Multifractal Characterization of Soil Particle‐Size Distributions

Abstract

(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.

Scaling in stream communities

“…By contrast, small species, such as rotifers, have a faster spatiotemporal turnover than larger ones (Schmid-Araya 2000) and may respond to microhabitat changes outside the spatial scale of the current study. Moreover, sediment particle-size distributions display single-fractal and multifractal patterns if smaller particle sizes are included in the analysis (Posadas et al 2001). These patterns suggest that a wider range of particle-pore sizes might display multifractal scaling, also affecting smaller invertebrate species of the benthic community.…”

Multifractal Characterization of Pore Size Distributions of Peat Soil

“…In soil science, the multifractal concept has been applied to analyze the pore size distribution and particles of soil [6][7][8], the image of a thin slice of soil [9], the structure of clay [10], the matrix pore structure of a porous medium [11], soil surface pressure [12] and soil spatial variability [13]. Muller and McCauley [4] were successful in applying the fractal method to characterize the properties of the fluid flow of sedimentary rocks.…”

Spatial Analyses of Soil Chemical Properties from a Remodeled Paddy Field as Affected by Wet Land Leveling

“…This method can apply to quantify the interpolation of spatial patterns from point data (semivariogram) and to estimate distribution of properties at the interest scale (kriging) (Western et al, 1998). Semivariogram analysis has been applied to quantify variability of soil physical property distribution, such as porosity or pore structure (Cislerova and Votrabova, 2002;Posadas et al, 2003), soil moisture distribution (Western et al, 1998;Western et al, 2004;Brocca et al, 2007), microbiological property distribution (Goovaaerts, 1998;Matumbu et al, 2014), crop yield distribution (Miller et al, 1987;Green and Erskine, 2004) and soil chemical property distribution (Markus and McBratney, 2001;Yasrebi et al, 2009;Li et al, 2010).…”