Relative cooling performance of urban trees: A CFD-based thermodynamic benchmark for diurnal design assessment

Urban trees mitigate outdoor heat through coupled shading, evapotranspiration, and aerodynamic effects, but a single area-aggregated indicator cannot describe where cooling occurs. This study defines the no-tree-normalized relative cooling performance index, RCP tree = (T ref − T tree )/(T ref − T inlet ), and extends it to spatially resolved windward and leeward locations using normalized coordinates ξ = x/D and η = y/D. The porous crown includes drag, turbulence modification, a volumetric water-vapour source, latent heat removal, and Beer–Lambert-derived solar attenuation. Solar beam direction was recalculated for each diurnal snapshot using the Fluent Solar Calculator and the ASHRAE Fair Weather Conditions option; the Perez diffuse-sky model was not used. The crown absorption coefficient was 0.585 m −1 , with zero scattering and unit refractive index. The dataset contained 1560 spatial samples from 39 tree cases and 12 matched no-tree reference simulations. Across all samples, local cooling ranged from 0.018 to 3.380 °C and averaged 0.652 °C. Mean leeward cooling was 0.837 °C, compared with 0.344 °C on the windward side. A histogram gradient-boosting surrogate using G, u, D, ξ, and η achieved case-grouped five-fold R 2 values of 0.953 for ΔT and 0.963 for RCP tree , with RMSE values of 0.151 °C and 0.040, respectively. Grouped-bootstrap permutation analysis assigned median normalized importance of 68.3% to ξ, 25.1% to η, 4.6% to wind speed, 1.3% to the coupled geometry index D, and 0.6% to DNI. In this design, DNI serves as a proxy for the diurnal boundary-condition state rather than as an independent solar-radiation effect. The framework provides spatially interpretable screening within the sampled domain. A targeted pedestrian-height check at 13:00 and 2 m/s showed area-averaged cooling of 0.40–0.78 °C at z = 1.1–1.5 m across the three crown diameters.