Discharge estimation in compound channels with converging and diverging floodplains using an optimised Gradient Boosting Algorithm

Q_fb

rate of flow of floodplain

Q

total discharge in the compound channel

Q_mc

main channel discharge

S_o

bed slope of the channel

n

Manning's coefficient

h

bank full depth of the main channel

B

width of the main channel

F_mc

main channel friction factor

F_fp

floodplain friction factor

F_f

relative friction factor

H

total flow depth over the main channel

A_R

area ratio

R_r

relative hydraulic radius

X_R

relative longitudinal distance

α

width ratio

β

relative flow depth

δ*

flow aspect ratio of the main channel

θ

angle of convergence and divergence

R²

coefficient of determination

L

length of the main channel

ANFIS

adaptive neuro-fuzzy interface systems

ANN

artificial neural networks

CatBoost

categorical boosting

DCM

Divided Channel Method

GBDT

Gradient Boosting Decision Trees

GEP

gene expression programming

LightGBM

light gradient boosting machine

MAPE

mean absolute percentage error

MARS

multivariate adaptive regression splines

ML

machine learning

PSO

particle swarm optimisation

RMSE

root mean square error

SHAP

SHapley Additive exPlanations

XGBoost

eXtreme Gradient Boosting

Throughout history, civilisations have established settlements close to rivers due to the advantageous combination of fertile arable land and convenient access to water resources for a range of human activities. In nature, most of the rivers are in the form of compound channels because of a combination of natural geomorphological processes and human settlement. Due to the continuous establishment of settlements along the riverbanks, the width of the river changes, becoming narrower in certain areas and wider in others. This results in a varying or fluctuating shape of the floodplain, known as non-prismatic floodplain. Non-prismatic floodplain in combination with the main channel forms a non-prismatic compound channel. During a flood water level rises and overflows the river bank and inundates nearby floodplains; therefore, the prediction of river discharge is crucial for flood defence management, water resource management, environmental protection, hydropower generation, infrastructure design and different research purposes.

During floods, estimating discharge becomes highly challenging, especially in the case of compound channel flow. Numerous researchers have endeavoured to develop empirical models for predicting discharge in prismatic compound channels. Among these approaches, the Single Channel Method (SCM) simplifies the entire section as uniform with a single roughness factor, often resulting in an overestimation of discharge. To address this limitation, researchers have explored various Divided Channel Methods (DCMs), which consider different interface planes originating from the junction regions between the main channel and floodplain. These methods, such as those proposed by Knight & Demetriou (1983), Myers (1987), Patra & Khatua (2006) and Khatua et al. (2012), aim to divide the section into subareas, thereby accounting for variations in apparent shear values. A novel approach, based on the Divided Channel Method (DCM), was introduced by Lambert & Myers (1998), wherein a correction weighting factor is applied to the computational velocity magnitude based on division subsections along vertical and horizontal lines. In the Weighted Divided Channel Method (WDCM), it is assumed that momentum exchange and apparent shear stress quantities are known on each imaginary boundary. This method calculates discharge by multiplying the mean velocity at each subsection by the corresponding area, determined from the vertical division line.

