Reach unified channel characteristics for the transverse advection-dispersion equation

Transverse dispersion is of interest in natural watercourses, especially near outfalls. The application of simple analytical solutions to the transverse advection-dispersion equation in these scenarios, however, is challenging due to variations in channel characteristics. Thus, a new method has been developed for averaging reach characteristics to account for longitudinal variability when using analytical solutions to the advection-dispersion equation by combining travel time and length weighting. The new ‘reach unification’ approach incorporates the characteristics (such as velocity, width, or dispersion coefficient) of each different sub-reach to the equivalent single reach values needed to make a direct downstream prediction. To demonstrate reach unification, synthetic concentration profiles from a continuous injection into a simplified rectangular channel with three sub-reaches of varying velocity, depth, and friction, have been generated using finite difference modelling. The characteristics of these sub-reaches when combined with reach unification made perfect downstream analytical predictions, confirming the approach. The use of the streamtube model to represent changes in channel width is investigated. It is also shown that reach unification is of significant benefit to the inverse problem, analysing recorded concentration profiles to estimate the dispersion coefficient and relating it to reach characteristics.