Clear sky solar illuminance using visual band irradiance

Abstract

Solar illuminance may be quantified by applying relevant efficacy functions to available full spectrum ground irradiance. Alternatively, illuminance may be determined by applying the Photopic function to ground level irradiance spectra obtained from the terrestrial irradiance spectrum adjusted using relevant atmospheric absorption and scattering coefficients. The Photopic function has finite values in the wavelength range of 400 nm to 700 nm and is concentrated around a mean wavelength of 555 nm with irradiance at wavelengths close to 555 nm contributing to the major portion of illuminance. Calculation of ground level direct, diffuse and hence global illuminance is simplified as absorption of irradiance in the atmosphere by water vapour and uniformly mixed gases is negligible and may be ignored. It is shown that due to the small variations in the overall irradiance over wavelengths in the visible bandwidth combined with the concentration effect of the Photopic function in this wavelength range illuminance may be calculated, with good accuracy, using constant extinction functions for both direct and diffuse illuminance. Due to the concentration of illuminance by the Photopic function global illuminance data were also correlated with a simplified description of illuminance attenuation through the atmosphere based on the Beer-Lambert-Bouger Law using a single constant effective extinction coefficient which accounts for all extinction processes under clear sky conditions over the visible range of wavelengths. Constants used in extinction functions for solar irradiance due atmospheric aerosols were obtained by fitting experimental data to analytical descriptions of atmospheric extinction while published constants were used for ozone and Rayleigh scattering. The analytical descriptions of global illuminance with solar elevation were compared with experimental data collected at Johannesburg over both summer and winter clear sky conditions. Correlations of measured and calculated global illuminance data for the method based on extinction of various atmospheric components was 4.47 % and 4.49 % for the method based on the Beer-Lambert-Bouger Law, both normalised using the terrestrial illuminance constant. While measurements were made at a specific site in Gauteng, the methods used to correlate the data are general and location independent but local climatic conditions may need to be taken into account to quantify the extinction coefficients for specific areas.