An Analytical Thermal Anisotropy Model for the Urban Canopy Over Sloping Terrain

Land surface temperature (LST) is an important parameter in many research fields. As a temperature characteristic, thermal radiation has an obvious directionality. In urban areas, the directional anisotropy (DA) in surface temperatures can reach 10 K during airborne measurements, limiting the applicability of urban surface temperature products. Notably, the intricate 3-D structures and heterogeneous temperature distributions in urban environments significantly influence this anisotropy. In recent decades, numerous models have been developed for urban thermal anisotropy (UTA) analysis; however, most of these models predominantly focus on horizontal surfaces, with little consideration of mountainous architectures. To balance the calculation efficiency and model complexity, this study introduces an analytical thermal anisotropy model applicable to urban areas. This model considers the effects of 3-D structures and slopes and is labeled as the AU3SM. The multiangle data used for the analysis are recorded by an unmanned aerial vehicle (UAV) with a multicircle observation scheme in Chongqing, China. Comparisons of the AU3SM simulated data with these measurement data yield root mean square error (RMSE) and coefficient of determination (
$R^{2}$
) values of 0.57 K and 0.89, respectively. Furthermore, similar comparisons with the discrete anisotropic radiative transfer (DART) model yield
$R^{2}$
and RMSE values of 0.98 and 0.12 K, respectively. Simulations reveal that slope influences the UTA, and the hotspot lies on the opposite side of the solar direction; ignoring slope values of 5°, 10°, 15°, and 25° results in UTA maximum biases of approximately 1.2, 3.5, 7, and 7.5 K, respectively, under certain conditions. These findings demonstrate that the proposed model can accomplish rapid UTA assessments in mountainous areas.