New Machine Learning Ensemble for Flood Susceptibility Estimation

Floods are among the most severe natural hazard phenomena that affect people around the world. Due to this fact, the identification of zones highly susceptible to floods became a very important activity in the researcher’s work. In this context, the present research work aimed to propose the following 3 novel ensembles to estimate the flood susceptibility in Putna river basin from Romania: UltraBoost-Weights of Evidence (U-WOE), Stochastic Gradient Descending-Weights of Evidence (SGD-WOE) and Cost Sensitive Forest-Weights of Evidence (CSForest-WOE). In this regard, a sample of 132 flood locations and 14 flood predictors was used as input datasets in the 3 aforementioned models. The modeling procedure performed through a ten-fold cross-validation method revealed that the SGD-WOE ensemble model achieved the highest performance in terms of ROC Curve-AUC (0.953) and also in terms of Accuracy (0.94). The slope and distance from river flood predictors achieved the highest importance in terms of flood susceptibility genesis, while the aspect, TPI, hydrological soil groups, and plan curvature have the lowest influence in terms of flood occurrence. The area with high and very high susceptibility represents between 21% and 24% of the Putna river basin from Romania.


Introduction
As part of the hydrological cycle, flooding has always been a natural part of the system, however, over the past decade, a gradual increase has been observed in the frequency and magnitude of flooding (Vojtek and Vojteková 2019;Zhang et al., 2022). In Romania, this has been a challenging task because many countries have found it difficult to develop effective flood prevention measures. As climate and land-use changes continue, flooding is expected to increase. This can largely be attributed to an increase in the occurrence of flood events (Pistrika et al. 2014;Afriyanie et al. 2020). As a result of these anthropogenic impacts, basins in which there has been substantial anthropogenic activity often experience increased runoff resulting in rapid erosion or increased evaporation processes (Chen et al. 2009;Chakrabortty et al. 2021). The mapping of flooding susceptibility is essential element of early warning systems intended to prevent and mitigate future flood risks since they identify the most prone zones based on the physical factors determining how much flooding will occur (Vojtek and Vojteková 2019;Janizadeh et al. 2021). Therefore, vulnerability assessment may also incorporate the notion of susceptibility. There is a series of conditions that have been recognized as necessary to construct flood susceptibility mapping techniques as they reflect the physical characteristics of the area under investigation (Arnell and Gosling 2016). These physical characteristics refer to several geographical components like lithology, land use, slope angle, river density, and other morphometric variables and hydrological soil groups. In selecting the appropriate conditioning factors for an assessment of flood susceptibility, one has to take into consideration the spatial scale of that analysis. For example, if the study zone is large (for example, the nation's territory), then using fewer variables would be reasonable. This is because it is more challenging to achieve the same data (thought at the same resolution or scale) for the whole area (Dodangeh et al. 2020). Some studies contend that fewer factors are possibly more likely to reduce the possibility of your receiving some overrated factors if there is a limited number of them. Local-scale (e.g., catchment) studies may integrate a variety of data and factors that are location-specific, allowing for an accurate description of flood predispositions because they utilize local data and variables.
Geographical information systems (GIS) have emerged as powerful tools to facilitate the synthesis of multiple input data sources Wang et al. 2021;Zhou et al. 2021aZhou et al. , 2021b, variables (Gao et al. 2021;Liu et al. 2021aLiu et al. , 2021bQuan et al., 2022), and ensuing logical and mathematical relationships to generate flood susceptibility maps, as flooding has both spatial and temporal aspects. There have been several methods developed over the years which have been used to identify and assess flood-prone areas in different geographic areas of the world. It should be noted the very strong development after 2010 of machine learning techniques Zhang et al. 2020;Zhang et al. 2021;Yin et al. 2022a;Zhan et al. 2022aZhan et al. , 2022b. Thus, they began to be used on a large scale in almost all scientific fields (Jafari-Asl et al. 2021;Rad et al. 2022). One of the factors that determined the accelerated increase in the degree of use of these modern techniques is represented by the development of software and the implementation of machine learning algorithms with the help of programming languages (Mehta and Devarakonda 2018). There were many advances in machine learning techniques used for mapping flood susceptibility in recent years, and several have revealed powerful features and demonstrated favorable results (Zhang et al. 2019;Liu et al. 2020;Liu et al. 2022;Li et al. 2022). These techniques include decision trees , artificial neural networks (Hong et al. 2018), random forest (Lee et al. 2017), Naive Bayes , logistic regression or support vector machine (Tehrany et al. 2015;Allahbakhshian-Farsani et al. 2020). Several studies have recently attempted to build flood susceptibility models by using hybrid strategies to determine their strengths and weaknesses. For example, machine learning was used to combine bootstrapping and subsampling methods (Dodangeh et al. 2020). Moreover, there were attempts to estimate the flood susceptibility using some advanced hybrid models that were generated by the combination of Dagging and Random Subspace algorithms ), on the one hand, with the random forest, support vector machine and artificial neural network, on the other hand (Islam et al. 2021). Other authors compute the flood susceptibility using the functional trees hybridized with bagging and rotational forest (Arabameri et al. 2020). A common practice in the assessment of flood-prone areas is to combine the bivariate statistics methods, like frequency ratio or weights of evidence, with models from the machine learning category like classification and regression tree, deep learning neural network, random forest, or support vector machine (Costache and Bui 2019;Bui et al. 2020). Hybrid machine learning algorithms provide excellent results for modeling natural hazards and many natural hazard models have been applied to hybrid machine learning algorithms for implementation and creation. While there was an agreement among the scientists that some tools would be useful to evaluate various hazards more effectively , there was no universal agreement on which tools were best suited to stimulate natural hazards such as floods. Flood susceptibility and other ways of stimulating natural hazards are among the research topics being discussed by researchers.
Therefore, in the present research work, the main scope of the developed workflow was to estimate the flood susceptibility across the Putna river basin from Romania, with the help of novel ensemble algorithms which were generated by the combination of Weight of Evidence bivariate statistics and the next three machine learning models: UltraBoost, Stochastic Gradient Descending and Cost Sensitive Forest.
The accuracy of the results was demonstrated with the Receiver Operating Characteristic (ROC) Curve method and by the computation of several statistical metrics. It should be also mentioned that the following sections are structured as follows: Study area; Data; Methods; Results; Discussions; Conclusions and future directions.
It is verified by government data in Romania that the worst flooding event which can be attributed to the Putna river catchment took place in 2005, and this catastrophe caused the death of a total of 15 people (Romanescu and Nistor 2011). A total of approximately €150 million was also generated by flooding that year as a result of the floods (Tîrnovan et al. 2014). Supplementary aspects of the Study area are provided in Sect. 1 (S1) of Online Supplementary Material.

