Reindl Sky Diffuse Model

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The Reindl sky diffuse irradiance model (Reindl et al., 1990;Reindl et al., 1990b; Loutzenhiser et al., 2007 ) represents three components of diffuse radiation on the POA, including isotropic, circumsolar brightening, and horizon brightening. This model extends the Hay and Davies model by adding an additional factor to the “brightening” term to account for horizon brightening.

As with the Hay and Davies model, an anisotropy index, $A_{i}$ , is defined as:

$A_{i}=\frac{DNI}{E_{a}}$ ,

where $DNI$ is the direct normal irradiance and $E_{a}$ is the extraterrestrial radiation.

The Reindl model formulation for sky diffuse radiation is then:

$E_{d}=DHI\times \left[ A_{i}\cos \left ( AOI \right )+\left ( 1-A_{i} \right )\frac{1+\cos \left ( \theta_{T} \right )}{2} \left( 1+\sqrt{\frac{DNI\times \cos \left ( \theta_{Z} \right )}{GHI}}\sin ^{3}\left ( \frac{\theta_{T}}{2} \right ) \right ) \right]$ .