Soil particle size distribution (PSD), a fundamental and vital soil physical property, influences the physical, chemical and biological processes in terrestrial ecosystems. However, the vertical and horizontal variations of soil PSD have not been fully elucidated in deep soil profiles due to observational constraints, with most knowledge gained from surface soils. Therefore, we obtained a total of 1320 soil samples from 22 soil profiles with a maximum depth of 21 m on a hillslope of the Chinese Loess Plateau, and applied fractal theory (single fractal and multifractal dimensions) to describe soil PSD. We found mean values of D (the single fractal dimension), D0 (the capacity dimension, representing the PSD's range), D1 (the information entropy dimension, representing the PSD's concentration), D2 (the correlation dimension, representing the PSD's uniformity), D1/D0, Δα (representing the distribution’s heterogeneity of the whole fractal structure) and Δf (representing the asymmetry characteristic of the singularity spectra) in loess deposits were 2.20 ± 0.06, 0.94 ± 0.02, 0.85 ± 0.01, 0.80 ± 0.02, 0.90 ± 0.02, 2.31 ± 0.45, and 0.57 ± 0.07 (mean ± standard deviation), respectively. Mean values of D, D0, D1, D2, Δα and Δf decreased with soil depth, while D1/D0 increased with depth, suggesting the overall homogeneity of PSD increased within 0–21 m soil profiles in the Loess Plateau. Additionally, D0 decreased significantly along deep soil profiles in both vertical and horizontal directions, indicating that the PSD occupied a relatively narrower range in deeper soil layers compared with the surface. In summary, our study confirms that the spatial heterogeneity of the PSD decreased with soil depth in loess deposits, mainly manifested in a reduced multifractal dimension D0 (i.e., the PSD's range decreased), which improves the fundamental knowledge for predicting deep soil properties in Earth's Critical Zone.
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