Flood Inventory
As part of this study, a map of flood risk was created using information collected from the General Inspection for Emergency Situations of Romania. The study zone was subsequently found to have 132 flood events, as a result of this investigation procedure. It was determined that an additional sample with 132 non-flood locations should be created since flood suscep-tibility mapping is a process related to the binary classification topic. Furthermore, to ensure that we have the opportunity to test the model's performance and to verify the accuracy of the prediction results, the flood and non-flood database samples were split into the training data set of 70% and the validation data set of 30%. Supplementary aspects of flood inventory are included in the Sect. 2 (S2) of the Online Supplementary File.

Flood Predictors
The flood predictors we chose to calculate the flood susceptibility for the entire region under study were comprised of 14 flood prediction models after careful consultation of the literature and taking into account the specific characteristics of the Putna River Basin. In order to create the Digital Elevation Model (DEM) across the area on which the study is focused, it was crucial to use the Shuttle Radar Topographic Mission at a resolution of 30 m. As a result, the DEM was used to derive the following nine morphometrical flood predictors, namely: slope angle ( which was used to generate the rainfall map for the study area. A short description of the predictors is provided in Sect. 3 (S3) and Table S1 of the Online Supplementary Material.

ReliefF Method
By using the ReliefF method, we will be able to make a preliminary evaluation of the predictive potential of the variables used as inputs to estimate flood susceptibility (Costache et al. 2021). Furthermore, it is important to emphasize that the ReliefF algorithm is capable of operating with continuous and discrete data. It is considered that the attribute value is assigned to the nearest instance of the same or a different class of the given attribute value (Costache et al. 2021). ReliefF was used in the present study as an analysis tool using Weka 3.9 software. Additional aspects of ReliefF method are included in Sect. 4 (S4) of Online Supplementary Material.

