## 3 Results  
### Spatiotemporal Evolution Analysis of Urbanization in Beijing-Tianjin-Hebei  
In Figure 5a, which displays the cumulative overlay of annual impervious surface data from 1985 to 2020, it can be clearly observed that the urban core areas of Beijing and Tianjin, as well as the urban agglomeration in southeastern Hebei, show obvious outward expansion trends. The color gradient from light to dark orange illustrates the temporal sequence of impervious surface development over the 35-year period. Specifically, Beijing, as the core city of the Beijing-Tianjin-Hebei urban agglomeration, demonstrated the highest mean annual expansion rate of 115.17 km\({}^{2}\)/year and has simultaneously driven the coordinated development of surrounding cities such as Langfang (90.63 km\({}^{2}\)/year) and Baoding (108.56 km\({}^{2}\)/year). In contrast, Chengde (21.44 km\({}^{2}\)/year) and Zhangjiakou (36.68 km\({}^{2}\)/year) in northern Hebei have experienced relatively slow urbanization due to factors such as topographical constraints and ecological protection policies, with their main development period concentrated after 2000. The urbanization process in the Beijing-Tianjin-Hebei region has undergone a transformation from rapid expansion to gradual deceleration over the past 30 years. Although  
Figure 5: Impervious surface change in the Beijing-Tianjin–Hebei (BTH) region. (**a**) Land cover change mapping using GAIA data from 1985 to 2020. (**b**) Expansion area and changing rate of GAIA from 1985 to 2020.  
the built-up area continues to grow, the expansion speed has significantly slowed in recent years. According to calculations, the impervious surface area in the Beijing-Tianjin-Hebei region increased from 7579.3 km\({}^{2}\) in 1985 to 37,484.0 km\({}^{2}\) in 2020, representing a total growth of 394.5% over the 35-year period, with an average annual increase of 854.4 km\({}^{2}\)/year (Figure 5b). In terms of growth rate, the impervious surface growth in the Beijing-Tianjin-Hebei region from 1985 to 2000 showed a pattern of initial decline, followed by increase, then decrease again. The expansion rate experienced a dramatic surge around 1990, with a growth rate of 800 km\({}^{2}\)/year; subsequently dropping sharply to reach the lowest point; then experiencing rapid growth again around 2010, reaching a peak during 2010-2015 at approximately 1700 km\({}^{2}\)/year; followed by a declining trend. The overall trend shows that the built-up land area in the Beijing-Tianjin-Hebei region continues to grow and has experienced two rapid expansion phases. To reveal the centroid changes in urban development in the Beijing-Tianjin-Hebei region, the impervious surface centroid at the regional scale was estimated using six-period ISC images. The weighted average center of impervious surfaces at the regional scale and its movement trajectory are shown in Figure 6.  
Figure 6a shows that the centroid of the Beijing-Tianjin-Hebei region exhibited a northward-then-southward transfer trend from 1990 to 2015. During 1990-2000, influenced by the early urbanization of Beijing and Tianjin, the centroid moved closer to the Beijing-Tianjin corridor. During 2005-2015, the urban centroid moved toward the south-east, reflecting the enhanced economic growth and population agglomeration effects in southeastern Hebei. The relatively short centroid movement distance indicates that regional overall development is relatively balanced, but there exists slight spatial imbalance. By separately analyzing the centroid transfer of high-density ISC areas and Hebei province (Figure 6c), it can be observed that the centroid transfer direction of high-density ISC areas is basically consistent with the overall Beijing-Tianjin-Hebei trend. The relocation of heavy industries such as Shougang in Tangshan and the rapid development of the Caofeidian Industrial Zone in the coastal economic belt have driven industrial transfer toward Hebei.