FRACTAL DIMENSIONS OF SOIL AGGREGATE-SIZE DISTRIBUTIONS CALCULATED BY NUMBER AND MASS

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 10(1) mm). Thus, the fractal dimension can be estimated from mass-distribution data within this range.