Multifractal and joint multifractal analysis of soil micronutrients extracted by two methods along a transect in a coarse textured soil

Understanding the spatial behaviour of soil nutrients is essential for fertilizer management. Traditionally, comparison of soil testing methods has been performed using simple correlation analysis. The aims of this work were: (a) to characterize patterns of spatial variability of micronutrient concentrations obtained by two different soil testing methods, using single multifractal spectra, and (b) to compare the scale-dependent relationship between the two datasets by joint multifractal analysis. The soil study site was located in Pernambuco state, Brazil. A 384-m transect was marked every 3 m on an Orthic Podzol, cropped to sugar cane, in Pernambuco state, Brazil. Both, Mehlich-3 and DTPA-extracted micronutrients were measured in each of the 132 collected soil samples. The spatial distributions of available Fe, Mn, Cu and Zn could be fitted with multifractal models, regardless of the soil testing method. The generalized dimension,D(q)versus q, and singularity spectra, f(alpha) versus alpha, showed a multifractal nature. Except for Fe, the scaling heterogeneity of the spatial distributions was higher for the Mehlich-3 than for the DTPA datasets. Moreover, Zn exhibited the highest multifractality in both cases. Joint multifractal analysis demonstrated strong positive correlations between the scaling indices of the studied micronutrients extracted by the two methods. There were, however, different degrees of association between the scaling indices of these micronutrients, which ranked as: Zn > Cu > Fe > Mn. Except for Mn, Pearson product moment correlations between concentrations of available micronutrients extracted by the two solutions at the single or point measurement scale were weaker than those of the respective scaling indices at multiple scales. Therefore, single multifractal analysis captured a great complexity in the spatial distribution of available Fe, Mn, Cu and Zn. Knowledge of the scaling behaviour of these available nutrients could be useful for transferring information about variability from one scale to another for soil fertility management. This study suggests that correlation analysis at the single or point measurement scale may not be sufficient to fully characterize the concentrations of microelements extracted by two different methods, whereas joint multifractal analysis showed potential to improve calibration of soil micronutrient testing. Highlights Mehlich-3 and DTPA-extracted micronutrients showed high statistical variability across a transect. All the spatial distributions of Fe, Mn, Cu and Zn displayed a well-defined multifractal structure. Joint correlations of extracted micronutrients were stronger than single statistical correlations. Our approach fully characterized complex spatial distributions arising from nonlinear processes.

Automated summary

The study investigated the spatial behaviour of soil nutrients through single multifractal spectra and joint multifractal analysis, revealing different associations between Fe, Mn, Cu, Zn concentrations obtained by Mehlich-3 and DTPA methods. Results showed that joint multifractal analysis could improve the calibration of soil micronutrient testing, highlighting the complexity of spatial distributions of available Fe, Mn, Cu, and Zn across scales.