Submitted to: Fractals In Soil Science
Publication Type: Book / Chapter
Publication Acceptance Date: 5/1/2000
Publication Date: 5/1/2000
Citation: Interpretive Summary: Measurements in soils depend on resolution. The more details a measurement provides, the larger values of length, volume, and area that 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 u 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 idea fractals in soils, a caution needs to be exercised in applications of fractal geometry. The content of the book is used to 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 agronomical 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 irregula 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. Fractal techniques provided a viable methodology to link processes and properties across scales. The use of fractal models in soil science was far from being straightforward. Subtleties in the application of the techniques were caused, in particular, by the complexity of the scale concept in soil science, by the wide use of indirect measurements, by the uncertainty in processes underlying fractal scaling, and by the absence of ideal fractals in soils. Although introducing distinct characteristic scales has important methodological advantages, working with characteristic scales in mind may lead to a quandary. 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. We use chapters of the book to demonstrate both the challenges and opportunities presented by fractals for process modeling in soils. Future applications of fractals in soil science are discussed.