Multifractal characteristics of particle size distributions (50–200 m) in soils in the vadose zone on the Loess Plateau, China

Abstract The soil particle size distribution (PSD) is an important and basic physical property that determines many other chemical, physical, and biological properties of soil. Thus, quantitatively characterizing the soil PSD is important. However, the PSDs have not been characterized previously in deep soil profiles on the Loess Plateau, China. Therefore, in the present study, we employed single fractal theory and multifractal theory to quantitatively characterize these PSDs. Soil samples (50–200 m) were collected from the top of the soil profile down to the bedrock by drilling at five sites on the Loess Plateau in China. The results showed that the sand content had the highest coefficient of variation (CV) whereas the silt content had the lowest CV. Single fractal dimension (D) analysis detected significant positive relationships between D and the silt and clay contents, but a significant negative relationship with the sand content. Multifractal analysis indicated that the capacity dimension (D0) values at five sites tended to increase from south to north, whereas a decreasing trend was determined for the information dimension/capacity dimension (D1/D0). Yangling had the lowest Δα and ΔD values, whereas Ansai had the highest. The Δf values were highest at Ansai and Shenmu. Our results are important to understand the soil physical properties and to estimate the soil hydraulic properties in deep profiles on the Loess Plateau.