Nonlinear Associations and Scale Dependence Between Yellow–Green–Gray Spatial Patterns and Carbon-Cycle-Related Indicators: A Case Study of Harbin

The nonlinear associations and scale dependence of yellow–green–gray spatial patterns with atmospheric CO2 and vegetation productivity remain insufficiently understood in cold-region cities characterized by mixed cropland–forest landscapes. Taking Harbin, China, as a case study, we integrated morphological spatial pattern analysis (MSPA), landscape metrics, and three-dimensional structural indicators with multiscale geographically weighted regression (MGWR), seven machine learning algorithms, and interpretable machine learning methods. Spatial block cross-validation was used to evaluate predictive performance at 3 km and 9 km grid scales. The results showed that (1) column-averaged atmospheric CO2 (XCO2) and vegetation net primary productivity (NPP) exhibited significant spatial clustering, with high-XCO2 areas generally corresponding to low-NPP areas; (2) cropland coverage (YC) ranked first in relative SHAP importance across all four scale-response combinations and was generally associated with higher predicted XCO2 and lower predicted NPP, whereas forest coverage (GC) showed the opposite patterns; (3) nonlinear predictive responses and non-additive interactions differed between the two response variables, with building-density-related combinations more prominent for XCO2 and cropland–forest combinations more prominent for NPP; and (4) the mean spatial cross-validation R2 values of random forest models were 0.524 and 0.660 for XCO2 and NPP at 3 km, respectively, compared with 0.597 and 0.630 at 9 km. These findings highlight the predictive relevance of cropland composition and landscape interactions while demonstrating the scale dependence of their associations with XCO2 and NPP. The results provide spatial planning insights for cold-region cities with mixed agricultural and forest landscapes.