Developing accurate flood forecasting models is necessary for flood control, water resources and management in the Mahanadi River Basin. In this study, convolutional neural network (CNN) is integrated with random forest (RF) and support vector regression (SVR) for making a hybrid model (CNN–RF and CNN–SVR) where CNN is used as feature extraction technique while RF and SVR are used as forecasting models. These hybrid models are compared with RF, SVR, and artificial neural network (ANN). The influence of training–testing data division on the performance of hybrid models has been tested. Hyperparameter sensitivity analyses are performed for forecasting models to select the best value of hyperparameters and to exclude the nonsensitive hyperparameters. Two hydrological stations (Kantamal and Kesinga) are selected as case studies. Results indicated that CNN–RF model performs better than other models for both stations. In addition, it is found that CNN has improved the accuracy of RF and SVR models for flood forecasting. The results of the training–testing division show that both models’ performance is better at 50–50% data division. Validation results show that both models are not overfitting or underfitting. Results demonstrate that CNN–RF model can be used as a potential model for flood forecasting in river basins.

  • CNN-based hybrid machine learning models are developed for flood forecasting and are compared with other ML models.

  • The impact of training–testing is analyzed and is selected for the best performance of models.

  • Four input models are tested for better input combinations for flood forecasting.

  • Sensitivity analysis of developed models is done for identifying the sensitive, insensitive and most sensitive parameters of models.

AI

artificial intelligence

ALLSSA

AntiLeakage Least-Squares Spectral Analysis

ANFIS

adaptive neuro-fuzzy inference system

ANN

artificial neural network

ARIMA

Auto-Regressive Integrated Moving Average

ARIMAX

Auto-Regressive Integrated Moving Average with eXplanatory variable

C

regularization parameter

CNN

convolutional neural network

DEM

digital elevation map

DL

deep learning

L

water level

LSTM

long-short-term memory

MAE

mean absolute error

MCM

million cubic meters

ML

machine learning

NASA

National Aeronautics and Space Administration

NSE

Nash–Sutcliffe Efficiency

PCS

projected coordinate system

Q

discharge

R

rainfall

RBF

radial basis function

R2

coefficient of determination

RF

Random Forest

RMSE

root mean square error

SARIMAX

Seasonal Auto-Regressive Integrated Moving Average with eXogenous factor

SRTM

Shuttle Radar Topography Mission

SVM

support vector machine

SVR

support vector regression

WRIS

Water Resources Information System

Floods are the most happening natural hazards which cause serious damage to the environment, human life, and livelihood (Khosravi et al. 2018). The damages caused by disasters like flooding are incalculable. Due to these tremendous and irreversible damages, it becomes extremely important to forecast the floods to reduce the flood risk and properly plan and manage the water resources systems (Kant et al. 2013; Sarker 2023; Sarker et al. 2023). Flow in rivers is nonlinear and affected by catchment characteristics, rainfall and climate conditions (Le et al. 2019). Therefore, more accurate and reliable models are required for flood forecasting. There are two types of models for forecasting, which are physically based hydrological models and data-driven models. Artificial intelligence (AI)-based machine learning models are data-driven models which create statistical relationships between input and output. These machine learning models have the ability to capture the nonlinearity form of time series and have made a lot of progress in research, especially in hydrology (Mosavi et al. 2018). The AI technique-based machine learning models have become popular in hydrology and water resources in recent years as they can analyse large-scale data and long-time series (Wang et al. 2009). Several machine learning models such as artificial neural networks (ANNs), support vector machine (SVM), adaptive neural-based fuzzy inference systems, decision trees and other regression-based models have been used for time series modelling in hydrology and water resources systems. The ANN is based on understanding the brain and nervous system and has been used in hydrology since the 1990s. The ANN model is used in conjunction with the flash flood routing model for forecasting the longitudinal stage profiles in rivers for flash floods (Hsu et al. 2010). Rezaeian-Zadeh et al. (2013) used ANN for monthly flood flow forecasting in arid and semi-arid regions. Neural networks based on bootstrap techniques have been used to quantify the parametric uncertainty involved in forecasting (Tiwari & Chatterjee 2010). The ANN model has worked better than the ARMA model for short-term rainfall prediction for real-time flood forecasting (Toth et al. 2000). A coupled wavelet-transformed neural network is developed for flood forecasting in non-perennial rivers in semi-arid watersheds (Adamowski & Sun 2010). The ANN has been useful for forecasting and analysis in hydrology and water resources (Campolo et al. 1999; Chao et al. 2008).

