Longitudinal Dispersion in Natural Streams

Abstract

When time‐series methods of parameter estimation are used to model the concentration of a pollutant in a natural waterway, the results may be grouped into a restricted class of models which are termed (j,n,m) models. It is shown that the dispersion as represented in conservative forms of these models has a temporal variance that increases linearly with time (thus mimicking the variance of a Fickian process) and is consistent with dead zone mixing within rivers and streams. Data from a variety of rivers are used to demonstrate that the (j,n,m) model provides an explanation of actual data that is superior to those obtained by manipulation of a Fickian equation. In addition, the model greatly simplifies computation of dead zone dispersive effects, is able to simply deal with non‐conservative pollutants and the results suggest that residence times are more meaningful physical parameters than dispersion coefficients in explaining dispersive phenomena.