Submitted to: Geoderma
Publication Type: Popular publication
Publication Acceptance Date: 1/11/2006
Publication Date: 5/2/2006
Citation: Pachepsky, Y.A., Perfect, E., Martin, M.A. 2006. Fractal Geometry applied to soil and related Hierarchical Systems. Geoderma. doi:10.1016/j.geodema.20067.03.002. Interpretive Summary: This paper contains an overview of discussion topics of the 6th International workshop on fractal mathematics applied to soil and related heterogeneous systems. Fractal geometry was developed to describe the hierarchy of ever-finer detail in the real world. Natural objects often have similar features at different scales. Measures of these features, e.g. total number, total length, total mass, average roughness, total surface area, etc., are dependent on the scale on which the features are observed. Fractal geometry assumes that this dependence is the same over a range of scales, i.e., it is scale-invariant within this range. As a result fractal objects look similar when observed at different scales. Fractal geometry has long been advocated as a better representation of complex porous media as compared with simple Euclidean models based on straight lines and circle arcs. Twenty-five years of applications of fractal geometry in soil science showed the utility of this geometrical model in describing soil structure and texture, in simulating soil hydraulic properties and parameters of contaminant transport, in discriminating between soils under different management, and in compressing measurement from data-rich advanced measurement technologies, such as laser diffractometry, scanning electron microscopy, computer-assisted tomography, and remote sensing, into meaningful and management-sensitive parameters. Fractal geometry is currently one of the best tools to address extreme events and rare occurrences. Rare occurrences at fine measurement scales tend to be the most important ones on coarse scales. For example, macropores are rare occurrences in traditional soil samples taken to measure hydraulic properties at the core scale. However, the hydrologic behavior of soil at the pedon scale is in many cases defined by macropores. Progress of the fractal geometry applications depends on resolving several methodological issues, such as identification of physical, chemical or biological processes that are able to produce fractal scaling, minimizing the subjective component by applying appropriate statistical techniques, and developing new fractal models tailored for specific applications, such as quantification and simulation pore connectivity to reveal the hierarchy of transport pathways. The research presented at the workshop provides a representative sample of the ongoing international effort to expand the use of fractal models in the Earth sciences.
Technical Abstract: This is an extended foreword for the of Geoderma special issue that contains a collection of selected papers from the 6th International workshop on fractal mathematics applied to soil and related heterogeneous systems. Although fractals should not be considered an ultimate model of scaling in the soil system, they do provide a balance between accuracy and clarity that may aid us in gaining insight into the sources and dynamics of complexity. Fractal geometry seemingly contradicts several commonly-held scientific viewpoints, such as natural scales and heterogeneity as a source of variability that have to be revisited. Rare occurrences at fine measurement scales tend to be the most important ones on coarse scales, and fractal geometry is currently one of the best tools to address extreme events and rare occurrences. The fractal theoretical and practical fractal framework for relating structure to function in natural porous media, and for understanding the associated feedbacks, needs to be expanded to quantify and simulate pore connectivity and reveal the hierarchy of transport pathways. Applications of fractal geometry remain dependent on human cognition and often contain a subjective component. Some degree of uncertainty is unavoidable in many such applications since the measure is defined by counting instead of actually measuring. Advanced measurement technologies, such as laser diffractometry, scanning electron microscopy, computer assisted tomography, and remote sensing, often provide new opportunities for determining the information content and complexity of natural systems. However, there is a clear need for protocols to collapse these data into meaningful and management-sensitive parameters. Fractal geometry has been instrumental in developing measures of the irregularity that are extremely useful for discriminating between natural systems. To ensure that the fractal tools are applied properly, physical, chemical or biological processes that are able to produce fractal scaling need to be identified. Interactions and discussions stimulated by this workshop suggest that there are many more avenues for research.