Weights of Evidence
To provide information as to how the Weights of Evidence method can be implemented in GIS environment, it is necessary to establish the following relationships (Armaş 2012): where N pix1 is the number of flood pixels within a class; N pix2 is the number of flood pixels outside the specific class; N pix3 is the number of pixels in a class without flood locations; N pix4 is the number of non-flood pixels outside a class; W + is equal to the positive weight, while W − represents the negative weight.
The final values of WOE coefficients (Wf) will be calculated using the next relation (Dahal et al. 2008): where Wplus is the positive weight of a class/category from a factor, Wmin is the negative weight of a category belonging to a specific factor, Wmin total represents the sum of all the negative weights in a multiclass map. The weights of evidence values were used as input data in the data mining models used in the present research. More aspects of Weights of Evidence can be found in Sect. 5 (S5) of Online Supplementary Material.

UltraBoost (U)
UltraBoost classifier represents a method used to boost heterogeneous learners. In the present research work, the UltraBoost algorithm is trained so as for each case to be assigned a specific probability of flooding (Moustafa et al. 2020). The attribute class forecast with the help of model is flood = 1 for the areas highly exposed to flood and 0 for non-flood -so the output probabilities of flood genesis is ranging between 0 and 1. Additional aspects of UltraBoost model are inserted in Sect. 6 (S6) of Online Supplementary Material.

Stochastic Gradient Descending (SGD)
The stochastic gradient descent method is a stochastic approximation of the gradient descent method, which is an iteration-based method for generating a derivative function (Hoang 2019). In addition to its high efficiency, and ease with which it can be implemented for datasets with redundant samples, this algorithm is very popular. In the flood susceptibility analyses, SGD is seldom applied, which is something that needs to be investigated more in-depth. The application of SGD in the present research work was possible through Weka 3.9 software. Additional aspects of the Stochastic Gradient Descending (SGD) model are presented in Sect. 7 (S7) of Online Supplementary Material.

Cost Sensitive Forest (CSForest)
The CSForest can be applied through the mean of the Classification Cost Reduction (CCR) function which replaces the Gain Ratio that was used as a splitting criterion (Siers and Islam 2015). The tree built by CSForest, before pruning, is deeper than that by CSTree. CSForest, by contrast, builds an ensemble of trees and then uses CSVoting for classifying records/ modules whereas the CSTree builds a single tree. In the present case study, the CSForest, for flood susceptibility modelling, was run in Weka 3.9 software. Additional aspects of Cost Sensitive Forest (CSForest) algorithm are included in Sect. 8 (S8) of Online Supplementary Material.

Receiver Operating Characteristic (ROC) Curve
ROC Curve suggests that a model can accurately predict flood susceptibility. Area Under Curve (AUC) measures the value of a curve of ROCs which is helpful for the user in getting the most important information (Xie et al., 2021a). The range of the AUC is between 0 and 1 (Xie et al., 2021b). Using the following mathematical relationship, we can estimate the AUC:

Statistical Metrics
The next 5 statistical indicators were involved also in the results validation procedure: Accuracy, Specificity, Sensitivity, Kappa Index, and Precision. In order to calculate the statistical metrics, we will be using the following equations (Canbek et al. 2017): where P is the sum of flood locations, N is the sum of non-flood locations, FP (false positive) and FN (false negative) are the numbers of flood and non-flood locations erroneously classified, k is the kappa coefficient, p o is the observed flood locations, and p e is the estimated flood susceptibility locations. A short description of the workflow followed in the present study is represented in Fig. 4.

Feature Selection Using ReliefF Method
The application of ReliefF method provided the following outcomes: Slope (0.653), Land use (

Weights of Evidence Coefficients
The WOE value is also a positive value as well as a negative value, and consequently, this procedure was necessary. The WOE of 3.56 assigned to the river land use class was the highest value and was followed by elevation below 200 m (3.1) and the class of distance from river lower than 50 m (2.9) ( Table S2). The WOE was used as an input dataset in the three machine learning models.

