Water Saving and Carbon Reduction (CO2) Synergistic Effect and Their Spatiotemporal Distribution Patterns

Under the dual constraints of rigid water resource management systems and China’s “dual carbon” national strategy, water resource management authorities face pressing practical demands for the coordinated governance of water conservation and carbon dioxide emission reduction. This study comprehensively compiles nationwide data on water supply/consumption, energy use, water intensity, and CO2 emissions across Chinese provinces. Employing a non-radial directional distance function (NDDF) model with multiple inputs and outputs, we quantitatively assess provincial water saving and carbon reduction performance during 2000–2021; measure synergistic effects; and systematically examine the spatiotemporal evolution, correlation patterns, and convergence trends of three key indicators: standalone water saving performance, standalone carbon reduction performance, and their synergistic performance—essentially addressing whether “1 + 1 > 2” holds true. Furthermore, we analyze the spatial convergence and clustering characteristics of synergistic effect across regions, delving into the underlying causes of inter-regional disparities in water–carbon synergy. Key findings reveal the following: ① Temporally, standalone water saving and carbon reduction performance generally improved, though the water saving metrics initially declined before stabilizing into sustained growth, ultimately outpacing carbon reduction gains. Synergistic performance consistently surpassed standalone measures, with most regions demonstrating accelerating synergistic enhancement over time. Nationally, water–carbon synergy exhibited early volatile declines followed by steady growth, though the growth rate gradually decelerated. ② Spatially, high-value synergy clusters migrated from the western to eastern regions and the northern to southern zones before stabilizing geographically. The synergy effect demonstrates measurable convergence overall, yet with pronounced regional heterogeneity, manifesting a distinct “high southeast–low northwest” agglomeration pattern. Strategic interventions should prioritize water–carbon nexus domains, leverage spatial convergence trends and clustering intensities, and systematically unlock synergistic potential.