A multi-scale assessment of supply–demand risk and ecological compensation in coal resource-based urban agglomerations of the Yellow River Basin from the perspective of carbon sink service flows

The compounded pressures of climate change and ecosystem degradation have heightened the role of carbon sink services (CSS) in sustaining resource-based regions. However, prior studies have largely emphasized carbon stocks or static supply–demand gaps, with insufficient consideration of spatial flows, supply–demand risks, and ecological compensation (EC) mismatches. Focusing on coal resource-based urban agglomerations (CRUA) in the Yellow River Basin (YRB), this study constructed a dynamic CSS supply–demand risk index to classify county-level risk. Carbon sink service flows (CSSF) were quantified across scales by coupling field-strength and breakpoint models, and a multi-level EC optimization scheme was developed based on CSSF. From 2003 to 2023, both CSS supply and demand increased, but demand rose far faster (257.70%) than supply (31.82%), widening the gap. Approximately 58% of counties faced "critically endangered" risk levels, primarily concentrated in key coal-producing regions such as Ordos. Within the CRUA, CSSF pathways declined and flow patterns shifted toward intra-provincial and intra-city transfers. Total county-level CSS flows increased from 2.60×10 6 to 3.61×10 6 t, accompanied by reduced dependence on external sinks and no exportable surplus. Actual EC in the CRUA fell from 1.44×10 8 to 1.18×10 8 CNY. These findings provide methodological and practical support for identifying high-risk CSS areas, improving carbon-sink governance, and refining EC mechanisms in the YRB and other resource-based regions. • In the YRB, the CRUA experienced increasingly acute CSS supply–demand tensions during 2003–2023. • 58% of counties in the CRUA face an “critically endangered” CSS supply–demand risk. • CRUA’s reliance on CSS in the YRB has declined, with no surplus available for export. • Develop an EC mechanism for resource-based cities based on CSSF. • Between the CRUA’s supply and demand areas, under-compensation and payment difficulties coexist.