Simplified dispersion analysis based on dye tests at a small stream

The modelling of solid transport in open channels requires good knowledge about parameters related to basic processes such as hydrodynamic dispersion, advection and decay rates. Such parameters are usually determined by dye tests. Numerous tracer studies have been performed on laboratory flumes and natural rivers. However, on-site sampling is often difficult, expensive and needs special apparatus. The main aim of the study was to justify simplified method based on the monitoring of the dye cloud shape in order to determine both longitudinal and transversal dispersion coefficients. In this study, four dye tests were carried out on a small local stream (the Lipkovsky) using Rhodamine WT fluorescein dye as a tracer. The tests were carried out in such a manner that both longitudinal and horizontal transversal dispersion data were obtained. For this purpose, the visually determined extent of the dye cloud was interpreted via the analytical solution of the advection-dispersion equation. The results obtained by this simplified approach indicated that the longitudinal dispersion coefficient D_x = 0.051–0.057 m²/s and the coefficient of horizontal transversal dispersion D_y = 0.00024–0.00027 m²/s. The method was justified by corresponding root mean square error (RMSE) counting RMSE = 0.65–1.02 m for the dye cloud centre, RMSE = 1.87–2.46 m for the head and tail of the cloud and RMSE = 0.025–0.11 m for the cloud width, the Nash-Sutcliffe efficiency coefficients ranged from 0.9 to 0.998. The comparison of these values with empirical formulae and other tracer studies indicated significant overestimation of the mentioned values of D_x, which can be attributed to the uniform velocity distribution along the width of Lipkovsky Stream. Much better agreement was achieved for D_y.