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Linear and Nonlinear Estimates of Fractal Dimension for Soil Aggregate Fragmentation

Research Station, Box 1030, Swift Current, SK, Canada S9H 3X2

E. Perfect and B. D. Kay

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

* Corresponding author.

ABSTRACT

Estimates of nonlinear parameters may vary with the fitting procedure (linear or nonlinear) used. The objectives of this study were to compare (i) values of the fractal dimension, D, and the constant, k, obtained using linear (defined D₁ and k₁) and nonlinear (defined D_nl and k_nl) fitting procedures and (ii) the sensitivity of D₁, D_nl, k₁, and k_nl to variations in cropping and tillage practices and soil properties. Using aggregate mass-size distribution data, from five different soils under two cropping and two tillage systems, obtained after wet sieving, 90 values were obtained for each of D₁, D_nl, k_nl, and k_l. The nonexistence of a 1:1 relation between D_nl and D₁ indicated that the population of D_nl was different from that of D₁. A similar trend was observed between k_nl and k₁. The standard error of the estimates of D_nl was less than that of D₁. Soil properties and cropping and tillage systems accounted for 84% of the variability in D_nl, 87% of k_nl, 81% of D₁, and 46% of k₁. The estimates of D_nl are accurate and can be predicted with greater confidence than those obtained using the linear procedure.

Received for publication December 21, 1993.