Influence of topography on the asymmetry of rill cross-sections in the Yuanmou dry-hot valley

Statistical characteristics of rill cross-sectional asymmetry (RCA)

The rill cross-sectional asymmetry (RCA) is a key parameter in describing rill morphology and includes the asymmetry ratio of the width (Aw) and the asymmetry ratio of the area (Aa). It reflects the differences in certain aspects of natural conditions resulting in inconsistent development speeds on both sides of a rill cross-section. The cross-section was classified as left-biased if Aw, Aa < 0, quasi-symmetrical if Aw, Aa = 0, and right skewed if Aw, Aa > 0. The left/right deflection reflects that erosion on the right happened faster than on the left, so the slope on the left is not as steep as on the right. The results of this study show that asymmetry is a common phenomenon in the cross-section of a rill. The Aw ranged from − 1.77 to 1.97, with an average value of − 0.034. There were 374 cross-sections whose RCA was less than or equal to 0, meaning that 53% of the cross-sections were right-biased. The Aa ranged from − 1.81 to 1.71, with an average of − 0.046. There were 374 cross-sections with an RCA of less than or equal to 0, meaning that 53% of the cross-sections were right-biased (Fig. 1).

Figure 2 shows that there are four Aw groups in the interval (− 1.7, − 1.5), 53 groups in the interval (− 1.5, − 1.0), 144 groups in the interval (− 1.0, − 0.5), 173 groups in the interval (− 0.5, 0), 174 groups in the interval (0, 0.5), 120 groups in the interval (0.5, 1.0), 39 groups in the interval (1.0, 1.5), and five groups in the interval (1.5, 2). The Aa has 15 groups in the interval (− 1.8, − 1.5), 63 groups in the interval (− 1.5, − 1.0), 130 groups in the interval (− 1.0, − 0.5), 166 groups in the interval (− 0.5, 0), 161 groups in the interval (0, 0.5), 110 groups in the interval (0.5, 1.0), 53 groups in the interval (1.0, 1.5), and 14 groups in the interval (1.5, 2). The RCA of most cross-sections is concentrated in the interval (− 0.5, 0.5). This interval of Aw contains 491 cross-sections, accounting for 68.96% of the total. There are 470 cross-sections in this interval of Aa, accounting for 66.01% of the total. This indicates that, although the rill cross-section exhibits some asymmetry, the difference between both sides of the section is small (Fig. 2).

The influence of a single topographic factor on the RCA

Correlation analyses of the Aw, Aa, and the slope difference on both sides (B), rill length (L), rill slope length (I), rill head catchment area (A), difference between the catchment areas of both sides (R), rill bending coefficient (K), and location of the section angle of turning of the rill (J) were carried out. The results show that the main factors that have a significant linear correlation with the Aw and the Aa are B (p < 0.01), with correlation coefficients of 0.32 and 0.22, respectively (Fig. 3). That is, the greater the difference in slope between the two sides, the more asymmetric the rill cross-section. R also has a significant linear correlation with the Aw (p < 0.05), with a correlation coefficient of 0.07. This means that the greater the difference in the catchments between the left and right sides of the rill, the greater the asymmetry of the rill cross-section. However, other topographic factors have no significant correlation with the RCA.

B is the difference in slope between the left and right sides of the rill cross-section catchment area. The closer B gets to 0, the smaller the difference in slope between the left and right sides of the rill cross-section catchment area. When the catchment area slope on the right side of the cross-section is greater than that on the left side, B < 0; and when the catchment area slope on the left side of the cross-section is greater than that on the right side, B > 0. Grouping B reveals that the average RCA increases as B increases (Fig. 4). When B is (− 30, − 20), Aw is − 0.48 and Aa is − 0.38; when B is (− 20, − 10), Aw is − 0.36 and Aa is − 0.31; when B is (− 10, 0), Aw is − 0.23 and Aa is − 0.22; when B is (0, 10), Aw is 0.21 and Aa is 0.16; when B is (10, 20), Aw is 0.47 and Aa is 0.40; and when B is (20, 40), Aw is 0.31 and Aa is 0.13. These are relatively low values because this group only has two sets of cross-sections which cannot represent the characteristics of interval B. The sign of the RCA is the same as the sign of B. The directionality of the RCA is significantly affected by B. When the slope of the left catchment area is large, RCA > 0, and the rill cross-section appears to be left-biased; when the slope of the right catchment area is large, RCA < 0, and the cross-section appears to the righ-biased.

The influence of multiple topographic factors on the RCA

In order to explore the influence of multiple topographic factors on the RCA, principal component analysis (PCA) was used to extract the main feature components of the topographic data. The PCA results show that the nine topographic factors can be reflected by two principal components at 61.84% (characteristic value: 3.117+1.211=4.328 variables) (Table 1). Therefore, the analysis of the first two principal components could reflect most of the information from all the data.

The contribution rate of the first principal component is 44.534%. The characteristic is that the factor variables have high positive loads for the four factors L, I, A, and K. L has the largest contribution rate at 88.5%, followed by A, I, and K, at 87.5%, 81.1%, and 60.2%, respectively. Therefore, the first component represents the rill slope and rill shape.

The contribution rate of the second principal component is 17.303%. The characteristic is that the factor variables have high positive loads for the three factors B, J, and R. B has the largest contribution rate at 83.5%, followed by J and R, at 57.4% and 55.7%, respectively. Therefore, the second component represents the effect of the difference between the two sides of the rill.

Based on the correlation between the topographic factors and the RCA of a rill cross-section in the Yuanmou dry-hot valley area, the following was observed: asymmetry in rill cross-sections is ubiquitous. The distribution range of Aw is − 1.77 to 1.97, the average value is − 0.034, and the cross-section that is right-biased accounts for 53%. A correlation analysis of the RCA and seven topographic factors shows that B has a significant positive correlation with the Aw and Aa (p < 0.01), the average RCA increases as B increases, and the directionality of the RCA is affected by B. When B > 0, RCA > 0, and the rill cross-section appears to the left; when B < 0, RCA < 0, and the cross-section appears to the right. The difference in catchment area between the sides has a significant linear correlation with the Aw (p < 0.05). Other single topographic factors have no significant correlation with the RCA. Principal component analysis and calculations show that the first principal component represents the influence of the rill slope surface and rill shape on the rill cross-sectional asymmetry. The contribution rate is 44.534%, which is characterized by a high positive load on the L, I, A, and K factors. The second principal component represents the effect of the difference between the two sides of the rill. The contribution rate is 44.534%, which is characterized by a high positive load on the B, J, and R factors.

Source: Ecology - nature.com