Analytical Solution of a Model of Contaminant Transport in the Advective Zone of a River

Abstract

An analytical solution of a model of contaminant transport in the advective zone of rivers is presented and evaluated. An existing model that accounts for transport in the advective zone by dividing the channel into flowing and stagnant zones is solved with Laplace transforms for the case of a Gaussian pulse injected into the center of the channel. The effects of the two main parameters of the model, the fraction of the channel occupied by the stagnant zone and a transfer coefficient, are consistent with expectations from the theory of shear dispersion. Another parameter, which is related to the streamwise width of the initial pulse, determines whether a separate pulse appears in the tracer-response curves. A procedure for determining the parameters from temporal moments of measured concentration curves is described and applied to measurements in the advective zone of a mountain stream. Predictions from the model of Reichert and Wanner fit the measurements—especially the peak concentration—better than predictions from the one-dimensional model.