Soil erosion is one of the main environmental problems affecting humans, and causes about 5 to 7 million hectares of farmland loss every year1. Gully erosion is one of the most important soil erosion processes and results in a soil loss rate of around 85%. Channel erosion includes rill erosion, ephemeral gully erosion, and gully erosion 2,3. Rill erosion is one of the initial forms of channel erosion 4, usually eventually forming a gully 5. Research on rill mainly focuses on the origin of rill cross-sectional morphology 6, describing the relationship between general rill cross-sectional morphology and rill erosion7–10. Rill morphological characteristics form the basis for understanding the underlying mechanisms of the evolution of rill, and are important for estimating the rill erosion volume and rill erosion rate. Therefore, it is paramount to study the morphological characteristics of rill erosion.
Rill morphology includes planar, cross-sectional, and longitudinal morphology, and the cross-section is the most important morphological feature reflecting development stage of rill 11. In the early stage of rill development, the rill cross-section generally presents a “V” shape 12. With the continuous evolution of a rill, a “U” or “box” cross-section gradually appears, but the rill is still dominated by a “V”-shape cross-section 13,14. The morphological characteristics of the rill cross-section constitute its length 15, depth 15, width 16, and asymmetry ratio 17, and these characteristics change with the evolution of the rill 12. The length of a rill has a significant positive correlation with the evolution rate of its morphology, and its width and depth increase with length 16. However, an increase in rill length and width leads to an increase in runoff and rill depth, and rill erosion becomes increasingly intense, which accelerates rill development 15,18. The cross-sectional area of a rill is positively correlated with the rill catchment area. The greater the flow of water into a ditch, the more serious is rill erosion, and the larger the rill cross-sectional area 19. Asymmetry in a cross-section is the main feature in the erosion of gullies, and it is an extremely important parameter used to describe the morphological and dynamic characteristics of a watershed 20,21. Cross-sectional asymmetry was first used to evaluate the morphologies of river beds, and was subsequently used to describe the cross-sectional morphologies of channels 20,22. However, systematic quantification of rill asymmetry is still lacking.
Cross-sectional asymmetry is the result of several combined factors, such as bedrock 23–25, climate 26, vegetation 27,28, and topography. With regard to bedrock, studies in loess areas have found that the slope of a cross-section is steeper on the exposed side of the bedrock, and gentler on the side covered by the loess layer. This is because eroding the bedrock becomes more difficult than eroding loess deposits24. With regard to climate, the sunward side is easily corroded by glacial melt runoff and expands to the rear side to form an asymmetric channel. This is because when the solar incident angle is large at noon and afternoon, the temperature of the sunward side groove wall increases, and it becomes more susceptible to erosion 26. With regard to vegetation, a slope with good vegetation development has relatively low levels of runoff and erosion; a slope with poor vegetation development, or bare patches, has relatively high levels of runoff and erosion. The varying levels of runoff and erosion are integral in forming an asymmetrical channel cross-section 27,28. With regard to topography, differences in topographic factors, such as slope 29, slope length 29, gully depth30, and catchment area, all affect the evolution of asymmetrical cross-sections. However, currently, scholars believe that topography affects small regional climates and vegetation conditions indirectly, creating channel cross-sectional asymmetry. Most studies concentrate on large-scale channels such as gullies, and there are few studies on the rill cross-sectional asymmetry ratio (RCA) 23,24,27,31.
Although there have been several studies on rill cross-sectional asymmetry, the influence of cross-sectional asymmetry on rill erosion, and the causes of cross-sectional asymmetry. However, quantitative research on the asymmetry characteristics of rill cross-sections is still lacking, and how topographic factors affect rill cross-sectional asymmetry remains to be resolved. The objectives of this study are: (1) To establish a rill cross-sectional asymmetric morphology index that describes the rill’s cross-sectional shape, and permits the selection of key topographic factors; (2) to analyze the relationship between rill cross-sectional asymmetry and rill topographic factors. This reveals the evolutionary laws and mechanisms underlying rill morphology, and provides a reference for ecological restoration and soil erosion management.