## 3 Results
### Spatio-Temporal Variation of Soil Erosion from 2000 to 2020
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Year**} & **Erosion** & **Modulus/** & **Proportion/** & **Effective Area/** \\  & **Grade** & **(t/ha per Year)** & **(\%)** & **(10\({}^{3}\) km\({}^{2}\))** \\ \hline \multirow{6}{*}{2000} & Slight & \textless{}200 & 60.69 & 2397.9 \\  & Mild & 200–2500 & 9.65 & 381.3 \\  & Moderate & 2500–5000 & 10.94 & 432.4 \\  & Strong & 5000–8000 & 8.58 & 339.0 \\  & Very strong & 8000–15,000 & 7.74 & 305.9 \\  & Extreme & \textgreater{}15,000 & 2.40 & 94.7 \\ \hline \multirow{6}{*}{2005} & Slight & \textless{}200 & 60.85 & 2411.6 \\  & Mild & 200–2500 & 10.65 & 422.0 \\  & Moderate & 2500–5000 & 12.07 & 478.2 \\ \cline{1-1}  & Strong & 5000–8000 & 8.60 & 340.9 \\ \cline{1-1}  & Very strong & 8000–15,000 & 6.79 & 269.0 \\ \cline{1-1}  & Extreme & \textgreater{}15,000 & 1.04 & 41.2 \\ \hline \multirow{6}{*}{2010} & Slight & \textless{}200 & 60.25 & 2388 \\  & Mild & 200–2500 & 10.47 & 415.0 \\ \cline{1-1}  & Moderate & 2500–5000 & 11.90 & 471.6 \\ \cline{1-1}  & Strong & 5000–8000 & 9.39 & 372.3 \\ \cline{1-1}  & Very strong & 8000–15,000 & 7.04 & 279.1 \\ \cline{1-1}  & Extreme & \textgreater{}15,000 & 0.95 & 37.8 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Statistics on the level of soil erosion in the forest farming subregion of the Loess Plateau between 2000 and 2020. Figure 4: Distribution of soil erosion severity across space in the research region in (**a**) 2000; (**b**) 2005; (**c**) 2010; (**d**) 2015; (**e**) 2020. When examining rates over 5-year periods, from 2000 to 2005, the proportion of very strong and extreme erosion areas decreased (0.95 and 1.36 percentage points, respectively); the percentage of erosion area at other intensity levels increased, and in general, the rate of soil erosion was trending downward. Specifically, very strong erosion replaced intense erosion at 0.36% of the area, and the region of soil erosion at all levels changed to the surrounding 75.32% of the slightly eroded area remains unchanged, 8.94% is converted to mild erosion, 7.36% is converted to moderate erosion, 4.28% is converted to strong erosion, 3.21% is converted to very strong erosion, and 0.90% is converted to extreme erosion. From 2005 to 2010, the transformation of soil erosion at every level was different from that of the previous period, except for the increase in the percentage of strong erosion and very strong eroded areas. The proportion of soil erosion area at all other intensity levels shows a decreasing trend, and the number of transformations from high-intensity levels to low-intensity levels increases significantly, especially the transformation of mild erosion to slight erosion (41.29% transformed to slight erosion), demonstrating a general downward trend in the severity levels of soil erosion over this time. From 2010 to 2015, the proportion of slight and moderate erosion declined considerably, while the percentage of extreme, strong, very strong, and mild erosion showed an increasing trend. Except for the decline in the area of slight and mild erosion and the growth in the area of other intensity categories, the transformation of the soil erosion area from 2015 to 2020 is comparable to that of the preceding time period. The percentage indicates a rising trend; specifically, the unchanged erosion intensity of slight erosion area rises to 81.45%, and the transfer of high-intensity to low-intensity area is mainly from mild and moderate erosion to slight erosion transformation, converting 40.65% and 34.33%, respectively. This suggests that the soil erosion intensity levels as a whole show a decreasing trend in this time period. It is complicated how soil erosion zones change over time and at various echelon levels.