Radiative Exchange in an Urban Street Canyon

The influence of building geometry on the radiation terms ofthe surface energy balance is a principal reason for surfacetemperature differences between rural and urban areas.Methods exist to calculate the radiation balance in an urban area,but their validity across the range of urban geometries andmaterials has not been carefully considered.Here the exchange of diffuse radiation in an urban street canyon isinvestigated using a method incorporating all reflections of radiation.This exact solution is compared to two commonly used approximationsthat retain either no reflections, or just one reflection of radiation.The area-averaged net radiative flux density from the facets of the canyondecreases in magnitude monotonically as the canyon aspect ratio increases.The two approximate solutions possess unphysical differences from thismonotonic decrease for high canyon aspect ratios or low materialemissivities/high material albedos.The errors of the two approximate solutions are small for near blackbodymaterials and small canyon aspect ratios but can be an order ofmagnitude for intermediate material properties and deep street canyons.Urban street canyon models need to consider at least one reflectionof radiation and multiple reflections are desirable for full applicability.