Three-dimensional emergy ecological footprint of the Central Plains Urban Agglomeration: spatial and temporal evolution, driving mechanisms and ecological compensation

• The improved three-dimensional emergy ecological footprint(EEF 3D ) model is used to explore urban sustainability. • The Interactive Geographical and Temporally Weighted Regression model is used to discuss the drivers of the EEF 3D . • The dynamic horizontal ecological compensation model is established. • This paper provides theoretical support for the research of harmonies between socioeconomic activities and ecological environment. Horizontal ecological compensation represents an environmental management approach, also a critical safeguard for addressing the external imbalance in ecosystem services, restructuring benefit redistribution mechanisms, and reshaping regional development dynamics. This paper employs three-dimensional emergy ecological footprint (EEF 3D ) analysis to assess the natural capital utilization within the Central Plains Urban Agglomeration (CPUA). We applied Interactive Geographically and Temporally Weighted Regression (IGTWR) model to investigate the spatio-temporally heterogeneous drivers and their interactions, then calculated ecological compensation quotas for 30 cities in CPUA. The findings revealed that: (1) The per capita emergy ecological footprint (eef) in the CPUA had fluctuating upward trend within a range of 6.240–7.742 hm 2 /cap, while the per capita emergy ecological carrying capacity (eec) was stable, leading to a persistent ecological deficit. (2) The per capita emergy ecological footprint size (eef size ) was stable, ranging from 0.602 to 0.659 hm 2 /cap, while the emergy ecological footprint depth (EEF depth ) ranged from 6.312 to 8.222. Cropland and construction land used the greatest flows of natural capital, whereas grassland and water area were the largest natural stocks used. (3) Interactions between two drivers had a greater influence on resource use than individual drivers. These interaction mechanisms operated through two coordinated pathways by both mitigating the positive effects of individual factors and restraining the expansion of EEF 3D . (4) Ecological compensation quotas across the CPUA were incredibly volatile over time. Payment zones predominantly clustered in central and eastern regions, with high-payment areas fragmented. Conversely, compensation zones concentrated in western and northern regions, where high-compensation areas formed contiguous clustering features.