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Title: Fractal Analysis in Agrophysics

item Pachepsky, Yakov
item San Jose Martinez, Fernando
item Martin, Miguel Angel

Submitted to: Encyclopedia of Agrophysics
Publication Type: Book / Chapter
Publication Acceptance Date: 12/27/2009
Publication Date: 10/1/2011
Citation: Pachepsky, Y.A., San Jose Martinez, F., Martin, M. 2011. Fractal Analysis in Agrophysics. In: Clinski, J., Horabik, J., Lkipiec, J., editors. Encyclopedia of Agrophysics. Heidleberg, Germany: Springer Verlag. p. 309-314.

Interpretive Summary: The interactions within soil-plant-atmosphere systems are complex. Identifying parameters that can characterize the general behavior of these systems has been challenging. Recently, fractals (a branch of mathematics) has proven to be useful in providing these types of parameters. Fractals have become very popular in agrophysical research because they can be used to characterize general changes in system properties with changes in the scale of observation. We provide here a concise introduction to the application of fractals in agrophysics. This overview is an important contribution to the first single source, comprehensive review of agrophysics. It is anticipated that this will be a widely used reference in the field.

Technical Abstract: The geometric irregularity is an intrinsic property of soils and plants. This geometric irregularity is easy to perceive and observe, but quantifying it has long presented a daunting challenge. Such quantifying is imperative because the geometric irregularity is the cause and the reflection of spatial and temporal variability that in turn strongly affects soil and crop management. Fractals have become an important tool to represent this irregularity. This entry provides a brief introduction in concepts and techniques behind those applications. Fractal objects and models are introduced. Physical processes are discussed that result in fractal scaling in agrophysics. Purposes and methods of fractal analysis are summarized. Measurements of scale dependence and fitting a fractal model to data are illustrated. The role of fractal analysis in agrophysics is discussed. The major contribution that fractal geometry makes in agrophysics is a general, simple and succinct representation of complex structures by a small number of fractal parameters. Fractals provide a balance between accuracy and clarity that may aid us in gaining insight into sources and consequences of the observed complexity of agrophysical systems and processes.