Assessing a transitional and turbulent overland flow resistance law for surfaces with different roughness

The control and management of soil erosion phenomena caused by rainfall and runoff is a significant issue in sloping landscapes, especially if they are scarcely or not vegetated. The study of the relationship between soil roughness and flow resistance is a fundamental step in improving the knowledge of erosion processes. In this study, the suitability of a theoretically deduced flow resistance law, based on a power-velocity profile, was assessed by transitional and turbulent overland flow data obtained in laboratory and available in the literature. These measurements were obtained in a sloping (slope in the range 1-40 %) rectangular flume, testing the effects of six different roughness conditions. At first, for each investigated roughness condition, the available measurements were used to calibrate and test the equation relating the Gamma function of the velocity distribution, the flow Froude number, and the channel slope. For all the investigated conditions, this analysis allowed for demonstrating that the flow resistance law gives a reliable estimate of the Darcy-Weisbach friction factor, with errors <=+/- 5 % for 89.8-100 % of the examined cases with reference to the considered roughness condition. Then, using coefficients b (1.05) and c (0.562) of the Gamma function available in the literature, the roughness effect was exclusively attributed to the a coefficient. In this case, the friction factor values calculated by the flow resistance law, with b = 1.05 and c = 0.562 and the a values corresponding to the different roughness conditions, are characterized by errors <=+/- 5% for 70.4-100 % of the cases. Finally, the power relationships between the calibrated a, b, and c coefficients of the Gamma function, and Manning's n values, corresponding to the roughness of the investigated surfaces, pointed out that the a coefficient is the most affected by the roughness conditions, as the exponent of Manning's assumes the highest value. The significance of this research is due to the fact that a relevant issue in modeling overland flow is to define the resistance coefficient for variable roughness, especially the vegetated ones.