A Geometric Model to Simulate Urban Thermal Anisotropy for Simplified Neighborhoods

Satellite-observed surface temperatures over heterogeneous urban pixels are generally determined by viewing and illumination angles, as well as by 3-D geometries and component temperature distributions of urban surfaces. This paper focuses on developing a Geometric model to simulate Urban Thermal Anisotropy considering overlaps of shadows on the ground for simplified neighborhoods (GUTA-osg). A Boolean model and projections for buildings are used to calculate the average fractions of urban components in a field of view. Simulation results derived from GUTA-osg are compared with those from the 3-D discrete anisotropic radiative transfer model. At view and solar zenith angles lower than 50°, GUTA-osg can be applied to urban scenes of <inline-formula> <tex-math notation="LaTeX">$h/w <2.0$ </tex-math></inline-formula> (building-height-to-spacing ratio) with confidence where errors of the estimated fraction of walls and shaded ground are less than 0.1. As <inline-formula> <tex-math notation="LaTeX">$h/w$ </tex-math></inline-formula> increases, GUTA-osg performs well when applied to urban scenes with smaller building plan area index values (e.g., <inline-formula> <tex-math notation="LaTeX">$\lambda _{p} < 0.3$ </tex-math></inline-formula> for <inline-formula> <tex-math notation="LaTeX">$h/w = 2.0$ </tex-math></inline-formula>–4.0). GUTA-osg accurately simulates the anisotropy of airborne measured temperatures, with <inline-formula> <tex-math notation="LaTeX">$R^{2} > 0.85$ </tex-math></inline-formula> and root mean square errors < 0.8 K. Biases of the model can result from: 1) the neglect of shadows on walls cast by adjacent buildings and 2) model simplifications, including constant building heights and random distributions of building location and orientation. GUTA-osg uses urban morphologic indexes as inputs, and coefficient values can be derived by fitting against multiangular thermal infrared observations. The model can be used to adjust the directional temperature to a common viewing geometry.