Ultraboost-Weights of Evidence (U-WOE)
The U-WOE ensemble model was trained through a ten-fold cross-validation method in Weka software. Following the training process, the Mean Absolute Error ( The importance values were imported in ArcGIS Map Algebra and the Flood Susceptibility Index (FSI) was calculated by the multiplication with WOE coefficients. The results of FSI U−WOE , were reclassified into 5 classes through the help of Natural Breaks method. The first class, that indicates the very low flood susceptibility values, appears on around 21% of the study area (Fig. 5a). Further, another 35.38% of the research area is covered by low FSI U−WOE values, while medium flood susceptibility has a total percentage of 19.41%. The high and very high flood susceptibility zones account for approximately 16% of the Putna river basin.

Stochastic Gradient Descending -Weights of Evidence (SGD-WOE)
The SGD-WOE model was also run in Weka software using the ten-fold cross-validation procedure. The next parameters were established in order to train the SGD-WOE ensemble: batch Size -100; epochs -100; epsilor -0.01; lambda -1.04E-4; learning rate -0.01; seed -1. The training procedure revealed the achievement of a Mean Absolute Error ( These values were used in the GIS environment through Map Algebra in order to estimate the flood susceptibility index. The very low flood susceptibility is presented on 41.62% of the Putna river catchment (Fig. 5b). The low flood susceptibility is spread on 33.04% of the study zone, while the medium values of flood exposure have only 4.28% of the Putna river basin. A total of 21% of the study area is characterized by high and very high flood susceptibility values.

Cost Sensitive Forest -Weights of Evidence (CSForest-WOE)
In order to train the CSForest-WOE model, a ten-fold cross-validation algorithm was applied. The structure that provides the best performance for CSForest was formed by 5 trees (Fig. S3). The value of Mean Absolute Error (MAE) was 0.095, while the Root Mean Squared Error (RMSE) was equal to 0.127. The very high performance of the CSForest-WOE algorithm was revealed by the Precision of 0.993.
The flood susceptibility values were split into 5 classes through the mean of Natural Breaks method. The very low values of FSI CSForest−WOE occupy around 26.51% of the Putna river basin, while the low flood susceptibility characterizes 34.31% of the research zone (Fig. 5c). Medium flood susceptibility has a total percentage of 14.93%, while the high class of FSI CSForest−WOE covers 7.67% of the area on which the present study is focused. The very high class reaches a total percentage of 16.57% of the study zone.

ROC Curve
The Success Rate associated with flood susceptibility maps shows that FSI SGD−WOE has the highest performance with an AUC of 0.953, followed by FSI U−WOE (AUC = 0.951) and FSI CFSorest (AUC = 0.95) (Fig. 6a). The results related to the Prediction Rate revealed that the best flood susceptibility maps were associated to the FSI SGD−WOE and FSI U−WOE both of them having an AUC of 0.947. The FSI CSForest−WOE has the lowest performance being characterized by an AUC of 0.945 (Fig. 6b).

Statistical Metrics
In terms of the training sample, the highest accuracy was achieved by SGD-WOE (0.94), followed by U-WOE (0.935) and CSForest-WOE (0.929). Regarding the results for k-index, it should be noted that the best value was obtained by SGD-WOE (0.88), followed by U-WOE (0.87) and CSForest-WOE (0.859). In regards to the validating sample, it should be seen that the maximum accuracy of 0.938 was attributed to SGD-WOE model, followed by U-WOE (0.925) and CSForest (0.913). The k-index revealed the same hierarchy with SGD-WOE in the first place with 0.875, followed by U-WOE (0.85) and CSForest-WOE (0.825) ( Table 1).

