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Analytical model for solar irradiance near a planar vertical diffuse reflector – formulation, validation, and simulations



Matthew Boyd


An analytical model is formulated for the irradiance on a surface (collector) with a rear (opposite the sun) planar vertical diffuse reflector, as is common for a lower roof on a multi-story building. The vast majority of research on solar reflectors has been for specular, or mirror, reflectors, with any diffuse reflections modeled about the specular reflection angle. This model is capable of calculating incident and reflected direct, diffuse, and ground-reflected radiation, using components borrowed from the HDKR irradiance model, and is easily implemented in any computation programming software capable of numeric integration. The model accounts for reflector edge effects and shading of diffuse and ground-reflected radiation by the reflector, but it does not account for shading of beam radiation by the reflector. The model shows good overall agreement with experimental tests, and is three percentage points more accurate than a standard radiation model for tilted surfaces. The model indicates that a planar vertical diffuse reflector increases the irradiance at high clearness indices and low reflector incidence angles, and decreases the irradiance otherwise. Increasing the reflector height and decreasing the collector pitch and distance between the collector and reflector increases the irradiance during clear periods, but decreases the irradiance, to a lesser absolute extent, during cloudy periods. Annual simulations show a gain in winter insolation and a loss in summer insolation for an average collector/reflector, with an increase in annual insolation for collectors near high albedo reflectors.
Solar Energy


solar irradiance model, diffuse reflector, experimental validation, annual simulation


Boyd, M. (2013), Analytical model for solar irradiance near a planar vertical diffuse reflector – formulation, validation, and simulations, Solar Energy, [online], (Accessed July 22, 2024)


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Created May 1, 2013, Updated November 10, 2018