In quantifying momentum transfer, Khatua et al. (2012) emphasised the importance of including/excluding interface length, which significantly affected discharge predictions for their channel. While the statistical analysis of flow data is occasionally used for river discharge forecasting, its practical application in real-world scenarios is limited. However, it can be employed to predict intended flow behaviour (Kilinc et al. 2000). Hydrodynamic and numerical models have started to replace conventional methods for modelling river floods, offering simulation capabilities. Nevertheless, these models are complex due to the multitude of factors requiring consideration in selecting the appropriate model for predicting river floods (Shrestha 2005). The Exchange Discharge Method (EDM), a 1D method for estimating discharge in compound channels, was introduced by Bousmar & Zech (1999), requiring two parameters: the turbulence exchange factor and the geometrical exchange correction factor. Abril & Knight (2004) anticipated the stage–discharge relationship using a depth-averaged method and finite element analysis, necessitating the calibration of three parameters: mean velocity, transverse eddy viscosity and local flow resistance coefficient. Liao & Knight (2007) used an analytical formula to determine the stage–discharge relationship in straight trapezoidal open channels, finding a good coincidence between analytical and experimental rating curves, albeit with the primary drawback of algebraic complexity when splitting the cross-section into several panels. Maghrebi (2006) employed a Single Point of Velocity Measurement (SPM) to calculate discharge in a rectangular laboratory flume, validating the model using data from the UK's Severn River, which demonstrated the method's reliability. Sun & Shiono (2009) estimated rating curves by employing an experimental model in straight compound channels, with and without one-line emergent vegetation along the floodplain boundary, developing novel friction factor formulas based on flow characteristics and vegetation density for both scenarios. Al-Khatib et al. (2013) computed discharge in compound symmetrical channels using data from multiple experiments and regression analysis. Yang et al. (2014) applied the momentum transfer coefficient to forecast discharge distributions of floodplains and the main channel. Fernandes et al. (2015) estimated the flow in the compound open channels using different stage–discharge predictors. Devi et al. (2021) developed an analytical method for predicting depth-averaged velocity in prismatic compound channels, while Das et al. (2022) proposed a multivariable regression model for predicting discharge across different sections of diverging compound channels.

Over the last six decades, many authors have investigated the flow of compound channels (Sellin 1964; Wormleaton et al. 1982; Knight & Demetriou 1983; Knight et al. 1989; Najafzadeh & Zahiri 2015; Devi et al. 2016). A few authors have investigated the non-prismatic compound channel. The very first investigation in skewed angles was conducted by James & Brown (1977) with diverse skew angles and observed that if the main channel is converging it increases the water level in the floodplain and when the main channel is diverging it reduces the water level in floodplain. Chlebek (2009) analysed the consequence of energy slope and behaviour in skewed non-prismatic compound channels. Bousmar (2002) was the first to perform an experimental study on the compound channel having converging floodplains with three different converging angles. Later, the consequence of convergence in an asymmetric compound channel with sharp narrowing on the floodplain with an angle of convergence of 22° was explored by Proust (2005). Bousmar et al. (2006) investigated diverging compound channels having two different diverging angles.

In general, the rate of flow in the main channel tends to be higher than in the floodplain. The interaction between the swift-moving water in the main channel and the slower-moving water in the floodplain creates significant flow resistance, making it challenging to predict discharge accurately. Due to these interactions exchange of mass and momentum is seen at the transition point and losses of momentum are observed due to this interaction. Changes in the cross-sectional area of the compound channel can result in a transition in the state of flow from being uniform to becoming non-uniform, which adds complexity to the hydraulic analysis. This transition has been addressed in the works of (Bousmar & Zech 2004; Rezaei & Knight 2009, 2011; Proust et al. 2010; Das 2018). Bousmar & Zech (2004) introduced a lateral distribution model (LDM) for uniform flow, which they subsequently adapted to account for non-uniform flow conditions. Rezaei (2006) experimented with the convergent compound channel and created an analytical model for the determination of the water surface profile. Using the first rule of thermodynamics, Proust et al. (2010) created a 1-D model to forecast the loss of energy for each subsection which are, the left floodplain, main channel and right floodplain. Yonesi et al. (2013) examined the effect of the roughness of floodplains on overbank flow in non-prismatic compound channels. Naik & Khatua (2016) used non-dimensional geometric parameters and developed a multivariate regression model to forecast the water level profile for compound channels. Das & Khatua (2018) developed two different non-linear regression equations for calculation flow resistance in converging and diverging compound channels. Das & Khatua (2019) proposed a regression model for predicting water surface profile in diverging compound channels.

