Beyond Provincial Averages: A Coupling-Embedded Sustainable Development Index for Multiscale Sustainability Diagnostics in China

Existing environmentally adjusted development indices can assign similar scores to regions with contrasting environmental–social configurations, while provincial averages conceal subprovincial variation. We developed a Coupling-Embedded Sustainable Development Index (CESDI), which retains the Sustainable Development Index (SDI) as baseline performance while incorporating an adjustment for the joint balance and overall development level of the environmental and social subsystems. CESDI was applied to 30 Chinese provincial-level units from 2002 to 2022. Exploratory predictions for 337 Chinese cities were generated using MOSAIKS-inspired Landsat features, nighttime lights, and dual-penalty ridge regression. CESDI preserved the interprovincial SDI gradient (Pearson r = 0.870 to 0.995) while differentiating provinces with similar SDI values but contrasting joint environmental–social conditions. National mean CESDI increased from 0.248 in 2002 to 0.465 in 2017 and declined to 0.371 in 2022. Nested province-grouped cross-validation yielded R2 = 0.4471 and RMSE = 0.1388. Feature-block ablation showed that the dual-penalty model outperformed daytime-only, nighttime-light-only, and equal-penalty specifications. The predicted share of high and very high classes increased from 12.5% to 37.1%, while within-province heterogeneity rose in 21 of 26 multi-unit provinces. The framework integrates baseline sustainability performance with a CCD-defined balance-and-level adjustment and provides an exploratory spatial-screening layer for identifying within-province variation.