Because of SVM's nonlinear regression and time series forecasting, it has been used much in hydrology and water resources engineering for forecasting. Lin et al. (2006) used SVM for long-term discharge forecasting and found that it had great potential for prediction of long-term discharge in comparison to ANN and auto-regressive moving average models. The SVM and random forest (RF) are also integrated with Google Earth Engine and have been utilized for lake and river monitoring and rainfall forecasting (Yu et al. 2017; Dehkordi et al. 2022). SVM and ANN are compared for flood forecasting with evolutionary strategy as an optimization technique for parameter optimization and it was concluded that SVM performs better than ANN (Bafitlhile & Li 2019). Nayak & Ghosh (2013) predicted the rainfall events using SVM classifiers and concluded that model predicted all the events in advance and was better in terms of false alarm and prediction. The performances of Auto-Regressive Integrated Moving Average (ARIMA), Auto-Regressive Integrated Moving Average with eXplanatory variable (ARIMAX), and Seasonal Auto-Regressive Integrated Moving Average with eXogenous factor (SARIMAX) models have been compared with the AntiLeakage Least-Squares Spectral Analysis (ALLSSA) for forecasting in Italian regions and it was shown that ALLSSA has a great potential for forecasting as it considers the seasonal and trend components (Ghaderpour et al. 2023). Gizaw & Gan (2016) analysed the performance of SVM for flood frequency analysis under historical and future climates and stated the SVM performed well based on goodness-of-fit. The support vector regression (SVR) is applied for regional flood frequency analysis in arid and semi-arid regions and compared with ANN, Adaptive Neuro-Fuzzy Inference System (ANFIS), and NLR (Sharifi Garmdareh et al. 2018). Results have indicated that SVR and ANFIS give better results than ANN and NLR for predicting peak flood discharge. A genetic algorithm-based SVM model is developed for predicting the monthly reservoir storage (Su et al. 2014). Wang et al. (2013) have employed SVM in conjunction with particle swarm optimization for improving the rainfall-runoff modelling. RF is the combination of classification and regression trees that overcomes the issues of overfitting a single decision tree (Breiman et al. 1984). The RF is a popular model due to its prediction capacity and processing speed (Mosavi et al. 2018). The RF has been used for the simulation of large-scale discharge (Schoppa et al. 2020). Tang et al. (2020) have used the hybrid RF based on flood hydrograph generalization for flood forecasting. RF based on flood hydrograph generalization was evaluated for flood forecasting (Tang et al. 2020). Wang et al. (2015) developed the flood hazard risk assessment model based on RF. Muñoz et al. (2018) developed a stepwise methodology for flash flood forecasting based on RF. Ali et al. (2020) used the hybridized RF for monthly rainfall forecasting. The RF model has the highest accuracy as compared to other machine learning models for the classification of snow cover area variation (Gogineni & Chintalacheruvu 2023). RF is compared with SVM for real-time radar-derived rainfall forecasting and it was concluded that RF outperforms SVM (Yu et al. 2017).

Ding et al. (2019, 2020), Le et al. (2019), Roy et al. (2022) and Yan et al. (2021) used long-short-term memory (LSTM) as a prediction model for flood forecasting. Cai & Yu (2022) have used a hybrid-based Recurrent Neural Network (RNN) model for flood forecasting in urban reservoirs. There are several other studies which state that deep learning (DL) techniques have great potential as a prediction model for flood forecasting. Fu et al. (2019) have used a hybrid model based on convolutional neural network (CNN) and LSTM for weather prediction. Shakir et al. (2022) have applied a CNN-based LSTM model for simulating groundwater levels. These studies show that hybrid DL models can improve the results. Tao et al. (2020) have highlighted that there is a need to extract highly correlated features for the development of hybrid ML models and DL has the advantage of utilizing the hidden layers for feature extraction. The DL models have great feature extraction capability. The CNN has been developed and used as a feature extraction technique in various studies. Mostly it has been in image classification and segmentation. These techniques improve the performance of models especially when multiple input variables are used. There has not been much study about combining DL models as feature extraction techniques with ML models as prediction models for flood forecasting.

The purpose of this study is to develop a CNN-based hybrid ML (CNN–RF and CNN–SVR) model for flood forecasting. This study includes the impact of training–testing data division on these hybrid models' performance. Multiple input variables and different combinations of these variables are tested for better input combinations for hybrid models. Sensitivity analysis of hybrid models is also included in this study. The performances of these models are evaluated by using the coefficient of correlation (R2), root mean square error (RMSE), mean absolute error (MAE) and Nash–Sutcliffe efficiency (NSE).

The Mahanadi River Basin is one of the largest basins in India, which lies between 80°–30′ to 86°–50′ of East Longitude and 19°–20′ to 23°–35′ of North Latitude geographically as shown in Figure 1. The total catchment area of the basin is 141,589 km2, out of which 53% of the basin is in Chhattisgarh and 46% of the basin is in Odisha and the remaining basin is in Jharkhand and Maharashtra. It originates from Dhamtari district of Chhattisgarh and travels a length of 851 km before draining into the Bay of Bengal (WRIS, 2014). The Mahanadi River Basin is mainly rainfed and there are large variations and fluctuations in river water. The average annual rainfall in the basin is 1,572 mm, which occurs mainly due to the south-west monsoon season from June to October (Jena et al. 2014). Hirakud Dam constructed over the Mahanadi Delta is the largest dam in the basin with a storage capacity of 7,189 MCM (million cubic meters) and with catchment area of 83,400 km2. The main study area is the middle reaches of Mahanadi River with a catchment area of 47,559 km2 located in Odisha, which extends from Hirakud dam to Naraj with a total length of 358.4 km. The channels' insufficient carrying capacity causes the basin to periodically experience severe flooding in the delta area (Visakh et al. 2019).
Figure 1

Study area map for the Mahanadi River Basin.

Figure 1

Study area map for the Mahanadi River Basin.

Close modal

Figure 1 illustrates the cartographic representation of the study area, derived from Digital Elevation Model (DEM) data. The DEM serves as a geospatial dataset illustrating the elevation characteristics of the investigated region (Gao et al. 2022). The NASA SRTM Plus DEM is imported into ArcMap 10.3 followed by automatic extraction of the river's sub-watershed using the hydrology tool from the Spatial Analyst Toolbox in ArcMap 10.3. Subsequently, rectification and correction of the downloaded DEM are performed. Sinks in the DEM are filled using the ‘fill’ option using the hydrology tool. This is followed by the derivation of the flow direction and flow accumulation and the stream network is extracted (Sarker 2021). Subsequently, sub-watersheds are delineated, and stream order is calculated. The extracted stream network and delineated sub-watersheds are then reprojected to the projected coordinate system (PCS) of the regional projection, specifically WGS-1984, UTM zone 44° N.

Dataset

Daily rainfall, daily discharge and daily water level measurements for 20 years from 1999 to 2018 for Kantamal and Kesinga stations are utilized in this study. Figures 2(a) and 2(b) show daily variation in discharge for Kantamal station and Kesinga station, respectively. The rainfall dataset is collected from the Indian Meteorological Department. Discharge and water level data are collected from the India Water Resources Information System (WRIS). The units of discharge, rainfall and water level are m3/s, millimetre (mm) and metre (m), respectively. Rainfall, discharge and water level of the present day are taken as input for the models for a one-day forecast of the discharge of the next day and so on.
Figure 2

Daily variation in discharge for (a) Kantamal station and (b) Kesinga station.

