A methodology for solute transport in unsteady, nonuniform streamflow with subsurface interaction

An advection-dispersion-reaction model can generally be used to describe one-dimensional stream solute transport if the flow is steady and if the channel is smooth and uniform. When applied to unsteady, nonuniform streamflows, a model based on the Fickian analogy needs to be modified to account for the temporal and spatial variation of the cross-sectional area of the stream channel. In this paper, we explore this topic with a simple approximation method as well as an elaborate one, both of which are incorporated into a conjunctive stream-aquifer transport model and are applied to a hypothetical stream-aquifer setting. The simple method, while easier to implement, displays a persistent pattern of error in simulation results. The elaborate method, while accurate in computation, results in a more complicated model and requires extensive procedures to overcome the efficiency problem when simulating complex stream-aquifer interactions. However, by coupling the latter with the adaptive stepsize control for the Runge-Kutta method in a conjunctive stream-aquifer model, it not only greatly improves model efficiency but also results in more realistic modeling than previously reported.