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Fractal Dimensions of Soil Aggregate-size Distributions Calculated by Number and Mass

Department of Land Resource Science, Univ. of Guelph, Guelph, ON N1G 2W1, Canada

* Corresponding author.

ABSTRACT

The fractal dimension, D, has been used to characterize soil aggregate-size distributions. However, D is based on the number-size relationship. In most soils applications, it is the mass-size relationship that is determined. A number-size distribution can be generated from the mass-size distribution, assuming scale-invariant shape and density. Variation in shape and density as a function of size may introduce errors in the calculation of D. We compared the fractal dimensions of soil aggregates estimated from mass-size distribution data (D_m), with those computed from actual number-size distribution data determined by counting (D_n). The fractal dimension ranged from 0.67 to 3.92 for D_n, and from 0.79 to 4.06 for D_m. A significant linear relation was found between D_m and D_n, with R² = 0.935. The resulting intercept and slope were not significantly different from zero and one, respectively, indicating a 1:1 relationship. This implies that the assumption of scale-invariant shape and density was valid across the range of aggregate sizes studied (5.0 x 10^–1 to 3.2 x 10¹ mm). Thus, the fractal dimension can be estimated from mass-distribution data within this range.

Received for publication November 8, 1991.

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