Extraterrestrial radiation

Extraterrestrial radiation (E_{a}) is the intensity (power) of the sun at the top of the Earth’s atmosphere.  It is usually expressed in irradiance units (Watts per square meter) on a plane normal to the sun.  It varies throughout the year because of the Earth’s elliptical orbit, which results in the Earth-Sun distance varying during the year in a predictable way.  This effect can be represented empirically with the following equations:

E_{a}=E_{sc}\times \left ( \frac{R_{av}}{R} \right )^{2}, where E_{sc} is the solar constant (1367 W/m^{2}).  R_{av} is the mean sun-earth distance and R is the actual sun-earth distance depending on the day of the year.

\left ( \frac{R_{av}}{R} \right )^{2}=1.00011+0.034221\cos \left ( b \right )+0.00128\sin \left ( b \right )+\cdots

0.000719\cos \left ( 2b \right )+0.000077\sin \left ( 2b \right ), where b = 2\pi \frac{DOY}{365} radians,

where DOY is the day of the year (integer).