Multifractal and joint multifractal analysis of the spatial variability of CO2 emission and other soil properties

Soil is a major source and also a sink of CO₂. Agricultural management practices influence soil  carbon sequestration. Identification of CO₂ emission hotspots may be instrumental in implemented strategies for managing carbon cycling in agricultural soils. We used multifractal analysis to assess the spatial variability of both, soil CO₂ emissions and associated soil physico-chemical attributes. The objectives of this study were: i) to characterize patterns of spatial variability of CO₂ emissions and related soil properties using single multifractal spectra, and ii) to compare the scale‐dependent relationship between soil CO₂ emissions and selected soil attributes by joint multifractal analysis. The study site was an experimental field managed as a sylvopastoral system, located in Selviria, South Mato Grosso state, Brazil. The soil was an Oxisol developed over basalt. Soil CO₂ emission, soil water content and soil temperature were measured at 128 points every meter. In addition, soil was sampled at the marked points to analyze clay content, macro and microporosity, air free porosity, magnetic susceptibility, bulk density, and humification index of soil organic matter in absolute values and relative to organic carbon content. The generalized dimension, D_q versus q, and singularity spectra, f(α) versus α, of the spatial distributions of the 11 variables studied showed various degrees of multifractality. In general, the amplitude of the generalized dimension and singularity spectra was much higher for negative than for positive q order statistical moments. Joint multifractal spectra show a positive relationship between the scaling indices of the spatial distributions of CO₂ and all of the other soil variables studied. However, contour plots were diagonally oriented for higher values of scaling indices and showed no distinct trend for the lower ones. Joint multifractal analysis corroborates different degrees of association between the scaling indices of CO₂ and all of the remaining variables studied. It also showed that CO₂ was stronger correlated at multiple scales than at the observation scale. Therefore, single scale analysis may not be sufficient to fully describe relationships between soil testing methods.Our study suggests that soil factors and processes driven the spatial variability of CO₂ and the associated variables studied may be not very different.