Figure 2

Daily variation in discharge for (a) Kantamal station and (b) Kesinga station.

Close modal
Figure 3 shows the trend, seasonality and randomness in the discharge data. From the trend, it can be seen that peak flows of stations have a negative trend after 2008. Randomness in the data is high for peak flows during monsoon season, and because of negative trend in peak flow laterally, the residuals also have negative trend. Seasonality is uniform in the whole data for both stations. The statistical description of data is shown in Table 1. The difference between minimum and maximum is very large. Because of high residuals and high variance in high flow and low flow, data needs to be scaled for the model's smooth performance. Data were scaled by using Standard Scalar to convert the values in the range of 0 and 1.
Table 1

Statistical description of discharge for Kantamal and Kesinga stations

Kantamal (m3/s)Kesinga (m3/s)
Mean 382.75 261.44 
Std 1,007.94 692.02 
Min 0.25 0.24 
Max 20,000 21,192.80 
Q50 114.96 94.15 
Q75 283.00 216.88 
Kantamal (m3/s)Kesinga (m3/s)
Mean 382.75 261.44 
Std 1,007.94 692.02 
Min 0.25 0.24 
Max 20,000 21,192.80 
Q50 114.96 94.15 
Q75 283.00 216.88 

Q50 and Q75 are the 50th and 75th percentile, respectively.

Figure 3

Decomposed graph of discharge data for (a) Kantamal station and (b) Kesinga station.

Figure 3

Decomposed graph of discharge data for (a) Kantamal station and (b) Kesinga station.

Close modal

In this study, two CNN-based hybrid models (CNN–RF and CNN–SVR) are applied for flood forecasting and compared with simple RF, SVR, and ANN. In this hybrid model, CNN is used as a feature extraction technique while RF and SVR are used for the prediction of discharge. The brief descriptions of these models are as follows:

Support vector machine

The SVM, developed by Vapnik in 1995, is a versatile model that can be used for classification and regression in various domains. It is a useful model for predictive modelling and decision-making due to its ability to manage complex and nonlinear data relationships (Pratap et al. 2024). The SVM is an approximation implementation method based on the principle of structural risk minimization which generalizes the errors of upper bound instead of reducing the training errors. The fundamental concept of the SVM method involves the initial selection of a nonlinear mapping algorithm, specifically identified as the support vector kernel function. This kernel function facilitates the transformation of input vectors into a high-dimensional feature space, thereby enabling linear classification. Subsequently, an optimal decision function is formulated within the feature space, aiming to achieve a nonlinear decision function in the original input space (Su et al. 2014). It reduces the problem of overfitting and minimizes the expected errors of learning rate. Based on this concept, the SVM achieves optimum network structure. For regression problems, it uses the loss function to draw the nonlinearity of data into higher dimensional space and applies linear regression. The regression function of SVM is described as SVR and is defined mathematically as follows:
(1)
where x is the input, is the regression function and is the nonlinear mapping function. w and b are the weight vector and bias term, respectively, and can be calculated by minimizing the structural risk minimization function.
(2)
where R is the structural risk minimization function and C is the trade-off between empirical risk and regularization term. With increasing value of , importance of empirical risk increases. is the Vapnik's insensitive loss function and N is the number of data points. C and are user defined parameters. The SVR problem can be formulated as the following optimization problem:
(3)
(4)
where and are dual Lagrange multipliers, is the target variable and T is the transpose of vectors. The regression function can be written as
(5)
(6)
where is the kernel function and n is the number of support vectors. The nonlinear kernel functions are used to convert the input data into high-dimensional space. There are various types of kernel functions in SVM such as linear, polynomial, sigmoid and Radial Basis Function (RBF). The RBF is the mostly used function, which is as follows:
(7)
where is a support vector and is a parameter that defines the width of the kernel.

Random Forest

The RF, introduced by Breiman (2001), is a powerful and versatile ensemble learning supervised ML algorithm which can be used for both classification and regression problems. It has the ability to make a relationship between input and output of very complex and nonlinear data (Alipour et al. 2020). It is an ensemble of multiple decision trees. A single decision tree is prone to overfitting on training data and performing poorly on testing data. To overcome this limitation of the single decision tree, the RF approach was devised. The RF model strategically addresses the overfitting vulnerability of regression trees by introducing bootstrap and robustness techniques for splitting the data into subsets for multiple decision trees and selecting input records and predictor variables during the training process (Sadler et al. 2018). The random selection of subsets for training the model provides variety for weak learners and helps in preventing the model from overfitting. The RF model computes its prediction by taking an average of the outputs of each individual decision tree. Large values of decision trees may result in wasting time in modelling, while small values of trees may result in increasing errors. The robustness technique helps in nullifying the unnecessary tree (Lee et al. 2017). Fine tuning technique of the RF model's hyperparameters makes it simple, reliable and efficient. It can be applied to small and complex data structures and in high-dimensional spaces. The basic RF structure is shown in Figure 4.
Figure 4

Structural map of RF.

Figure 4

Structural map of RF.

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Artificial neural network

ANN is a computer-based programming model that draws inspiration from the structural complexity of the human brain, characterized by extensive networks of interconnected neurons. The ANN was pioneered by McCulloch and Pitts in 1943. The ANN consists mainly of three layers: the input layer, the hidden layer and the output layer. The first layer receives data input, processes it through hidden layers, and outputs predictions through the output layer (Lohani et al. 2014). This algorithm involves a feed–forward phase where external input information at the input nodes is propagated forward to compute the output information signal at the output unit, utilizing randomly assigned connection strengths or weights. Subsequently, a backward phase follows, during which the weights are updated based on the error between the computed and observed values at the output units (Hsu et al. 2010). Most importantly, the ANN demonstrates an amazing ability to learn on its own, which enables it to solve problems proficiently without requiring external knowledge or adhering to particular physical behaviour (Adamowski & Sun 2010). A feed–forward-based neural network has been used in this study. The basic ANN structure is shown in Figure 5.
Figure 5

Structural map of the ANN.

