Unbiased estimation of the fractal dimension of soil aggregate size distributions

  • Perfect E
  • Kay B
  • Rasiah V
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Abstract

The fractal dimension has been used to characterize the size distribution of soil aggregates produced by tillage. The fractal dimension is normally estimated from the slope of the cumulative number-size distribution plotted on a log-log scale, D1. It can also be estimated non-linearly from the cumulative number-size distribution, Dn1. In both methods, the fitting is done over the entire range of scales for which data are available. However, fractal models indicate deviations from ideal behavior during the initial stages of fragmentation. Inclusion of data from the early stages of fragmentation may result in biased estimates of D1and Dn1. We used the derivative of the cumulative number-size distribution plotted on a log-log scale after the fourth stage of fragmentation as an unbiased estimator of the fractal dimension, Dd. Values of D1Dn1and Ddwere compared for soil aggregate size distributions resulting from the fragmentation of dry clods collected from seven cropping/ tillage treatments and crushed at five specific energy levels. Estimates of the fractal dimension ranged from 1.179 to 2.803. The range in D1was much wider than the ranges in Dn1or Dd. No significant relationship existed between D1and Dd. The relationship between Dn1and D1had an R2of only 0.183 (P

Author-supplied keywords

  • Aggregate size distribution
  • Crushing energy
  • Fractal dimension
  • Fragmentation
  • Tillage

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Authors

  • E. Perfect

  • B. D. Kay

  • V. Rasiah

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