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 h_a 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 s_ta 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 s_t 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 – s_t 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.

本文提出了一种确定小溪和临时沟渠断面极限的新方法。该方法基于对每个横截面的实际深度h _a的估计，该实际深度h _a是将通道与山坡区域区分开的特定深度。分析表明，实际深度对应于在水力半径R的最大值时出现的特定坡度s _ta。该方法使用体积方法来计算水力半径，该水力半径是整个调查通道的体积与其边界侧面之间的比率。岸坡s _t的值由整个通道侧面的DEM得出。Castillo等人还将该新技术（最大化水力半径，MHR）与直角梯形（RAT）方法进行了比较。以及Casalì等人的差异DEM（DoD）方法。MHR方法是通过在人工地球通道上，以小区规模和使用两个临时沟渠进行的测量来测试的。对于地球通道，必须为每个侵蚀特征专门建立关系R – s _t，并且通过MHR技术发生的通道体积估计误差可忽略不计。在样地规模上，MHR和RAT在表面宽度和横截面积方面均具有可比性。关系通道长度L-体积V确认这一协议，而国防部的方法却系统地低估了交易量。在临时沟壑尺度上，MHR方法使用体积方法来计算水力半径，因此能够考虑沿所研究通道的横截面形状变化的影响。最后，分析表明，通过MHR方法获得的LV对在通过现场测量获得的可用文献数据的散射范围内。