Water, energy, and food are lifelines for modern societies. The continuously rising world population, growing desires for higher living standards, and inextricable links among the three sectors make the water-energy-food (WEF) nexus a vibrant research pursuit. For the integrated delivery of WEF systems, quantifying WEF connections helps understand synergies and trade-offs across the water, energy, and food sectors, and thus is a critical initial step toward integrated WEF nexus modeling and management. However, current WEF interconnection quantifications encounter methodological hurdles. Also, existing calculation results are scattered across a wide collection of studies in multiple disciplines, which increases data collection and interpretation difficulties. To advance robust WEF nexus quantifications and further contribute to integrated WEF systems modeling and management, this study: (i) summarizes the estimate results to date on WEF interconnections; (ii) analyzes methodological and practical challenges associated with WEF interconnection calculations; and (iii) points out opportunities for enabling robust WEF nexus quantifications in the future.

In the context of China's resolute advancement of dual carbon goals (carbon peaking and carbon neutrality), urban agglomerations emerge as pivotal areas for carbon emission mitigation due to their dense economic activities and rapid urbanization. Previous studies overlook regional disparities in carbon emission prediction, disregarding the variations and policy directives across different provinces or cities. Therefore, this study addresses the research gap by investigating synergistic strategies to foster regional carbon peaking within the Beijing-Tianjin-Hebei region. Employing a novel approach tailored to regional segmentation policies, we provide more accurate predictions reflecting real-world conditions and distinct policy landscapes. Meanwhile, we integrate carbon emission efficiency into our analysis, emphasizing the dual goals of emission reduction and quality economic growth. Our empirical investigation in the Beijing-Tianjin-Hebei region, utilizing the Super-SBM and extended STIRPAT models, reveals upward trends in carbon emission efficiency, with varying trajectories across cities. Scenario simulations informed by the "14th Five-Year Plan" demonstrate that under the green development scenario, carbon peaking accelerates, alongside enhanced efficiency, supporting long-term emission reduction. Moreover, we design seven regional synergy carbon peak strategies for scenario simulations to facilitate the rational layout of dual carbon policies for collaborative development. We find that synergistic strategies have proven more effective in reducing regional carbon emission and increasing efficiency than strategies focusing solely on economic development or energy conservation. This innovative finding emphasizes the necessity of comprehensive green development in the Beijing-Tianjin-Hebei region and provides strong evidence for policymakers. Our research contributes to targeted strategies for improving carbon emission efficiency and reducing emissions, emphasizing the importance of synergistic approaches for regional carbon reduction.