Multifractal scaling of soil spatial variability

Soils data exhibit great complexity that spatial analyses try to understand. The geostatistical approach studies soil variability as the outcome of random processes and is characterized by means of the variogram. Multifractal analysis introduces a new methodology based on the determination of the scaling properties of the data set which are summarized by the multifractal spectrum. However, there are different types of multifractal spectra which are computed using different algorithms, each of them carrying its own numerical problems of implementation and, further, having different conceptual foundations. This paper first focuses on the ability of two of these spectra, the singularity spectrum and the Rényi spectrum, to characterize the variation of certain soil properties (electrical conductivity, organic matter (OM) content, soil pH, depth of Bt horizon) measured along transects. Secondly, the features of both spectra corresponding to the organic matter content measured along two transects of equal length and a third longer transect are analyzed and compared. st majority (96%) of the coefficients of determination R2 of the linear fittings leading to multifractal dimensions were greater than 0.93 for the singularity spectrum and greater than 0.99 for the Rényi spectrum, indicating a somewhat better definition of the spectrum in the second case. Both multifractal spectra distinguished two patterns for the variation of OM content, one corresponding to the short transects and another corresponding to the long transect, with features close to spectra corresponding to monofractal and multifractal noises, respectively. concluded that singularity and Rényi spectra are useful for characterizing soil variability and can distinguish between different patterns of soil variation corresponding to the different degrees of randomness present in the data.