A new model to predict direct normal instantaneous solar radiation, based on laws of spectroscopy, kinetic theory and thermodynamics

Abstract

The attenuation of solar radiation by the atmosphere is caused by two simultaneous processes: (a) scattering by air molecules and by the atmospheric turbidity; and (b) absorption by O 3, H 2O and CO 2. Since the atmospheric turbidity is closely related to horizontal visibility, V (meteorological optical range), the terrestrial direct normal solar radiation can be expressed as: I bn =I on exp(−N s K s − K t V −N o K o −N c K c −N w K w )mƒ where I on is direct normal extraterrestrial solar radiation; N o, N s, N c, and N w are thickness of the ozone layer in precipitate cm, the total number of gas moles, the number of CO 2 moles and the number of H 2O moles in the vertical atmosphere column, respectively; V is visibility in km; K s, K t, are the Rayleigh and the modified turbidity scattering coefficients; K o, K c, K w are the absorption coefficients of ozone, carbon dioxide and water vapour, respectively; m is relative air mass; f is the empirical function for air mass correction. Based on experimental measurements of direct normal solar radiation at different locations: Murmansk (polar zone), St Petersburg, Moscow, Kharkov, Crimea (Russia and Ukraine), Kabul (Afghanistan), and Gaborone (Botswana), a new physical model to calculate all variables and coefficients involved in the above equation is proposed. The model is based on laws of spectroscopy, kinetic theory and thermodynamics. A special software to predict direct normal solar radiation is developed. Comparison of the model proposed with the experimental measurements of I bn showed that the accuracy of the direct normal solar radiation obtained with this program is within 5% of the experimental data. For countries where the meteorological conditions do not change very much the accuracy can be improved to 3%. The model can be used at any location from the Northern to the Southern Pole, with only meteorological input data (pressure, temperature, relative humidity and visibility).