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:
$$E_d=DHI\times \left[A_i\cos\left( AOI\right)+\left(1-A_i\right)\frac{1+\cos\left(\theta_T\right) }{2} \left(left( 1+\sqrt{\frac{DNI\times \cos\left( \theta_Z \right)}{GHI}}\sin^{3}\left(\frac{\theta_T} {2}\right)\right)\right]$$.
$$DHI$$ is the diffuse horizontal irradiance, $$AOI$$ is the angle of incidence, $$DNI$$ is the direct normal irradiance, $$GHI$$ is the global horizontal irradiance, $$\theta_T$$ is the tilt angle of the array, and $$\theta_Z$$ is the solar zenith angle.
This model is implemented in the PV_LIB Toolbox and the function: pvl_reindl1990.