Relationship between the fractal dimension of soil aggregates and erosion in degraded lands in the Qinling–Ba mountainous area of China

Abstract The aggregate size distribution (ASD) is an important soil characteristic that is influenced by soil erosion processes and land degradation. However, very few studies have aimed to explore the responses of the soil ASD to land degradation. With respect to the Qinling–Ba mountainous area in southern Shaanxi Province, China, this study aimed to investigate the soil ASD in different degraded land ecosystems and their responses to erosion using fractal theory. Thirty‐three plots (7 m 2 ) classified into five land use types representing different degrees of degradation (agriculture, horticulture, grassland, coppices and mature forest) were established to determine and compare runoff and sediment yield. A total of 99 soil samples were collected, and the soil ASD was analysed to determine the fractal dimension (FD). The results revealed that the aggregate FD values ranged from 2.21 to 2.44 for the dry‐sieving method (FD dry ) and from 2.70 to 2.82 for the wet‐sieving method (FD wet ). The average FD dry values followed the order of coppices > agriculture > mature forest > horticulture > grassland, whereas the average FD wet values followed the order of grassland > horticulture > agriculture > coppices > mature forest. Lower FD wet values were associated with soil dominated by larger aggregates. Statistically significant differences in runoff and sediment were found between agriculture, horticulture, grassland and coppices and mature forest at the 0.05 level of significance. The erosion rate was positively and linearly related to the FD wet value ( R 2 = 0.74, p < 0.05) and negatively related to the FD dry value ( R 2 = 0.136, p < 0.5). The results indicated that erosion is more notably related to the FD wet value than to the FD dry value. This study highlights the importance of understanding the soil ASD and its implications for erosion processes, which can inform sustainable land management practices and strategies for soil conservation in this region.