## 5 Conclusions  
The following findings are made from this study's calculations of the spatio-temporal variations in soil erosion in the forest farming subregion of the Loess Plateau from 2000 to 2050 and analysis of the elements that affect soil erosion.  
The forest farming subregion of the Loess Plateau experiences mostly slight soil erosion, with the proportion of slight erosion to the total area being no less than 67.46%. In the research region, soil erosion is distributed in a highly diverse manner, with very strong and extreme erosion mainly in the wooded plots of Jincheng City, the temperate deciduous scrub plots of Anyang City, and the cultivated vegetation plots in the eastern part of Jinzhong City. There is a small distribution in the eastern part of the wooded plots in Changzhi City and a small distribution in the southwestern part of the shrubland dry-land plots in Jiyuan, and in the northwestern part of the wooded dry-land plots in eastern Linfen City.  
From 2000 to 2020, there was more change in land use, with cropland, woodland, and grassland decreasing by 2554.0, 670.6, and 82.2 km\({}^{2}\), respectively. Soil erosion has significantly increased as a result of the conversion of arable and construction land to woodland. Therefore, by 2050, certain environmental protection measures should be adopted based on the protection of arable land, which successfully restricts the growth of constructing land to mitigate the rate at which soil erosion is escalating. Soil erosion (t/ha per year) in 2025, 2030, and 2050 is 4885, 4984, and 4761, respectively, with an increasing trend in soil erosion in all three years compared to soil erosion in 2020.  
In the forest farming subregion of the Loess Plateau, the analysis of the numerous factors influencing land use types using the geographical detector revealed that vegetation cover is a dominant factor in land use type. The ability of vegetation covering and altitude to explain the kind of land usage is 0.081 and 0.013, respectively, when acting as a single factor and rises to 0.112 when acting as a two-factor superposition. The two elements' interplay has the most explanatory potential, leading to the recommendation that vegetation cover be enhanced in locations with higher relief. The kind of land use is the primary determinant of the geographical distribution pattern of soil erosion. The interaction detector demonstrates that the interaction between the plant cover and land use type parameters has a bigger impact on soil erosion than each component acting alone. Areas with LUCC of grassland, NDVI of 0.9 to 1, a slope greater than 35 degrees, a terrain elevation between 1595 and 2559 m, and rain between 0.805 and 0.854 m are areas at high risk of soil erosion. In this context, the prevention and management of areas at high risk of soil erosion should focus on the combined effects of many factors.  
Conceptualization: J.M.; methodology: J.M. and H.L.; formal analysis: R.W.; writing--original draft preparation: [PERSON] and X.L. ([PERSON]); writing--review and editing: [PERSON]. ([PERSON]); funding acquisition: [PERSON]. ([PERSON]).; resources: [PERSON]. ([PERSON]). All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Natural Resources Integrated Survey Command Center of China Geological Survey, Project No. DD20230514. This work was supported by The Science and Technology Innovation Fundation of the Comprehensive Survey & Command Center for Natural Resources, China Geological Survey (KC20220015).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding [PERSON].  
The authors would like to thank [PERSON], [PERSON], and [PERSON] for helpful discussions on topics related to this work.  
The authors declare that they have no conflicts of interest.