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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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.

Groundwater is a vital source of freshwater, supporting the livelihood of over two billion people worldwide. The quantitative assessment of groundwater resources is critical for sustainable management of this strained resource, particularly as climate warming, population growth, and socioeconomic development further press the water resources. Rapid growth in the availability of a plethora of in-situ and remotely sensed data alongside advancements in data-driven methods and machine learning offer immense opportunities for an improved assessment of groundwater resources at the local to global levels. This systematic review documents the advancements in this field and evaluates the accuracy of various models, following the protocol developed by the Center for Evidence-Based Conservation. A total of 197 original peer-reviewed articles from 2010–2020 and from 28 countries that employ regression machine learning algorithms for groundwater monitoring or prediction are analyzed and their results are aggregated through a meta-analysis. Our analysis points to the capability of machine learning models to monitor/predict different characteristics of groundwater resources effectively and efficiently. Modeling the groundwater level is the most popular application of machine learning models, and the groundwater level in previous time steps is the most employed input data. The feed-forward artificial neural network is the most employed and accurate model, although the model performance does not exhibit a striking dependence on the model choice, but rather the information content of the input variables. Around 10–12 years of data are required to develop an acceptable machine learning model with a monthly temporal resolution. Finally, advances in machine and deep learning algorithms and computational advancements to merge them with physics-based models offer unprecedented opportunities to employ new information, e.g., InSAR data, for increased spatiotemporal resolution and accuracy of groundwater monitoring and prediction.

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