1 Introduction

During the past few decades, the frequencies of extreme weather events and related disasters have increased due to incessant changing climate and global warming (Hettiarachchi et al. 2018; Nam et al. 2015). Evidence suggests that the extreme weather events have occurred more frequently after the mid 20th century and have occurred in that region which does not have such in the history (Hoeppe 2016). Among all, the occurrences of flooding are maximum across the globe and causes higher damage than other natural disasters (Yang et al. 2018; Hirabayashi et al. 2013). It has been estimated that from 1995 to 2015, flood hazard affected more than 100 million people and the damages estimated at 75 billion USD in every year (Mohanty et al. 2020; Alfieri et al. 2017). In the countries like Bangladesh, the casualty due to flood is higher than any other natural calamities during recent past (Dewan 2015; Azad et al. 2013) as a large section of populations lives in the floodplains under the varying degree of vulnerability to flooding, river erosion etc. (Tingsanchali and Karim 2005). Many parts of Bangladesh have experienced a number of devastating flood events during past decades which has caused huge loss of both property and lives (Ferdous et al. 2019). In northern Bangladesh, flash floods are periodic events that often happen in the downstream riparian areas, especially in the lower Teesta River basin. For instance, a very recent flash flood observed in the lower Teesta River basin, especially in Nilphamari, Lalmonirhat, and Kurigram districts in August-2017, which caused the submergence of considerable landmass, and five people were swept away. According to the network for information, response and preparedness activities on disaster (NIRAPAD), about 6.8 million people and over 560,000 hectares of croplands were badly damaged by the flash flood. FAO (2017) estimated that the destruction of the flash flood of August 2017 caused the damages of up to US$ 10 million (FAO 2017). Although natural along with anthropogenic activities are resulting in the flooding, the climate change has been identified as the principal cause behind the manifestation of flooding in the world, which affects the pattern, intensity and magnitude of floods (Hettiarachchi et al. 2018; Zhao et al. 2018; Gill and Malamud 2017; de Kraker 2015; Taubenböck et al. 2011). Some natural factors such as elevation, soil texture, drainage density, distance, vegetation etc. act as the prompting factors of flood in different parts of the world (Azareh et al. 2019; Hosseini et al. 2020). The occurrences of flooding are natural, which cannot be stopped, however the damages done by floods can be mitigated by appropriate planning and management (Abebe et al. 2019). Hence, the prediction and delineation of flood prone areas is an important aspect of alleviation of flood hazards, which reduces the fatalities due to the flooding (Pyatkova et al. 2019; Sarhadi et al. 2012). Further, a study by Ward et al. (2013) pointed that the South and South-east Asia, especially India and Bangladesh has the highest share of population and GDP exposed to flood risk. Therefore, to cope with such looming conditions, the knowledge of vulnerability through the quantification and identification of spatiotemporal characteristics of flood prone areas are indispensable for the effective management and mitigation of flood hazards (Mohanty et al. 2020). Therefore, a flood susceptible model (FSM) is a useful tool which is required to identify regions at risk and to safeguard these high-risk regions and natural resources as well (Maaks et al. 2020).

The development of flood susceptibility maps is very challenging and difficult as several factors are involved. These factors are heterogeneous and very complex in nature (Ardıçlıoğlu and Kuriqi 2019; Kuriqi et al. 2020; Costache and Bui 2019). However, of late, regional data with very detailed information can be obtained from satellite images or remote sensing databases (Pourghasemi et al. 2020a; Nikolaos et al. 2019; Li et al. 2019; Talukdar and Pal 2017). Nowadays very high resolution data like synthetic aperture radar (SAR) and optical sensor images are available in some places, which can highly improve the flood susceptible maps (Bui et al. 2020a; Talha et al. 2019; Arora et al. 2019). However, these state-of-art techniques can handle spatial datasets and produce high resolution and prediction performances (Uthayakumar et al. 2020; Abba et al. 2020; Ma et al. 2020). Therefore, the integration of remote sensing databases and GIS technology have been widely applied to study the relationships between these factors and the occurrences of flood hazards (Choubin et al. 2019; Jahangir et al. 2019) and made the flood susceptible models less challenging and highly accurate. Consequently, researchers have used these technologies for predicting the natural hazards including flood susceptible models (Bui et al. 2020a, b; Wang et al. 2020; Pourghasemi et al. 2020a, b; Chen et al. 2020; Dodangeh et al. 2020).

