Assessing the cross-scale spillover effect of urban Heat Island (UHI): an indicator-based approach in the Beijing-Tianjin-Hebei region

Due to rapid urbanization, urban heat island (UHI) effects have expanded from city-level phenomena to continuous cross-city UHI belts, posing challenges to regional ecological security and public health. However, a critical research gap remains: the spatial structure, formation mechanisms, and cross-scale transmission processes of continuous UHI belts are insufficiently quantified, primarily due to a reliance on isolated, single-scale analyses. In this study, an indicator-based, multiscale analytical framework was developed at the Beijing-Tianjin-Hebei (BTH) region, city, and 1-km grid scales. Landscape metrics, a coupled random forest-geographic SHAP (RF-GeoSHAP) model, and generalized additive mixed models (GAMMs) were used to investigate the hierarchical transmission pathways of continuous UHI belts. Our results show that these belts emerge as structurally connected regional heat sources once heat island dominance (HID) surpasses a nonlinear threshold of approximately 7%. At the agglomeration scale, HID, along with climatic and ecological backgrounds (PRE, NDVI, TMP), are identified as the dominant thermal predictors, while at the fine grid scale, local thermal accumulation is substantially amplified by building height (BH) and sky view factor (SVF) under structural forcing. Crucially, the influence of these key driving indicators exhibits clear threshold effects that are nonlinearly amplified by regional UHI connectivity. Overall, this study enhances the understanding of UHI dynamics across scales and offers valuable insights for indicator-guided UHI mitigation strategies at the urban agglomeration scale.