Spatial heterogeneity of surface roughness on tilled loess slopes in erosion stages

The main soil erosion areas of the Chinese Loess Plateau are tilled slopes. The knowledge of their spatial heterogeneity will contribute to the understanding of erosion mechanisms on a microtopographic scale. In this study, the spatial heterogeneity of four conventionally tilled slopes was examined under simulated rainfall conditions using a semivariogram-based methodological framework. Results show that all tilled slopes have a relatively stable spatial structure and the erosion stages of all tilled slopes have a similar spatial variability. The rainfall in the splash, sheet, and rill erosion stages has a degree of relief effect, strengthening effect, and relief effect on the surface roughness, respectively. However, the effects of tillage practices and slope gradient on the spatial heterogeneity are much larger than those of the rainfall. The spatial heterogeneity decreases with increasing slope gradient. The general autocorrelation scale of the tilled slopes is 3.15 m and their fractal dimension ranges from 1.59 to 1.85. The tilled slopes have certain anisotropy with respect to the slope direction from 10° to 22.5° while they show isotropy or weaker anisotropy in other directions. In this work, a semivariogram-based methodological framework was established for the spatial heterogeneity of microtopographic-scale slopes. The results also provide a theoretical foundation for future tillage measures on sloping fields of the Loess Plateau.