Extra-Terrestrial Beam Irradiation

The extra-terrestrial Beam Irradiation \(G_0 \left( n \right)\) is a required input to the various models, and is calculated as follows:

$$G_0 \left( n \right) = \frac{G_\text{sc}}{R_0^2\left( n \right)}$$

Where \(G_\text{sc}\) is the Solar Constant, and \(R_0 \left( n \right)\) is the distance of the Earth from the Sun relative to its mean value. These are given by:

$$G_\text{sc} = 1367\ \left\lbrack W/m^2 \right\rbrack$$

$$R_0^2 \left( n \right) = \left\lbrack 1.000110 + 0.034221 \cos \Gamma \left( n \right) + 0.001280 \sin \Gamma\ \left( n \right) + 0.000719 \cos \left( 2\Gamma \left( n \right) \right) + 0.000077 \sin \left( 2\Gamma \left( n \right) \right) \right\rbrack^{- 1}$$

Where \(\Gamma\) is given by:

$$\Gamma = \frac{2\pi \left(n - 1\right)}{365}$$

\(n\) being the day of the year.

\(G_0 \left(n\right)\) is the normal component so whenever the horizontal component is needed then \(G_0 \left(n\right)\) needs to be multiplied by the cosine of the sun's zenith angle.