A geometric model to simulate thermal anisotropy over a sparse urban surface (GUTA-sparse)

Remote measurements of land surface temperature are prone to significant directional anisotropy. This anisotropy is strong over urban surfaces because of three-dimensional structures and the resulting heterogeneous temperature distributions. However, the development of models that correct urban thermal anisotropy and consider the two factors is rare. In this study, with the assumption of random building orientations, we developed a Geometric model to simulate Thermal Anisotropy over a sparse Urban surface (GUTA-sparse), which does not consider the mutual shadowing effect. GUTA-sparse assumes that anisotropy is the sum of three parts: the vertical wall background temperature contribution, vertical wall orientation effects and shadow contribution. The simulation data provided by the 3-D Discrete Anisotropic Radiative Transfer (DART) model and airborne measurements over the city of Marseille were employed to evaluate model performance. The results show that in this model, the solar zenith angle influences the ability of the fitted coefficients to characterize surface features. GUTA-sparse is applicable over urban surfaces that have aspect ratios smaller than 1.0, where the mutual shadowing effect is negligible. The proposed model can also well simulate the airborne measured anisotropy with root mean square errors (RMSEs) of 0.44, 0.44, 0.56 and 0.40 K, and the anisotropy amplitudes at the four flight times all exceed 8 K. The model is independent of surface parameters that are difficult to obtain, which makes it suitable for remote sensing applications. Because the model is linear with respect to surface parameters, it can be applied to heterogeneous urban surfaces. This model aids in better understanding the relationships among urban surface geometry, component temperatures and thermal anisotropy, and this model may potentially correct the directional temperature values to a common viewing geometry.