A Maximizing Hydraulic Radius (MHR) method for defining cross-section limits in rills and ephemeral gullies

In this paper, a new method for determining the cross-section limits in rills and ephemeral gullies is proposed. This method is based on the estimate of the actual depth ha of each cross-section, which is the particular depth distinguishing the channel from the hillslope areas. The analysis showed that the actual depth corresponds to a particular bank slope sta occurring for the maximum value of the hydraulic radius R. The method was applied using a volumetric approach for calculating the hydraulic radius as the ratio between the volume of the whole investigated channel and its boundary lateral surface. The value of the bank slope st was derived by the DEM of the whole channel lateral surface. This new technique (Maximizing Hydraulic Radius, MHR) was also compared with the Right-Angled Trapezoid (RAT) method by Castillo et al. and the method of DEM of difference (DoD) by Casalì et al. The MHR approach was tested by measurements carried out in artificial earth channels, at plot scale and using two ephemeral gullies. For the earth channels, the relationship R – st has to be specifically established for each erosion feature and negligible estimate errors of the channel volume by the MHR technique occurred. At plot scale, MHR and RAT are comparable in terms of both surface width and cross-section area. The relationship channel length L- volume V confirmed this agreement while the DoD method systematically underestimated the volume. At ephemeral gully scale the MHR method, which uses a volumetric approach for calculating the hydraulic radius, was able to take into account the effect of the variability of the cross-section shape along the investigated channels. Finally, the analysis demonstrated that the pairs L-V obtained by the MHR method fall within the scattering of the available literature data obtained by field measurements.