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.
Hydrological processes research remains a field that is severely measurement limited. While conventional tracers (geochemicals, isotopes) have brought extremely valuable insights into water source and flowpaths, they nonetheless have limitations that clearly constrain their range of application. Integrating hydrology and ecology in catchment science has been repeatedly advocated as offering potential for interdisciplinary studies that are eventually to provide a holistic view of catchment functioning. In this context, aerial diatoms have been shown to have the potential for detecting of the onset/cessation of rapid water flowpaths within the hillslope-riparian zone-stream continuum. However, many open questions prevail as to aerial diatom reservoir size, depletion and recovery, as well as to their mobilisation and transport processes. Moreover, aerial diatoms remain poorly known compared to freshwater species and new species are still being discovered. Here, we ask whether aerial diatom flushing can be observed in three catchments with contrasting physiographic characteristics in Luxembourg, Oregon (USA) and Slovakia. This is a prerequisite for qualifying aerial diatoms as a robust indicator of the onset/cessation of rapid water flowpaths across a wider range of physiographical contexts. One species in particular, (Hantzschia amphioxys (Ehr.) Grunow), was found to be common to the three investigated catchments. Aerial diatom species were flushed, in different relative proportions, to the river network during rainfall-runoff events in all three catchments. Our take-away message from this preliminary examination is that aerial diatoms appear to have a potential for tracing episodic hydrological connectivity through a wider range of physiographic contexts and therefore serve as a complementary tool to conventional hydrological tracers.