Comparison of roughness models to simulate overland flow and tracer transport experiments under simulated rainfall at plot scale

Abstract

The Saint-Venant equations have consistently proved capable of accurately simulating hydrographs at plot scale. However, recent works showed that even though the hydrograph is satisfyingly reproduced, the flow velocity field within the plot might be wrong, with the highest velocity largely underestimated. Moreover, the choice of roughness models to be used in the Saint-Venant equations is most often done in the purpose of increasing the hydrograph quality, while the actual travel time of water is ignored. This paper presents a tracer experiment made on a 10-m by 4-m rainfall simulation plot, where travel time and tracer mass recovery as well as local flow velocity have been measured. Four roughness models are tested: (i) Darcy-Weisbach's model, (ii) Lawrence's model, (iii) Manning's model with a constant roughness coefficient, and (iv) Manning's model with a variable roughness coefficient which decreases as a power law of the runoff water depth. Models with a constant friction factor largely underestimate high velocities. Moreover, they are not able to simulate tracer travel-times. Lawrence's model correctly simulates low and high velocities as well as tracer breakthrough curves. However, a specific set of parameters are required for each breakthrough curve from the same experiment. The best results are obtained with the Manning's model with a water-depth dependent roughness coefficient: simulated velocities are consistent with measurements, and a single set of parameters captures the entire set of breakthrough curves, as well as tracer mass recovery. The study reported here brings the following findings: (i) roughness coefficient is flow-dependent, (ii) faithful simulation of the velocity fields does not imply a good prediction of travel time and mass recovery, (iii) the best model is a Manning type model with a roughness coefficient which decreases as a power law of water depth. The full dataset used in this work is available on request. It can be used as benchmark for overland flow and transport models.