Longitudinal dispersion coefficient modeling in natural streams via newly proposed explainable ensemble learning...

Precise estimation of the longitudinal dispersion coefficient (Kₓ) is vital for pollutant transport modeling in rivers. In this study several Machine Learning (ML) models, including Feed Forward Neural Networks (FFNN), Adaptive Neuro-Fuzzy Inference System (ANFIS), Support Vector Regression (SVR), and Convolutional Neural Networks (CNN) were used to estimate K_x. These three Ensemble learning (EL) techniques, of Simple Averaging Ensemble (SAE), Weighted Averaging Ensemble (WAE), and Neural Averaging Ensemble (NAE), were employed to combine the outputs of single models. The analysis utilized data from natural streams in the United States and the United Kingdom, incorporating variables such as channel width (W), flow depth (H), average velocity (U), and shear velocity (U_⁎). Model interpretability was finally examined using Shapley Additive Explanations (SHAP) method, which identified W and H as the most influential estimators, but with different powers across models. Modeling performance evaluation using Root Mean Square Error (RMSE) and Determination Coefficient (DC) metrics demonstrated that NAE achieved higher accuracy, reducing RMSE by 11% and improving DC by over 7% compared to Deep Learning (DL)-based CNN, the best-performing individual model. Stream-wise cross-validation (CV) results showed that FFNN could achieve the highest Area Under the Curve (AUC of 0.909), while ensemble techniques, especially WAE (AUC = 0.902 ± 0.016) and NAE (AUC = 0.886 ± 0.024), exhibited superior stability and generalization, consistently outperforming single models.