A method for calculating the oblique cross-slope tillage factor

In regions with rolling hills, oblique cross-slope tillage is more common than contour or up-and-down slope tillage. However, its role in soil erosion assessments has been largely overlooked, and the impact of contour tillage has often even been disregarded due to the limitations of existing evaluation methods. To address these gaps, a novel soil erosion factor—the oblique cross-slope tillage subfactor (T_o)—was proposed, and a raster-based method was developed to accurately quantify the influence of the furrow direction on soil erosion. Using a 28 km² watershed in northeastern China as a case study, tillage lines were digitized from satellite images, and furrow contour angles were computed on the basis of their relationships with contour lines. The furrow direction modification coefficient relative to contour tillage was then used to derive T_o. Soil erosion was assessed both with and without T_o. The results showed that oblique cross-slope tillage covered 46.1 % of the study area, and the exclusion of T_o resulted in a 26.5 % overestimation of erosion rates, highlighting the importance of incorporating T_o into soil erosion assessments. The furrow contour angle varied significantly within parcels, with an average variation of 70.8°. The grid-based method for calculating T_o was more accurate and practical than traditional parcel-based approaches. T_o effectively captures the impact of oblique cross-slope tillage at various angles and could serve as a universal substitute for specific cases of contour and up-and-down slope tillage. Incorporating T_o into soil erosion models could increase their accuracy and provide more reliable guidance for soil conservation planning.