Multifractal Analysis of Soil Properties along Two Perpendicular Transects

Abstract

The spatial variability of soil properties can be best characterized through concepts of scale invariance, fractals, and multifractals. The objectives of this study were to analyze and to compare the scaling patterns and structural heterogeneity of soil properties across two transects in Campinas, SP, Brazil, using the multifractal formalism. Two transects were marked parallel and perpendicular to land slope, with a length of 2.28 and 1.98 km, respectively. Soil samples were collected at the 0 to 20 cm depth every 30 m. The soil properties analyzed were: texture (sand, silt, clay), pH (H2O and KCl), organic carbon (OC) content, exchangeable Ca, H, and Al, exchangeable bases (SB), cation exchange capacity (CEC), and percent base saturation (V). Spatial variability of soil properties was controlled by natural causes, including parent material and topography, and by soil use and management. The variability of pH across the two transects was characterized by either quasi‐monofractal behavior or by a relatively low degree of multifractality. The other soil properties studied showed stronger degrees of multifractality. Hence, the multifractality for OC and silt content was much higher at the transect perpendicular to land slope. Variables from the soil exchange complex, particularly exchangeable Al, Ca, and SB, were characterized by higher multifractal indices in the two transects. Patterns of spatial distribution assessed by multifractal analysis were linked to soil forming factors and processes. Our results suggest that scale heterogeneity in the spatial distribution of soil properties was enhanced by the interaction of various natural or anthropogenic sources of variability.

Multifractal analysis of soil fauna diversity indexes

“…The method of moment was used to determine the multifractal parameters of the soil fauna. A transect of 381 m was divided into successive smaller segments, generating partition functions in k (k = 1, 2, 3 ...) and generating scales of d segment numbers, N (δ) = 2 k of characteristic length, δ = L × 2 -k (Evertsz and Mandelbrot 1992;Vidal-Vázquez et al 2013).…”

Multifractal Analysis of Vertical Profiles of Soil Penetration Resistance at Varying Water Contents

“…Multifractal analysis has been conducted in different ways. The method of moments (Evertsz and Mandelbrot, 1992) has been frequently used to perform multifractal analysis of one‐dimensional soil datasets measured across transects, either in the horizontal (Folorunso et al, 1994; Caniego et al, 2005; Zeleke and Si, 2006; Vidal‐Vázquez et al, 2013) or in the vertical (San José Martínez et al, 2010; Paz‐Ferreiro et al, 2013; Siqueira et al, 2013) directions at several scales. Therefore, multifractal concepts and procedures used in our work are only briefly outlined here.…”

“…In practice, accuracy also depends on the range of q moments used to implement multifractal analysis. This is because the correlation coefficients between the logarithms of normalized measures versus the logarithm of the scale used to construct the partition function decrease as q increases (Vidal‐Vázquez et al, 2013). We computed partition functions for successive segment sizes in steps of 2 k , 0 ≤ k ≤ 6 in the range −5 < q < 5, and results were satisfactory.…”

“…Multifractal analysis has been conducted in different ways. The method of moments (Evertsz and Mandelbrot, 1992) has been frequently used to perform multifractal analysis of one-dimensional soil datasets measured across transects, either in the horizontal (Folorunso et al, 1994;Caniego et al, 2005;Zeleke and Si, 2006;Vidal-Vázquez et al, 2013) To implement multifractal analysis, suppose m(S) represents a measure (field) defined on a set S in R D , where D = 1, 2, or 3. To assess the heterogeneity of the measure, m i , the space R D can be split into n boxes of the same linear size d, that is, equal intervals in R 1 (Evertsz and Mandelbrot, 1992).…”

“…Also, Millán et al (2012) conducted a geostatistical study to analyze the spatial structure of soil PR and other soil properties measured in this field. Furthermore, multifractal analysis has provided valuable information to assess several soil properties and processes, including soil particle size distribution (Posadas et al, 2001; Miranda et al, 2006), soil pore size distributions (Posadas et al, 2003; Caniego et al, 2003; Vidal Vázquez et al, 2008; Paz‐Ferreiro et al, 2010), and spatial variability of soil properties (Kravchenko, 2008; Caniego et al, 2005; Zeleke and Si, 2006; Vidal‐Vázquez et al, 2013). Similarly, the multifractal formalism has been used to analyze patterns of spatial variation of PR datasets measured along transects (Folorunso et al, 1994) or on a grid (Roisin, 2007).…”