Multifractal Analysis of Vertical Profiles of Soil Penetration Resistance at Varying Water Contents

The objective of this work was to characterize the scaling properties of depth-dependent penetration resistance (PR) profiles using multifractal analyses and to explore the effects of increasing soil water deficit on the scaling heterogeneity of the studied data series. Soil PR was recorded at 11 successive dates with decreasing soil water content on a Mollisol (Argiudoll) from Entre Rios Province, Argentina. For each date, 10 replicated PR vertical profiles were measured every centimeter from 0 to 80 cm. Both singularity and Renyi spectra showed that all PR datasets exhibited a well-defined multifractal structure, so that the multifractal approach provided considerable detailed information on their depth-dependent structure. The entropy dimension, D-1, significantly (P < 0.05) increased with decreasing soil water content, and its mean values ranged from 0.976 to 0.981. Therefore, the drier the soil, the more the homogeneity and evenness of the PR depth-dependent profiles. Moreover, the amplitude of the branches of the Renyi and singularity spectra accounting for the most positive statistical moments, [0, 5], significantly (P < 0.05) decreased with increased soil water deficit. However, for the most negative counterparts, [0, -5], these amplitudes tended to increase, although not significantly. Subsequently, increasing soil dryness increased the homogeneity of the highest PR values, but had no significant effect on the homogeneity of the lowest PR values. The multifractal approach was useful to characterize changes in inner structure, heterogeneity, and evenness of PR vertical profiles over a period with increasing soil water deficit.