Comparing multifractal characteristics of soil particle size distributions calculated by Mie and Fraunhofer models from laser diffraction measurements

Abstract

Particle size distribution (PSD) is a basic soil property, closely related to main soil physical and chemical attributes. Soil PSD determined by laser diffraction (LD) may provide additional information to soil texture determined by traditional methods. In turn, LD may be implemented using either Mie or Fraunhofer calculation methods, based on different assumptions. The multifractal approach has been demonstrated to be useful for characterizing the inner structure of soil PSD. We analysed the PSDs of 18 soil horizons sampled on the most characteristic soil types from Argentina with a wide range of textural classes, from clayey to sandy, mainly developed over loess material. Our aims were to assess the multifractality between PSDs computed using either Mie scattering or Fraunhofer diffraction models, and to compare the scaling properties and multifractal behavior of PSDs from soils with contrasting textures. Fraunhofer model provided PSD curves, which were shifted toward coarser particles compared to those obtained with Mie model. Regardless calculation method, all the PSDs studied displayed a well-defined multifractal structure, as shown by singularity, f(α) versus α, and by Rènyi spectra, Dqvs q. Moreover, all singularity spectra were strong asymmetric, right deviating curves, which is consistent with a greater heterogeneity of the low values of volume frequencies for all the PSDs analysed. Soil PSDs computed by Fraunhofer model showed higher asymmetry than those computed by Mie model for 16 out of 18 horizons studied; this suggests that scaling heterogeneity mainly depends on the support length, which is larger for the PSDs computed by Mie. In addition, other features of the PSDs stemming from soil processes such as weathering intensity of loess materials may also influence multifractality. Stronger correlations were found between multifractal parameters from PSDs calculated by the two models for the most positive q moments of singularity and Renyi spectra, i.e. α10, D10, than for those gathered from the central and negative q moments. The entropy dimension, D1, significantly (P<0.05) increased with increasing clay content, in contrast to previous findings; this may be due either to differences in the inner structure of various PSD data sets compared, or to shortcomings of standard PSD measurement and calculation procedures.