Spatiotemporal disparity of water scarcity risk and sharing responsibility: an integrated framework for urban agglomerations

Water scarcity increasingly threatens regional economies through cascading supply chain disruptions, making it essential to understand how risks propagate and how responsibilities should be shared. This study develops a water-constrained mixed-MRIO model integrated with responsibility-sharing mechanisms, and applies it to the Beijing-Tianjin-Hebei (BTH) urban agglomeration. Results show that indirect losses can exceed direct losses by over 50% in high-APL sectors, highlighting the amplifying role of network topology beyond water intensity. Scenario analysis reveals contrasting outcomes: targeting high-water-use sectors concentrates direct losses, whereas exempting livelihood-related sectors shifts the burden to manufacturing and construction, leading to extensive downstream spillovers. Across the three responsibility allocation schemes (value-added retention, Ghosh distance-based proximity, and APL-driven propagation), the results consistently reveal a misalignment: upstream Hebei cities absorb disproportionate production-side losses, whereas Beijing and Tianjin retain consumption-side benefits supported by infrastructure and institutional advantages. Robustness checks with substitution, buffering, and structural perturbations confirm that these asymmetries persist across parameter variations. The findings underline that without cross-regional eco-compensation, water rights trading, or differentiated quota systems, current governance perpetuates structural inequities. By linking loss propagation with responsibility allocation, this framework provides actionable diagnostics for balancing competitiveness with hydrological sustainability in urban agglomerations.