Many scholars have developed and utilized several types of models and algorithms for preparing flood susceptible models (Sahana et al. 2020). Therefore, based on the previous literature, the models, have been used for preparing flood susceptibility maps, can be several types (Siahkamari et al. 2018; Chen et al. 2019a; Termeh et al. 2018; Hong et al. 2018a; Bui et al. 2019a; Mahmood et al. 2019), such as (1) expert knowledge based FSMs like analytical hierarchy process (AHP) (Costache et al. 2020a; Dano et al. 2020; Nachappa et al. 2020; Souissi et al. 2019), (2) bivariate and statistical based models, such as weights-of-evidence (Chen et al. 2019b; Paul et al. 2019), fuzzy logic (Wang et al. 2019; Sahana and Patel 2019), information value (Xu et al. 2013; Chen et al. 2014), frequency ratio (Chen et al. 2020a; Moghaddam et al. 2019; Khosravi et al. 2019a, Sahana et al. 2020), logistic regression (Tien Bui et al. 2019a; Shafapour Tehrany et al. 2019a, b; Pham et al. 2020a; Ali et al. 2020), analytical network process (Ali et al. 2020; Akay and Koçyiğit 2020), certainty factor (Costache et al. 2020a), neuro fuzzy logic (Termeh et al. 2018; Hong et al. 2018b) (3) machine learning algorithms (Shahabi et al. 2020; Dodangeh et al. 2020; Wang et al. 2020; Costache et al. 2020b; Costache and Bui 2020; Tang et al. 2020), and (4) hydrological models such as soil water assessment tool (SWAT) (Oeurng et al. 2011; Busico et al. 2020; Uniyal et al. 2020; Bhattacharya et al. 2020) and Hydraulic Engineering Centre-River Analysis System among others (Getahun and Gebre 2015; Joshi and Shahapure 2020; Huţanu et al. 2020). Recently, machine learning techniques have drawn more and more attention, which have been employed in FSMs by many researchers (Bui et al. 2020a; Chen et al. 2019a; Hong et al. 2018a; Wang et al. 2020). The most popular machine learning techniques are artificial neural networks (Falah et al. 2019; Moghaddam et al. 2019; Pham et al. 2020b; Bui et al. 2020b), random forest (Avand et al. 2019; Paul et al. 2019; Achour and Pourghasemi 2020; Chen et al. 2020b; Nhu et al. 2020; Vafakhah et al. 2020), support vector machines (Termeh et al. 2018; Khosravi et al. 2019a), and decision trees (Choubin et al. 2019; Moghaddam et al. 2019; Yariyan et al. 2020; Nhu et al. 2020; Chen et al. 2020c; Costache et al. 2020c), radial basis function (Choubin et al. 2019), which predict the areas at risk of flooding very accurately. However, FSM experiences many challenges, such as selecting the proper methods for modelling among vast numbers of methods, and each method produces different results (Costache et al. 2020a, b; Shafizadeh-Moghadam et al. 2018). Even, each of these models have some drawbacks for predicting the FSMs. Therefore, very recently, to overcome these limitations of several algorithms, researchers have been applied hybrid ensemble machine learning algorithms, which have shown better performance than the conventional and single models (Pham et al. 2016, 2017a; Wang et al. 2020; Shahabi et al. 2020; Nachappa et al. 2020; Costache et al. 2020a; Costache and Bui 2020). The widely applied and popular ensemble machine learning algorithms, which showed very high accuracy to prepare flood susceptibility models, are random subspace (Pham et al. 2020b; Chen et al. 2019a), Reptree (Chen et al. 2019a; Ghasemain et al. 2020), bagging (Shahabi et al. 2020; Chen et al. 2019b; Yariyan et al. 2020), naive Bayes (Ali et al. 2020; Pham et al. 2020c; Tang et al. 2020), logistic tree (Chapi et al. 2019), ensemble of bootstrapping (Dodangeh et al. 2020), ensemble of boosted generalized linear model (Hosseini et al. 2020). The outstanding findings of the hybrid machine learning algorithms for several natural hazard’s models inspire researchers to apply and develop the hybrid machine learning algorithms. However, no general agreement has been found on the selection of the best method for different types of natural hazards modelling such as landslide or flood susceptibility (Chen et al. 2019b). Researchers recommend developing and testing new models for flood susceptibility mapping and other kinds of natural hazards modelling (Chen et al. 2019a).

The flood hazards and susceptibility mapping is not a new area of research in Bangladesh and researches have been already carried out (Hoque et al. 2019; Islam and Sado 2000). Further, the studies have been carried out in the upper Teesta River basin (Indian part of Teesta river) for flood susceptibility analysis (Roy et al. 2019; Mandal and Chakarbarty 2016), but no such comprehensive study for flood susceptibility analysis has been carried out in the Lower Teesta River basin of Bangladesh. To fill these gaps in research, this study designed to develop the new ensemble of bagging algorithms by integrating four other machine learning algorithms, which have not applied till date, for deriving the highly accurate prediction of the susceptibility to flood hazards in the Lower Teesta River basin of Bangladesh. The predicted models comparisons are highly recommendable work for exploring the performances of each model. For this, we used Kruskal–Wallis test and Kolmogorov–Smirnov test to compare the models with each other. Although we used two commonly used non-parametric tests, such as the Friedman test and Wilcoxon Signed-Rank test for model comparison. Based on this line of thinking, we set main objectives of this research were (1) to develop new ensembles of bagging algorithms for flood susceptibility analysis, (2) to delineate and prepare the flood susceptible zones in Lower Teesta River basin, and (3) to validate and compare the flood susceptibility models of the Lower Teesta River basin.

2 Study area

Lower Teesta River basin, which situated in the northern part of Bangladesh has been selected as the study area for this research which is located between 25° 30′ 02′′ N and 26° 18′ 37′′ N latitudes and 88° 52′ 58′′ E and 89° 45′ 34′′ E longitude (Fig. 1). The basin covers about 2284 km2 area and includes five districts of Bangladesh namely Lalmanirhat, Nilphamary, Rangpur, Kurigram and Gaibandha. As per the 2011 Census, the total population of the area was about 10.42 million. The average elevation of the region varies between 05 and 100 meters and the slope is from north-west to south-east. The climate of the basin is subtropical monsoon type (Koppen: CWA) with highest temperature goes beyond 40° C during May, while lowest climate hardly goes below 15 °C during December. The mean annual rainfall of the region is more than 250 cm in which more than 80 per cent of the total rainfall occurs during monsoon season (June to September).

Fig. 1
figure 1

The location of the study area having the training and validation flood points

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The flood-plain of the region is made up of the Teesta and several other small and medium sized rivers. This river deposits sediments each year during flooding period and makes its plain fertile and favorable for agriculture (Mandal and Chakarbarty 2016). The morphology of the lower Teesta basin is demarcated by the low depressions as well as the moribund river channel valley formed by long morphological alters in the basin pathways. Hence the basin is susceptible to flooding and flash flood is a common phenomenon and occurs each year during monsoon season. The sediments deposited are mostly recent making the surface a fertile alluvial plain which are composed of clay, silt and fine to medium sized alluvium (Saha et al. 2019).

3 Materials and methods

3.1 Materials and databases

As the study area has experienced frequent flooding each year; therefore, based on the field survey and local people perception, the historical flooding inventories were prepared. In the present study, we obtained several data types for flood susceptibility modelling. We obtained Landsat 8 operational land imager (OLI) for preparing land use land cover (LULC) maps (path/row: 138/42, spatial resolution: 30 m, date: 19/03/2019), which was downloaded from the United States Geological Survey (USGS) website. For deriving topographical factors and hydrological factors, we used ASTER GDEM (Version 2) (spatial resolution: 30 m). The rainfall data were collected from the Bangladesh Meteorological Department (BMC), Dhaka, Bangladesh. We used a soil taxonomy map, which was collected from the Natural Resources Conservation Service (NRCS)-United States Department of Agriculture (USDA). The drainage map was prepared by utilizing the topographic maps with a scale of 1:250,00 obtained from the Bangladesh water development board. A detailed procedure of methodology of this study is presented by Fig. 2.

