## 3 Results
### Spatial Dynamics of Rangeland Degradation  
Although rangeland degradation change statistics can be generated by other measures, such as census tracts, they shed little light on where the rangeland degradation changes are occurring. However, by constructing a change detection map, the advantages of remote sensing could be fully appreciated. Using raster calculation, spatial change maps of rangeland degradation were constructed (Figure 6) for each study interval, and the elements of maps were defined as follows: (1) a one-level increase of degradation during study interval indicates \"developed\" (e.g., a change from Non-DR to SI-DR); (2) a cross-level increase indicates \"seriously developed\" (e.g., a change from Non-DR to M-DR). Conversely, a one-level decrease indicates \"reversed\"; and a cross-level decrease indicates \"notably reversed\". No change between two study periods was expressed as \"stable\" ([PERSON] et al., 2011). Meanwhile, to further evaluate the results of degraded rangeland conversions, matrices of degraded rangeland from 1996 to 2001, 2001 to 2006, and 2006 to 2011 were created (Tables 5-7). Unchanged pixels in this table are located along the major diagonal of matrix and conversion values were calculated by area (km\({}^{2}\)). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Degraded Rangeland Type** & **1996–2001 (\%)** & **2001–2006 (\%)** & **2006–2011 (\%)** \\ \hline SI-DR & –5.98 & +3.71 & +3.83 \\ M-DR & +9.32 & \(-4.77\) & \(-2.41\) \\ Se-DR & +10.22 & \(-4.58\) & \(-0.81\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Annual change rate of degraded rangeland from 1996 to 2011 (positive values mean an increase, negative values represent a decrease). Figure 6: Rangeland degradation spatial dynamics for Linxia rangeland during 1996–2001, 2001–2006, and 2006–2011. The base map was the hillshade result of digital elevation model (DEM) topographical analysis. From 1996 to 2001, 532.36 and 102.19 km\({}^{2}\) of SI-DR converted to M-DR and Se-DR, and 169.92 and 102.22 km\({}^{2}\) of M-DR changed into SI-DR and Se-DR, respectively. The amount of Se-DR area that changed into SI-DR and M-DR was relatively small (16.27, and 4.63 km\({}^{2}\), respectively) (Table 5). Meanwhile, 176.87, 185.82, and 4.63 km\({}^{2}\) of Non-DR converted to SI-DR, M-DR, and Se-DR, respectively. In the first study interval (1996-2001), only 283.36 km\({}^{2}\) of degraded rangeland was either reversed or notably reversed, with the change being dispersedly distributed in the study region. Conversely, 1104.49 km\({}^{2}\) of rangeland was developed or notably developed, which was widely distributed in the study region. In this period, due to overgrazing and lack of effective policy guidance, the total area of developed and seriously developed degraded rangeland was 3.90 times that of the reversed and notably reversed degraded rangeland, which indicates that during the 1996-2001 interval, rangeland degradation in the study region was in a state of deterioration (Figure 6). In the second period (i.e., from 2001 to 2006), 283.12 km\({}^{2}\), 3.17 km\({}^{2}\), and 453.29 km\({}^{2}\) of SI-DR changed to M-DR, Se-DR, and Non-DR, respectively, with the largest proportion changing to Non-DR among study periods. An area of 122.79 km\({}^{2}\) of M-DR changed to Se-DR, and 646.93 km\({}^{2}\) of M-DR changed to SI-DR, which is 5.27 times the area that changed to Se-DR. In addition, 50.80 and 172.03 km\({}^{2}\) of Se-DR changed to SI-DR and M-DR, respectively (Table 6), which was much greater than the total area changed during the previous interval. In this period (2001-2006), 1480.22 km\({}^{2}\) of degraded rangeland was reversed or notably reversed and was mainly distributed in western Xiahe County; an area of 698.28 km\({}^{2}\) of DR was developed in the study region (Figure 6).