Figure 5

Structural map of the ANN.

Close modal

Convolutional neural network

The CNN is a powerful class of DL algorithms mostly used for image-related tasks such as image classification, object detection, and segmentation. The CNN is widely recognized as a feature extraction technique for its exceptional feature extraction capability. The CNN is a specially designed structure which trains fast and captures the spatial information of complex data efficiently due to its translation variance and weight-sharing characteristics (Yang et al. 2019). The CNN has the capability to abstractly extract features from data in its shallower layers, subsequently aggregating these features in the deeper layers, which facilitates a comprehensive understanding of the data. The CNN is structured with multiple convolution layers, pooling layers, and one or more fully connected layers (Figure 6). Convolutional layers use convolutional filters to generate distinct feature maps from the input data. These maps are integrated together to produce the convolutional layer's final input. The pooling layer downsamples and reduces the size of each feature map, which helps in reducing the overfitting concerns and training time. These extracted feature maps are connected together to make a fully connected layer which is linked to the forecasting models (Barzegar et al. 2021). The output of the CNN can be calculated as follows:
(8)
where * is an operator of convolution. is the cnth feature of map of the convolutional layer. f represents activation function applied to the results. X represents input data structure. and represent weight function and bias of the structure, respectively.
Figure 6

Structural map of the CNN.

Figure 6

Structural map of the CNN.

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Model evaluation methods

Model performance is evaluated by comparing the model output and observed data using evaluation methods. These evaluation methods determine the efficiency of the model. In this study, RMSE, coefficient of determination (R2), mean square error and NSE are used for model evaluation. The coefficient of determination (R2) measures the correlation between observed and predicted values (Adamowski & Sun 2010). The NSE has the ability to measure the relation of observed and predicted values that are different from the mean. The MAE measures goodness-of-fit that is related to moderate flows, while the RMSE is related to high flow values (Kisi 2010; Ghaderpour et al. 2023).

Root mean square error

It is an error index statistic. It measures the overall performance of models across the entire range of datasets. It is sensitive towards small differences and more weighted towards higher magnitude errors because of squared measures. It is defined as:
(9)

Coefficient of determination (R2)

It is a widely used method for model evaluation. It describes the collinearity between the observed data and predicted data. It measures the proportion of statistical variance in the dataset which can be described by the model. It is defined as:
(10)

Mean absolute error

It is also the measure of the difference between observed data and predicted data as RMSE. It gives no idea about underestimation and overestimation. It evaluates all the deviations from the observed values in an equal manner regardless of sign. It is defined as:
(11)

Nash–Sutcliffe Efficiency

It is sensitive to extreme values and yields sub-optimal results when the dataset contains large outliers. It describes the accuracy of model outputs other than the discharge. It is defined as:
(12)
where is the predicted value, is the observed value, q is the mean of observed values and n is the number of observations.

Model development

The available dataset includes some missing values. These missing values are filled with the average of the last ten years' values of the same date. The dataset is divided into training and testing equally (50–50%). It is taken after testing different combinations of training and testing percentages for all models. The discharge data is time series data which consists of seasonal variations and randomness. That is why it has large variations, which make it non-stationary data. Working on non-stationary data is difficult and it also affects the performance of the model. So, the dataset needs to be stationary for smooth performance of models and high accuracy, which is done by scaling the data. The dataset was scaled by Standard Scalar, which is a function of sklearn library in Python. It scales the data into a given range, mostly between 0 and 1, without changing the shape of the original distribution. Figure 7 shows the basic flowchart of model development.
Figure 7

Flowchart of hybrid model development.

Figure 7

Flowchart of hybrid model development.

Close modal

The scaled data are processed to the CNN model for feature extraction. The output of the CNN model is taken as input to machine learning models for forecasting. Models are tested with various training–testing data divisions. Then models are tested for four input models to get a better input combination for the model's performance. Sensitivity analysis is done for CNN-based models to analyse the effective and non-effective hyperparameters of models and to get the optimum values of effective parameters. Non-effective hyperparameters are eliminated and optimum values of effective hyperparameters are set for best performance of the models. After deciding the model's parameters, models are trained on training data and the performance is tested with a test dataset. For evaluating the model's performance, R2, RMSE, MAE and NSE are used as evaluation parameters.

This study consists of the application of hybrid machine learning models for river flow forecasting for Kantamal and Kesinga stations in the Mahanadi River Basin. Two CNN-based hybrid models (CNN–RF and CNN–SVR) are developed in this study, where CNN is used as a feature extraction technique and RF and SVR are used as forecasting methods. These models are tested for training–testing data division, and the most effective division was chosen for model development (Figure 8). Three types of variables are tested with different grouping with each other or better accuracy of models (Tables 2 and 3). Both models consist of various parameters which affect the model's performance. Some parameters are most important for the accuracy of models, and some may not have any effect on the model's performance for this data. To analyse the sensitive and insensitive parameters, sensitivity analysis is done and the insensitive parameters are excluded from the developed models (Figures 9 and 10). Finally, both models with selected training–testing division, input variables and model parameters are applied and compared with RF, SVR, and ANN (Table 4). The Mahanadi River Basin has been the subject of extensive research for flood forecasting, with several studies employing various machine learning models and hybrid approaches (Kar et al. 2016; Majhi et al. 2022; Nivesh et al. 2022; Samantaray & Sahoo 2023). These studies have significantly contributed to the understanding of flood prediction in the region. However, the present study aims to demonstrate superior results by introducing innovative methodologies and refining existing approaches.
Table 2

