Fractal and Compositional Analysis of Soil Aggregation

Parent, Léon-Étienne
Parent, Serge-Étienne
Kätterer, Thomas
Egozcue, Juan José
A soil aggregate is made of closely packed sand, silt, clay, and organic particles building up soil structure. Soil aggregation is a soil quality index integrating the chemical, physical, and biological processes involved in the genesis of soil structure and tilth. Aggregate size distribution is determined by sieving a fixed amount of soil mass under mechanical stress and is commonly synthesized by the mean weight diameter (MWD) and fractal dimensions such as the fragmentation fractal dimensions ( ). A fractal is a rough object that can be broken down into a number of reduced-size copies of the original object. Equations have been developed to compute bounded and unbounded scaling factors as measures of fractal dimensions based on assumptions about average diameter, bulk density, shape and probability of failure of sieved particles. The log-log relationship between particle diameter and cumulative number or mass of aggregates or soil particles above a given diameter often shows more or less uniform fractal patterns. Multi-fractal (slopes showing several values ≤ 3) and non fractal patterns or incomplete fragmentation ( ) have been reported. Scaling factors are curvefitting parameters 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 assumptions and dimensional constraints of fractal analysis. Our objective was to compare MWD, fractal scaling factors and ilr coordinates using published data. In the first dataset, MWD was found to be biased by excessively high weight being given to the largest aggregate-size. Eight ilr coordinates contrasting micro- vs. macro-aggregates were related to fragmentation fractal dimensions, most of which were below 2 or above 3, a theoretical impossibility for geometric fractals. The critical ilr value separating scaling factors 3 and > 3 was close to zero. In a second dataset, the Aitchison distance computed across ilr coordinates proved to be a useful measure of the degree of soil aggregation, agradation or degradation against a reference composition such as that of primary particles, bare fallow or permanent grass. The individual contributions of ilr coordinates to the Aitchison distance can be interpreted in terms of sign and amplitude and be related to soil properties and processes mediated by soil aggregation ​
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