It is complicated to estimate the discharge of the compound channel because of its complex geometry, complex flow patterns and the existing method requires complex calculation and provides poor results for non-prismatic compound channels. In the last thirty years, a range of machine learning (ML) algorithms have been adopted for developing the model for estimating the discharge of channels. Zahiri & Dehgahani (2009) using ANN calculated the discharge in the compound channel. Later Azamathulla & Zahiri (2012) used the GEP and M5 Tree model to successfully estimate the flow in a compound channel section. Najafzadeh & Zahiri (2015) computed the discharge in a prismatic compound channel using the neuro-fuzzy group method for data handling (NF-GMDH) and found that the method has a better predictive ability compared to the genetic programming, non-linear regression and the vertically DCM. Zahiri & Najafzadeh (2018) proposed gene expression programming (GEP), model tree (MT) and the evolutionary polynomial regression (EPR) model for predicting discharge in compound channel sections using three non-dimensional parameters, such as relative flow depth, coherence parameter and discharge computed by the vertical division method. Khuntia et al. (2018) developed an ANN model for boundary shear stress distribution in prismatic compound channels and found that the developed model produces better results than existing empirical equations. Das et al. (2018, 2020) used soft computing techniques ANFIS and GEP to estimate the rate of flow of compound channels. Shekhar et al. (2023) used hybrid ANN-PSO and MARS soft computing techniques and compared them with traditional and empirical methods.

Gradient Boosting Decision Tree (GBDT) algorithms (XgBoost, CatBoost, LightGBM) have been used in different hydrologic and hydraulic modelling (Yu et al. 2020; Demir & Sahin 2023; Eini et al. 2023). However, the applicability of these ML approaches is not explored in the domain of compound channels. So, in the present manuscript, an attempt has been made to check the usefulness of six ML models, namely Xgboost, LightGBM, CatBoost, PSO-XgBoost, PSO-LightGBM and PSO-CatBoost, in discharge prediction for compound channels having converging and diverging flood.

A total of 290 datasets from experiments on non-prismatic compound channels were collected from various studies. Table 1 provides a range of datasets used to build ML models, 75% of the data (218 datasets) were randomly chosen for training, while the remaining data were reserved for validation/testing. Based on insights from previous research conducted by Das et al. (2018, 2020) and Yonesi et al. (2022), a set of critical parameters have been identified as pivotal for predicting the discharge of non-prismatic compound channels. Using Buckingham's theorem, nine dimensionless parameters have been obtained to model discharge as given in the following equation.

PCA is a multivariate statistical technique commonly employed for statistical analysis, specifically in the context of dimensionality reduction through factor analysis. This method organises complex datasets into uncorrelated variables, which are linear combinations of the original variables, resulting in a significant simplification of the information contained in the original data (Pandey et al. 2023). To assess the appropriateness of the dataset for PCA, the Kaiser–Meyer–Olkin (KMO) and Bartlett's spherical tests were utilised, with criteria set at KMO > 0.5 and a significance level of p < 0.05 in Bartlett's test (Mukherjee & Singh 2022). Depending on the absolute values, the component loadings are classified as strong (>0.75), moderate (0.5–0.75) and weak (0.3–0.5) (Wang et al. 2017).

GBDT is an ensemble method that was introduced by Friedman (2001). GBDTs use a boosting mechanism to create a robust learner through the combination of numerous weak learners characterised by relatively lower accuracy This paper focuses on applying three newly introduced GBDT modifications, namely XGBoost, CatBoost and LightGBM, to develop predictive models for discharge estimation in a compound channel with converging and diverging flood plain. Subsequent sections provide descriptions and highlight the key features of these algorithms.

Ke et al. (2017) introduced the Light Gradient Boosting Machine (LightGBM) technique, which gained popularity due to its efficiency and accuracy in gradient boosting. It employs various techniques to enhance its computational power and predictive performance. One notable feature is the histogram algorithm, which discretises continuous feature values into integers and constructs histograms to guide the decision tree-building process. Additionally, LightGBM utilises a leaf-wise algorithm that selects the leaf with the highest splitting gain among existing leaves for further division. To mitigate the risk of overfitting, LightGBM incorporates a maximum depth constraint on this leaf-wise approach, ensuring efficiency and robustness in model training. Overall, LightGBM's combination of innovative algorithms and controls makes it a widely recognised and efficient gradient boosting model in the ML community.

