Rényi dimensions analysis of soil particle-size distributions

Dynamism and complexity are terms that have been related to soils. New approaches and points of view have been researched during past decades considering soil’s multiple functions and integrating physical, chemical, and biological soil attributes. Also new mathematical models have been explored such as fractal sets and multifractal measures. Characterization of soil particle-size distribution is a key move towards modeling of soils and their behavior with respect to water movement and retention or soil erosion. Modeling soil physical properties related with soil production or degradation and finding indexes of characterization have been set as priorities in many programs related to ecology, sustainable agriculture, etc. Combination of multifractal techniques and laser diffractometry of soil particles have a potential to develop such characterization via analysis of rarely explored regions of the interval of sizes. Multifractal analysis can be applied using Rényi dimensions to detect scaling properties in soil particle distributions. However, specifics of the laser diffraction data require the construction of a new measure with which multifractal techniques may be applied. We developed such a measure and applied the Rényi dimension analysis to 20 soil particle-size distributions obtained by laser diffractometry. These distributions showed, in general, suitable scaling properties, generating Rényi dimensions spectra similar to those obtained for theoretical multifractal properties and showing great variety in their multifractal behavior. Results suggest the applicability of Rényi dimensions spectra to soil characterization for modeling empirical data and generating synthetic data by means of algorithms capable of generating such kind of measures.