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Linear and Nonlinear Estimates of Fractal Dimension for Soil Aggregate Fragmentation
Author(s) -
Rasiah V.,
Perfect E.,
Kay B. D.
Publication year - 1995
Publication title -
soil science society of america journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.836
H-Index - 168
eISSN - 1435-0661
pISSN - 0361-5995
DOI - 10.2136/sssaj1995.03615995005900010012x
Subject(s) - mathematics , fractal dimension , tillage , linear regression , nonlinear system , dimension (graph theory) , nonlinear regression , fractal , aggregate (composite) , population , statistics , mathematical analysis , physics , combinatorics , regression analysis , materials science , agronomy , demography , quantum mechanics , sociology , biology , composite material
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 D 1 and k 1 ) and nonlinear (defined D nl and k nl ) fitting procedures and (ii) the sensitivity of D 1 , D nl , k 1 , 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 D 1 , D nl , k nl , and k l . The nonexistence of a 1:1 relation between D nl and D 1 indicated that the population of D nl was different from that of D 1 . A similar trend was observed between k nl and k 1 . The standard error of the estimates of D nl was less than that of D 1 . Soil properties and cropping and tillage systems accounted for 84% of the variability in D nl , 87% of k nl , 81% of D 1 , and 46% of k 1 . The estimates of D nl are accurate and can be predicted with greater confidence than those obtained using the linear procedure.