Extending spatial regression to the analysis of subsurface urban heat islands

Abstract

Spatial regression models have been widely employed in the analysis of surface urban heat islands to investigate the relationship between urban morphology and surface temperature. In contrast, the employment of such approaches in the study of subsurface urban heat islands, which are a hidden yet central problem in urban climate, remains vastly untapped. This study is the first to apply classical spatial regression approaches to the modeling of subsurface urban heat islands, focusing on the influence of underground heat source density and depth on the subsurface temperature field. Using the Chicago Loop district as a case study, we apply Moran's I coefficient to confirm the presence of spatial autocorrelation in the underground temperature field. We then evaluate six different grid sizes using Pearson correlation coefficients to determine the optimal spatial resolution, identifying 60 m as the most appropriate scale. Based on this resolution, we implement and compare four models to simulate subsurface heat island patterns: the ordinary least squares, the spatial error model, the spatial lag model, and the geographically weighted regression. Results show that geographically weighted regression consistently outperforms other models by capturing spatial heterogeneity, achieving R² values exceeding 0.85 in all scenarios. This work advances the application of spatial analysis in underground urban climate studies and provides a valuable foundation for efficient modeling and harvesting of underground waste heat resources.