## 3 Research Ranges, Objects and Methods
### The Spatial and Temporal Evolution of One-Star Green Residences  
According to the visualization results shown in Figure 2, the spatial and temporal evolution of one-star green residences can be divided into two stages.  
During 2008 to 2009, the center of gravity was always in Xuancheng in Anhui province, and only shifted 81.80 km to the northeast. The weighted standard deviation ellipses only cover an area of less than 0.13 million km\({}^{2}\) in the Yangtze River Delta, showing an obvious east-west distribution pattern. The major and minor axes standard deviations were shortened by 37.45 km from 783.15 to 745.70 km and 10.94 km from 211.26 to 200.32 km, respectively, and the axial ratio remained unchanged at 0.27, indicating that the direction and shape of the spatial distribution change trend of one-star green residences were not significant. This is because before 2010, except for Wuhan, Ningbo, Wuxi and Shanghai, there were no one-star green residences in other cities.  
During 2010 to 2016, the center of gravity moved gradually from east to west with slight fluctuations in the north-south direction with a displacement of 358.5 km. It can be found that during this period, the development speed of one-star green residences in the northern and southern regions of China was similar, but the development rate in the western region was faster than in the eastern region, which made the centers of gravity move westward every year. There was a obvious trend of southward movement in 2013, which was due to the rapidly development of one-star green residences in Guangdong province. The area of ellipse fluctuates between 135.47 and 167.87 km\({}^{2}\), covering mainly the eastern coastal regions of Shandong, Jiangsu, Shanghai, Zhejiang, Fujian and Guangdong, and the central regions of Hebei, Henan, Hubei, Hunan, Anhui and Jiangxi. It indicated that cities in these regions had a relatively large number of one-star green residences. It's worth noting that the ellipse began to spread significantly westward, covering parts of Shanxi, Shaanxi, Chongqing, Guizhou and Guangxi from 2013. This is mainly related to the vigorous development of one-star green residences in central and western regions in China. The rotation angle decreased by 29.94\({}^{\circ}\) from 50.77\({}^{\circ}\) in 2014 to 20.83\({}^{\circ}\) in 2014, and  
Figure 4: Weighted standard deviation ellipse of three-star green residences and their center of gravity change in China (2009–2016).  
then increased to 24.78\({}^{\circ}\) in 2016. It is obvious that the ellipse has a northeast-southwest distribution pattern. The major axis standard deviation increased first and then decreased. It first increased from 1670.89 km in 2010 to 1875.09 km in 2014, and then decreased to 1766.21 km in 2016, with a fluctuation of 204.2 km. The minor axis standard deviation had a more obvious fluctuation. The minimum value appeared in 2012 with 1023.18 km, and the maximum value appeared in 2016 with 1191.37 km, with a difference of 181.09 km, and the axial ratio also fluctuated around 0.6. It can be seen that the one-star green residences were mainly distributed in the central and eastern regions in China during the study period, and this presents the main trend of development in the northeast-southwest direction. However, due to the rapid development of one-star green residences in the western region, the east-west expansion speed of the ellipse range was obviously greater than that in the north-south direction, and the center of gravity moved westward obviously.