Quantifying the Relationship between Slope Spectrum Information Entropy and the Slope Length and Slope Steepness Factor in Different Types of Water-Erosion Areas in China

Abstract

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.