Input combination results for the Kantamal station

Training
Testing
R2RMSEMAENSER2RMSEMAENSE
 CNN–RF 
Input 1 0.92 337.00 96.51 0.90 0.37 629.36 152.40 0.37 
Input 2 0.95 265.55 79.95 0.94 0.57 517.49 109.22 0.62 
Input 3 0.90 370.86 170.41 0.85 0.87 286.47 166.27 0.79 
Input 4 0.93 312.83 133.85 0.90 0.90 248.00 129.62 0.86 
 CNN–SVR 
Input 1 0.59 758.06 143.92 −0.17 0.60 499.57 108.58 0.07 
Input 2 0.75 597.33 116.21 0.64 0.61 494.75 108.23 0.58 
Input 3 0.98 166.63 53.08 0.98 0.88 273.71 55.66 0.88 
Input 4 0.99 130.67 42.11 0.99 0.91 234.34 57.23 0.91 
 RF 
Input 1 0.71 637.98 173.89 0.54 0.56 508.20 158.73 0.59 
Input 2 0.76 580.65 195.85 0.53 0.64 474.61 183.33 0.46 
Input 3 0.93 309.38 184.61 0.92 0.85 310.19 193.39 0.79 
Input 4 0.92 336.12 141.92 0.88 0.89 265.62 134.64 0.83 
 SVR 
Input 1 0.64 711.22 138.17 0.32 0.59 504.79 109.72 0.16 
Input 2 0.78 552.19 105.85 0.70 0.53 540.95 111.36 0.60 
Input 3 0.98 180.78 64.59 0.98 0.83 326.14 67.42 0.83 
Input 4 0.99 102.67 34.31 0.99 0.89 262.62 63.93 0.89 
 ANN 
Input 1 0.63 718.78 167.50 0.42 0.63 484.02 128.97 0.50 
Input 2 0.70 652.45 169.41 0.53 0.65 471.35 138.91 0.55 
Input 3 0.80 524.71 161.98 0.74 0.82 340.29 123.96 0.80 
Input 4 0.87 432.55 150.21 0.84 0.85 311.68 131.36 0.85 
Training
Testing
R2RMSEMAENSER2RMSEMAENSE
 CNN–RF 
Input 1 0.92 337.00 96.51 0.90 0.37 629.36 152.40 0.37 
Input 2 0.95 265.55 79.95 0.94 0.57 517.49 109.22 0.62 
Input 3 0.90 370.86 170.41 0.85 0.87 286.47 166.27 0.79 
Input 4 0.93 312.83 133.85 0.90 0.90 248.00 129.62 0.86 
 CNN–SVR 
Input 1 0.59 758.06 143.92 −0.17 0.60 499.57 108.58 0.07 
Input 2 0.75 597.33 116.21 0.64 0.61 494.75 108.23 0.58 
Input 3 0.98 166.63 53.08 0.98 0.88 273.71 55.66 0.88 
Input 4 0.99 130.67 42.11 0.99 0.91 234.34 57.23 0.91 
 RF 
Input 1 0.71 637.98 173.89 0.54 0.56 508.20 158.73 0.59 
Input 2 0.76 580.65 195.85 0.53 0.64 474.61 183.33 0.46 
Input 3 0.93 309.38 184.61 0.92 0.85 310.19 193.39 0.79 
Input 4 0.92 336.12 141.92 0.88 0.89 265.62 134.64 0.83 
 SVR 
Input 1 0.64 711.22 138.17 0.32 0.59 504.79 109.72 0.16 
Input 2 0.78 552.19 105.85 0.70 0.53 540.95 111.36 0.60 
Input 3 0.98 180.78 64.59 0.98 0.83 326.14 67.42 0.83 
Input 4 0.99 102.67 34.31 0.99 0.89 262.62 63.93 0.89 
 ANN 
Input 1 0.63 718.78 167.50 0.42 0.63 484.02 128.97 0.50 
Input 2 0.70 652.45 169.41 0.53 0.65 471.35 138.91 0.55 
Input 3 0.80 524.71 161.98 0.74 0.82 340.29 123.96 0.80 
Input 4 0.87 432.55 150.21 0.84 0.85 311.68 131.36 0.85 

The bold values are the best input combinations to the models.

