An analytical urban temperature model with building heterogeneity using geometric optical theory

The enhancement of the living conditions in big cities since the end of the last century is closely related to changes in the thermal environment and besides in urban microclimate, particularly for metropolitan areas. In this context, a knowledge of the spatial and temporal variability of urban heat island (UHI) became an increasing matter of concern, which can be measured from land surface temperature (LST). Actually, LST can be derived from thermal infrared (TIR) remote sensing observations to ensure the necessary spatial and time frequency coverage. But a full exploitation of satellite TIR data cannot be achieved without accounting for the strong anisotropy of urban landscape. Hitherto, a poor investigation was focused on the modeling and the analysis of the directional anisotropies of LSTs considering the complexity of urban building surfaces (e.g., heterogeneity of building morphology and temperature distribution) whereas it is fundamental to establish reliable critical indicators derived from energy balance. Herein, we propose an analytical model to simulate the angular signatures of urban temperatures, in which the geometric optical theory is considered to model the direct radiances of the main components (i.e., sunlit and shaded street, roof and wall). The built model assumes a random distribution of low/middle-rise and high-rise buildings, which depicts realistically the heterogeneity of urban architectural distribution. We evaluated the proposed model using both measured datasets from airborne and satellite sensors and a simulated dataset from a 3D ray-tracing model so-called discrete anisotropic radiative transfer (DART). Results indicate that 1) the proposed model is effective for simulating directional anisotropies of LSTs, with a root mean square error (RMSE) lower than 0.90 C and R-2 > 0.49 for comparison with measured datasets; and 2) the directional anisotropies of LSTs are significantly affected by variations in building height, with values possibly exceeding 1.5 degree celsius. The proposed model can be perceived as a useful tool to analyze the contribution of each component and to assess the impact of urban structure. Furthermore, it can serve to improve urban radiation budget estimations in mixed pixels.