Submitted to: Encyclopedia of Soils in the Environment
Publication Type: Peer reviewed journal
Publication Acceptance Date: 11/17/2003
Publication Date: 10/27/2004
Citation: Pachepsky, Y.A., Crawford, J.W. 2004. Fractal analysis of soils. Encyclopedia of Soils in the Environment. pp.85-97. Interpretive Summary: Measurements in soils depend on resolution. The more details gives a measurement, the larger values of length, volume, and area are observed. Soils are studied at resolutions from nanometers to megameters. Laws are needed to relate results of studies and measurements at different resolutions. The scale dependence of measurements stems from the irregularity and roughness of soil structure. Recently, mathematics came up with a new, fractal geometry tailored to measure rugged objects. The application of fractal geometry in soil science is a fast developing field as demonstrated by the exponential growth in the number of publications. Fractal techniques provided a viable methodology to link processes and properties across scales. Fractal laws were applicable to many soil properties. Using these laws allowed researchers to predict soil parameters that are difficult to measure, in particular, soil hydraulic parameters. These achievements are documented in this paper. Because there are no ideal fractals in soils, a caution needs to be exercised in applications of fractal geometry. We illustrate both challenges and opportunities presented by fractals for process modeling in soils, including solute transport in soils in water quality predictions, compression of the remote sensing data in hydrological and agronomic studies, using temporal fractals in research of the global changes in atmospheric carbon content and carbon sequestration in soils, and predictability of soil behavior in changing environment.
Technical Abstract: Geometric properties of soil elementary particles, aggregates, peds, pores, exposed soil surfaces, contours, etc., are of utmost importance for understanding and managing soils. Ideal geometrical objects, such as spheres, circles, and segments, are widely used in measurements in soil science, and this introduces uncontrollable errors. Fractal geometry appeared not more than 30 years ago. It was developed to describe irregular natural shapes having hierarchies of ever-finer detail and to relate features of natural objects observed at different scales. The application of fractal models in soil science is a new developing field as demonstrated by the exponential growth in the number of publications. We present a compendium of methods applied to perform fractal analysis of soils and demonstrate both the challenges and opportunities presented by fractals in soil studies. Fractal techniques provided a viable methodology to link processes and properties across scales. Relationships of fractal geometry can be only approximately true in soils. Indirect measurements as a source of data may be an impediment in application of fractal models. Current and prospective use of fractal analysis in soil studies is summarized.