A diagnostic equation for understanding courtyard thermal radiation environments: Evidence from courtyards in central Guangdong, China

A well-thermalized courtyard serves as a common outdoor space for urban residents to combat high temperatures and relax. Thermal radiation is a key variable affecting thermal comfort in courtyards. However, the extent to which various spatial features induced by diverse courtyard design schemes couple and influence changes in the courtyard's radiation components, ultimately affecting overall radiation, remains unclear. This study establishes a holistic diagnostic equation to quantitatively elucidate the complex relationships and coupling effects between various spatial indices and radiation components, aiding in the understanding of the courtyard thermal radiation environment. Utilizing the indexization of critical spatial variables and a multiple linear regression method from the previously developed GPU-parallel quasi-physical courtyard thermal radiation model CMRT, the diagnostic equation is constructed. Results indicate that the NRMSE for the proposed diagnostic equation ranges from 0.02 to 0.16, with MAE between 2.5 and 16 W/m², comparable to mainstream simulation software in peer studies. The sensitivity ranking within the diagnostic equation reveals that exposure factor series, solar transmittance series, and background meteorological variable series are the most sensitive, while the average spatial variable series exhibit lower sensitivity. The Diagnostic Equation exhibits clear advantages in interpretability and efficiency compared to traditional simulation methods, although its adaptability is relatively limited. However, its potential for flexible extensibility can compensate for this drawback. The research outcomes will enhance understanding of the courtyard thermal radiation environment and can be directly applied to climate-adaptive design practices in courtyards.