Citation: Sihag, P.; Nouri, M.; Ahmadpari, H.; Seyedzadeh, A.; Kisi, O. Approximation of the Discharge Coefficient of Radial Gates Using Metaheuristic Regression Approaches. Sustainability 2022, 14, 15145. https://doi.org/10.3390/ su142215145 Academic Editors: Andrzej Walega and Miklas Scholz Received: 24 September 2022 Accepted: 11 November 2022 Published: 15 November 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). sustainability Article Approximation of the Discharge Coefficient of Radial Gates Using Metaheuristic Regression Approaches Parveen Sihag 1 , Meysam Nouri 2,3 , Hedieh Ahmadpari 4 , Amin Seyedzadeh 5 and Ozgur Kisi 6,7, * 1 Department of Civil Engineering, Chandigarh University, Punjab 43521-15862, India 2 Department of Water Engineering, Faculty of Agriculture, Urmia University, Urmia 57561-51818, Iran 3 Department of Civil Engineering, Saeb University, Abhar 45717-74783, Iran 4 Department of Irrigation and Reclamation Engineering, College of Aburaihan, University of Tehran, Tehran 57561-51818, Iran 5 Department of Water Engineering, Faculty of Agriculture, Fasa University, Fasa 57561-51818, Iran 6 Department of Civil Engineering, Technical University of Lübeck, 23562 Lübeck, Germany 7 Department of Civil Engineering, Ilia State University, 0162 Tbilisi, Georgia * Correspondence: ozgur.kisi@th-luebeck.de Abstract: Radial gates are widely used for agricultural water management, flood controlling, etc. The existence of methods for the calculation of the discharge coefficient (C d ) of such gates are complex and they are based on some assumptions. The development of new usable and simple models is needed for the prediction of C d . This study investigates the viability of a metaheuristic regression method, the Gaussian Process (GP), for the determination of the discharge coefficient of radial gates. For this purpose, a total of 2536 experimental data were compiled that cover a wide range of all the effective parameters. The results of GP were compared with the Group Method of Data Handling (GMDH), Multivariate Adaptive Regression Splines (MARS), and linear and nonlinear regression models for predicting C d of radial gates in both free-flow and submerged-flow conditions. The results revealed that the radial basis function-based GP model performed the best in free-flow condition with a Correlation Coefficient (CC) of 0.9413 and Root Mean Square Error (RMSE) of 0.0190 while the best accuracy was obtained from the Pearson VII kernel function-based GP model for the submerged flow condition with a CC of 0.9961 and RMSE of 0.0132. Keywords: gates; submerged flow; free-flow; discharge coefficient; estimation models 1. Introduction Flow controller and flow regulator structures play important roles in flow distribution in irrigation systems and the success rate of irrigation systems depends on the performance of these structures [1]. The maximum discharge condition is the main criteria for designing irrigation systems, while in practice, in the majority of cases, the maximum discharge is not observed. So, in such systems, flow controller and flow regulator structures are used for providing gravity irrigation conditions and for setting the water level at required water levels [2]. Gates are the most common types of structures that are commonly utilized in irrigation networks [3]. In addition, flow discharge measurement is another important application of gates in these systems, and estimation of flow discharge under gates can be classified as one of the most important issues in hydraulic engineering [3]. In other words, the precision of flow discharge information has a direct influence on operational management and water-saving policies [4]. According to gate applications all over the world, the hydraulic performance of gates has been studied by many researchers. Gibson [5] and Henry [6] carried out the earliest studies on gates. Henry [6] presented the slice gate discharge coefficient (C d ) in the form of a graph considering a dimensionless form of effective parameters in both submerged and free-flow conditions. The study by Henry [6] is the basis of some other studies and some other C d equations. After that, Rajaratnam Sustainability 2022, 14, 15145. https://doi.org/10.3390/su142215145 https://www.mdpi.com/journal/sustainability