Particle fractal dimension and total phosphorus of soil in a typical watershed of Yangtze River, China

Phosphorous (P) is an essential nutrient in soil which can lead to eutrophication when eroding into rivers or lakes. As a new method to represent soil properties, fractal theory was applied to study soil characteristics and related process. To understand the correlation of total soil P (TSP) and fractal dimension (D) with the effect of soil depth and slope gradient, soil grid samples were collected at 0–10, 10–20 and 20–40 cm depths in Yingwugou watershed, Yangtze River, China. The physico-chemical properties of the samples were analyzed to determine the TSP content and D. Fractal scaling theory was then applied to establish the relationship between D and TSP. With silt as the dominant particle size, the D values of the study area were in the range of 2.42–2.55. On the flat ground, more fine particles (clay and silt) were reserved and on the contrary relatively high content of coarse sand was retained on steep slope. D values decreased with slope and soil depth increased. The average TSP contents of the three layers were 0.65, 0.63 and 0.57 g/kg for 0–10, 10–20 and 20–40 cm, respectively, showing a decreasing tendency with increased soil depth. With increasing slope gradient, the TSP contents decreased first and then increased slowly. The TSP contents were positively related to silt content (P < 0.05) and clay content (P < 0.05) and negatively associated with sand contents (P < 0.01). There was an one-dimensional linear relationship (n = 530, R ² = 0.16, P < 0.01) between TSP content and D values. The correlation would improve when concrete slope was taken into account. To better understand and control soil erosion, the relationship between D value and soil nutrients deserves more attention.