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United States Department of Agriculture

Agricultural Research Service

Title: Conventional and Fractal Geometry in Soil Studies

Author
item Pachepsky, Yakov

Submitted to: International Workshop on Fractal Mathematics Describing Soil and Heterogeneous Systems
Publication Type: Abstract Only
Publication Acceptance Date: June 17, 2002
Publication Date: June 28, 2002
Citation: Pachepsky, Y.A. 2002. Conventional and fractal geometry in soil studies. International Workshop on Fractal Mathematics Describing Soil and Heterogeneous Systems. p.5.

Technical Abstract: Applying the conventional geometry to measure lengths, areas, and volumes in soils is always based on introducing a measurement scale, that is, length, area, or volume unit within which actual irregular boundary of a soil unit is replaced with a segment of a smooth line, or with a smooth surface. In indirect, or proxy measurements, physical parameters are converted into soil geometric parameters using a model of porous media composed of simple geometric bodies, like cylinders, squares, or spheres. The use of the conventional geometry ignores the irregularity of boundaries. At the same time, the irregularity perceived as roughness, tortuosity, non-homogeneity, etc., has long been sensed as an important feature affecting soil functioning in environment and important for soil management. Fractal geometry capitalizes on the fact that the dependencies of conventionally measured geometric parameters on the measurement scale can be used to determine parameters of irregularity. Broader interpretation of fractal geometry, or fractal mathematics, allows extension of those concepts for time series, diversity and variability patterns, and growth dynamics. Examples demonstrate both applicability of the fractal geometry to soils and relationships between fractal parameters and soil management, as well as between those parameters and contaminant transport in soils.

Last Modified: 11/23/2014