Modeling of Solute Transport and Macrodispersion by Unsteady Stream Flow under Uncertain Conditions

Abstract

A numerical simulation for a longitudinally one-dimensional upscaled solute transport model is developed in order to predict the mean solute concentration in natural streams subject to irregular variations in various flow and transport parameters and forcing conditions. A solute transport equation at the local scale of a river cross section is deterministic, but the equation at the river reach scale is stochastic due to various uncertainties in flow and transport parameters in every reach. The upscaling transformation makes a transport equation at the river reach scale deterministic. Compared with the transport equation at local scale, the upscaled equation at the river reach scale has seven covariance integrals, which incorporate the influence of the stream variabilities on the mean value of solute concentration. One of these integrals provides the explicit model of the macrodispersion coefficient as it varies in time and space under varying flow conditions. Lagrangian trajectories of flow are simulated to compute the time-space covariance integrals (including macrodispersion) of the flow properties. The Monte Carlo simulation of the stochastic solute transport is implemented to verify the upscaling methodology. The validation exercise confirms that the upscaled model is accurate, feasible, and physically meaningful. The Monte Carlo simulation with the stochastic Saint-Venant flow model also supplies all the random flow information used in both the predictive transport model and the validation transport model.