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

International audience

English. Enhancement of the living conditions in the big cities since the end of the last century is closely related to changes in 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) -the gradient of temperature between the downtown and the first green ring -became an increasing matter of concern in regard to health population. UHI can be measured from land surface temperature (LST), provided the required accuracy assessment is reached. 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, 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 mimic the angular signatures of urban temperatures, in which the geometric optical and spectral invariant theories are considered to model, respectively, the direct and scattering 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 [[EQUATION]] and [[EQUATION]] > 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.