Fig. 2
figure 2

Methodology flowchart of this study

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3.2 Flood inventory

The primary step for preparing the flood susceptibility map is the creating of flood inventory maps of the study basin because the probable flood susceptible zones are predicted based on the mathematical relationship between the past flood events and its influencing factors (Bui et al. 2020a; Sarkar and Mondal 2020). However, for collecting the past common flood points in the present study area, we used the historical inundation maps, topographical map and survey on the perception of local people. We collected 207 flood points from the study area (Figs. 1, 3). Subsequently, the collected 207 flooded points were randomly partitioned into 80% (165 points) and 20% (42 points) groups to build and validate the flood susceptible models. However, flood susceptibility mapping is considered as the binary classification in which flood inventory has been classified into two classes, such as flood points and non-flood points. Therefore, in order to construct the training flood inventory, which is considered as the dependent factor for building the model, the binary values like 1 as flood points and 0 as non-flood points are required. Here, flood points have been considered as the exact points where frequent floods have been observed, while the non-flood points considered the points where floods were not recorded in the last few years. Similar to flood points, we had to obtain negative samples or non-flood points. To avoid bias, several researchers recommended choosing the similar number of non-flood points as the positive or flood samples (Tang et al. 2020). Therefore, we randomly collected 206 non-flood points based on the topographical map, historical flood data, field survey and NDWI maps. Subsequently, we randomly classified the non-flood points into 80% (165 points) and 20% (41 points) groups. Thus, we prepared a dependent factor as training datasets which comprised 165 flood points as 1 and 165 non-flood points as 0.

Fig. 3
figure 3

Field photographs of the flooding situation in the Teesta river basin representing a, c, d flooded road, b damaged houses due to flooding, e flooded village, f, h destroyed road due to devastating flooding, g overflow on the culvert, and i camping on the national road by the people affected by flooding

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Similarly, we also prepared testing datasets for evaluating the final models, which comprised 42 flood points as 1 and 41 non-flood points as 0. Both the training and validation datasets were shown in Fig. 1. We extracted data from twelve flood conditioning parameters (spatial datasets) based on the training datasets by using the ‘extract values to point’ tools in ArcGIS 10.5 software. Subsequently, we imported these datasets into WEKA (version 3.9.3) software, and the whole modelling was done over there.

3.3 Methods for generating the flood conditioning parameters

The flood susceptible model is usually very complex and comprehensive, as it requires several topographical and hydrological factors in geospatial format. We selected and prepared twelve flood conditioning parameters for the present work based on the previous literature on flood susceptibility modelling (Chen et al. 2019b; Sturzenegger et al. 2019; Bui et al. 2019b; Arabameri et al. 2019; Moghaddam et al. 2019; Paul et al. 2019; Janizadeh et al. 2019). The parameters were elevation, curvature, aspect, slope, topographic roughness index (TRI), topographic wetness index (TWI), stream power index (SPI), sediment transport index (STI), LULC, distance to the river, soil type, and rainfall. As the collected parameters had different spatial resolution, we applied resampling technique to make them uniform (30 m spatial resolution). The details procedure for preparing the flood conditioning parameters were discussed as follows:

3.3.1 Elevation

The elevation has been identified as a major dominant factor for the modeling of flood (Choubin et al. 2019; Bui et al. 2016). The flood frequency and elevation are inversely related to each other, as one of them (flood) decreases with increase in another (elevation) and vice versa. The areas with low elevation are supposed to be more susceptible to floods while the areas with higher elevation are supposed to be less susceptible to the floods (Khosravi et al. 2016a, b). The Teesta River basin is prone to the frequent flooding as it is located in a low elevation area with a flat topography.

3.3.2 Aspect

Maximum slope of the surface in a definite direction is known as aspect. Several studies considered aspect as significant parameters in the modeling of flood susceptibility (Bui et al. 2020; Bui et al. 2016; Chen et al. 2019). It determines the direction of flow of flood water and hence is an important parameter for flood study (Costache 2019a; Lei et al. 2020). The aspect has been prepared using the ASTER GDEM data.

3.3.3 Slope

Slope gradient is an important physiographic characteristic, which is directly related to the flooding as it contributes to the runoff velocity and vertical percolation of the water (Choubin et al. 2019; Rahmati et al. 2016). The chances of flooding increases with decline in the slope angle and decreases with an increase in slope angle(Costache 2019b). Therefore, the Teesta River basin is supposed to be more prone to flooding as it has flat topography with low elevation.

3.3.4 Curvature

The curvature is another determinant in flood susceptibility modeling which is prepared using ASTER GDEM in ArcGIS 10.2 domain. The convergent and divergent runoff regions were separated by the curvature. The activity of runoff is associated with the regions with negative value (Costache and Bui 2020) and these regions are highly susceptible to flooding.

3.3.5 Topographic roughness index (TRI)

Flooding also occurred by TRI which depends on the local topography of a basin. The occurrence of flooding highly depends on the TRI and the higher floods are always associated with lower TRI and the high TRI leads to either no or low floods (Tehrany et al. 2019a, b). In this research, stretch format was used for preparing TRI map with values ranging between 0 and 27 (Fig. 6a).

3.3.6 Topographic wetness index (TWI)

TWI is the indication of watersheds’ wetness by spatial variation first proposed by Beven and Kirkby (1979). It is used to spatially represent the variation of wetness of a river basin (Meleset al. 2020). The TWI shows the quantity of water accumulated in a pixel size of a watershed area or basin and can be expressed as Eq. 1.

$$TWI = \frac{{{ \ln }(A_{s} )}}{\tan \beta }$$
(1)

where, As represents the explicit catchment area (m2 m−1) and β represents the slope gradient (in degrees). The higher TWI values and the flood events have strong correlation with each other (Shit et al. 2020). In this research, the TWI value ranges between 0 and 7.72 (Fig. 6b).

