Water-heat-carbon nexus for understanding mechanisms and response thresholds across urbanization gradients

• A new water-heat-carbon nexus was proposed to explore urbanization impacts. • Mechanisms of urbanization's impact on WHC differ across threshold-based sub-areas. • The relationship between WHC and urbanization has an inverted S-shape. • The number of direct and positive pathways increases with urbanization gradients. • Priority zones were identified based on the likelihood of crossing thresholds. Urbanization significantly affects the balance of key elements such as water, heat, and carbon in cities. However, previous studies have not integrated these factors for comprehensive analysis. Here we proposed a water-heat-carbon (WHC) nexus model to provide a holistic understanding of urbanization's impacts. Furthermore, we employed the model to identify the mechanisms and response thresholds of urbanization through this coupling approach. Our findings reveal three key insights: (1) WHC exhibits a nonlinear, inverted S-shaped response to urbanization. (2) The mechanisms through which urbanization influences WHC differ significantly across urbanization gradients. As urbanization intensifies, the complexity of environmental pathways increases, with direct effects becoming more pronounced and positive impact pathways emerging progressively. (3) We identified priority zones for restoration and protection based on the likelihood of units shifting between low- risk and high-risk categories. Our study enhances understanding of the WHC-urbanization nexus and underscores the importance of accounting for threshold effects and environmental interactions when examining the drivers of WHC. This framework can be adapted to other urban areas experiencing similar challenges.