Multiscaling analysis of soil roughness variability

Soil surface roughness (SSR) is a parameter highly suited for the study of soil susceptibility to wind and water erosion. The development of a methodology for quantifying SSR has typically been based on field techniques to obtain data, rather than on the indexes used for interpreting soil roughness variability. One of the most used indexes to evaluate SSR is the random roughness (RR), easily calculated from the heights obtained with a pin meter. The RR index was obtained from soil elevation measurements collected at the intersections of a 2 × 2-cm² grid in a 100 × 400-cm² plot from three different types of soil. SSR values for all soil types were obtained after passing three different tillage tools (chisel, tiller, and roller) through three types of soils at field conditions. The RR index was calculated using the standard deviation (SD) of the lines parallel to the direction of tillage. Lines were 20 mm apart.Since RR assumes vertical random roughness without correlation, the variability of SSR was assessed using structure function (SF) to complement the study. Therefore, the main objective of this analysis was to better illustrate the variability of SSR in relation to spatial distribution. The SF was highly sensitive to soil roughness variability and depended on the tillage tool treatments and soil types, thereby illustrating the origin of the soil roughness variability, either from the soil itself or from the tillage tool used. We also demonstrate that the concept of a generalised Hurst exponent derived from the SF improves our ability to differentiate among the cases.