3.3.7 Stream power index (SPI)

The SPI refers to the power of erosion (erosive power) of the flowing water and it has considerable impact on the fluvial systems (Tehrany et al. 2015). The sediment transportation capacity and erodibility of a river from its own bed is known as the SPI (Chen et al. 2020). The SPI was calculated using Eq. 2.

$${\text{SPI}} = {\text{A}}_{\text{s}} \;\tan\upbeta$$
(2)

where, As represents the specific catchment area and β represents the slope gradient.

3.3.8 Sediment transport index (STI)

Erosion as well as deposition processes in a specific basin are described by STI. It is used to reflect the erosive capacity of a surface/terrain and can be calculated using Eq. (3).

$${\text{STI}} = \left( {\frac{{{\text{A}}_{\text{s}} }}{22.13}} \right)^{0.6} \left( {\frac{{\sin\upbeta}}{0.0896}} \right)^{1.3}$$
(3)

where, β refers to the slope pixels while the As refers to the upstream area. The STI was calculated based on the geomorphologic as well as hydro-climatic attributes. The change in the channel’s bed due to sediment deposition affects the water storing capability of the basin which leads to the increase in flood risk (Antoniazza et al. 2019). In the present research, the STI value ranges between 0 and 140.64 (Fig. 6d).

3.3.9 Land use land cover

The LULC affects the surface runoff and sediment transportation both directly and indirectly (Zhang et al. 2010). The flood events are more frequent in settlement areas than the forest and open areas because the built-up lands do not allow water to infiltrate and block surface runoff (Costache 2019c), while the forested and open surfaces does not put obstacles in the movement of water (Yin et al. 2017). In this research, the LULC mapping has been done using the Landsat 8 (OLI) dataset using ANN algorithm on ENVI software version 5.3. Six LULC classes have been identified in this study, i.e. built-up area, vegetation cover, bare land, agricultural land, sand bar and water body (Fig. 7a).

3.3.10 Distance to river

The areas next to the rivers are most exposed to the flooding and hence, the distance from the river is identified as an important flood conditioning factor. Chances of flooding increases with the decrease in distance from the river and decreases with increase in distance from the river (Talukdar and Pal. 2019; Costache et al. 2020d; Binh et al. 2020). Topographic maps (scale 1:50,000) and Google Earth were used to prepare the distance to the river map.

3.3.11 Soil types

Flooding is also affected by soil as the properties soil determines the infiltration of water and surface runoff (Costache et al. 2019; Phillips et al. 2019). The infiltration rate and surface runoff are inversely related to the flooding. The soil map has been classified into 12 classes based on the USDA soil taxonomy classification using the USDA map as the base map.

3.3.12 Rainfall

Rainfall has been also identified as a major influencing factor of flooding as the intense rainfall for even a short time-period can cause flooding (Pham et al. 2019a, b; Ali et al. 2020; Costache et al. 2020e; Pourghasemi et al. 2020a, b). Data of rainfall was sourced from Bangladesh Meteorological Department and the spatial distribution of rainfall done by the well known interpolation technique kriging in ArcGIS version 10.3. The kriging method was employed because the rainfall data obtained was from only four meteorological stations and this technique has been suggested to plot less number of observations (Kourgialas and Karatzas 2011).

3.4 Methods for analyzing importance of flood conditioning parameters

Several spatial techniques as well as models have been proposed and applied for the mapping of flood susceptibility modeling and hazard zonation in order to delineate the flood prone areas. The preparation of flood hazard models involves the building of a set of parameters related to floods (Chen et al. 2019). The flood conditioning factors are used to enhance and increase the quality of the results. Total 12 factors have been used in this study as the flood conditioning factors; i.e. aspect, slope, curvature, stream power index (SPI), elevation, sediment transport index (STI), topographic roughness index (TRI), topographic wetness index (TWI), LULC, type of soil, distance to the river, and rainfall. Further, to identify the parameters influencing the prediction of flood susceptibility modeling, the information gain ratio (IGR) has been used because of its ability to identify the significance of each factor influencing flood susceptibility modeling (Bui et al. 2020a, b; Al-Abadi 2018). The IGR values have been assigned based on the significance of the factor. The IGR was employed in the present study because of its efficacy and was calculated using Eq. (4).

$${\text{Gain ratio}}\left( {{\text{x}}, {\text{Z}}} \right) = \frac{{{\text{Entropy }}\left( {\text{Z}} \right) - \mathop \sum \nolimits_{1}^{\text{n}} \mathop \sum \nolimits_{{{\text{i}} = 1}}^{\text{n}} \frac{{\left| {{\text{Z}}_{\text{i}} } \right|}}{{\left| {\text{Z}} \right|}} {\text{Entropy }}({\text{Z}}_{\text{i}} )}}{{ - \mathop \sum \nolimits_{{{\text{i}} = 1}}^{\text{n}} \frac{{\left| {{\text{Z}}_{\text{i}} } \right|}}{{\left| {\text{Z}} \right|}}{ \log }\frac{{\left| {{\text{Z}}_{\text{i}} } \right|}}{{\left| {\text{Z}} \right|}}}}$$
(4)

Further, identification of the importance of the factors responsible for flooding has been done by utilization of the Karl Pearson’s correlation coefficient used by Xu and Li (2020) and the variance inflation factors (VIF) used by Javidan et al. (2020) techniques in this study. A VIF value more than 9 and the very low correlation coefficient shows the problem of multicollinearity in the factors employed. Therefore, it is recommended to exclude those conditioning factors with VIF more than 9 or very low coefficient of correlation in the modeling.

3.5 Methods for flood susceptibility mapping

3.5.1 Bagging

The bagging is a popular technique used for the construction of ensembles (Prasad et al. 2006). Bagging refers to an ensemble algorithm, which can constitute multiple models of different subsets of a training dataset. It combines the prophecy from all models. It is the application of bootstrapping and aggregating procedure to a high variance machine learning technique and was called Bagging by an American Statistician Breiman (1996).

