Successful application of one-dimensional advection–dispersion models in rivers depends on the accuracy of the longitudinal dispersion coefficient (LDC). In this regards, this study aims to introduce an appropriate approach to estimate LDC in natural rivers that is based on a hybrid method of granular computing (GRC) and an artificial neural network (ANN) model (GRC-ANN). Also, adaptive neuro-fuzzy inference system (ANFIS) and ANN models were developed to investigate the accuracy of three credible artificial intelligence (AI) models and the performance of these models in different LDC values. By comparing with empirical models developed in other studies, the results revealed the superior performance of GRC-ANN for LDC estimation. The sensitivity analysis of the three intelligent models developed in this study was done to determine the sensitivity of each model to its input parameters, especially the most important ones. The sensitivity analysis results showed that the W/H parameter (W: channel width; H: flow depth) has the most significant impact on the output of all three models in this research.

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Sediment load in fluvial systems is one of the critical factors shaping the river geomorphological and hydraulic characteristics. A detailed understanding of the total sediment load (TSL) is required for the protection of physical, environmental, and ecological functions of rivers. This study develops a robust methodological approach based on multiple linear regression (MLR) and support vector regression (SVR) models modified by principal component analysis (PCA) to predict the TSL in rivers. A database of sediment measurement from large-scale physical modelling tests with 4759 datapoints were used to develop the predictive model. A dimensional analysis was performed based on the literature, and ten dimensionless parameters were identified as the key drivers of the TSL in rivers. These drivers were converted to uncorrelated principal components to feed the MLR and SVR models (PCA-based MLR and PCA-based SVR models) developed within this study. A stepwise PCA-based MLR and a 10-fold PCA-based SVR model with different kernel-type functions were tuned to derive an accurate TSL predictive model. Our findings suggest that the PCA-based SVR model with the kernel-type radial basis function has the best predictive performance in terms of statistical error measures including the root-mean-square error normalized with the standard deviation (RMSE/StD) and the Nash–Sutcliffe coefficient of efficiency (NSE), for the estimation of the TSL in rivers. The PCA-based MLR and PCA-based SVR models, with an overall RMSE/StD of 0.45 and 0.35, respectively, outperform the existing well-established empirical formulae for TSL estimation. The analysis of the results confirms the robustness of the proposed PCA-based SVR model for prediction of the cases with high concentration of sediments (NSE = 0.68), where the existing sediment estimation models usually have poor performance.

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Discharge of pollution loads into natural water systems remains a global challenge that threatens water and food supply, as well as endangering ecosystem services. Natural rehabilitation of contaminated streams is mainly influenced by the longitudinal dispersion coefficient, or the rate of longitudinal dispersion (Dx), a key parameter with large spatiotemporal fluctuations that characterizes pollution transport. The large uncertainty in estimation of Dx in streams limits the water quality assessment in natural streams and design of water quality enhancement strategies. This study develops an artificial intelligence-based predictive model, coupling granular computing and neural network models (GrC-ANN) to provide robust estimation of Dx and its uncertainty for a range of flow-geometric conditions with high spatiotemporal variability. Uncertainty analysis of Dx estimated from the proposed GrC-ANN model was performed by alteration of the training data used to tune the model. Modified bootstrap method was employed to generate different training patterns through resampling from a global database of tracer experiments in streams with 503 datapoints. Comparison between the Dx values estimated by GrC-ANN to those determined from tracer measurements shows the appropriateness and robustness of the proposed method in determining the rate of longitudinal dispersion. The GrC-ANN model with the narrowest bandwidth of estimated uncertainty (bandwidth-factor = 0.56) that brackets the highest percentage of true Dx data (i.e., 100%) is the best model to compute Dx in streams. Considering the significant inherent uncertainty reported in the previous Dx models, the GrC-ANN model developed in this study is shown to have a robust performance for evaluating pollutant mixing (Dx) in turbulent environmental flow systems.