Dye-tracer technique for rill flows by velocity profile measurements

Water flow on hillslope soil surface supplies energy which is required to detach soil particles, to transport and deposit sediments, therefore flow velocity is a key variable related to hillslope hydrodinamics of soil erosion processes. Among the different methods available for measuring velocity of shallow interrill and rill flow, the trace technique is widely used. Trace technique is applied by adding a material (salt, magnetic material, water isotope, floating object) and then measuring the speed of the material to travel a known distance from the injection point. When flow velocity is measured using a dye-tracing method, the mean velocity is calculated by multiplying the measured surface velocity of the leading edge of the tracer plume by a correction factor which was generally empirically deduced. The main uncertainty of the dye-tracing technique stands in the estimate of this correction factor, which is the ratio between the mean flow velocity and the surface velocity. The main goal of this paper is establishing a theoretical relationship for calculating the correction factor by using a power velocity profile. At first, the developed analysis demonstrated that the correction factor only depends on the exponent of the power velocity distribution (Eq. (5)). Then, this theoretical expression of the correction factor was applied using the velocity profiles measured by Baiamonte and Ferro for the condition of sediment-free flow in motion on a rough bed and by Coleman for a sediment-laden flow moving on a smooth flume. Using the correction factor values calculated by the velocity measurements carried out for the sediment-free flow in motion on a rough bed, the relationship between the correction factor and roughness height was established. In agreement with a previous study by Ali et al., for a sediment-free flow the correction factor increases with roughness height. Finally, the velocity profile measurements carried out for a sediment-laden flow in motion on a smooth bed were used to state the effect of sediment load on the correction factor. This last analysis allowed to conclude, in agreement with Li and Abrahams and Zhang et al., that the correction factor decreases when the sediment load increases.