## 3 Results
### Projected Variations of Land Use Types and Soil Erosion
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Land Use Type** & & **2025** & **2030** & **2050** \\ \hline \multirow{3}{*}{Arable land} & Area/(10\({}^{3}\) km\({}^{2}\)) & 35.16 & 34.87 & 32.60 \\  & Soil erosion/ & 2442 & 2412 & 2483 \\  & (t/ha per year) & 27.52 & 27.07 & 26.85 \\ \multirow{3}{*}{Woodland} & Soil erosion/ & 4885 & 4984 & 4761 \\  & (t/ha per year) & 4895 & 4984 & 4761 \\ \multirow{3}{*}{Grassland} & Area/(10\({}^{3}\) km\({}^{2}\)) & 32.37 & 34.92 & 24.15 \\ \cline{1-1}  & Soil erosion/ & 1439 & 1321 & 1254 \\ \cline{1-1}  & (t/ha per year) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Structure of land use and soil erosion in the period 2025 to 2050.  
and NDVI was the most important factor, with an explanatory power of 0.112. The results suggest that the forest farming subregion of the Loess Plateau should pay more attention to vegetation cover in areas with high elevation and in places with significant geographic relief to boost the planting of plants. In the research region, there are a variety of factors that have varying degrees of explanatory power for soil erosion. The q-values for the five variables are rainfall (0.021), NDVI (0.179), terrain elevation (0.103), slope (0.129), and LUCC (0.199). Among them, the LUCC factor with the highest q-value and the strongest explanatory power was the dominant factor affecting the research area's soil erosion's geographic spread. The interaction detector's findings demonstrate that the degree of synergy between the factors affecting soil erosion is significantly greater than the single factor's capacity for explanation. Among these, the most significant element determining the explanatory power of the geographical distribution of soil erosion is the synergistic influence of LUCC and other parameters. Particularly, the non-linearly increased interaction between the two factors strengthens the inhibitory influence on soil erosion. The interaction with rain is around 10 times larger than the single factor. This means that soil erosion is very different between land use types with different amounts of rainfall or between land use types with the same amount of rainfall. Local soil erosion can be effectively controlled through rational and orderly land use. This result is in line with other researchers' findings [43; 44; 45] about how different areas' land use impacts soil erosion. Soil erosion is a high-risk area if the LUCC is grassland, the NDVI is 0.9 to 1, the slope is greater than 35\({}^{\circ}\), the terrain elevation is 1595-2559 m, and the rain is 0.805-0.854 m when the average value of soil erosion intensity reaches the maximum (Figure 10). In summary, soil erosion is a complex process influenced by a combination of factors. It is therefore recommended that the process of prevention and restoration not only focus on the dominant factors but also require regional coordination and integrated management. For example, in sensitive areas such as slopes and grasslands, measures such as reforestation are taken to increase vegetation cover and strengthen local capacity for water and soil conservation. Figure 9: Explaining potential of the two-factor interaction depending on (**a**) the different forms of land usage and (**b**) soil erosion.