For 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. Indeed, when the solar incident angle is high in the afternoon and at noon, the temperature of the groove wall on the sunward side rises, making it more susceptible to erosion 26. Regarding climate, the sunward side is easily corroded by glacial melt runoff and expands to the rear side to form an asymmetric channel 26. This is because it is more difficult to erode bedrock than to erode loess deposits 25.
With regard to bedrock, studies in loess areas have revealed that a cross-slope section is steeper on the exposed side of the bedrock and gentler on the side covered by the loess layer. However, a method for the systematic quantification of rill asymmetry is still lacking.Ĭross-sectional asymmetry is the result of several combined factors, such as bedrock 24, 25, climate 26, vegetation 27, 28, and topography. Cross-sectional asymmetry was first used to evaluate the morphologies of river beds and then to describe the morphologies of channels 23. Asymmetry in a cross-section is the main feature in eroding gullies and it is an extremely important parameter used to describe the morphological and dynamic characteristics of a watershed 22. The greater the flow of water into a ditch, the more serious the rill erosion, and the larger the rill cross-sectional area 21. The cross-sectional area of a rill is positively correlated with the rill catchment area. 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 17, 20.
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 18. The morphological characteristics of a rill cross-section include its length 17, depth 17, width 18, and asymmetry ratio 19, and these characteristics change with the evolution of the rill 14. With the continuous evolution of a rill, a “U” or “box” cross-section gradually appears, but the rill is still dominated by a “V”-shaped cross-section 15, 16. In the early stages of rill development, the rill cross-section generally presents a “V” shape 14. Rills can exhibit a planar, cross-sectional, or longitudinal morphology, and the cross-section is the most important morphological feature reflecting the development stage of the rill 13. Therefore, it is paramount to study the morphological characteristics of rill erosion. The morphological characteristics of rills form the basis for understanding the underlying mechanisms of the evolution of rills and are important for estimating rill erosion volumes and rates 10, 11, 12. Research on rills has mainly focused on the origin of rill cross-sectional morphologies 5, and describing the relationship between general rill cross-sectional morphology and rill erosion 6, 7, 8, 9. Rill erosion is one of the initial forms of channel erosion 3, usually eventually forming a gully 4. Gully erosion is one of the most important soil erosion processes and results in a soil loss rate of around 85% 2. Soil erosion is one of the main environmental problems affecting humans and leads to around 5 to 7 million hectares of farmland loss every year 1. (3) Seven topographic factors were divided into two types of principal components: the first represents the rill slope surface shape and the rill shape, and the second represents the difference between the two sides of the rill. The difference between the catchment areas on both sides has a significant linear correlation with the asymmetry ratio of the width (r = 0.07, p < 0.05). (2) There is an extremely significant positive correlation between the slope difference and the rill cross-section asymmetry ratio ( p < 0.01) the asymmetry ratio increases as the slope difference on both sides ( B) increases, and the directionality of the asymmetry ratio is affected by B. The results of correlation analysis and principal component analysis to investigate the topographical conditions of rill development show that: (1) asymmetry is the main feature in rill cross-sections 53% of rill cross-sections are right-biased and 47% are left-biased. To explore the relationship between rill topography and rill cross-sectional asymmetry, we used the microtopographic profiler method to measure 712 groups of rill cross-sections in the Yuanmou dry-hot valley area. Rill erosion is one of the most common types of erosion, and the development conditions of the asymmetric characteristics of rill cross-sections are still relatively poorly understood.
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