Multifractal and joint multifractal analysis of general soil properties and altitude along a transect

Multifractal characterisation of soil spatial variability has the potential for providing a better understanding of the distribution patterns of data values, and may contribute to improved resource management. We examined the scaling heterogeneity and multiple scale relationships of soil general properties and topography using multifractal and joint multifractal techniques. Soil samples were collected down to 0.20 m depth and altitude was recorded at equal intervals of 3 m along a 396 m transect in an Orthic Podzol at Pernambuco, Brazil. Soil properties studied were: textural fractions, pH, organic carbon (OC), exchangeable cations, exchangeable acidity (H + Al), sum of bases (SB), cation exchange capacity (CEC) and percent base saturation (V). The spatial distribution of altitude and soil general properties, characterised through generalised dimension, Dq, and singularity spectra, f(α)-α, showed a well-defined multifractal structure. Notwithstanding, these variables displayed several degrees of scaling heterogeneity, which was lowest for pH, sand and clay contents and highest for exchangeable cations and silt content. Joint multifractals showed that correlations between pairs of variables may or may not be stronger at the observation scale than across a range of spatial scales. Hence, soil OC and pH showed higher relationships to CEC, (H + Al), SB and V at the observation than at multiple spatial scales, while local topography effects on pH and CEC were greater at multiple scales. Multifractal and joint multifractal analysis provided new insights to characterise the spatial patterns and the relationships between soil properties at multiple scales, and to evaluate the effect of topography on soil heterogeneity.