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Fractal and Compositional Analysis of Soil Aggregation

A soil aggregate is made of closely packed sand, silt, clay, and organic particles building upsoil structure. Soil aggregation is a soil quality index integrating the chemical, physical, andbiological processes involved in the genesis of soil structure and tilth. Aggregate sizedistribution is determined by sieving a fixed amount of soil mass under mechanical stress andis commonly synthesized by the mean weight diameter (MWD) and fractal dimensions such asthe fragmentation fractal dimensions ( ). A fractal is a rough object that can be broken downinto a number of reduced-size copies of the original object. Equations have been developed tocompute bounded and unbounded scaling factors as measures of fractal dimensions based onassumptions about average diameter, bulk density, shape and probability of failure of sievedparticles. The log-log relationship between particle diameter and cumulative number or massof aggregates or soil particles above a given diameter often shows more or less uniform fractalpatterns. Multi-fractal (slopes showing several values ≤ 3) and non fractal patterns orincomplete fragmentation ( ) have been reported. Scaling factors are curvefittingparameters that are very sensitive to the choice of the fractal domain about breakpoints.Compositional data analysis using sequential binary partitions for isometric log ratio (ilr)coordinates with orthonormal basis provides a novel approach that avoids the assumptionsand dimensional constraints of fractal analysis. Our objective was to compare MWD, fractalscaling factors and ilr coordinates using published data. In the first dataset, MWD was foundto be biased by excessively high weight being given to the largest aggregate-size. Eight ilrcoordinates contrasting micro- vs. macro-aggregates were related to fragmentation fractaldimensions, most of which were below 2 or above 3, a theoretical impossibility for geometricfractals. The critical ilr value separating scaling factors 3 and > 3 was close to zero. In asecond dataset, the Aitchison distance computed across ilr coordinates proved to be a usefulmeasure of the degree of soil aggregation, agradation or degradation against a referencecomposition such as that of primary particles, bare fallow or permanent grass. The individualcontributions of ilr coordinates to the Aitchison distance can be interpreted in terms of signand amplitude and be related to soil properties and processes mediated by soil aggregation

Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada

Other contributions: Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Author: Parent, Léon-Étienne
Parent, Serge-Étienne
Kätterer, Thomas
Egozcue, Juan José
Abstract: A soil aggregate is made of closely packed sand, silt, clay, and organic particles building upsoil structure. Soil aggregation is a soil quality index integrating the chemical, physical, andbiological processes involved in the genesis of soil structure and tilth. Aggregate sizedistribution is determined by sieving a fixed amount of soil mass under mechanical stress andis commonly synthesized by the mean weight diameter (MWD) and fractal dimensions such asthe fragmentation fractal dimensions ( ). A fractal is a rough object that can be broken downinto a number of reduced-size copies of the original object. Equations have been developed tocompute bounded and unbounded scaling factors as measures of fractal dimensions based onassumptions about average diameter, bulk density, shape and probability of failure of sievedparticles. The log-log relationship between particle diameter and cumulative number or massof aggregates or soil particles above a given diameter often shows more or less uniform fractalpatterns. Multi-fractal (slopes showing several values ≤ 3) and non fractal patterns orincomplete fragmentation ( ) have been reported. Scaling factors are curvefittingparameters that are very sensitive to the choice of the fractal domain about breakpoints.Compositional data analysis using sequential binary partitions for isometric log ratio (ilr)coordinates with orthonormal basis provides a novel approach that avoids the assumptionsand dimensional constraints of fractal analysis. Our objective was to compare MWD, fractalscaling factors and ilr coordinates using published data. In the first dataset, MWD was foundto be biased by excessively high weight being given to the largest aggregate-size. Eight ilrcoordinates contrasting micro- vs. macro-aggregates were related to fragmentation fractaldimensions, most of which were below 2 or above 3, a theoretical impossibility for geometricfractals. The critical ilr value separating scaling factors 3 and > 3 was close to zero. In asecond dataset, the Aitchison distance computed across ilr coordinates proved to be a usefulmeasure of the degree of soil aggregation, agradation or degradation against a referencecomposition such as that of primary particles, bare fallow or permanent grass. The individualcontributions of ilr coordinates to the Aitchison distance can be interpreted in terms of signand amplitude and be related to soil properties and processes mediated by soil aggregation
Document access: http://hdl.handle.net/2072/273642
Language: eng
Publisher: Universitat de Girona. Departament d’Informàtica i Matemàtica Aplicada
Rights: Tots els drets reservats
Subject: Estadística matemàtica -- Congressos
Mathematical statistics -- Congresses
Anàlisi multivariable -- Congressos
Mathematical statistics -- Congresses
Biologia -- Mètodes estadístics -- Congressos
Biology -- Statistical methods -- Congresses
Fractals -- Congressos
Title: Fractal and Compositional Analysis of Soil Aggregation
Type: info:eu-repo/semantics/conferenceObject
Repository: Recercat

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