Multifractal analysis of soil surface roughness

Soil surface roughness (SSR) is a parameter highly suited to the study of soil susceptibility to wind and water erosion. The development of a methodology for quantifying SSR is therefore instrumental to soil evaluation. We developed such a method, based on the multifractal analysis (MFA) of soil elevation measurements collected at the intersections on a 2- by 2-cm(2) grid in a 200- by 200-cm(2) plot. Samples were defined using the gliding box algorithm (GB), in which a box of a given size glides across the grid map in all possible directions. The advantage of the GB over the box counting algorithm is that it yields a greater number of large sample sizes, which usually leads to better statistical results. Standard deviation, semivariogram fractal dimension, and semivariogram crossover length were estimated for all scenarios to compare the results of SSR multifractal analysis to indices found with traditional techniques. For its high sensitivity to the spatial arrangement implicit in a data set, MFA appears to be better suited than classical indices to compare plots tilled under different management criteria. The results showed that MFA is able to effectively reflect the heterogeneity and complexity of agricultural SSR. Based on this type of analysis, two new indices have been defined to compare the multifractal spectrum characteristics of the raw data to the characteristics of a random field with the same average and SD.