Table 3

Input combination results for the Kesinga station

Training
Testing
R2RMSEMAENSER2RMSEMAENSE
 CNN–RF 
Input 1 0.87 321.19 78.38 0.80 −0.04 474.53 114.44 0.24 
Input 2 0.92 249.56 0.67 0.88 0.44 348.96 88.10 0.53 
Input 3 0.94 206.94 80.03 0.92 0.88 161.56 78.74 0.86 
Input 4 0.98 113.58 30.54 0.98 0.90 146.65 41.12 0.92 
 CNN–SVR 
Input 1 0.39 672.47 112.71 −1.74 0.53 319.50 77.13 −0.30 
Input 2 0.52 594.50 105.10 −0.80 0.61 290.62 73.21 0.17 
Input 3 0.67 495.20 84.04 0.01 0.88 162.58 50.29 0.82 
Input 4 0.71 465.26 79.67 0.19 0.89 153.53 46.03 0.84 
 RF 
Input 1 0.59 549.28 130.22 0.10 0.40 361.50 110.34 0.34 
Input 2 0.77 411.19 128.87 0.60 0.41 357.78 118.99 0.40 
Input 3 0.93 221.43 118.84 0.91 0.81 203.62 126.01 0.78 
Input 4 0.96 165.59 75.83 0.95 0.86 175.37 78.83 0.86 
 SVR 
Input 1 0.42 653.59 112.88 −0.88 0.56 310.22 78.29 0.21 
Input 2 0.51 601.26 109.66 −0.51 0.62 287.58 77.04 0.35 
Input 3 0.73 445.72 81.60 0.35 0.86 175.15 56.62 0.80 
Input 4 0.76 425.93 0.82 0.43 0.87 166.59 57.77 0.82 
 ANN 
Input 1 0.42 655.84 128.38 −0.42 0.58 303.25 92.85 0.40 
Input 2 0.62 536.48 118.48 0.31 0.57 305.42 91.90 0.56 
Input 3 0.77 415.11 112.58 0.67 0.80 206.33 69.64 0.87 
Input 4 0.89 286.46 97.26 0.87 0.82 199.48 95.22 0.88 
Training
Testing
R2RMSEMAENSER2RMSEMAENSE
 CNN–RF 
Input 1 0.87 321.19 78.38 0.80 −0.04 474.53 114.44 0.24 
Input 2 0.92 249.56 0.67 0.88 0.44 348.96 88.10 0.53 
Input 3 0.94 206.94 80.03 0.92 0.88 161.56 78.74 0.86 
Input 4 0.98 113.58 30.54 0.98 0.90 146.65 41.12 0.92 
 CNN–SVR 
Input 1 0.39 672.47 112.71 −1.74 0.53 319.50 77.13 −0.30 
Input 2 0.52 594.50 105.10 −0.80 0.61 290.62 73.21 0.17 
Input 3 0.67 495.20 84.04 0.01 0.88 162.58 50.29 0.82 
Input 4 0.71 465.26 79.67 0.19 0.89 153.53 46.03 0.84 
 RF 
Input 1 0.59 549.28 130.22 0.10 0.40 361.50 110.34 0.34 
Input 2 0.77 411.19 128.87 0.60 0.41 357.78 118.99 0.40 
Input 3 0.93 221.43 118.84 0.91 0.81 203.62 126.01 0.78 
Input 4 0.96 165.59 75.83 0.95 0.86 175.37 78.83 0.86 
 SVR 
Input 1 0.42 653.59 112.88 −0.88 0.56 310.22 78.29 0.21 
Input 2 0.51 601.26 109.66 −0.51 0.62 287.58 77.04 0.35 
Input 3 0.73 445.72 81.60 0.35 0.86 175.15 56.62 0.80 
Input 4 0.76 425.93 0.82 0.43 0.87 166.59 57.77 0.82 
 ANN 
Input 1 0.42 655.84 128.38 −0.42 0.58 303.25 92.85 0.40 
Input 2 0.62 536.48 118.48 0.31 0.57 305.42 91.90 0.56 
Input 3 0.77 415.11 112.58 0.67 0.80 206.33 69.64 0.87 
Input 4 0.89 286.46 97.26 0.87 0.82 199.48 95.22 0.88 

The bold values are the best input combinations to the models.

Table 4

Final results of all models for Kantamal and Kesinga stations

Kantamal station
Training
Testing
R2RMSEMAENSER2RMSEMAENSE
CNN–RF 0.99 96.36 34.63 0.99 0.95 172.83 54.19 0.95 
CNN–SVR 0.98 150.83 48.75 0.98 0.92 226.26 56.31 0.92 
RF 0.97 179.13 99.30 0.97 0.93 215.09 109.60 0.91 
SVR 0.99 112.08 37.98 0.99 0.91 239.31 58.69 0.91 
ANN 0.87 422.00 133.61 0.85 0.86 298.48 108.58 0.86 
Kesinga station
Training
Testing
R2RMSEMAENSER2RMSEMAENSE
CNN–RF 0.97 157.29 33.13 0.96 0.91 137.25 41.06 0.92 
CNN–SVR 0.95 195.71 33.13 0.93 0.91 143.49 44.64 0.87 
RF 0.96 173.92 76.95 0.95 0.88 160.50 77.56 0.88 
SVR 0.97 158.23 31.07 0.96 0.88 158.47 43.68 0.90 
ANN 0.90 265.71 81.19 0.89 0.84 186.35 72.99 0.89 
Kantamal station
Training
Testing
R2RMSEMAENSER2RMSEMAENSE
CNN–RF 0.99 96.36 34.63 0.99 0.95 172.83 54.19 0.95 
CNN–SVR 0.98 150.83 48.75 0.98 0.92 226.26 56.31 0.92 
RF 0.97 179.13 99.30 0.97 0.93 215.09 109.60 0.91 
SVR 0.99 112.08 37.98 0.99 0.91 239.31 58.69 0.91 
ANN 0.87 422.00 133.61 0.85 0.86 298.48 108.58 0.86 
Kesinga station
Training
Testing
R2RMSEMAENSER2RMSEMAENSE
CNN–RF 0.97 157.29 33.13 0.96 0.91 137.25 41.06 0.92 
CNN–SVR 0.95 195.71 33.13 0.93 0.91 143.49 44.64 0.87 
RF 0.96 173.92 76.95 0.95 0.88 160.50 77.56 0.88 
SVR 0.97 158.23 31.07 0.96 0.88 158.47 43.68 0.90 
ANN 0.90 265.71 81.19 0.89 0.84 186.35 72.99 0.89 

Bold values are the values of the best model's results.

Figure 8

Performance evaluation graphs for train test split for R2, NSE, RMSE and MAE at (a) Kantamal station and (b) Kesinga station.

Figure 8

Performance evaluation graphs for train test split for R2, NSE, RMSE and MAE at (a) Kantamal station and (b) Kesinga station.

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Figure 9

Performance evaluation graphs for RF parameters in CNN–RF at the Kantamal station and the Kesinga station.

Figure 9

Performance evaluation graphs for RF parameters in CNN–RF at the Kantamal station and the Kesinga station.

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Figure 10

Performance evaluation graphs for SVR parameters in CNN–SVR at the Kantamal station and the Kesinga station.

Figure 10

Performance evaluation graphs for SVR parameters in CNN–SVR at the Kantamal station and the Kesinga station.

