Analytical solutions of the advection-dispersion equation and related models are indispensable for predicting or analyzing contaminant transport processes in streams and rivers, as well as in other surface water bodies. Many useful analytical solutions originated in disciplines other than surface-water hydrology, are scattered across the literature, and not always well known. In this two-part series we provide a discussion of the advection-dispersion equation and related models for predicting concentration distributions as a function of time and distance, and compile in one place a large number of analytical solutions. In the current part 1 we present a series of one- and multi-dimensional solutions of the standard equilibrium advection-dispersion equation with and without terms accounting for zero-order production and first-order decay. The solutions may prove useful for simplified analyses of contaminant transport in surface water, and for mathematical verification of more comprehensive numerical transport models. Part 2 provides solutions for advective-dispersive transport with mass exchange into dead zones, diffusion in hyporheic zones, and consecutive decay chain reactions.
Contaminant transport processes in streams, rivers, and other surface water bodies can be analyzed or predicted using the advection-dispersion equation and related transport models. In part 1 of this two-part series we presented a large number of one- and multi-dimensional analytical solutions of the standard equilibrium advection-dispersion equation (ADE) with and without terms accounting for zero-order production and first-order decay. The solutions are extended in the current part 2 to advective-dispersive transport with simultaneous first-order mass exchange between the stream or river and zones with dead water (transient storage models), and to problems involving longitudinal advectivedispersive transport with simultaneous diffusion in fluvial sediments or near-stream subsurface regions comprising a hyporheic zone. Part 2 also provides solutions for one-dimensional advective-dispersive transport of contaminants subject to consecutive decay chain reactions.