Decomposition
Decomposition is the process whereby diffuse horizontal irradiance \(G_\text{dif}\) is estimated from global horizontal irradiance \(G_\text{h}\), typically when a direct measurement of \(G_\text{dif}\) is not available.
Erbs
The Erbs decomposition model is based on experimental observations [12]. The ratio of diffuse to global horizontal irradiance is given as a function of the clearness index \(k_\text{T}\) as follows:
For hourly irradiance values, the diffuse fraction is defined as follows:
$$\begin{align} \text{for}\ k_\text{T} \leq 0.22 &\quad \frac{G_\text{dif}}{G_\text{h}} = 1.0 - 0.09 k_\text{T} \\ \text{for}\ 0.22 < k_\text{T} \leq 0.80 &\quad \frac{G_\text{dif}}{G_\text{h}} = 0.9511 - 0.1604 k_\text{T} + 4.388 k_\text{T}^2 - 16.638 k_\text{T}^3 + 12.336 k_\text{T}^4 \\ \text{for}\ k_\text{T} > 0.80 &\quad \frac{G_\text{dif}}{G_\text{h}} = 0.165 \end{align}$$
The clearness index \(k_\text{T}\) is the ratio of global horizontal irradiance \(G_\text{h}\) to Extraterrestrial radiation:
$$k_{T} = \frac{G_\text{h}}{G_0 \left( n \right) \cos \left( \theta_\text{z} \right) }$$
DIRINT
The DIRINT algorithm by Perez and Ineichen determines Direct Normal Irradiance (DNI) from GHI, an improvement of the DISC method also developed by Perez [19].