Multifractal parameters of soil particle size as key indicators of the soil moisture distribution

Determining the soil moisture content (SMC) distribution is indispensable for field management, especially in arid and semiarid regions. Effective parameters can contribute to the optimization of SMC models for accurate SMC prediction. Therefore, in this study, the relationships between the SMC and multifractal parameters (D-2, D-v, D-s, A(v), and F-v denote the correlation dimension, property of small probability and large probability, spectrum width, and symmetry of spectrum shape, respectively) of the soil particle size distribution (PSD) were explored in the hilly loess region of China. A grid method was adopted (20 m x 20 m, total = 384 points) to sample the SMC in the 0-40 cm and 40-80 cm soil layers on the second, eighth, and twelfth days after the first rainfall, which were defined as the early sampling (ES), medium sampling (MS), and late sampling (LS), respectively. We found that the variation in the SMC explained by the multifractal parameters increased as SMC decreased, where they accounted for 40.07% and 75.75% of the SMC in the 0-40 cm and 40-80 cm soil layers in LS, respectively. The variation in the SMC in the 0-40 cm explained by the multifractal parameters was lower than that in the 40-80 cm soil layer in all sampling stages. The equations fitted for the whole soil layer were significant in all sampling stages (P < 0.01). A(v) (31.95%) and D-v (13.59%) had negative correlations with SMC, and their relative importance values with respect to SMC were high in all sampling stages (P < 0.05). SMC at higher values had a positive correlation with F-v, whereas SMC at lower values had a significant positive correlation with D-2 and negative correlation with D-s, and these two parameters in the MS and LS stages explained more than 75% of the variation in the SMC in the 40-80 cm soil layer. These results suggest that the characteristics of the soil PSD can be described in detail by the multifractal parameters, which can directly reflect the SMC. Thus, we conclude that SMC is closely related to the multifractal parameters of the PSD (A(v), D-v, D-s, D-2, and F-v) and it can be applied to optimize SMC models.