Solar Zenith Angle and Air Mass

When the attenuation of solar radiation penetrating to the earth s atmosphere is caused by the absorption of O2 and O3, the solar irradiance at the altitude zq and wavelength X on the surface perpendicular to the sun is expressed according to the Beer-Lambert law. 

Iq is the extraterrestrial solar irradiance, and are absorption cross section and molecular density of each molecular species, respectively. 

The distance I of a certain point on the earth surface from the sun gets longer with the solar zenith angle 6 than the vertical distance z, as shown in Fig. 3.8, and more photons are absorbed by the molecules. Considering the horizontal earth surface, the relationship between / and0 is expressed as. 

The ratio of the distance I, the direct radiation of the sun passes through the atmosphere, and the vertical distance z from the sun is called air mass m. The air mass can be closely approximated for 0 60°, by 

The solar zenith angle 6 necessary to calculate air mass in Eq. (3.4) can be obtained from the latitude q (degree), solar declination 5 (radian), and hour angle h (radian). 

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