Simplified global irradiance model
We have shown in earlier work how a simplified model can be used to achieve a good fit to the global irrad - iance data . The following expression shows that the global irradiance on a horizontal surface IG as the sum of two terms: the first term expresses the direct solar beam irradiance, and the second term expressed the diffuse irradiance due to Rayleigh and Mie scattering from molecules and aerosols in the sky and from clouds.
Ic = U0 F, a1 slnV - I,
I0 = 1367 W/m2 is the solar constant. FJ takes account of the yearly variation of the solar irradiance due to the elliptical orbit of the earth around the sun. A practical equation for FJ is available in reference . The factor aL accounts for the attenuation of direct beam irradiance due to absorption and scattering, where L is the Rayleigh air mass. Finally, the factor sin V takes the geometry of the situation into account for a solar elevation angle V. The solar elevation angle can be computed with knowledge of the latitude, the solar declination angle and the local time. The equation required is widely available in the literature of solar energy design .
The air mass L through which the direct rays of the sun must pass depends of course on the angle V between the horizontal and a line from the observer to the center of the sun. For angles V > 250 a simple drawing will show that the air mass L = 1/sin V, for in this case it is reasonable to assume that the earth is a flat surface with a thin layer of atmosphere. However, for angles less than 250 with the sun low on the horizon it is essential to take the curvature of the earth and temperature gradients into account. Fritz Kasten and Andrew