LINEAR AND NONLINEAR ESTIMATES OF FRACTAL DIMENSION FOR SOIL AGGREGATE FRAGMENTATION

Estimates of nonlinear parameters may vary with the fitting procedure (linear or nonlinear) used. The objectives of this study were to compa re (i) values of the fractal dimension, D, and the constant, k, obtain ed using linear (defined D-l and k(l)) and nonlinear (defined D-nl and k(nl)) fitting procedures and (ii) the sensitivity of D-l, D-nl, k(l) , and k(nl) to variations in cropping and tillage practices and soil p roperties. Using aggregate mass-size distribution data, from five diff erent soils under two cropping and two tillage systems, obtained after wet sieving, 90 values were obtained for each of D-l, D-nl, k(nl), an d k(l). The nonexistence of a 1:1 relation between D-nl and D-l indica ted that the population of D-nl was different from that of D-l. A simi lar trend was observed between k(nl) and k(l). The standard error of t he estimates of D-nl was less than that of D-l. Soil properties and cr opping and tillage systems accounted for 84% of the variability in D-n l, 87% of k(nl), 81% of D-l, and 46% of k(l). The estimates of D-nl ar e accurate and can be predicted with greater confidence than those obt ained using the linear procedure.