For this study, a learning set C has been considered, which consists of n independent observations (Chen et al. 2018). Here, the independent observations are the flood conditioning factors, where C = {(Xi, Yi), i = 1, 2, 3 … n}. For this, firstly, the set Cb (b = 1, 2, 3 …. n) represents the bth bootstrap sample of training set C, acquired by illustration with substitution n components of the C. Later, to calculate the bootstrap estimator g * (·) by the plug in the code: g * (·) = hn ((X1, Y1), …. (Xn, Yn)) (·). Finally at last, replicate the above mentioned steps m times, in which the m could be either 50 or 100, based on the need, yielding g*k(·) (k = 1, 2, 3 …. m). Hence, the Bagging calculator will be as Eq. 5

$$gBag\left( \cdot \right) = \frac{{\mathop \sum \nolimits_{k = 1}^{m} g^{*k} ()}}{m}$$
(5)

Further, the Bagging estimator can be illustrated as Eq. (6).

$$gBag \left( \cdot \right) = *\left[ {g*\left( \cdot \right)} \right]$$
(6)

where the speculative quantity matches to m = ∞ and this infinite number m directs the precision of Monte Carlo estimation.

3.5.2 Ensembles of bagging

REPTree


The REPTree algorithm follows the idea of computing the information gain with entropy and minimizing the error occurring due to the variance (Witten and Frank 2005). Suggested by Quinlan (1987), this algorithm produces the regression tree by means of node statistics like information gain or the variance diminution calculated from the up-down phase, and trims it by using reduced-error cutting.


M5P


M5P is a tree based regression algorithm proposed by Quinlan (1992) which produced values at the trees’ leaves for future prediction. The trees produced by this algorithm have some multivariate linear techniques. This algorithm can solve problems with high dimensionality equal to 100 characters. It is efficient and gives more accurate results by building comparatively smaller trees. This model works with continuous variables rather than discrete variables (Sihag et al. 2019).


Random forest


Random forest is a well admired ensemble learning algorithm proposed by Breiman (2001), which is a permutation of the decision trees for the classification as well as regression for making predictions. It is a combination of two subsets, i.e. bagging idea of Breimanand the random selection features of Ho. In a bagging ensemble, poor classifiers can give high accuracy by producing a number of strong classifiers with Random forest. A wide variety of samples were created along with generating various similar regression trees in the training phase by this ensemble. Then, based on the results of multiple classifiers, it classified the data. Lastly, it selects the classification, which has a majority vote over all trees in a forest.


Random tree


The random tree is also known as RTree, a regression model based on a decision tree algorithm. The trees are created by RTree considering randomly chosen attributes (K) at every node without pruning. Further, it gives an alternative to allocate the evaluation of the class probabilities on the basis of a hold-out set, i.e. Back-fitting.

3.6 Validation and comparisons of flood susceptibility models

3.6.1 Receiver operating curve

Receiver operating characteristics (ROC) curve is the graph of sensitivity along with 1-specificity, which produces an area under itself called AUC (Hajian-Tilaki 2013). AUC is very useful which helps to evaluate the performances of prediction accuracy and also for interpreting the results. ROC is also utilized for assessing the risk of any vulnerable situation or object. ROC curve is expressed by the following formula:

$${\text{ROC}} = \frac{Sensitivity}{Specificity}$$
(7)

3.6.2 Confusion matrix

In the present study, for evaluating the accuracy assessment of the four flood susceptibility maps, we calculated confusion matrix apart from the ROC curve. We calculated sensitivity, specificity, Youden index J, predicted positive value, predicted negative value, and optimal criterion for validating the flood susceptible models (for details: Hong et al. 2020).

3.6.3 Friedman test

Friedman test is an ideal nonparametric test used for comparing several matching groups among them developed by Milton Friedman (Lindman 1974). It is a two way analysis. This test presumes that the sources of all the variables having equivalent continuous distribution and all variables are communally self-determining (Cieslak and Chawla 2009). The Friedman test is described by the following equation:

$$X^{2} = \frac{12}{{kn \left( {k + 1} \right)}}\mathop \sum \limits_{j = 1}^{k} r_{j}^{2} - 3n\left( {k + 1} \right)$$
(8)

where, X2 is the probable p value, k is number of variables, n denotes number of examples under each variable and r denotes the rank.

3.6.4 Wilcoxon signed-rank test

Wilcoxon Signed-Rank test is the nonparametric technique for testing the variations of paired data based on ordinal scale (Suchmacher and Geller 2012). It is well known as the backup test of t test in which self-determining variables are binary based. This test is employed for detecting whether any variable is shifted by the influence of other variables. Four main steps should have been done for doing this test. First, calculate the variation of every pair of datasets. Secondly, rank the derived variation. Thirdly, assigning the respective sign (+ or – sign) of the ranked values. Finally, both sums (sums of positive sign and sums of negative sign) are computed.

3.6.5 Kruskal–Wallis test

Kruskal–Wallis test is the one way nonparametric test for evaluating the performance of several similar groups among them (Gibbons 1985). This test is recognized as a very useful test for performance evaluation. The statistical form of Kruskal–Wallis test is following below:

$$K = \left( {N - 1} \right)\frac{{\mathop \sum \nolimits_{i = 1}^{g} n_{i} \left( {\underline{{r_{i} }} - \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{r} } \right)^{2} }}{{\mathop \sum \nolimits_{i = 1}^{g} \mathop \sum \nolimits_{j = 1}^{n = i} \left( {r_{ij} - \underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{r} } \right)^{2} }}$$
(9)

where, N means total samples, \(n_{g}\) denotes number of total samples in g group, \(r_{jg}\) denotes overall rank of j samples in group and \(\underline{{r_{g} }}\) means rank of samples in g group and \(\underset{\raise0.3em\hbox{$\smash{\scriptscriptstyle-}$}}{r}\) denotes mean rank of samples among all samples.

3.6.6 Kolmogorov–Smirnov test

Kolmogorov–Smirnov test also known as KS test is a common nonparametric test which compares two observations on the basis of performances (Kolmogorov 1933; Smirnov 1939). It is a less sensitive model compared to other models, because it produces no assumptions on data distribution. Statistical equation of this test is noted below:

$$X^{2} = \frac{{4D^{2} n_{1} n_{2} }}{{n_{1} + n_{2} }}$$
(10)

where, X gives the values of p, \(n_{1}\) and \(n_{2 }\) is the number of examples in two different observations.

