Global Radiation Resulting from Multiple Scattering in a Rayleigh Atmosphere

<jats:p>Using Chandrasekhar’s solution for the radiative transfer problem in a plane-parallel model of the earth’s atmosphere, under the assumption of perfect, conservative scattering according to the Rayleigh law, expressions are derived for the relative global and sky radiation received on a horizontal surface, as a function of normal optical thickness and inclination of incoming parallel radiation. The corrections representing the effect of ground reflection are also expressed in terms of certain functions already defined by Chandrasekhar. These expressions, which include the effect of all orders of scattering, are then used to compute the absolute global and sky radiation as a function of wavelength and solar zenith distance, based on the solar extraterrestrial energy curve as given recently by Nicolet. The results show that, under these assumptions, the global radiation received at the surface of the earth should remain essentially constant in spectral distribution for a wide range of solar altitudes, and that the pure sky radiation should have two maxima, centered at 3,300 Å and 4,100 Å respectively, for solar zenith distances ranging between o° and 45°. The theoretical work is compared with Bernhardt’s results obtained by means of certain simplifying assumptions about the successive orders of scattering. The absolute global and sky radiation is integrated over the range 0.29 μ to 4.00 μ, and it is shown that in general the computation is in good agreement with existing measurements under clear sky conditions.</jats:p>