Multifractal Analysis of Soil Properties along Two Perpendicular Transects

The spatial variability of soil properties can be best characterized through concepts of scale invariance, fractals, and multifractals. The objectives of this study were to analyze and to compare the scaling patterns and structural heterogeneity of soil properties across two transects in Campinas, SP, Brazil, using the multifractal formalism. Two transects were marked parallel and perpendicular to land slope, with a length of 2.28 and 1.98 km, respectively. Soil samples were collected at the 0 to 20 cm depth every 30 m. The soil properties analyzed were: texture (sand, silt, clay), pH (H2O and KCl), organic carbon (OC) content, exchangeable Ca, H, and Al, exchangeable bases (SB), cation exchange capacity (CEC), and percent base saturation (V). Spatial variability of soil properties was controlled by natural causes, including parent material and topography, and by soil use and management. The variability of pH across the two transects was characterized by either quasi-monofractal behavior or by a relatively low degree of multifractality. The other soil properties studied showed stronger degrees of multifractality. Hence, the multifractality for OC and silt content was much higher at the transect perpendicular to land slope. Variables from the soil exchange complex, particularly exchangeable Al, Ca, and SB, were characterized by higher multifractal indices in the two transects. Patterns of spatial distribution assessed by multifractal analysis were linked to soil forming factors and processes. Our results suggest that scale heterogeneity in the spatial distribution of soil properties was enhanced by the interaction of various natural or anthropogenic sources of variability.