4 Results and analysis

4.1 Importance of flood conditioning parameters

The determination of the influence of flood conditioning factors were evaluated by using the values of IGR for each parameter. It was calculated by using a tenfold cross validation technique. Figure 4 showed that the LULC (0.52), slope (0.495), DR (0.12) and elevation (0.11) were the most important flood conditioning factors with higher IGR values than TRI (0.03), SPI (0.03), STI (0.02), TWI (0.01), and curvature (0.01). Further, the IGR value of aspect factor was zero (0), hence it could be considered as the less influential parameter for flooding.

Fig. 4
figure 4

Determination of influence of flood conditioning parameters by using information gain ratio

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4.2 Characteristics of flood conditioning parameters

To explore the spatial relationship between natural hazard occurrences and influencing factors is significantly needed in modeling study (Pham et al. 2016). Flooding occurrences are influenced by several factors (Fernández and Lutz 2010; Pradhan 2010). In the present study, 12 influencing factors, such LULC, distance to road, elevation, slope, topographic wetness index, stream power index, sediment transport index, curvature, topographic roughness index, curvature and aspect were selected. The likelihood of flooding decreases with the increases of elevation. Elevations for the study area were ranged from 18 to 69 m, which remained in line with the flood occurrence (Fig. 5a). The ground surface, which is possessed by the curvature. The range of curvature value between 1.0 and 2.0 was considered as sensitive to flooding (Hudson and Kesel 2000). Curvature map, which was produced by using the DEM ranged from 0.32–0.82 (Fig. 5b). An aspect map was generated and classified into 9 categories: (0–22.5), (22.5–67.5), (67.5–112.5), (112.5–157.5), (157.5–202.5), (202.5–247.5), (247.5–292.5), (292.5–337.5), (337.5–360) (Fig. 5c). Due to the regional flood risk assessment, ground slope is a momentous element, which can increase runoff (Tehrany et al. 2015b). In this study, slope was ranged from 0 to 5.75 (Fig. 5d). TRI ascertained the confrontment pose on the water flow by the underlying surface (Straatsma and Baptist 2008). Teesta river located around the lowest TRI, which caused speedy water flow due to the hilly slopes around the river.

Fig. 5
figure 5

Influencing factors of flood occurrence a elevation, b curvature, c aspect and d slope

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Consequently, the flooding has been happening in those regions, where the lowest TRI is observed. The highest value of TRI was 27 in this study (Fig. 6a). Flood plain is strongly correlated with the high TWI values. In Fig. 6b, the range of TWI value was − 1.54 to 7.72 (Fig. 6c). Flood occurrence is affected by the STI. The highest value of STI in this study was 140.64 (Fig. 6d).

Fig. 6
figure 6

Influencing factors of flood occurrence a TRI, b TWI, c SPI and d STI

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In flood occurrences, LULC played a vital role, vegetated land turning into bare land resulting in the increase of runoff (García-Ruiz et al. 2008). In this study, LULC was classified into 6 categories, such as vegetation, bare land, built up, sand bar, agricultural land, and water body (Fig. 7a). For the flood discharge, river flow played a key role as a main track and caused flooding in those areas, which are near to the river (Opperman et al. 2009). Figure 7b showed that the highest distance from the river of this region was 1503 m. For accounting surplus precipitation and infiltration, soil data played a significant role (Johnson 2000). In this study, 12 soil types were found, such as water, usterts, aquults, humults, udults, ustults, aqualfs, ustalfs, ochrepts, aquepts, aquents, and psamments (Fig. 7c). For flood assessment, the amount of rainfall played a key role (Kay et al. 2006). The highest rainfall in this region was 550.411 mm (Fig. 7d).

Fig. 7
figure 7

Influencing factors of flood occurrence a land use land cover, b distance to river, c soil types and d rainfall

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4.3 Flood susceptibility mapping

Four novel ensemble machine learning algorithms, such as Bagging with Reptree, Bagging with M5P, Bagging with Random forest, and Bagging with Random tree methods were developed and employed to predict the flood susceptibility areas in the Teesta flood region area.

We classified flood susceptibility zones into five classes, such as very low, low, moderate, high and very high (Fig. 8). 1071.71 km2 area, largest area to the total area of the basin, was predicted as a very high susceptible zone and the moderate susceptibility zone was covered by the smallest area (395.49 km2). These were predicted by Bagging with Random forest (Fig. 9c). Bagging with REPtree predicted 1045.72 km2 and 521.65 km2 area as very high and high flood susceptible zones (Fig. 9a). 1060.811 and 831.89 km2 area as very high flood susceptible zone were predicted by Bagging with M5P and Bagging with random tree algorithms, while the very low flood susceptibility zone was covered by 951.82 km2 1038.31 km2 respectively (Fig. 9b, d).

Fig. 8
figure 8

Flood susceptibility mapping using a bagging with Reptree, b bagging with M5P, c bagging with random forest, d bagging with random tree

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Fig. 9
figure 9

Area coverage of predicted flood susceptible models by a bagging with Reptree, b bagging with M5P, c bagging with random forest, d bagging with random tree

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4.4 Evaluation and comparisons of flood susceptibility models

Four individual models (BgReptree, BgM5P, BgRf andBgRt) were used to implement and develop flood susceptibility maps in this study. The AUC and significant level of the ROC curve (Fig. 10) were used to assess the evaluation of these models. The values of 4 individual models were statistically significant (significant level, 0.00) in this study. Figure 10 showed that BgM5P model (AUC = 0.945) was the best performed model followed by BgRf (AUC = 0.912), BgReptree (AUC = 0.876) and BgRt (AUC = 0.844). Several measures of confusion matrix were calculated for validating the flood susceptible models (Table 1). Higher sensitivity (86.25), specificity (8.75), Youden index J (0.75), predicted positive (88.46%) and negative values (86.59%), and optimal criterion (> 0.214) were calculated for the BgM5P based FSM model (Table 1). Based on the all values of different measures of confusion matrix, it could be stated that BgM5P algorithm selected as the representative for flood susceptible modelling in the present study area, followed by the BgRf, BgReptree, and BgRt.

