The effects of overall slope on soil surface roughness estimation

Soil surface roughness (SSR) is essential for understanding and modeling soil erosion processes, while whether the overall slope of the investigated terrain surface must be corrected before SSR estimation is still unknown. This study aims to investigate the effects of overall slope on SSR and associated temporal change estimates by using the high-resolution digital elevation models (DEMs) from the rainfall simulation experiments of Nearing et al. (2017) wherein medium-term rainfalls (ca. 10–20 years) were simulated on a 2 m by 6.1 m stony plot under three slope treatments (5 %, 12 %, and 20 %). Square moving windows with different sizes ($W_Z$) covering the topographic DEMs were used to estimate SSR for each slope treatment before and after each rainfall simulation under the slope-detrending (DT) and no-detrending (NDT) scenarios. Results showed that: (1) The estimated SSR linearly increased with $W_Z$ under the NDT scenario while it increased rapidly for small $W_Z$ and tended toward asymptotes for large $W_Z$ under the DT scenario. (2) With increasing window size, the standard deviations of SSR increased under the NDT scenario but decreased under the DT scenario. (3) Without correcting the overall slope effects, SSR was overestimated while the temporal change of SSR was significantly underestimated reaching up to −175 % as compared to the DT scenario, and the underestimation was positively correlated with slope gradient, the true SSR temporal change, and window size. We mathematically illustrated that the estimated SSR under the NDT scenario in fact consisted of oriented roughness that was resultant from the systematic elevation variation rather than soil surface random roughness alone, and the overall slope effects must be corrected before SSR estimation for effectively tracking SSR temporal changes. The results provide guidance about the level of accuracy one might expect in evaluating SSR and associated temporal changes at hillslopes with different overall slopes.