Spatial arrangement of soil pores determines soil structure and is important to model soil processes. Geometric properties of individual pores can be estimated from thin sections, but there is no satisfactory method to quantify the complexity of their spatial arrangement. The objective of this work was to apply a multifractal technique to quantify properties of ten contrasting soil pore systems. Binary images (500 by 750 pixels, 74.2 μm pixel−1) were obtained from thin sections and analyzed to obtain f(α) spectra. Pore area and pore perimeter were measured from each image and used to estimate a shape factor for pores with area larger than 0.27 × 106 μm2 Mean area of the lower (MAL) and upper (MAU) one‐half of cumulative pore area distributions were calculated. Pore structures with large (MAU > 10 × 106 μm2) and elongated pores exhibited “flat” f(α)‐spectra typical of homogenous systems (three soils). Massive type structure with small (MAU < 1 × 106 μm2) rounded and irregular pores resulted in asymmetric f(α)‐spectra (two soils). Well defined and symmetric f(α)‐spectra were obtained with soil structures having elongated pores of intermediate size (1 × 106 < MAU < 10 × 106 μm2) clustered around relatively small structural units (five soils). Multifractal parameters defining the maximum of the f(α)‐spectra were correlated to total porosity (P < 0.001), and silt content (P < 0.05). This study demonstrates that the spatial arrangement of contrasting soil structures can be quantified and separated by the properties of their f(α)‐spectra. Multifractal parameters quantifying spatial arrangement of soil pores could be used to improve classifications of soil structure.

(1999), using the model of Turcotte (1986) and Tyler and Wheatcraft (1992), also found that three domains A particle-size distribution (PSD) constitutes a fundamental soil characterized the cumulative PSD of 19 soils. They assoproperty correlated to many other soil properties. Accurate representations of PSDs are, therefore, needed for soil characterization and ciated the power exponent in each domain with fractal prediction purposes. A power-law dependence of particle mass on dimensions defining scaling in the clay, silt, or sand particle diameter has been used to model soil PSDs, and such powerdomains. law dependence has been interpreted as being the result of a fractal A distribution of particle sizes reflects the relative distribution of particle sizes characterized with a single fractal dimenbalance of weathering and pedogenetic processes. Prision. However, recent studies have shown that a single fractal dimenmary minerals, generally present in the sand-and siltsion is not sufficient to characterize a distribution for the entire range size fractions, originate from weathering of a parent of particle sizes. The objective of this study was to apply multifractal material, while clay minerals are the result of weathering techniques to characterize contrasting PSDs and to identify multifracand synthesis of new minerals. The different origin of tal parameters potentially useful for classification and prediction. The the various size fractions may explain the various scaling multifractal spectra of 30 PSDs covering a wide range of soil textural classes were analyzed. Parameters calculated from each multifractal domains observed in soil PSD (Wu et al., 1993; Bittelli spectrum were: (i) the Hausdorff dimension, f(␣); (ii) the singularities et al., 1999). Grout et al. (1998) found that a single of strength, ␣; (iii) the generalized fractal dimension, D q ; and (iv) fractal dimension obtained from the model of Tyler their conjugate parameter the mass exponent, (q), calculated in the and Wheatcraft (1992) did not describe adequately the range of moment orders (q) of between Ϫ10 and ϩ10 taken at 0.5 distribution of particle sizes of three soils, and proposed lag increments. Multifractal scaling was evident by an increase in the multifractal techniques as a promising alternative to difference between the capacity D 0 and the entropy D 1 dimensions characterize PSD. Multifractal distributions may be best for soils with more than 10% clay content. Soils with Ͻ10% clay suited to represent the multiplicative action of the varicontent exhibited single scaling. Our results indicate that multifractal ous pedogenetic processes acting on a parent material parameters are promising descriptors of PSDs. Differences in scaling and resulting in a given distribution of particle sizes. properties of PSDs should be considered in future studies.

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