Estimation of the Dispersion Coefficient in Natural Rivers Using a Granular Computing Model

Because pollutant dispersion in rivers is strongly influenced by the longitudinal dispersion coefficient ($K_x$), its accurate estimation is critical in the field of environmentally sound hydraulic engineering. In this study, a granular computing (GC) model was explored for the first time to overcome problems in accurately estimating $K_x$. Because GC is a black-box model that is not user friendly, an appropriate nonlinear regression (NLR) method was also applied to precisely predict $K_x$. The inclusion of the generally ignored parameter of river curvature in $K_x$ estimation significantly improved NLR model performance. In so doing, both GC and NLR model estimations of $K_x$ achieved high linear coefficients of determination ($R^2$) and small error indices [root mean square error (RMSE) and mean absolute error (MAE)] with respect to measured $K_x$ values. The same analysis showed that the GC model (with $R^2$, RMSE, and MAE values equal to 0.997, 8.11, and 2.18, respectively), outperformed the NLR model, particularly for extreme high values of $K_x$. Similarly to previous studies, it was also found that the most effective parameters on $K_x$ were the channel aspect ratio, friction term, and river curvature, respectively, in descending order of importance. Moreover, a comparison between some well-known $K_x$ models and the developed GC and NLR alternative presented here showed the latter to have outperformed the former, indicating that the GC and NLR models are a good choice for $K_x$ prediction.