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.

纵向弥散系数（LDC）在模拟天然河流中污染物和沉积物的运输中起着重要作用。由于运输过程，污染物的浓度沿河而变化。已经进行了各种研究以提供用于估计LDC的简单方程式。在这项研究中，研究了机器学习方法，即支持向量回归，高斯过程回归，M5模型树（M5P）和随机森林以及多元线性回归，以预测自然流中的LDC。收集了来自全球60条具有不同水力和几何特征的河流的数据集，以开发LDC估算模型。统计标准，包括相关系数（CC），均方根误差（RMSE）和平均绝对误差（MAE），被用来审查模型。将这些模型估计的LDC值与常见经验模型的相应结果进行比较。使用泰勒图对模型进行评估，结果表明，在机器学习模型中，M5P具有优越的性能，CC为0.823，RMSE为454.9，MAE为380.9。Sahay和Dutta模型的CC值为0.795，RMSE为460.7，MAE为306.1，比其他经验模型给出的结果更为精确。M5P模型的主要优点是它们提供实用公式的能力。总之，结果证明，所开发的具有简单公式的M5P模型优于其他机器学习模型和经验模型。因此，它可以用作估算河流中最不发达国家的适当工具。