Relationships between soil detachment rate and flow sediment deficit with rill length on deforested and burned soil

The variability of soil detachment rate (D_r) with rill length is essential to understand the complex process of rill erosion. Moreover, an important variable of rill erosion, such as the ‘flow sediment deficit’ (FSD)–the difference in D_r between the two extreme points of a rill–has been scarcely investigated. Soil disturbances, such as fire and deforestation, strongly aggravate the natural rates of rill erosion, leaving the soil bare and unprotected by vegetation. Therefore, it is essential to explore and model how D_r and FSD depend on rill length in these land conditions. In this study, we have measured D_r and FSD in rills with length of 0.75, 1.5, and 2.5 m, using an experimental flume (3.5-m long) and soil samples collected in a burned and deforested site in Northern Iran. Soil slope and flow discharge were from 5.4 to 21.2 %, and from 0.55 to 0.94 L m⁻¹ s⁻¹, respectively. The highest D_r (on average 0.072 kg m⁻² s⁻¹) was measured at the upstream side of the rill (being equal to the maximum rate). Downstream of the rill, this rate was lower (by −64 % for a rill length of 0.75 m to −9.5 % for 2.5 m) and the minimum value (0.026 kg m⁻² s⁻¹) was measured for the shortest rill (0.75 m). D_r monotonically increased with slope and flow discharge for a given rill length. The variability rate of D_r can be estimated with very high precision by power equations, adopting the shear stress (Nash and Sutcliffe’s coefficient of efficiency, NSE, over 0.94) and stream power (NSE > 0.89) as input variables. Despite our study being limited by the small scale and the local soils, the results quantify the variability of D_r and flow sediment deficit along a rill in the experimental field conditions. The proposed equations are useful to predict these variables depending on rill length in physically-based erosion models in areas with climatic and geomorphological characteristics similar to the experimental sites.