Hyperparameter tuning is of paramount significance in ML algorithms as it governs the behaviour of training algorithms and plays an important role in improving model performance. In this paper, the PSO approach is applied for fine-tuning hyperparameters of XGBoost, LightGBM and CatBoost ML algorithms. The PSO algorithm relies on various controlling parameters, including fitness criteria (such as RMSE, MSE and R²), local coefficient (c1), global coefficient (c2), inertia coefficient (w), maximum iterations and population/swarm size (s). Table 2 provides a detailed overview of the PSO control parameters, the hyperparameters subjected to tuning, explanations of these parameters and the specified value ranges for optimising each ML model.

Various statistical parameters were employed for quantitative comparisons to assess the performance of ML models (Najafzadeh & Oliveto 2020; Najafzadeh & Anvari 2023). The performance evaluation parameters considered in the study are given below.

The significance of uncertainty, reliability and resilience analyses in evaluating model performance is paramount for ensuring the credibility and utility of predictive models (Saberi-Movahed et al. 2020). Uncertainty analysis aims to define a reliable uncertainty interval, denoted as U95, indicating the range within which the true outcome of an experiment is likely to fall. U95 is estimated based on errors in the experimental measurement process, with the understanding that in around 95 out of 100 trials, the true outcome would lie within this interval. The U95 formula involves the weighted summation of squared differences between observed and predicted values. Reliability analysis assesses a model's overall consistency, expressed as a percentage computed through the relative average error (RAE). The reliability factor is set to 1 if RAE is less than or equal to a threshold (typically 20%) and the reliability of the model is determined as the average of these factors. Resilience analysis, related to reliability, is expressed as a percentage and evaluates a model's ability to recover from inaccurate predictions. Collectively, these analyses contribute to a comprehensive understanding of model behaviour, empowering decision-makers to make more informed choices and enhancing the overall robustness and trustworthiness of predictive models in various domains.

SHAP is a feature attribution method rooted in game theory. It addresses the challenge of the inherent black-box characteristics of certain ML models by introducing a reliable interpretability framework (Lundberg & Lee 2017; Chang et al. 2022). SHAP employs Shapley values as a means to quantitatively express the individual contributions of input features to model output, thus providing transparency and understanding of model behaviour. In this study, SHAP analysis has been performed on the best models (PSO-CatBoost and PSO-XgBoost) to find the contribution of each input feature for predicting discharge in a compound channel having converging and diverging flood plain.

Recent years have witnessed substantial advancement in the practical application of the ML algorithm for regression tasks. The traditional ML framework involves crucial stages such as data preprocessing, model selection, development, evaluation and deployment. Hyperparameter optimisation is an essential element of the ML algorithm and effective optimisation of these hyperparameters is crucial for enhancing ML algorithm performance. In this study, XGBoost, LightGBM and CatBoost were utilised for predicting discharge in a compound channel and PSO was used to fine-tune their hyperparameters, aiming to boost their effectiveness in the task. Subsequently, three hybrid models, PSO-XGBoost, PSO-LightGBM and PSO-CatBoost were developed, incorporating PSO for hyperparameter optimisation. These models were evaluated by comparing their performance to models trained with default hyperparameters, providing insights into the efficacy of PSO in optimising the algorithms. This section incorporates a detailed discussion of results obtained from the present models and existing models for the estimation of discharge in a compound channel of converging and diverging flood plain.

