Although it is desirable to estimate the surface temperatures of buildings and other objects on the ground by performing a fully coupled conductive, radiative, and convective heat transfer simulation in three dimensions, the following simplified method is adopted in the present study. First, an unsteady heat conduction analysis is performed for individual cover types, such as asphalt and grassland. In the analysis, one-dimensional vertical heat conduction is assumed and evaluated according to the meteorological condition of the day of the simulation. The surface temperature of a cover type is calculated for the case with no shading from the sun and the case with shading from the sun. Subsequently, from the solar position for the hour for analysis, the sunlit and shaded conditions of the urban surfaces are determined in every grid cell of the three-dimensional analysis domain. The sunlit and shaded conditions of the urban surfaces are determined by taking into account the building arrangement within the city to be investigated by the CFD analysis. Finally, the surface temperature of the urban surface within an individual grid cell is assigned according to the surface cover types and the sunlit and shaded conditions.
When the surface heat energy budget is solved, parameters such as albedo, emissivity, and evaporation efficiency are required. Ichinose et al. (1999) evaluated values for five parameters relevant to the surface heat energy budget (i.e. albedo, evaporation efficiency, density, specific heat, and thermal diffusion coefficient) of ten land cover types. Ihara et al. (2003) evaluated values for a different set of five parameters relevant to the surface heat energy budget (i.e. albedo, emissivity, thermal diffusion coefficient, heat capacity, and thermal conductivity) of eight land cover types. The relevant parameters and the corresponding values from Ichinose et al. (1999) and Ihara et al. (2003) which are used in the present study are summarized in Table IV Although the value of the thermal diffusivity is influenced by the wind speed, it is set constant at 11.6 W m−2 K−1 (Yoshida et al., 2000) in the present study. The mass transfer coefficient is estimated using Lewis's law.
In the present study, a simple method is adopted for determining sunlit and shaded areas on the ground, building walls, and building roof surfaces in individual grid cells (Figure 2(a)). For each vertical column of grid cells, the lowest height reached by the solar radiation is determined. The lowest height reached by the solar radiation and the relevant building heights are taken into consideration for determining the sunlit and shaded areas for each vertical column of grid cells. The vector normal to the building wall, Si, j, k, and the solar-radiation vector, es, are defined as:
where Δxi, Δyj, and Δzk are the widths of grid cells in the east–west, north–south, and vertical directions, respectively; GA, i+1/2, GA, i−1/2, GA, j+1/2, and GA, j−1/2 are the open area ratios of the east, west, north, and south sides of an individual grid cell in the three-dimensional grid system (i, j, k), respectively; θs is the solar elevation angle (0 ≤ θs ≤ π/2), and ϕs is the solar azimuth angle (−π ≤ ϕs ≤ π). Figure 2(b) illustrates geometrical patterns between a building wall and the solar-radiation vector. When Si, j, k· es ≥ 0, the building wall is determined to be sunlit. In contrast, when Si, j, k· es ≥ 0, the building wall is determined to be shaded.