The Hay and Davies diffuse model  divides the sky diffuse irradiance into isotropic and circumsolar components.  Horizon brightening is not included.  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 Hay and Davies model formulation for sky diffuse radiation is:

$E_{d}=DHI\times\left&space;[&space;A_{i}&space;R_b&space;+\left&space;(&space;1-A_{i}&space;\right&space;)\frac{1+\cos&space;\left&space;(&space;\theta_{T}&space;\right&space;)}{2}&space;\right&space;]$,

where $DHI$ is the diffuse horizontal irradiance, $R_b=\cos \left( AOI \right) / \cos \left( Z \right)$, $AOI$ is the angle of incidence, $Z$ is the solar zenith, and $\theta_{T}$ is the tilt angle of the array.

This model is implemented in the PV_LIB Toolbox as the function: pvl_haydavies1980.

References:

• [1] Loutzenhiser P.G. et al. “Empirical validation of models to compute solar irradiance on inclined surfaces for building energy simulation” 2007, Solar Energy vol. 81. pp. 254-267
• [2] Hay, J.E., Davies, J.A., 1980. Calculations of the solar radiation incident on an inclined surface. In: Hay, J.E., Won, T.K. (Eds.), Proc. of First Canadian Solar Radiation Data Workshop, 59. Ministry of Supply and Services, Canada.

Content contributed by Sandia National Laboratories