To determine the most contributing parameter for the estimation of discharge in a compound channel having a converging and diverging flood plain, PCA was performed. Prior to performing the PCA, Bartlett's test and KMO test were performed on all the parameters to assess its aptness for the PCA analysis. The significance value of Bartlett's test on the input dataset was close to zero and the KMO test was 0.549 showing the appropriateness of the dataset for PCA analysis. PCA extracts the essential parameter for representing information within the whole dataset, four principal components (PC1, PC2, PC3 and PC4) reflecting the total variance of 78.16%, as presented in Table 3. PC 1 explains 31.07% of the variance within the variables. Area ratio (A_R) and width ratio (α) are loaded above 0.75 which is strong loading (highlighted in bold, Table 3), flow aspect ratio (δ*) and converging or diverging angle (θ) exhibit moderate loading and other parameters have weak loading. PC2, PC3 and PC4 explain variance variables of 19.72,15.001 and 1.112%, respectively. Relative longitudinal distance (X_R) and bed slope of the channel (S₀) exhibit strong loading for PC 3 and PC 4, respectively. PCA analysis suggests that the variables F_f, S₀, δ*, α, X_R and θ play a significant role in explaining the variance in the dataset as they have high loadings on the primary principal component (PC 1). However, in this study, all the input parameters are selected for modelling discharge as the cumulative variability of all the principal components is 78.16% to have a more efficient model.

Performance evaluation of ML models is critical for assessing the prediction capability of the models. In the present study, ML algorithms (XgBoost, CatBoost and LightGBM) with a default value of hyperparameters have been developed for the prediction of discharge. The PSO algorithm was used for the optimisation of hyperparameters and developed hybrid models, namely PSO-XgBoost, PSO-CatBoost and PSO-LightGBM. All the base models were compared with their hybrid model counterparts to assess the effectiveness of optimisation using PSO. Different statistical performance parameters, such as RMSE, R² and MAPE, have been used for assessing the comparative effectiveness of models.

The XgBoost model has been developed using five important and effective hyperparameters for the learning processes, namely n_estimators, learning_rate, max_depth, max_delta_step and min_child_weight. Default values of these hyperparameters have been taken for the development of the XgBoost model, as given in Table 4. The PSO algorithm was used for fine-tuning the hyperparameters of the XgBoost. The best hyperparameters have been chosen by performing 100 iterations under different hyperparameter guesses and the best hyperparameters, are presented in Table 4.

In order to check the efficacy of hyperparameter optimisation using PSO, it is compared with the default value of the model in the previous section. The modified algorithm finetunes the hyperparameters of XgBoost, CatBoost and LightGBM models to minimise the objective function (i.e. RMSE for the present case). The default hyperparameters of XgBoost, CatBoost, LightGBM and optimised hyperparameters using PSO have been given in Tables 4–6, respectively. PSO optimisation enhances the performance of the models, as observed in Table 7. All models developed in the study using ML approaches perform reasonably well for predicting discharge in the compound channel with converging and diverging flood plains. XgBoost and CatBoost model performance are excellent and further enhanced by the application of the PSO optimising algorithm. The optimised hyperparameters of the models capture the relation between input parameters and discharge more accurately for the prediction of discharge in a compound channel having converging and diverging floodplains. The best-performing model based on R² value in the testing phase is PSO-XgBoost while PSO-CatBoost is in the training phase (highlighted in bold, Table 7). However, the error indices, such as RMSE and MAPE values, are lower for the PSO-CatBoost model in the training stage while in the testing stage, it is lower for the PSO-XgBoost model. The PSO-CatBoost model performs better than other ML models used in the study for all data, so it is considered a better model for the prediction of discharge in a compound channel.

The philosophy behind using these four empirical equations is to assess the applicability of the existing methods for the estimation of discharge in the compound channel with converging and diverging flood plains. These empirical equations consider the width ratio and aspect ratio as the input parameters to compute %Qmc. Though these methods are used to calculate the discharge in a prismatic compound channel section, the efficacy of these models is not tested for non-prismatic compound channels. So, for comparison purposes, the aforementioned methods are used. The present study highlighted that the existing empirical equations are not accurate for estimating discharge in a non-prismatic compound channel with a diverse range of datasets used in this study. So, there is a requirement of the other models, for accurate prediction of discharge in compound channels with converging and diverging flood plains.

