## 3 Results
### Spatial-Temporal Patterns of Multi-Scale BCEs
#### 3.2.3 County-Level BCEs in the BTH and Municipality-Level BCEs in the NCRJ  
According to the Lorentz curve of county-level emissions of the BTH, the curves deviate from the mean line, showing significant scale differences in BCEs between counties in the BTH (Figure 7a). The degree of curve deviating from the mean line increases continuously from 2000 to 2010, indicating that scale differences between counties' BCEs increase due to high-emission counties' growth rate being faster than middle- and low-emission counties. However, with the acceleration of the growth of middle- and low-emission counties' BCEs, the differences in the BCE scale between counties are reduced and the curves of 2015 and 2019 are relatively approaching the mean line. Similarly, 10% of counties' BCEs accounted for 50% of the total BCEs in 2010, and this proportion increased to 17% in 2019. The Lorentz curves of municipalities' BCEs in the NCRJ also deviate far from the mean line, but the multi-year curves almost overlap, which means that there are significant differences in the scale between municipalities' BCEs but the differences remain stable and show barely interannual changes (Figure 7b). Since the municipalities' BCEs maintain similar growth and decline rates, the proportion of high-emission municipalities accounting for 50% of the total BCEs was about 15.8% from 2000 to 2019. From the perspective of spatial patterns, there are significant interannual changes in BCEs at the county level within the BTH (Figure 8). The BCE of most counties ex  
Figure 6: BCEs of prefectures in the NCRJ. Figure 7: Lorentz curve of county-level emissions of the BTH and municipality-level emissions of the NCRJ. ceeded 200,000 tons in 2000. Chaoyang, Haidian, Fengtai, Changping, Shunyi, Tongzhou, Daxing, and Fangshan in Beijing and Dongli, Beichen, Xiqing, and Binhai New District in Tianjin's BCEs exceeded 1 million tons, forming a significant high-emission cluster. With the emissions of the BTH increasing rapidly between 2005 and 2010, the number of counties generating more than 1 million tons in Beijing and Tianjin increased significantly. In addition, counties' BCEs in Tangshan, Shijiazhuang, and Handan also continued to increase. For example, the BEC of Fengrun and Qianan in Tangshan, and Wuhan in Handan exceeded 1 million tons. The number of counties with BECs over 200,000 tons in Chengde and Langfang also increased. The BEC of most counties in the BTH still maintained a significant growth trend from 2010 to 2015, and the main patterns include the concentration of high-emission counties in Beijing and Tianjin, the distribution of counties with emissions higher than 1 million tons in Shijiazhuang and Baoding, and the increase in the number of counties with emissions exceeding 500,000 tons in Shijiazhuang, Baoding, Cangzhou, and Handan. Compared with the previous period, the number of counties with high emissions increased in Tianjin, Shijiazhuang, and Tangshan in 2019. In general, counties' BCEs in the BTH observably increased from 2000 to 2019. Due to the rapid speed of development with a relatively large population size and dense buildings, the change in BECs of counties surrounding core areas in Beijing, Tianjin, Shijiazhuang, and Tangshan exceeded 500,000 tons. Figure 8: Spatial–temporal evolution of and change in BCEs at the county level in the BTH. Municipalities' BCEs in the NCRJ are more stable and vary within a smaller range (Figure 9). Most municipalities' BCEs reached 100,000 tons, and the emissions of most municipalities in Tokyo, Kanagawa, Saitama, and Chiba prefectures exceeded 200,000 tons. Most of the high-emission municipalities with emissions above 1 million tons are concentrated in Tokyo including Hachioji, Machida, Shinjuku, Koto, Ota, Setagaya, and other areas located on the fringes of the special ward. The changes in most municipalities' BCEs in the NCRJ were less than 50,000 tons, but the changes in BECs of parts of municipalities in Ibaraki, Saitama, and Chiba were between 50,000 tons and 100,000 tons.