Multifractal analysis of vertical profiles of soil penetration resistance at the field scale

Soil penetration resistance (PR) is widely used as an indirect indicator of soil strength. Soil PR is linked to basic soil properties and correlated to root growth and plant production, and as such it is extensively used as a practical tool for assessing soil compaction and to evaluate the effects of soil management. This study investigates how results from multifractal analysis can quantify key elements of depth-dependent soil PR profiles and how this information can be used at the field scale. We analysed multifractality of 50 PR vertical profiles, measured from 0 to 60 cm depth and randomly located on a 6.5 ha sugar cane field in northeastern Brazil. The scaling property of each profile was typified by singularity, and Rényi spectra estimated by the method of moments. The Hurst exponent was used to parameterize the autocorrelation of the vertical PR data sets. The singularity and Rènyi spectra showed that the vertical PR data sets exhibited a well-defined multifractal structure. Hurst exponent values were close to 1, ranging from 0.944 to 0.988, indicating strong persistence in PR variation with soil depth. Also, the Hurst exponent was negatively and significantly correlated to coefficient of variation (CV), skewness and maximum values of the depth-dependent PR. Multifractal analysis added valuable information to describe the spatial arrangement of depth-dependent penetrometer data sets, which was not taken into account by classical statistical indices. Multifractal parameters were mapped over the experimental field and compared with mean and maximum values of PR. Combination of spatial variability survey and multifractal analysis appear to be useful to manage soil compaction.