Uncertainty quantification of granular computing-neural network model for prediction of pollutant longitudinal dispersion coefficient in aquatic streams

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 (D(x)), a key parameter with large spatiotemporal fluctuations that characterizes pollution transport. The large uncertainty in estimation of D(x) 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 D(x) and its uncertainty for a range of flow-geometric conditions with high spatiotemporal variability. Uncertainty analysis of D(x) 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 D(x) 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 D(x) data (i.e., 100%) is the best model to compute D(x) in streams. Considering the significant inherent uncertainty reported in the previous D(x) models, the GrC-ANN model developed in this study is shown to have a robust performance for evaluating pollutant mixing (D(x)) in turbulent environmental flow systems.