One-dimensional numerical modeling of the conservation equation for non-reactive stochastic solute transport by unsteady flow field in stream channels

Numerical predictions of solute transport by open-channel flow are complicated by uncertainty due to spatial and temporal variability, measurement error and limited sampling of the parameters that represent the system physical properties, boundary and initial conditions, and sinks/sources. Over several decades, a number of simplified approaches to stochastic solute transport with the assumption of steady and deterministic flow condition, have been explored. Under this kind of assumption, the modeling approaches are limited to the consideration of the complete physical random features affecting transport. This study overcomes this deficiency by including most of the physical uncertainties in the flow and solute transport models.; This study first presents the Monte Carlo method to simulate the one-dimensional unsteady flow fields using the Saint-Venant model as a set of stochastic partial differential equations whose channel geometry parameters, initial and boundary conditions, and sources (lateral input) are spatiotemporal random fields.; Then, the random flow fields are applied to the predictive ensemble-average nonreactive solute transport equation, developed by Kavvas(2001), which is then implemented to compute the mean solute concentration field in time and space. The mean solute transport equation is generated from the general convection-dispersion transport equation using cumulant expansion approach. In the mean solute concentration equation, seven integral covariance terms are computed at every point in the numerical spatiotemporal grid, based on the information supplied by the random flow fields.; As an alternative approach, the Monte Carlo simulations of the solute transport, using the general convection-dispersion transport equation, are used to verify the predictive results of the mean solute transport equation according to the same random flow fields as the predictive method uses.; Comparison of the predictive mean concentration with the average of 1000 realizations generated by the Monte Carlo simulations showed that the predictive results are very close to the average solute concentration of 1000 realizations at any time and space location. This result proves that the predictive mean solute transport equation for transport under heterogeneous and transient open-channel flow (Kavvas, 2001) is quite accurate and feasible.