On the relative role of hydrodynamic dispersion for river water quality

Neglecting hydrodynamic dispersion in models of river water quality has important implications in terms of simplifying the equations which describe the system and for model calibration. In this paper we analyze the behavior of a river system subjected to a time-variable point source input of a degradable solute using frequency response techniques applied to one-dimensional solute transport models, considering the combined effect of amplitude attenuation and phase shift due to hydrodynamic dispersion. We derive exact and simplified expressions that can be used for establishing whether dispersion is negligible at a desired level of accuracy. Finally, we present an application of the analysis to the river Lambro in northern Italy which receives diurnally varying solute loads from an undersized sewage treatment plant. The results obtained show the following: (1) In the case of a time-constant solute input, exact analytical expressions of the error incurred by neglecting dispersion can be derived which show that dispersive transport is negligible in most quasi steady state cases. (2) When solute input varies sinusoidally with time, the error due to neglecting dispersion is strongly dependent on the input frequency and may be significant if the input frequency is high. The error is practically independent of the decay rate coefficient, k, except when k is significantly greater than the input frequency. (3) Ignoring solute transport upstream from the outfall, due to dispersion, in the solution to the advection dispersion equation (ADE) can result in significant errors if the input frequency is sufficiently high. In some cases the choice of the ADE solution employed may have a larger impact than neglecting dispersion altogether.