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Training and testing

There is no study about the division of data into training and testing which verifies any specific division of data into training and testing. The division has been varied in different studies. In this study, data is tested for different data division percentages for training and testing for hybrid models. From Figure 8, it can be seen that the results of CNN–RF are either better or the same by dividing data into 50–50% as compared to 60–40% division for both stations, while the results of CNN–SVR are slightly better with 60–40% division at Kantamal station in terms of RMSE and MAE only. However, the results of CNN–SVR are better with 50–50% division at Kesinga station. As most of the results are better with 50–50% division, it is chosen in this study as training–testing data division.

Input selection

This study consists of the forecasting based on multivariate modelling procedures. Two more variables, rainfall(R) and water level(L), are added with discharge (Q) for model development. Different input combinations, input 1 (Q), input 2 (R, Q), input 3 (L, Q) and input 4 (R, L, Q), are tested with all models to analyse the relationship of these variables as input for discharge forecasting. The accuracy of all models is low for input 1 as shown in Tables 2 and 3. With adding rainfall as input in input 2, accuracy is improved for some models while it was not affected for other models. Adding water level as input to discharge in input 3 improves the accuracy of all models to a high extent. Results are better when all three variables are used as input for forecasting. Adding rainfall and water level separately with discharge improves the accuracy of models shown in Tables 2 and 3; however, water level had more impact than rainfall on the model's accuracy. So, all variables together are more effective for model performance and were chosen for this study.

Model parameters sensitivity analysis

All ML models contain many parameters which derive the model's performance. These parameters derive the accuracy of models. Some parameters may be more sensitive than other parameters, and some parameters may be insensitive in a model's performance. To analyse all these types of parameters, sensitivity analyses are performed on CNN–RF and CNN–SVR.

The RF is mainly constructed with n-estimators, depth of tree, minimum sample split, maximum features, minimum sample leaf and criterion. The depth of the tree represents the longest path between the root node and the leaf node. N-estimator represents the number of trees in a model. Minimum sample split (Min_sample_split) represents the minimum number of observations required in a given node in order to split it. Maximum features (Max_features) are the maximum number of input features for each tree in a model. The minimum sample leaf (Min_sample_leaf) specifies the number of samples that should be present in the leaf node after splitting the node.

The SVR model's accuracy depends on the values of C, gamma and epsilon mainly. The values of these parameters depend on the data and change with different sets of datasets and their length. C is a regularization parameter which represents the trade-offs between the expected errors and the model's complexity. A higher value of C means a smaller margin of decision functions, and a lower value of C means a larger margin of decision functions. Gamma defines the distance of influence of a single training point. The low value of gamma means the distance is far, and the high value means the distance is close. Epsilon defines the range of prediction from support vectors up to which no penalty is applied in training loss.

The main parameters in CNN are the number of layers, the number of nodes in each layer, batch size and epochs. A number of hidden layers and a number of nodes in the hidden layer are set experimentally. Batch size represents the group of numbers of datasets. These groups are called batches and the model is trained on a sample of the same size of batches. Epochs are the number of training of the model on the whole dataset.

To find out the sensitive parameters, the accuracy of models is tested by changing one parameter value and keeping the other parameter value the same. The CNN model in both CNN–RF and CNN–SVR is developed with one input layer, two hidden layers, one flattening layer and one output layer. The model is tested with different numbers of hidden layers, and it is found that more hidden layers do not improve the model's accuracy. Also, changing the number of nodes in these layers is not improving the model. So, the hidden layers are chosen as two layers and the number of nodes is taken as 128 for both models for both stations.

RF has many parameters for model fitting such as n-estimator, minimum sample leaf, minimum sample split, maximum depth, and maximum features. In all these parameters, minimum sample split and minimum sample leaf have no role in the model's performance for both stations. The minimum value of the sample split is two, which is the default value for the model, and the minimum value for the sample leaf is two. The accuracy of the model increases with increasing the value of the n-estimator up to a certain value, and after that it becomes constant. As RF has a bootstrap technique, the accuracy of the model can vary with every run of the model for the same value of n-estimator, but this variation is very small. The performance of CNN–RF with an n-estimator of more than 100 is the same for Kantamal station while it is reduced for Kesinga station. So, the n-estimator value is taken as 100 in model development. As the model consists of three input variables, the maximum feature value goes up to 3. The range of maximum depth varies from 1 to 10 and it is found that after a value of 5, the results are the same. From Figure 9, it can be seen that maximum depth is more sensitive for CNN–RF than other parameters, followed by n-estimator and maximum features for both stations. The chosen values of the n-estimator, maximum features and maximum depth are 100, 3 and 10, respectively, for both models (Figure 9). The results are shown in the form of R2 and are found to be the same using other evaluation matrices such as RMSE, MAE and NSE.

The SVR consists of three important parameters, which are C, gamma and epsilon. Epsilon has no role in the model's performance. So, it can be taken as 0 or neglected. C has a large effect on model performance. Gamma is taken as 0.001 for C, and epsilon is 0 for testing both C and gamma. It can be seen from Figure 10 that at a lower value of C, accuracy is very low and increases with increasing the value of C. The accuracy of the model depends more on the C value than the gamma value, but gamma is also important to increase the accuracy of the model, as shown in Figure 10. So, both parameters are sensitive to the model's performance. A value of C of more than 10,000 is suitable for model performance for Kantamal and Kesinga stations. C is taken as 10,000 for both stations. Increasing the value of C further does not contribute to increasing the accuracy of the model, as shown in Figure 10. The value of C is taken as 25,000 for testing gamma. The model's accuracy increases with increasing the gamma value up to a certain value of gamma, and then it starts decreasing. The model's accuracy is high at a value of gamma equal to 0.1 for the Kantamal station and 0.05 for the Kesinga station. Only two parameters are sensitive and to be considered for this study. The results are shown in the form of R2 and it follows the same for RMSE, MAE, and NSE.

