Study on the Spatiotemporal Evolution and Migration Path Coupling of the “Water–Land–Energy–Carbon” Nexus System in the Beijing–Tianjin–Hebei Region

This study investigates the spatiotemporal evolution and migration path coupling of the “water–land–energy–carbon” nexus system in the Beijing–Tianjin–Hebei region from 2002 to 2023 using multi-source data. The Coefficient of Variation and Shannon entropy were employed to assess the stability of elements, while Dynamic Time Warping (DTW) was applied to couple their migration paths. The results reveal the following: (1) Terrestrial water and groundwater exhibited similar evolution patterns, though groundwater showed greater volatility. Land use remained stable, with primary conversion being cropland to impervious. Nighttime light intensity increased significantly in urban areas, reflecting growth in energy consumption. Carbon emissions increased in most areas but decreased in some urban centers. (2) Element centroids displayed differentiated migration: water resources and cropland shifted southwest, and ecological land expanded northwest, while impervious, carbon emissions, and nighttime light concentrated in the southeast and northeast. (3) Two strongly coupled paths were identified: “terrestrial water–groundwater–cropland,” reflecting agricultural dependence on water resources, and “impervious –nighttime light–carbon emissions,” revealing the linkage between urban expansion, energy consumption, and carbon emissions. This study reveals the migration patterns of factors driven by both natural factors and human activities, providing quantitative support for resource optimization and low-carbon development policies in the Beijing–Tianjin–Hebei region.