3 random variables (mtry) was implemented for each node and 1000 trees (ntree).

RF algorithm is based on a handful of decision trees and is currently one of the best learning algorithms. The OOB (Out-Of-Bag) was used to evaluate the performance of the model. As shown in Fig. 8, OOB is a function of trees and is reduced when more trees are added to the RF algorithm.

Fig. 8
figure 8

The overall error rate for RF model (OOB (black line); no flood (red line); flood (green line)

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The performance results of the RF algorithm are presented in Table 4 and Fig. 8. OOB and mean squared error (MSE) values were calculated as 0.36 and 0.29, respectively. Considering OOB and MSE values, flood modeling of the study area can be carried out well. As can be seen from the Table 4, out of 154 flood pixels, 54 pixels were mistakenly predicted without flood, 100 pixels were correctly predicted, and among 154 pixels without flood, 97 pixels were properly predicted without flood, and 57 pixels were mistakenly predicted as flood.

Table 4 Error matrix of RF model
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Flood susceptibility map results using RF model

After preparing the effective factor maps, the flood inventory map containing 154 flood points and 154 non-flood points were discontinued and the value of each of the effective factors was obtained for each point. Then, the data were entered into the R software, using the RF package, using the quantile classification method; it was divided into four classes of low, moderate, high, and very high sensitivity. By studying Table 5, it is obvious that the moderate class has the largest area percentage (25.47%), followed by high (25.36%), very high (25.11%), and low (24.06%) classes (Fig. 9).

Table 5 The number and percentage of floods in FSM using RF model
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Fig. 9
figure 9

Flood susceptibility map using RF model

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Prioritizing effective factors in flood

The mean of Gini reduction was used to determine the priority of effective flood factors (Table 6).

Table 6 Accuracy mean decrease and mean decrease Gini of effective flood factors in RF model for the preparation of FSM in the Gilan Province
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As can be seen from the Table 6, distance from rivers, altitude, and drainage density is the most important factor for flood and the least important factor is geology. The results of Tehrany et al. (2015) found that altitude and slope angle factors were the most important factors affecting on flooding. Therefore, the importance of variables in the flood map was influenced by the method used in the research and the characteristics of the study area. In other words, different geological conditions, topography, and weather in a region can change the priority of the factors affecting the flood mapping.

Evaluation of the model efficiency

One of the most methods for determining accuracy and evaluation of models is the ROC curve. In this study, 30% of the floods were used for validation stage. The results of evaluation of FR, ANFIS, and RF using ROC curve (Fig. 10) showed that the obtained AUC for models were 68.6, 63.9, and 71.3%, respectively.

Fig. 10
figure 10

ROC curve for three models

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Rahmati and Pourghasemi (2017) compared the evidential belief function (EBF), RF, and boosted regression trees (BRT) models for mapping flood susceptibility in the Galikesh region, Iran. They found that the EBF and BRT models with the AUC values of78.67% and 78.22%, respectively, were superior to the RF model with an AUC value of 73.33%. Although the EBF and BRT models were outperformed than the RF model, There are several advantages for the RF model over other models, as it can work with data lost in calibration and validation data, and because of its hybrid design, it can estimate even when some inputs are lost. In addition, in the modeling process, the importance of the factors are identified which can be useful (Ball et al. 2009). Another benefit of RF model is able to model non-linear relationships between the flood occurrence and related conditioning factors. Also, the RF model do not need to check statistical assumptions (e.g., outliers and data normalization). As shown in Fig. 10, the RF model with an AUC value of 71.3% had a good performance and the FR and ANFIS models with AUC values of 68.6% and 63.9%, respectively, had a moderate performance in providing FSM. This study shows that the performance of FR and ANFIS models is similar, whereas Razavi Termeh et al. (2018) indicated that a combination of ANFIS with metaheuristic optimization was superior to the FR model. In addition, Tien Bui et al. (2018) proposed three new hybrid artificial intelligence optimization models, namely, ANFIS with cultural (ANFIS-CA), bees (ANFIS-BA), and invasive weed optimization (ANFIS-IWO) algorithms for FSM in the Haraz Watershed, Iran. They found that the AUC values of ANFIS-CA, ANFIS-BA, and ANFIS-IWO were 92.1%, 93.9%, and 94.4%, respectively.

The current research like other studies has some limitation. Most importantly, non-flood locations were randomly selected in the study area, the locations are considered as non-flood locations that did not have flood occurrence (Chen et al. 2019a). Thus, the new methods must be applied to select reliable non-flood locations. The generated flood map can be used in management and enforcement work to prevent and reduce floods in the future.

Conclusions

The results of this study showed that by integrating geographic information system (GIS) and factors influencing flood conditions and the historical data of recorded flood, the interaction between factors influencing watershed floods can be studied. In general, GIS is one of the most powerful tools for analyzing and displaying spatial data in the management of watersheds. For this purpose, eleven factors were used as effective factors for FSM. Among the effective factors on flood, the physical characteristics of the basin are very important due to the high stability and low variability. These properties directly affect the hydrological regime and indirectly affect the climate of the area. The prioritization of effective factors using the mean decrease Gini showed that distance from rivers, altitude, and drainage density had the most effect, respectively, and SPI and geology had the least effect on flooding in the study area. Meanwhile, FSM with RF and ANFIS models and its accuracy evaluation using ROC revealed a reasonable accuracy of the RF model (71.3%) compared with ANFIS model (63.9%) in the study area. Therefore, RF model is suitable for identifying areas with flood susceptibility. Finally, use of RF model is proposed for FSM, especially in developing countries.