Abstract:
|
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 |