Forecasting results of developed models

The evaluation methods interpret the model's accuracy. The training and test results are good for all models. Results are acceptable for all models for both stations (Table 4). However, the results of CNN–RF are better than other models for training and testing for both stations in terms of all evaluation methods. The R2 values are 0.95, 0.92, 0.93, 0.91, and 0.86 for CNN–RF, CNN–SVR, RF, SVR and ANN, respectively, for Kantamal station. Similarly, the R2 values are 0.91, 0.91, 0.88, 0.88, and 0.84 for CNN–RF, CNN–SVR, RF, SVR, and ANN, respectively, for Kesinga station. A similar trend is followed for RMSE values for both stations. However, MAE results are better for CNN–SVR and SVR models than RF mode for both stations. It is concluded that the SVR model is more accurate for moderate flows while the RF model works on high flows. Also, it is clear that CNN improves the accuracy of models, as shown in Table 4. However, its impact as a feature extraction technique is more on the RF model as compared to the SVR model.

Figures 11 and 12 show the scatter plot for all models for Kantamal and Kesinga stations, respectively. For Kantamal station, the CNN–RF and CNN–SVR are able to forecast high flows also and are less scattered as compared to other models, as shown in Figure 11. But CNN–SVR has one unexpectedly high prediction and is a little more scattered for medium and peak flows. For Kesinga station, CNN–RF and CNN–SVR are almost the same, but medium flows are less scattered for CNN–RF, which made this model more accurate. Both developed models are better than other models for forecasting. Figures 13 and 14 show the observed and forecasting discharge for Kantamal and Kesinga stations, respectively. The peak flow forecast is good for Kantamal station but not very good for Kesinga station. It is showing some over-predictions for peak flows. It is happening because the peak flows in the training dataset are higher and have higher values as compared to the test dataset, and this limitation can be improved using more data.
Figure 11

Scatter plot of observed and forecasted data at the Kantamal station.

Figure 11

Scatter plot of observed and forecasted data at the Kantamal station.

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Figure 12

Scatter plot of observed and forecasted data at the Kesinga station.

Figure 12

Scatter plot of observed and forecasted data at the Kesinga station.

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Figure 13

Plot of observed and forecasted data at the Kantamal station in left panel and observed minus forecasted data in the right panel.

Figure 13

Plot of observed and forecasted data at the Kantamal station in left panel and observed minus forecasted data in the right panel.

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Figure 14

Plot of observed and forecasted data at the Kesinga station in left panel and observed minus forecasted data in the right panel.

Figure 14

Plot of observed and forecasted data at the Kesinga station in left panel and observed minus forecasted data in the right panel.

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Significance, limitations and future scope

Accurate flood forecasting is crucial for meeting downstream demands, including agricultural, industrial, and drinking water needs. The present study highlights the effectiveness of hybrid machine learning models compared to simpler models, providing enhanced streamflow forecasts. The implications of this research extend to enhancing proper water resource planning and management, crucial for sustainable environmental protection and addressing the challenges posed by climate change. The developed models show great potential for forecasting. The CNN performs well as a feature extraction technique for improving the performance of RF and SVR models for forecasting. Three input features (rainfall, discharge, and water level) are used in this study. More input features can be examined for flood forecasting, such as temperature and evapotranspiration. The influence of training–testing data division on models is analysed to fix the division of data for this study. This is limited to this study because the division may be different for different input features and in different study areas. In this study, values of hyperparameters are selected based on the experiment by keeping other hyperparameters constant while selecting one. This process does not give the ideal combination of hyperparameters' values. Optimization techniques can be used to solve this problem and it can save some computational time. In future research, expand the present study by analysing historical land cover changes in the basin over the past three decades, investigating their relationship with streamflow patterns and water resource management. Additionally, we plan to explore the reciprocal impact between land use alterations and streamflow dynamics, emphasizing their role in environmental protection and climate change challenges. Integrating these aspects will enhance our understanding of streamflow forecasting factors and aid in proactive water resource planning for sustainable environmental management amidst evolving climate conditions.

This study investigates flood forecasting using hybrid models in the Mahanadi River Basin. This study's significance lies in its application for accurate streamflow forecasting, crucial for meeting downstream demands such as agricultural, industrial, and drinking water needs. This work highlights the effectiveness of hybrid machine learning models compared to simpler models, offering improved streamflow forecasts.

The present study has been conducted on flood forecasting using two hybrid machine learning models based on CNN, namely CNN–RF (combining CNN with RF) and CNN–SVR (combining CNN with SVR). The performance of the models has been assessed using statistical indicators including R2, RMSE, MAE, and NSE. The two hybrid models have been evaluated using various distinct data splits for training and testing. From the results, it can be concluded that a discernible trend has been observed: the CNN–SVR model shows higher performance with a 60:40 split for RMSE and MAE only at the Kantamal station. Conversely, the 50:50 split gives better performance of two models at both stations. Furthermore, the results of input data selection on the Mahanandi River basin indicate that among the four input models, the input 4 model (all three variables together) shows a greater influence on the model outputs. Sensitivity analyses of model parameters help in finding the effective parameters and their values for the model's best performance. Among the two models, CNN–RF shows higher performance in two stations compared to the CNN–SVR and other models. Therefore, CNN can be considered as a valuable feature extraction technique for flood forecasting, with the potential to enhance overall predictive results.

While this study encourages the use of developed models for other works, some aspects can be improved further. A 20-year dataset is sufficient for forecasting but more length of data may be useful for improving the hybrid models' results especially for peak flows. Optimization techniques can be used for these hybrid models for better performance and reducing time consumption for model development. Also, more variables like temperature and evaporation can be explored for model development. Future work will include the use of optimization techniques, more weather data, and the exploration of more ML models for further hybridization for flood forecasting.

We gratefully acknowledge the Central Water Commission of India and the Indian Meteorological Department of India for their support of the data.

All relevant data are included in the paper or its Supplementary Information.

The authors declare there is no conflict.

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