This study investigates whether the intensity of human activities conducted by urban populations and carried by urban land follows a wave-shaped diffusion rule using a harmonized DMSP-like NTL dataset during 1992–2018 in 234 cities of China. The results show that variations in the intensity of human activities are diffused in a wave-shaped manner from the urban center to the periphery in cities of different sizes and structures. The results demonstrate that variations in the intensity of human activity also exhibit a wave-shaped diffusion pattern, which is best modeled by a Gaussian function with an average R² of 0.79 and standard deviation of 0.36 across all fitted functions. The outward movement of these waves in monocentric cities with an urban population <8 million occurred at a pace of ~0.5–1.0 km per year, reaching an average distance of ~18 km from the urban centers. While the pace decreased to ~0.2–0.6 km per year in larger or polycentric cities, the average distance of the waves from the urban centers increased to ~22–25 km in these larger cities. In addition, a process-pattern link between the distance-decayed rule and the wave-shaped rule of human activity dynamics was established. Moreover, a spatiotemporal Gaussian function was further discussed to enable modelers to forecast future variations in the intensity of human activities. The disclosed wave-shape rule and model can benefit the simulation of urban dynamics if integrated with other simulation technologies, such as agent-based models and cellular automata.

Research on the coupling coordination relationship between land–use carbon emissions (LUCE) and ecosystem service value (ESV) is vital for achieving China’s “dual carbon” goals and advancing ecological civilization. Applying the carbon emission coefficient method, equivalent factor method, coupling coordination degree model, and Geographically and Temporally Weighted Regression (GTWR) model, this study examined spatiotemporal patterns of land–use changes, carbon emissions per unit area (ACE), and ecosystem service value per unit area (AESV) across China (excluding Xizang, Hong Kong, Macao, and Taiwan) from 2000 to 2020, along with their coupling relationship and driving forces. Results showed that grassland, forest, and cropland accounted for more than 70% of China’s land area, with a total land–use conversion area of 1.42 × 106 km². ACE increased while AESV generally decreased, both displaying strong spatial heterogeneity and agglomeration. The average Dagum Gini coefficients were approximately 0.70 for ACE and 0.58 for AESV. Coupling coordination degree mostly fluctuated around 0.20, rising initially and then falling, with distinct spatial variations in coordinated development types. Population density, Normalized Difference Vegetation Index (NDVI), and average elevation were negatively correlated with the synergistic effect between LUCE and ESV, whereas GDP density, annual precipitation, and average slope showed positive correlations. These findings provided theoretical support for formulating scientific land–use policies, optimizing carbon emission management, and implementing effective ecological protection measures.