Data processing.

Five national urban agglomerations are selected according to the Fourteenth Five-Year Plan, namely the Yangtze River Delta, the Pearl River Delta, Beijing-Tianjin-Hebei, the Middle reaches of the Yangtze River, and Chengdu-Chongqing. The study on synergistic effects of such national strategic planning urban agglomerations, defined as coordinated degrees, and their time-series trends from 2016 to 2021 is significant for the practice of the national "double carbon" goal. Spatial differentiation of coordinated degree in five agglomerations is analyzed based on the Theil Index, along with regional linkage strength of coordinated degree under the gravity model. Conclusions include: (1) a downward trend is shown from 2016 to 2021 for the coordinated degree, along with the Pearl River Delta is the best among the five agglomerations; (2) the Middle reaches of the Yangtze River is the highest, followed by the Pearl River Delta and the Yangtze River Delta of coordinated degree in 2021; (3) the main cause of downwards in coordinated degree combined by a stable decline in carbon emissions and fluctuating increase in pollutants; (4) intra-regional differences in the Yangtze River Delta and the Middle reaches of the Yangtze River are relatively large, compared with the smallest in the Pearl River Delta measured by Theil Index; (5) coefficients of variation are relatively higher in the Middle reaches of the Yangtze River and the Yangtze River Delta, followed by the Beijing-Tianjin-Hebei, the Pearl River Delta and Sichuan-Chongqing urban. Consequently, countermeasures are proposed from the perspective of government, including technology and regional cooperation, policy innovation by overall coordination, synergy promotion by technological innovation, and regional synergy by win-win cooperation.