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Title: Estimating longitudinal dispersion coefficient in natural streams using empirical models and machine learning algorithms
Authors: Kargar, K
Samadianfard, S
Parsa, J
Nabipour, N
Shamshirband, S
Mosavi, A
Chau, KW 
Issue Date: 2020
Source: Engineering applications of computational fluid mechanics, 2020, v. 14, no. 1, p. 311-322
Abstract: The longitudinal dispersion coefficient (LDC) plays an important role in modeling the transport of pollutants and sediment in natural rivers. As a result of transportation processes, the concentration of pollutants changes along the river. Various studies have been conducted to provide simple equations for estimating LDC. In this study, machine learning methods, namely support vector regression, Gaussian process regression, M5 model tree (M5P) and random forest, and multiple linear regression were examined in predicting the LDC in natural streams. Data sets from 60 rivers around the world with different hydraulic and geometric features were gathered to develop models for LDC estimation. Statistical criteria, including correlation coefficient (CC), root mean squared error (RMSE) and mean absolute error (MAE), were used to scrutinize the models. The LDC values estimated by these models were compared with the corresponding results of common empirical models. The Taylor chart was used to evaluate the models and the results showed that among the machine learning models, M5P had superior performance, with CC of 0.823, RMSE of 454.9 and MAE of 380.9. The model of Sahay and Dutta, with CC of 0.795, RMSE of 460.7 and MAE of 306.1, gave more precise results than the other empirical models. The main advantage of M5P models is their ability to provide practical formulae. In conclusion, the results proved that the developed M5P model with simple formulations was superior to other machine learning models and empirical models; therefore, it can be used as a proper tool for estimating the LDC in rivers.
Keywords: Gaussian process regression
Longitudinal dispersion coefficient
M5 model tree
Random forest
Support vector regression
Publisher: Taylor & Francis
Journal: Engineering applications of computational fluid mechanics 
ISSN: 1994-2060
EISSN: 1997-003X
DOI: 10.1080/19942060.2020.1712260
Rights: © 2020 The Author(s).
.This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use,distribution, and reproduction in any medium, provided the original work is properly cited.
The following publication Katayoun Kargar, Saeed Samadianfard, Javad Parsa, Narjes Nabipour,Shahaboddin Shamshirband, Amir Mosavi & Kwok-wing Chau (2020) Estimating longitudinaldispersion coefficient in natural streams using empirical models and machine learningalgorithms, Engineering Applications of Computational Fluid Mechanics, 14:1, 311-322 is available at
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