The complete surface temperature (T_c) in urban areas, defined as the mean temperature of the total active surface area, is an important variable in urban micro-climate research, specifically for assessment of the urban surface energy balance. Since most vertically-oriented building facets are not observed by a nadir-viewing remote imaging radiometer, the radiometric surface temperature (T_r) measured at a specific view angle cannot be used with existing heat transfer equations to estimate radiative and convective fluxes in the urban environment. Thus, it is necessary to derive T_c for city neighborhoods. This study develops a simple method to estimate T_c from T_r with the aid of the Temperatures of Urban Facets in 3D (TUF-3D) numerical model, which calculates 3-D sub-facet scale urban surface temperatures for a variety of surface geometries and properties, weather conditions and solar angles. The effects of geometric and meteorological characteristics – e.g., building planar area index (λ_p), wall facet area index (F), solar irradiance – on the difference between T_c and T_r were evaluated using the TUF-3D model. Results showed the effects of geometric and meteorological characteristics on the difference between T_c and T_r differ between daytime and nighttime. The study then sought to predict the relationship between T_r and T_c, using λ_p, F, and solar irradiance for daytime and only using λ_p and F for nighttime. Based on the simulated data from TUF-3D, the resulting relationships achieve a coefficient of determination (r²) of 0.97 and a RMSE of 1.5 K during daytime, with corresponding nighttime values of r² = 0.98 and RMSE = 0.69 K. The relationships between T_r and T_c are evaluated using high resolution airborne thermal images of daytime urban scenes: r² = 0.75 and RMSE = 1.09 K on August 6, 2013 at 12:40 pm; and r² = 0.86 and RMSE = 1.86K on October 24, 2017 at 11:30 am. The new relationships were also applied to estimate T_c from T_r in Hong Kong retrieved from Landsat 5 Thematic Mapper (TM) and the Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER). In the present climatic context, the difference between T_c and T_r can reach 10 K during daytime in summer, and 6 K during daytime in winter, with seasonal variation attributable to the variations in shortwave irradiance. The nighttime difference between T_c and T_r can also reach 2 K in both summer and spring seasons.

This study aims to evaluate the effects of urban geometry on retrieval of emissivity and surface temperature in urban areas. An improved urban emissivity model based on sky view factor (IUEM-SVF) was further enhanced to consider all radiance contributions leaving the urban canopy, including (i) emission by all facets within an instantaneous field of view (IFOV); (ii) reflection by all facets of emission from surrounding facets; and (iii) propagation of emitted and reflected radiation with multiple reflections (scattering) within a complex 3D array of urban objects. The effective emissivity derived from IUEM-SVF was evaluated with a microscale radiative transfer and energy balance model: Temperatures of Urban Facets in 3-D (TUF-3D). IUEM-SVF performs well when urban facets have uniform emissivity and temperature; e.g., root mean square deviations (RMSD) are less than 0.005 when material emissivity is larger than 0.80 (ɛ ⩾ 0.80). However, when material emissivities are variable within the observed target, differences of effective emissivity between IUEM-SVF and TUF-3D become larger, e.g., RMSD of 0.010. When the effect of geometry is not considered and a mixed pixel emissivity is defined, the difference is even much larger (i.e. 0.02) and this difference increases with the decrease of sky view factor. Thus, the geometry effect should be considered in the determination of effective emissivity. Effective emissivity derived from IUEM-SVF was used to retrieve urban surface temperature from a nighttime ASTER thermal infrared image. Promising results were achieved in comparison with standard LST products retrieved with the Temperature and Emissivity Separation (TES) algorithm. IUEM-SVF shows promise as a means to improve the accuracy of urban surface temperature retrieval. The effect of thermal heterogeneity on the effective emissivity was also evaluated by TUF-3D, and results show that the thermal heterogeneity cannot be neglected since the RMSD between the effective emissivity based on TUF-3D and IUEM-SVF is relatively large.