Comparison of novel physics-guided machine learning models with empirical equations for predicting longitudinal dispersion coefficient in diverse natural river systems

Abstract

Accurate calculation of the longitudinal dispersion coefficient (LDC) is crucial for assessing river fate and transport processes. Traditional methods, including experimental, analytical, and empirical equations, each have their challenges, such as complexity and susceptibility to errors. This study introduces and evaluates advanced physics-guided machine learning (ML) models, including hybrid hydrodynamic-particle simulation (HHPS), physics-enhanced ML (PEML), and physics-regularized regression trees (PRRT). Our dataset includes hydraulic and geometric parameters collected from 50 diverse rivers across the US and the UK, encompassing variables such as river width (W), flow depth (H), average flow velocity (U), flow shear velocity (U*), concentration of the solute (μgL) and LDC (ε). Input parameters were dimensioned using the UU∗ and WHratios, while the dimensionless LDC (εHU∗) served as the model output. By embedding core hydrodynamic principles such as continuity, mass and momentum conservation, and Navier-Stokes equations into the ML algorithms, these models achieved high predictive accuracy. Specifically, the HHPS model reached a coefficient of determination of 0.997, and both PEML and PRRT demonstrated Nash-Sutcliffe efficiencies exceeding 0.950, significantly outperforming traditional empirical equations. Additionally, SHapley Additive exPlanations (SHAP) sensitivity analysis revealed the substantial influence of channel width and flow conditions on LDC predictions. Our study highlights the superior performance of physics-guided ML models in providing accurate and reliable tools for river water quality management, demonstrating their substantial improvements over traditional methods and their potential broader applications in environmental studies.