The performance of all ten models i.e., present models Xgboost, LightGBM, CatBoost, PSO-XgBoost, PSO-LightGBM, PSO-CatBoost and four empirical methods, i.e., Knight & Demetriou (1983), Khatua & Patra (2007), Devi et al. (2016) and Das et al. (2022) for different ranges of width ratio and relative flow depth are shown in Tables 8 and 9. This assessment clearly specifies the appropriateness of different models for different input ranges of width ratio and relative flow depths. All present models developed in the study perform well for all ranges of width ratio (α) and relative flow depth (β). For the width ratio (α) <2, the PSO-XgBoost model has lower values of RMSE and MAPE while for width ratio (α) > 2, the PSO-CatBoost model has lower values of RMSE and MAPE. Out of all the models used in the study, PSO-CatBoost performs better for the width ratio (α) > 2 while PSO-XgBoost performs better for the width ratio (α) < 2. It is evident from in Table 8 that the PSO-CatBoost model has minimum values of RMSE and MAPE for all ranges of relative flow depth (β). NSE and Index of agreement (Id) values for both PSO-CatBoost and PSO-XgBoost are similar and close to 1 for all the range of width ratio (α). NSE is negative for all the empirical methods all ranges of width ratio and relative flow depth, which shows that predicted discharge by empirical methods is unsatisfactory as it suggests that the observed mean is a better predictor than the model. The NSE value of all the developed ML models in the present study is close to 1 for all ranges of width ratio and relative flow depth, which suggests that developed models have more prediction capability. However, LightGBM has lower values of NSE ranging from 0.97 to 0.65 for different ranges of width ratio and relative flow depth, but still better than the empirical models. Despite LightGBM exhibiting a lower NSE value, which ranges from 0.97 to 0.65 across various width ratios and relative flow depths, it still outperforms the empirical models. The index of agreement (I_d) values is close to one across different ranges of width ratios and relative flow depths, which suggests a perfect match. The performance of empirical models is relatively acceptable, indicated by the index of agreement (I_d) value, particularly for width ratios less than 1.5. However, for other ranges of width ratio and relative flow depth, the empirical models exhibit lower Index of Agreement values. ML models developed in the present study have also outperformed M5, GEP and EPR models developed in the study of Zahiri & Najafzadeh (2018) for the estimation of discharge in compound channels with converging and diverging flood plains. Range-wise error analysis for width ratio (α) and relative flow depth (β) given in Tables 8 and 9 shows that M5, GEP and EPR models developed in the study of Zahiri & Najafzadeh (2018) have good MAPE values compared to other empirical performance but other statistical performance parameters such as RMSE, I_d and NSE have poor values. The unsatisfactory performance of empirical methods can be attributed to two primary factors. Firstly, data collected from different researchers often lack consistency and can introduce variability and bias and secondly, empirical equations may have limited validity, particularly when applied outside the range for which they were originally derived, leading to potential inaccuracies.

The SI, BIAS and DI offer insights into the performance of various ML models and empirical equations for predicting discharge in a compound channel are provided in Table 10. Among the ML models, PSO-XgBoost stands out with the lowest SI of 0.228, indicating precise predictions. Although exhibiting a negative BIAS of −1.02, suggesting a tendency for underestimation, the high DI of 0.976 signifies a strong alignment between true and predicted values. Other ML models, including LightGBM, PSO-LightGBM, XgBoost, CatBoost and PSO-CatBoost, also demonstrate favourable performance with low scatter indices and discrimination indices close to 1. Conversely, empirical equations, such as Knight & Demetriou (1983), Khatua & Patra (2007), Devi et al. (2017) and Das et al. (2022), display higher scatter indices, indicating lower accuracy in predicting discharge in a compound channel. Das et al. (2022) particularly exhibit a negative DI, suggesting a weaker correlation between true and predicted values. The observations underscore the superior performance of ML models over empirical equations in accurately predicting discharge. Despite variations in scatter indices and BIAS values, PSO-CatBoost emerges as an effective model with a low SI (0.229), minimal BIAS (−0.755) and a DI of 0.974, highlighting its robustness and reliability for discharge prediction in the compound channel. Therefore, based on these results, PSO-CatBoost is suggested as the most suitable model for discharge prediction.

