Guanghe Zhang

Topography critically affects the occurrence of soil erosion, and computing slope spectrum information entropy (SSIE) allows for the convenient mirroring of the patterns of macroscopic topographic variation. However, whether SSIE can be effectively utilized for the quantitative assessment of soil erosion across various types of water-erosion areas and the specific methodology for its application remain unclear. This study focused on the quantitative relationship between SSIE, the slope length and slope steepness (LS) factor within various types of water-erosion areas across different spatial scales in China using multi-source geographic information data and technical tools such as remote sensing and geographic information systems. The results revealed (1) clear consistency in the spatial patterns of SSIE and the LS factor, which both displayed a distinct three-step distribution pattern from south to north. (2) The power model (Y = A·X^B) demonstrated a superior capacity to explaining the relationship between SSIE and the LS factors compared to the linear or exponential models, as evidenced by a higher coefficient of determination (R²). R² values of different evaluation units (second-grade water-erosion area, third-grade water-erosion area, 30 km × 30 km grid, and 15 km × 15 km grid) were 0.88, 0.88, 0.81, and 0.79, respectively. (3) Despite a range of variances across various spatial scale evaluation units and different types of water-erosion areas, no significant disparities were evident within the power model. These findings offer a new topographic factor that can be incorporated into models designed for the expedited evaluation of soil erosion rates across water-erosion areas. Information about the proximity of the SSIE to the LS factor is valuable for enhancing the practical utilization of SSIE in the quantitative evaluation of soil erosion.

Non-homogeneous soil’s high gravel content (also known as the “soil-rock dual structure”) may render it more prone to erosion and the significant development of gullies. In order to reveal the morphological characteristics and erosion rate of gullies in “soil-rock dual structure” areas, this study focused on the Shagou Reservoir basin in the Yimeng mountain area as the study area. Based on a complete digital orthophoto map (DOM, 0.03 m) and a digital elevation model (DEM, 0.03 m) acquired by an unmanned aerial vehicle (UAV), the researchers calculated the length (L), top width (TW), depth (D), area (A) and volume (V) of 19 gullies and built and optimized the volume estimation model. The DOM and the DEM were used to modify the morphological parameters of 43 gullies extracted from high-resolution remote sensing (RS) stereopair images (Worldview, 0.5 m), and the development and evolution of gully erosion were evaluated in large scale. The results showed that: (1) after correction, the average relative errors of parameters L, TW, D and A computed from the UAV data and the high-resolution RS stereopair image data fell below 0.005%; (2) the mean of TW/D was 5.20, i.e., the lateral erosion development of gullies far outweighed the downcutting erosion. The retrogressive erosion, lateral erosion and downcutting erosion rates of gullies were 0.01~0.83 m/a (averaged at 0.23 m/a), 0.01~0.68 m/a (averaged at 0.25 m/a) and 0.01~0.19 m/a (averaged at 0.09 m/a), respectively, between 2014 and 2021; (3) the volume-area (V-A) model for gullies is the optimal one (p < 0.01, R² = 0.944).A total of 90.7% of the gully volume was growing at an erosion rate of 0.42~399.39 m³/a and the total erosion rate of the gullies was 3181.56 m³/a from 2014 to 2021. These research findings can serve as a basis for the quantitative modeling of gully erosion in water-eroded locations with a large-dimension “soil-rock dual structure”.