Temporal moments of one-dimensional advective-dispersive transport with exchange represented via memory function models: Application to river corridor transport

Abstract

Practical simulation of solute transport in river corridors often relies on one-dimensional transport models with solute flux between river and hyporheic zone governed by a mass exchange term, perhaps most generally expressed using the ‘memory function’ formalism. While expressions for temporal moments of solute breakthrough curves (BTCs) are available for a number of such models, those for memory function forms are not, to our knowledge. Here we report closed-form BTC temporal moment expressions for memory function forms, found by exploiting the connection to phase exposure-dependent exchange (PhEDEx) formulations. We use these results to investigate the general capability of the memory function form to accommodate specific scaling of river tracer temporal moments reported in the literature, and we apply the method to identification of parameters in application to two recent tracer tests. The applications involve a simple numerical solution to the memory function river corridor transport model calibrated using measured temporal moments of the tracer test BTCs. The numerical model is validated only for the classical case of the transient storage model without lateral inflow, the analytical solution for which we adapt from the Lassey solution for mobile-immobile exchange in porous media. It should be noted that the temporal moments results obtained here in the context of river corridor transport also apply to one-dimensional transport in two-domain (mobile-immobile) porous media, when governed by a two-domain memory function model.