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Statistical and Fractal Evaluation of the Spatial Characteristics of Soil Surface Strength

Department of Land, Air and Water Resources, Univ. of California, Davis, CA 95616

*Corresponding author.

ABSTRACT

In order to understand processes causing soil crusting and to optimize sampling schemes, improved understanding of crust spatial characteristics is needed. For this purpose, statistical and fractal analyses of soil surface strength, as measured by a 1.59-mm-diam. flat-tipped micropenetrometer, were carried out for a variety of soils and under a variety of sampling schemes. Specifically, this work considered maximum penetration forces sampled at intervals of 0.005, 0.01, 0.05 and 0.5 m along four parallel transects 0.25 m apart, for nine different sites within California's Central Valley. Force measurements were non-homogeneous in space. For eight of the nine sites, both the mean and the variance were non constant; and for all sites, the range and nugget variance of fitted semivariograms were scale dependent. Fractal analysis of the measurements allowed qualitative discrimination among soils, despite small variations across scales. For all sites, fractal dimensions of sampled series at alternative scales were similar, but the smallest deviations across scales were observed on high-strength silt loam, and the largest on low-strength loamy sand soils. Multifractal spectra (for data sets normalized and interpreted as probability measures) gave similar entropy dimensions for all sampling schemes, with very small deviations across scales for silt loam soils and largest again for loamy sands. Results suggest that the fractal attributes (fractal and entropy dimensions), being scale-independent attributes, may be relevant qualifiers of the intrinsic variability of penetration measurements and that this variability can be modeled as a fractal process.

Received for publication January 4, 1993.

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