Performance metrics of various ML models, shedding light on their predictive capabilities and robustness using uncertainty, reliability and resilience analysis are summarised in Table 11. LightGBM exhibits a wider confidence interval, indicating higher uncertainty, while CatBoost stands out with the highest reliability index among the non-optimised models. PSO enhances model performance by reducing uncertainty and improving reliability, as seen in PSO-LightGBM, PSO-CatBoost and PSO-XgBoost. Especially, PSO-CatBoost displays the most consistent and robust performance, boasting the lowest mean resilience index and standard deviation of the resilience index. This analysis suggests that the PSO-CatBoost Model provides a more consistent, reliable and resilient model for the prediction of discharge in a compound channel with converging and diverging flood plains.

The comparison between SHAP analysis and sensitivity analysis reveals consistent and meaningful insights into the factors influencing the estimation of discharge in a compound channel with converging and diverging floodplains. Bed Slope (So) and Flow Aspect Ratio (δ*) emerge as pivotal contributors in both analyses, with so positively impacting discharge and δ* exhibiting a negative influence. The wide distribution of So and δ* in SHAP analysis underscores their critical roles in differentiating predictions and suggests a substantial impact on discharge. Sensitivity analysis reinforces these findings by ranking So and δ* with high sensitivity scores. While other features (Rr, α, Ar, Ff, θ, β and Xr) exhibit narrower distributions in SHAP analysis, indicating consistent impacts on predictions, sensitivity analysis acknowledges their relevance by assigning lower sensitivity scores. Overall, the agreement between SHAP and sensitivity analyses enhances the reliability of the identified influential parameters, providing a comprehensive understanding of the dynamics affecting discharge estimation in compound channels.

In the present study, six ML models, namely Xgboost, LightGBM, CatBoost, PSO-XgBoost, PSO-LightGBM and PSO-CatBoost, have been developed for the prediction of discharge in a compound channel with converging and diverging flood plain. To validate the results obtained from the ML models it is compared using different statistical performance parameters with four existing empirical methods, i.e., Knight & Demetriou (1983), Khatua & Patra (2007), Devi et al. (2016) and Das et al. (2022). The following conclusions were drawn from the study.

• The PSO-CatBoost model is found to be the better model for the prediction of discharge in compound channels out of the six ML methods used in the present study.

• SHAP and sensitivity analysis show that the influential factor among the nine parameters considered for predicting discharge is ‘So’, while ‘Xr’ has the least impact on the prediction of discharge in a compound channel with converging and diverging plains.

• The study highlights the importance of choosing the right model based on the width ratio (α). PSO-CatBoost is best for α > 2 (wider features), and PSO-XgBoost is superior for α < 2 (narrower features), improving predictive accuracy in various applications.

• PSO enhances model performance by reducing uncertainty and improving reliability. PSO-Catboost displays the most efficient and robust models based on uncertainty, reliability and resilience analysis.

• The study emphasises the superior performance of ML models, particularly PSO-CatBoost, which exhibits a low SI (0.229), minimal BIAS (−0.755) and a DI of 0.974, making it more suitable for discharge prediction in a compound channel with converging and diverging flood plains.

• Empirical methods suffer from unsatisfactory performance primarily due to the heterogeneity of datasets collected from different researchers, leading to variability and biases. Additionally, limitations in the validity of empirical equations within specific ranges hinder accurate predictions and generalisability.

The limitation of the present study is the diverse range of datasets employed in the modelling of discharge in a compound channel with converging and diverging floods. The model will provide better results if the input parameter value lies in the same range, as mentioned in Table 1. Further research is needed to improve the accuracy of the model by incorporating more datasets on converging and diverging compound channels.

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

The authors declare there is no conflict.