Model of Spectral and Directional Radiative Transfer in Complex Urban Canopies with Participating Atmospheres

Thermal heat transfers, including solar and infrared radiation in cities, are key processes for studying urban heat islands, outdoor human thermal comfort, energy consumption, and production. Thus, accurate radiative transfer models are required to compute the solar and infrared fluxes in complex urban geometry accounting for the spectral and directional properties of the atmosphere and city fabric materials. In addition, these reference models may be used to evaluate existing parametrization models of radiative heat transfer and to develop new ones. The present article introduces a new reference model for outdoor radiative exchange based on the backward Monte Carlo method. The integral formulations of the direct and scattered solar, and the terrestrial infrared radiative flux densities are presented. This model can take into account the ground (e.g., roads, grass), different types of buildings and vegetation (e.g., trees consisting of opaque leaves and trunks) with their spectral and directional (Lambertian and specular) reflectivity of materials. Numerical validations of the algorithm are presented against the results of a state-of-the-art model based on the radiosity method for the particular case of an infinitely long street canyon. In addition, the convergence of urban solar radiation budgets is studied for a selection of urban complex geometries including or not the window glazing. Good convergence is found for all geometries, even in the presence of rare events due to specular reflections.