Radiative exchange in an urban street canyon

The influence of building geometry on the radiation terms of the surface energy balance is a principal reason for surface temperature 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 and materials has not been carefully considered. Here the exchange of diffuse radiation in an urban street canyon is investigated using a method incorporating all reflections of radiation. This exact solution is compared to two commonly used approximations that retain either no reflections, or just one reflection of radiation. The area-averaged net radiative flux density from the facets of the canyon decreases in magnitude monotonically as the canyon aspect ratio increases. The two approximate solutions possess unphysical differences from this monotonic decrease for high canyon aspect ratios or low material emissivities/ high material albedos. The errors of the two approximate solutions are small for near blackbody materials and small canyon aspect ratios but can be an order of magnitude for intermediate material properties and deep street canyons. Urban street canyon models need to consider at least one reflection of radiation and multiple reflections are desirable for full applicability.