Fig. 10
figure 10

Validation of flood susceptible models by using RoC curve

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Table 1 Confusion matrix estimated for all flood susceptible models
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Wilcoxon signed rank tests were employed to evaluate the performance of the four models. The p value for the BgM5P-BgReptree, BgRf- BgReptree, BgRt- BgM5P, BgRt- BgRf placed at a 95% significant level (< 0.05), whereas the values of Z exceeded the critical level (− 1.96 and + 1.96). The performance of the four models for flood susceptibility mapping was significantly different from each other. The Freidman test did not compare the differences between individual models and the Chi square value was 30.015 found by Friedman test (Table 2). The average ranking values of the Freidman tests for the four hybrid models (BgReptree, BgM5P, BgRf and BgRt) were 2.63, 2.12 2.38, 2.87, respectively. Therefore, the Wilcoxon Signed-Rank test was used for exploring the differences between individual models. The z value and p value of Wilcoxon signed rank test of Bg-Rt vs Bg-Reptree, Bg-Rf vs Bg-M5P were not exceed the critical level (− 1.96 and +1.96) and statistically significant (< 0.05) (Table 3). This indicated that the performance of these two models were not significantly different.

Table 2 Friedman test for all flood susceptible models
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Table 3 Result of Wilcoxon signed-rank test for comparing the flood susceptible models
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Kruskal–Wallis test revealed that all the four ensemble models were significant at 0.01% level (Table 4) for flood susceptibility modeling. Among four models, BgM5P performed best, because it achieved the lowest mean rank (44.90) in lower part and highest mean rank (116.10) in upper part and produced highest Chi Square value (94.462) compared to other three models. The order of the other models based on their mean rank and Chi Square values were Bg-Rf > Bg-Reptree > Bg-Rt. Following the mentioned three statistical tests, Kolmogorov–Smirnov test also explored that four Bagging with ensemble models provided significant (p < 0.01) results of flood susceptibility modeling (Table 5). Most extreme differences of four models ranged from 0.500 to 0.750. z values produced by this test ranged from 3.162 to 4.743. BgM5P again outperformed in this test. Ranks of other models were Bg-Rf > Bg-Reptree > Bg-Rt.

Table 4 Results of Kruskal–Wallis test for comparing the flood predictive models
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Table 5 Results of Kolmogorov–Smirnov test for all flood susceptible models
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5 Discussion

Extreme flood has been becoming a common miserable scene in the northern part of Bangladesh every year due to its geological structure and inappropriate law enforcement. It is a paramount need to take a prediction and mitigation approach in order to reduce property damage and loss of life. Flood modeling and flood susceptibility mapping are the essential approach to assess risk. Four Bagging ensemble models were used to make flood susceptibility maps in this study. In general, the flooding susceptible models cut off the exposed areas considering several flood conditioning parameters (Hong et al. 2018). Tehrany et al. (2015a) suggested that floods usually are affected by the particular area’s morphological, geological, topographical and hydrological conditions. Therefore, choosing the appropriate flood-conditioning parameters is the most important and essential part in modeling of flood susceptibility. The IGR method, utilized in the present work, evaluated the influence of the selected parameters for flooding. Arora et al. (2019) pointed out that the importance of the flood conditioning factors varies from one, location to another. This is because the nature and cause of the flooding are not always similar at different locations (Rubinato et al. 2019). The result of IGR showed that the most effective factors were LULC, while, TRI, SPI, STI, TWI and curvature were evaluated as least effective conditioning factors and aspect had no effect in the flood susceptibility mapping in this study. This is because the study area lies in the lower part of Teesta River basin having a flat topography with low elevation, low slope angle and moderate drainage density (Mondal and Islam 2017). These findings are quite similar with the findings of Khosravi et al. (2018), Khosravi et al. (2016a, b), Khosravi et al. (2019). They reported that the most important flood conditioning factor was altitude and less important factors were rainfall, SPI and curvature. Similar findings were found by Tehrany et al. (2015), Moghadam et al. (2018), Termeh et al. (2018), Chapi et al. (2017).

Li et al. (2012) reported that in the low elevated areas (areas having elevation lower than 300 m) the likelihood of flood occurrence was high which demonstrate that the study area of this study is very vulnerable to the susceptibility of flood occurrence as the elevation of this study area is low enough (69 m). Hong et al. (2017) also reported the similar kind of results in their study.. The curvature range found in this study was 0.82–0.32. Hudson and Kesel (2000) stated that the range of curvature value between 1.0 and 2.0 had the probability of flooding. Almost similar results were obtained by Cao et al. (2016), Chapi et al. (2017) and Khosravi et al. (2016a, b) in their studies. The aspect was ranged between 337.5 and 360 and the IGR value was 0.00. Therefore, present study excluded aspect for flood susceptibility modelling following Rahman et al. 2019. Khosravi et al. (2016a, b) also reported the similar results in their study. The slope angle found in this study ranges from 0 to 5.75° which determines the water velocity and Fernandez and Lutz (2010) described it as a vital parameter of causing flood. Rahmati and Pourghasemi (2017), Tehrany et al. (2014) reported that the probability of flood occurrence would be higher, if slope angle was lower. The findings of this study demonstrated that the study region had high likelihood of flood occurrence due to the lower slope angle.

