## 3 Results
### Gravity Center Migration of Vegetation NPP  
In order to explore the discreteness and bias of vegetation NPP distribution in the study area [38], the gravity center model was utilized to analyze the migration trend of vegetation NPP gravity center from 2000 to 2022 (Figure 6). In the polar coordinate system, the distance (polar diameter) and deflection angle (polar angle) of the gravity center of NPP from 2000 to 2022 were calculated to reflect its dynamic migration (Table 3). Figure 6: _Cont._  
center (northwest and northeast quadrants) accounted for 56% of the total gravity centers, indicating that the vegetation NPP increments in the northern half were greater than that of the southern half. The western half of the gravity center (northwest and southwest quadrants) accounted for 56%, indicating that the vegetation NPP increments in the western half were greater than that of the eastern half. The vegetation NPP gravity centers in East China are mostly distributed in Kaihua County, Quzhou City, and Zhejiang Province (Figure 6(b1,b2)). The standard deviation ellipse angle was 167.459\({}^{\circ}\), which was significantly different from that of Northeast China (170.617\({}^{\circ}\)), showing a northwest-southeast distribution pattern. The standard deviation ellipse area of 182.429 km\({}^{2}\) was the smallest among the six distribution areas. The standard deviations were 3.068 km and 18.925 km along the x- and y-axes, respectively. In 2001, the gravity centers deviated the farthest (29.651 km) from the origin, distributed at the southern end, indicating that, in 2001, the vegetation NPP increments were more significant in the corresponding area. The vegetation NPP gravity centers in North China were concentrated in Keshiketeng Banner, Chifeng City, and Inner Mongolia (Figure 6(c1,c2)). The ellipse angle was small (21.81\({}^{\circ}\)), showing a northeast-southwest distribution pattern. The standard deviation ellipse area was large, indicating that the gravity center distribution in North China was more discrete. Approximately 56% of the gravity centers were distributed in the north. The vegetation NPP gravity centers in Northwest China were mainly distributed in Gangcha County and Haibei Tibetan Autonomous Prefecture, with a standard deviation ellipse angle of 114.625\({}^{\circ}\), showing a northwest-southeast distribution pattern (Figure 6(d1,d2)). The area of standard deviation ellipse was the largest, at 1621.429 km\({}^{2}\). The distribution was the most discrete. The gravity center was the farthest from the origin in 2001, with a distance of 70.931 km, indicating that, in 2001, the increase in vegetation NPP was more significant in the corresponding area. In the polar coordinate system, the distribution of the gravity centers in the north-south direction was relatively uniform. Most of the gravity centers were distributed in the northwest quadrant, indicating that the vegetation NPP increments in the northwest were greater than those in the southeast. The vegetation NPP gravity centers in Southwest China were concentrated in Yanyuan County and Liangshan Yi Autonomous Prefecture, with a deflection angle of 72.350\({}^{\circ}\) (Figure 6(e1,e2)). The area of standard deviation ellipse was 275.257 km\({}^{2}\), and the dispersion degree was not large. According to the polar coordinate image, 2006 and 2015 had the farthest distances from the origin, at 18.857 km and 22.432 km, respectively, indicating that the vegetation NPP changed considerably in the corresponding area. Moreover, 2009 and 2012 had the smallest distances from the origin, at 3.412 km and 1.595 km, respectively, indicating that the vegetation NPP changed slightly in the corresponding area. The vegetation NPP gravity centers in the central and southern regions were concentrated in Dong'an County and Yongzhou City, with a north-south spatial distribution (Figure 6(f1,f2)). The standard ellipse angle was 7.17\({}^{\circ}\), and the standard ellipse area was small, indicating that its dispersion was small.