Surface roughness effects on the solar reflectance of cool asphalt shingles

We analyze the solar reflectance of asphalt roofing shingles that are covered with pigmented mineral roofing granules. The reflecting surface is rough, with a total area approximately twice the nominal area. We introduce a simple analytical model that relates the “micro-reflectance” of a small surface region to the “macro-reflectance” of the shingle. This model uses a mean field approximation to account for multiple scattering effects. The model is then used to compute the reflectance of shingles with a mixture of different colored granules, when the reflectances of the corresponding mono-color shingles are known. Simple linear averaging works well, with small corrections to linear averaging derived for highly reflective materials.Reflective base granules and reflective surface coatings aid achievement of high solar reflectance. Other factors that influence the solar reflectance are the size distribution of the granules, coverage of the asphalt substrate, and orientation of the granules as affected by rollers during fabrication.