Multifractal analysis in soil properties: Spatial signal versus mass distribution

- Multiscale analysis of three different variables on a soil transect revealing their behaviour
- Generalized Structure Function and multifractal spectrum method comparison.
- Variables present a distinctive multifractal character.
- Relation between methods, was verified.

The spatial variability of soil properties is a constant expected factor that must be considered in soil studies. This variability is composed of “functional” variations and random fluctuations or noise. Multifractal formalism is suitable for variables with self-similar distributions on a spatial domain. Multifractal analysis can provide insight into the spatial variability of soil parameters. In soil science, it has been quite popular to characterize the scaling property of a variable measured along a transect as a mass distribution of a statistical measure on a length domain of the studied transect. The analysed variable is divided into a number of self-similar segments, and the partition function and mass function are estimated. Based on these estimations, the multifractal spectrum (MFS) is calculated. Another technique that can be applied focuses on the variations of a measure by analysing the absolute differences in the soil property values at different scales, such as the Generalized Structure Function (GSF) and the Universal Multifractal Model (UMM). The aim of this study was to compare both types of multifractal methods on a set of soil physical properties measured on a common 1024 m transect across arable fields at Silsoe in Bedfordshire, East-Central England. The studied properties were total porosity (Porosity), gravimetric water content (GWC) and nitrous oxide flux (N2O flux). The results showed that when using both methods, the N2O flux exhibits a distinctive multifractal character, and weak multifractal characters are detected in the GWC and Porosity cases. Additionally, several parameters were calculated and discussed.Finally, the relationship between the mass exponent function (τ(q)) and the GSF (ζ(q)) found in the literature, was positively verified for the three variables. On the contrary, the relationship between ζ(q) and the scaling exponent function based on UMM (K(q)) showed discrepancies in N2O flux and GWC for q values higher than 3. This is the first time that these comparisons have been made on soil property data.