The morphological factor of TRI is highly related with flooding (Werner et al. 2005). Findings showed that the study area had the highest value of TRI (27) which could cause flooding and this finding is similar to the findings of Tehrany and Kumar (2018). STI which is considering another flood occurrence factor defines the movement of the sediments in water bodies (Mojaddadi et al. 2017). The highest STI value explored in this study was 14.64. Almost similar result of STI found in the work of Tehrany and Kumar (2018). SPI and TWI are two important hydrological factors responsible for the spatial variation of flooding. The TWI values ranged from 1.54 to 7.72 in this study. Topographical effects are quantified by the TWI (Lee et al. 2017). The LULC, distance to river, soil type and rainfall were the remarkable flood conditioning factors in this study. The findings of these parameters matched with the findings of Tehrany and Kumar (2018), Brath et al. (2006). Azareh et al. (2019) revealed that soil texture, land use, elevation and frequently occurring heavy rain storms were the most influential factors of flood in Iran which is analogous to this study. Hosseini et al. (2020) found that elevation (similar to this study); drainage density; vegetation and distance were the influential factors of flash flood in Iran. Five flood susceptible zones were predicted by BgReptree, BgM5P, BgRf and BgRt. High and very high flood susceptibility zones were covered by 20–29% areas of the total area of Teesta basin. Janizadeh et al. (2019) reported that 26.1% and 12.9% of area predicted as very high susceptibility according to QDA and ADT model respectively. According to fuzzy WofE-LR; WofE-RF and fuzzy WofE-SVM model, very high susceptibility area was 10.41%, 15.89%, and 17.65% in China, respectively (Hong et al. 2017). In their study, Choubin et al. (2018) reported that 80.6 km2 and 10.1 km2 area were, respectively, predicted as low and very high flood susceptibility classes revealed by using the MDA model. Pham et al. (2019) explored that very low, low, moderate, high, and very high susceptibility classes were covered by approximately 26%, 34%, 20%, 12%, and 8% area of the total land area, respectively, predicted by RSSFT model. Bui et al. (2019), Shahabi et al. (2020), Chen et al. (2019) reported that 15–24% area was predicted as high flood susceptible zone. Similar findings as this study were found by Tsakiri et al. (2018), Tehrany et al. (2019a, b), Ma et al. (2019), Costache et al. (2019). Therefore, it can be stated that the findings of the present study are highly correlated with the findings of previous literatures. These findings can be used as the basic foundation for flood management in the present study area.

To evaluate the model performance, several previous studies used the AUC values of the ROC curve (Bui et al. 2018; Choubin et al. 2018; Khosravi et al. 2019). The AUC values of the BgM5P and BgRf used in this study were 0.945 and 0.912, respectively. Bui et al. 2018 reported that the ANFIS-ICA (AUC = 0.947) model performed better by comparing with the Bagging-LMT (AUC = 0.940), BLR (AUC = 0.936), LMT (AUC = 0.934), ANFIS-FA (AUC = 0.917), LR (AUC = 0.885) and RF (AUC = 0.806) models. Choubin et al. (2018) used AUC for validation of the flooding susceptible models and considered the flood susceptible models as valid because of achieving the higher AUC values, such as ensemble model (AUC = 0.91), followed by CART (AUC = 0.83), SVM (AUC = 0.88), MDA (AUC = 0.89) models. Hosseini et al. (2020) used GLMBoost based Random forest and BayesGLM algorithms for flood modeling and revealed high performance accuracy of both the algorithms for modeling flood. Khosravi et al. (2019) found that the NBT had the highest predictive accuracy than the VIKOR (AUC = 0.965), TOPSIS (AUC = 0.968), SAW (AUC = 0.97), NB (AUC = 0.979) models. Hong et al. (2020) developed and applied the ensemble of bagging-LogitBoost alternating decision tree (LADT) and forest by penalizing attributes (FPA) for modelling the landslide susceptibility maps and reported that bagging-LADT model achieved the very high accuracy for both training and testing datasets. Therefore, it could be stated that the ensemble of bagging could be improved significantly for any kinds of natural hazard prediction. Dodangeh et al. (2020) used BT-GAM, BT-MARS and BT-BRT ensemble algorithms for flood susceptibility prediction and BT-GAM (AUC = 0.98) found as the outperformed model followed by BT-MARS (AUC = 0.97) and BT-BRT (AUC = 0.95). Therefore, we can state that the algorithms which were used in the present study had higher accuracy. For assessing the performance of the models, Wilcoxon signed-rank test, Friedman test, Kruskal–Wallis test and Kolmogorov–Smirnov test were also conducted in this study. The findings of these tests are identical with the work of Bui et al. (2018), Khosravi et al. (2018), Hong et al. (2017). Kruskal–Wallis test and Kolmogorov–Smirnov test found that all the four ensemble models performed significantly (p < 0.01) for flood susceptibility mapping of Teesta River basin, Bangladesh.

6 Conclusion

In the present study, we developed and utilized four ensembles of bagging algorithms, such as bagging with REPtree, bagging with RF, bagging with M5P, and bagging with RT for the first time for modelling the flood susceptibility mapping in the Teesta River basin, Bangladesh (Northern). A total of 413 flooding points with twelve parameters, such as elevation, slope, curvature, aspect, SPI, TWI, STI, LULC, rainfall, distance to the river, TWI, and soil types, which affect the flooding, were selected for modelling. The importance of flood condition parameters were determined by employing the IGR technique. Based on the feature selection outcomes, aspect was not considered for flood susceptible modelling. The ROC curve was used to validate the flood susceptible models. The Friedman test, Wilcoxon signed-rank test, Kruskal–Wallis test and Kolmogorov–Smirnov test were employed to explore the differences of performance of the flood susceptible models with each other. The highest flexibility and predictive ability were obtained in case of the bagging with M5P algorithm, followed by bagging with RF, bagging with REPtree and bagging with RT. The application of the ROC Curve in the outcome validation phase depicted that bagging with the M5P algorithm had the highest efficiency in comparison with other models (AUC = 0.945). However, the performance of all models for the mapping of flood susceptibility were excellent. The findings of the study stated that bagging with M5P and bagging with RF are one most capable tool for flood susceptible modelling. As an optimal model, a total area of 30% was identified as highly vulnerable to flooding. However, the major drawback is that the application of these models did not consider the changes over time for some factors, including SPI and LULC, because these are dynamic. Based on the availability of temporal datasets of these factors, future research on the temporal scale will be performed. Furthermore, these models can be upgraded by performing the sensitivity analysis concerning various influential factors. Bagging with the M5P algorithm, in comparison with the other models, had advantages, including fewer candidate parameters, high optimization capability, and fast convergence for preparing flash flood susceptibility maps.

In recent times, the strategies for the management of flood are considered as the top priority, particularly in Bangladesh, where flash floods occur every year. However, other basins and regions have not yet been appraised for flood mitigation plans. Hence, the present study was taken place in the Teesta River basin using some advanced machine learning algorithms, which will provide valuable information concerning methods to be adopted for supporting the local authorities and other parties in developing efficient alleviation strategies of flash flood and land-use policy planning not only Bangladesh but also other basins of the world.