Discussions
There is no doubt that atmospheric emissions of greenhouse gases have been increasing in the past few decades, and these emissions have become increasingly pronounced because of the occurrence of weather-related and climate-related events such as flooding, droughts, storm surges, and sea-level rises (Dimeyeva et al. 2015;Yin et al. 2022b). Natural risk evaluation research works also include the flood susceptibility models, which are among the most challenging. Flood susceptibility prediction accuracy is strongly influenced by the effects of particular conditions relevant to the study area(s) and by the method used in making the prediction (Islam et al. 2021). As in many other similar studies, in this paper, the authors wanted to estimate the susceptibility to floods by comparative use of 3 machine learning models. These were also combined with a bivariate statistical method, the latter allowing uniform input data to be obtained for all flood predictors. The ensemble approach used in flood susceptibility mapping between researchers has been quite useful in some cases. An ensemble model was applied for bivariate and multivariate statistical analysis by Bui et al. (2019), and they found the ensemble model to be better than the individual models. The 3 machine learning models are represented by UltraBoost, Stochastic Gradient Descending and Cost Sensitive Forest, while the bivariate statistics method was represented by Weights of Evidence. The performance of the 3 models of flood susceptibility was performed using the ROC curves, the Area Under the Curve (AUC) and several statistical metrics (sensitivity, specificity, accuracy and k-index) results. All the results showed that the models were able to perform reasonably well in assessing flood-prone areas. All 3 models had associated AUC values greater than 0.945, which indicates a very high performance and a high accuracy of flood susceptibility maps. These performances far exceeded the performance obtained by Nachappa et al. (2020), in which ensemble methods between machine learning and bivariate statistics were also used and in which all AUC values were below 0.9. The aforementioned study focused on the Salzburg province from Austria which has a multitude of common climatic and relief characteristics as in the high and middle altitude regions of the present study area. Another study whose central topic was the determination of flood susceptibility using machine learning combined with bivariate statistics was conducted by Liuzzo et al. (2019) in Devon County, in the United Kingdom. And in this case, the AUC values obtained by the authors of the previously mentioned study were generally more than 0.91, being, therefore, lower than those obtained in the present study. This demonstrates once again that the use of the 3 algorithms in the present study may be more efficient than other machine learning models used in the literature. Another example of a study on flood susceptibility calculated by state-of-the-art algorithms was conducted by Wang et al. (2020). The authors of the study used a combination of Support Vector Machine (SVM) and Convolutional Neural Network (CNN) to estimate flood exposure in Shangyou County from China. In this case, the highest AUC value was 0.937 and was associated with the 2D-CNN algorithm. Even in this situation where very powerful computational algorithms were used in estimating flood susceptibility, the performance of the models applied in the present study was not exceeded.
The findings of the present study are generally expected to have a significant impact on refining flood risk management plans and activities as well as the principles in the region for making certain that additional damages caused by flooding are avoided.

Conclusions and Future Directions
The central topic of this scientific article is the estimation of flood susceptibility through 3 advanced machine learning models in the hydrographic area of the Putna River Basin in Romania. The combination of the bivariate statistical method represented by Weights of Evidence with the following 3 machine learning models allowed the generation of ensemble models that provided very good results: UltraBoost, Stochastic Gradient Descendent and Cost Sensitive Forest. The application of ROC Curve and Area Under Curve showed that the best performance was obtained by SGD-WOE ensemble whose AUC value was 0.953. Also, statistical metrics showed that the same model obtained the highest Accuracy, equal to 0.94. According to the flood susceptibility maps generated by the three ensemble models, the surfaces with a high and very high degree of flood exposure are found on surfaces that fall between 21.04% (FSI SGD−WOE ) and 24.24% (FSI CSForest−WOE ). These areas with high and very high exposure to floods are spread mainly in the plain area of the study area but also along the main valleys in this region.
The main novelty of the present study is the application for the first time in the literature of the three ensemble models in order to estimate the susceptibility to floods. Their very high performance is a strong reason for these three ensemble models to be taken over in other research papers and applied to other study areas. At the same time, the authors of the study consider, as future research directions, the integration of the methodology for estimating the susceptibility to floods within a wider methodology for estimating the risk of these phenomena. Thus, in future works, the socio-economic objectives of the studied area will also be taken into account. It is also considered to carry out detailed case studies on floodplains through hydraulic modeling and the use of digital land models with high spatial resolution.
Funding This work was supported by a grant of the Romanian Ministry of Education and Research, CNCS -UEFISCDI, project number PN-III-P1-1.1-PD-2019-0424-P, within PNCDI III.

Availability of Data and Materials
The data used in this research are available by the corresponding author upon reasonable request.

Ethics Approval
The authors confirm that this article is original research and has not been published or presented previously in any journal or conference in any language (in whole or in part).

Consent to Participate and Consent to Publish Not applicable.
Competing Interests The authors have no conflict of interest.