Characterization of Spatial and Temporal Coupling of Digital Economy and Carbon Emission in Yangtze River Delta Urban Agglomerations and the Influence Factors by Integrating GWRF and SHAP

Against the strategic backdrop of "Digital-China" and the "Dual-Carbon" goals, the synergistic advancement of digital economy and carbon emission reduction is crucial for achieving high-quality, sustainable development. As a leading region in China's economic and digital transformation, the Yangtze River Delta (YRD) urban agglomeration provides a critical-case study for examining the complex interplay between digital growth and decarbonization. In this study, we aimed to systematically analyze the spatiotemporal-coupling characteristics and underlying influence mechanisms between the digital economy and carbon emissions in the YRD region from 2011 to 2023. Moving beyond aggregate-analysis and linear-assumptions, this study seeks to reveal the spatial heterogeneity, nonlinear-relationships, and threshold-effects to provide a nuanced empirical basis for differentiated-regional policymaking. Methodologically, we integrated the Geographically Weighted Random Forest (GWRF) model with SHapley Additive exPlanations (SHAP). We constructed comprehensive evaluation systems for both the digital economy and carbon emissions, and calculates the coupling coordination degree (D) between these two systems for 41 cities. The core analytical approach uses the GWRF model, which embeds a spatial-weight matrix into the Random Forest algorithm to simulate the spatially-varying and nonlinear effects of multiple influencing factors on the degree of coordination. Subsequently, the SHAP framework was applied to interpret the GWRF " black-box model and quantify the global-importance, directional-contribution, and potential nonlinear or threshold-behavior of each explanatory variable. This study yielded several key findings. Regarding temporal evolution, the overall coupling coordination degree of the YRD urban agglomeration shows a clear upward trend, increasing from 0.411 in 2011 to 0.505 in 2023, marking a transition from an "imminent-imbalance" to a "barely-coordinated" stage. However, this progression is not monotonic; the significant dip observed in 2021 reflects dynamic tension and potential lagged-adaptation between technological-advancement cycles and stringent emission-reduction targets. In terms of spatial patterns, a distinct hierarchical "core-corridor-periphery" radial structure has formed. Shanghai, leveraging its advanced technological foundation and institutional advantages, remains at the forefront, achieving "high-quality coordination" by 2023. The provinces of Jiangsu and Zhejiang exhibit follow-up growth, entering the "barely-coordinated" stage. In contrast, Anhui province, despite exhibiting the fastest growth rate, remains at the threshold of "imminent-imbalance," highlighting persistent regional disparities within the agglomeration. At the city level, high-coordination cores were concentrated along the Shanghai-Nanjing-Hefei-Hangzhou development axis, with coordination levels gradually diffusing along major transport corridors and weakening in northern Anhui and southwestern Zhejiang. Concerning the model validation and identification of key drivers, the GWRF model demonstrated significantly superior explanatory power and predictive accuracy compared to the standard-Random Forest model, confirming its efficacy in capturing spatial-non-stationarity. The SHAP analysis identified variables from the digital economy subsystem, specifically, the number of mobile phone subscribers, employees in information transmission and software services, and postal business volume, as important positive drivers. Their intensity-of-influence exhibited a spatial-diffusion pattern, radiating outward from core metropolitan areas to key manufacturing nodes and emerging industrial zones. Conversely, variables from the carbon emissions subsystem, particularly carbon emissions intensity and per-capita carbon emissions, act as primary inhibitors of coupling coordination. In summary, this study elucidates a dual-path mechanism, wherein the agglomeration of digital elements drives synergistic improvements, whereas high-carbon economic structures exert inhibitory pressure. This study makes substantive contributions to both the theoretical and methodological fronts. Theoretically, it provides robust empirical evidence for the complex, nonlinear-interdependencies between digital and green transitions, challenging simplistic linear-assumptions and enriching the understanding of their coupling dynamics in a regional context. Methodologically, the integrated GWRF-SHAP framework was validated as a powerful tool for dissecting high-dimensional and spatially-heterogeneous problems in urban and regional studies, offering a replicable-analytical pathway. These findings provide actionable-insights for policymakers to advocate tailored-strategies that reinforce positive digital diffusion, especially in lagging areas, while implementing targeted measures to decouple economic growth from carbon emissions in high-pressure zones. Ultimately, this approach aims to foster a more balanced and synergistic development pathway for the YRD and similar regions.