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:

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

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

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

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