Evaluating Discharge Coefficient of Rectangular Sharp Crested Weirs Using Machine Learning Models

Mrinmoy Dhar (), Sanjog Chhetri Sapkota (), Prasenjit Saha () and Sameer Arora ()
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Mrinmoy Dhar: ICFAI University
Sanjog Chhetri Sapkota: Sharda University
Prasenjit Saha: ICFAI University
Sameer Arora: National Institute of Urban Affairs

Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), 2025, vol. 39, issue 8, No 28, 4171 pages

Abstract: Abstract In the realm of flow measurement using rectangular sharp-crested weirs, the stage-discharge relationship, primarily represented by the discharge coefficient (Cd), holds paramount significance. In order to comprehend and predict the behavior of Cd effectively, six machine learning (ML) algorithms, namely, Support Vector Machine (SVM), Decision Tree (DT), Random Forest (RF), Adaboost (ADB), Xgboost (XGB) and Catboost (CATB), are assessed. The performances of each of these approaches have been evaluated based on statistical criterions and using Taylor diagram. It is revealed that all six techniques can predict the discharge coefficient with excellent accuracy, with the Catboost model outperforming the other models. In the prediction of Cd, the values of the coefficient of determination and root mean square error obtained from the CATB model are 0.9782 and 0.0064, respectively. The extensive nonlinear behaviour exhibited by the ML models is also addressed using shapely additives explanation (SHAP) framework. Further, a comparison of the predictions of ML approaches with the results of existing empirical formulas has been made. The accuracy of ML approaches is found to be much higher than that of either of the existing empirical formulas, indicating the superior prediction capability of ML models.

Keywords: Discharge; Flow Measurement; Ensemble Machine Learning; Machine Learning Model (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s11269-025-04152-3

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