Terrain Complexity and Infrastructure–Carbon Decoupling: Evidence from Sichuan Province, China

Against the backdrop of China’s dual carbon goals, understanding how terrain complexity affects the decoupling linkage between infrastructure investment and carbon emissions is crucial for developing differentiated low-carbon strategies. This study focuses on Sichuan Province, a region characterized by significant topographical heterogeneity, to investigate how terrain constraints influence carbon emission decoupling. We construct a Terrain Constraint Index (TCI) using three indicators (Digital Elevation Model (DEM), Coefficient of Variation of elevation (CV), and Terrain Position Index (TPI)) weighted by a game theory-based combination of entropy and Criteria Importance Through Intercriteria Correlation (CRITIC) methods and employ the Tapio decoupling model combined with group comparison analysis to examine the correlation between terrain complexity and decoupling performance. The key findings are as follows. (1) The TCI exhibits a “high in the west, low in the east” spatial pattern, ranging from 0.151 (Zigong) to 0.591 (Ya’an), with five distinct terrain complexity levels identified. (2) During 2001–2021, good decoupling states (strong + weak decoupling) accounted for 76.8% of all observations, indicating overall improvement in carbon emission efficiency. (3) A monotonic negative association is observed between terrain complexity and decoupling performance: the good decoupling ratio decreases from 82.5% in Low TCI regions to 62.5% in Very High TCI regions, with Mann–Whitney tests showing suggestive differences (raw p < 0.05, though not significant after Bonferroni correction). (4) Average decoupling elasticity increases from 0.182 in Very Low TCI regions to 0.705 in Very High TCI regions, demonstrating that higher terrain complexity is associated with worse decoupling outcomes. (5) Geodetector analysis reveals that infrastructure investment has the highest explanatory power (q = 0.401, p < 0.01), and the interaction between terrain factors and investment shows significant nonlinear enhancement effects (q = 0.544–0.830). These findings suggest that terrain complexity is associated with worse carbon emission decoupling, plausibly through affecting infrastructure investment efficiency, and point to the need for differentiated low-carbon strategies for regions with varying topographical conditions.