Representative elementary area for multifractal analysis of soil porosity using entropy dimension

Abstract

Abstract. The notion of representative elementary area (REA) developed to address heterogeneity and scale problems in quantitative soil pedology comes from the notion of representative elementary volume of fluid dynamics in porous media. The REA allows the identification of the minimum area of a soil block section that is required to represent the pedofeature of interest based on its distribution in soil space. In this paper eight samples were imaged with two different techniques: the confocal microscope and the conventional film camera. These techniques provided information about pore sizes between 3.62 µm and 161.98 µm, and between 39.72 µm and 1776.34 µm, respectively. Sixteen of the resulting digital images were then analyzed to investigate the representative elementary area of the multifractal patterns of the spatial distribution of voids related to the micro and macroporosity by means of the entropy dimension. Our results permit the location of the REA region over the domain of the microstructures rendered by the analysis of the microscope images. They also suggest that this region seemingly spans scales of the macrostructures as revealed by the analysis of the camera pictures.

Multifractal analysis of discretized X-ray CT images for the characterization of soil macropore structures

“…The binarization algorithm was coded in MATLAB® (version R2007). Matrox® Inspector v.4.1 (Matrox Electronic Systems Ltd.) was used to describe the porosity for each of the 2-D sectional binarized images (San José Martínez et al, 2007). It was assumed that single pixel objects were artifacts of the imaging process (Hatano et al, 1992;VandenBygaart and Protz, 1999) and only voids with more than four connected pixels were considered, which corresponds to macropores with an equivalent diameter of 0.78 mm.…”

Quantitative evaluation of pore characteristics of sodic soils reclaimed by flue gas desulphurization gypsum using X‐ray computed tomography

“…Previous review articles and research papers have offered sufficient study cases in exploring the reliability of applying X‐ray CT to quantify the soil pore characteristics (Cnudde & Boone, ; Haeffneff, ; Naveed et al, ; Taina et al ., 2008; Zhou, Mooney, & Peng, ). For example, studies have been widely carried out on segmentation of X‐ray CT images (Baveye et al, ; Iassonov, Gebrenegus, & Tuller, ; Schlüter, Sheppard, Brown, & Wildenschild, ) involving image resolution selection (Sleutel et al, ; Wildenschild et al, ), representative elementary area identification (San José Martínez, Caniego, García‐Gutiérrez, & Espejo, ), and optimal thresholding methods (Elliot & Heck, ; Smet, Plougonven, Leonard, Degré, & Beckers, ; Wang, Kravchenko, Smucker, & Rivers, ); quantification and reconstruction of the pore structure (Marcelino, Cnudde, Vansteelandt, & Carò, ) such as characterization of macropores (Garbout, Munkholm, & Hansen, ; Luo, Lin, & Schmidt, ), extraction of three‐dimensional (3D) typical pore parameters (Al‐Raoush & Willson, ; Luo, Lin, & Li, ), and assessing the spatial variability of soil structure (Carducci, Zinn, Rossoni, Heck, & Oliveira, ); as well as the relationship between pore characteristics and soil functions (Helliwell et al, ) including correlations with soil physical properties (Anderson, Gantzer, Boone, & Tully, ; Munkholm, Heck, & Deen, ) and explanation of the hydraulic conductivity (Luo, Lin, & Halleck, ; Naveed et al, ; Paradelo et al, ; Tracy et al, ). Although the majority of current case studies focus on naturally cultivated soils, there are still some reports confirming that images extracted from X‐ray CT are effective in quantifying pore characteristics of unnaturally soils such as reconstructed, degraded, and reclaimed soils (Dowuona, Taina, & Heck, ; Langmaack, Schrader, Rapp‐Bernhardt, & Kotzke, ; Li, Shao, & Jia, ; Wang, Guo, Bai, & Yang, ).…”

Lacunarity of soil macropore space arrangement of CT images: Effect of soil management and depth

“…When the logarithm of lacunarity is very close to zero before the size of the largest cubic box is attained, no new information is gained about the spatial arrangement of the geometrical structure under investigation with cubic boxes of larger size. In this case, it could be said that a representative elementary volume (REV) is attained within the size of the sample (VandenBygaart and Protz, 1999;San José Martínez et al, 2007;Luo and Lin, 2009). Therefore, lacunarity could provide a new approach to estimating REV.…”