Hay–Davies

Method

The Hay–Davies model splits the diffuse sky into a circumsolar part that follows the direction of the sun and a uniform part. The share of the circumsolar part is the anisotropy index, which is the direct normal irradiance divided by the irradiance outside the atmosphere. On a clear day the index is high and most of the diffuse light comes from near the sun. The model has no horizon band.

The math

$$D_{plane} = D\left[A_i\frac{\max(0,\ \cos\theta)}{\max(\cos 85°,\ \cos\theta_z)} + (1-A_i)\frac{1+\cos\beta}{2}\right],\qquad A_i = \min\!\left(1,\ \frac{\text{DNI}}{E_0}\right) \tag{1}$$

where

Symbol	Meaning	Unit
$D_{plane}$	the diffuse light on the module plane	W/m²
$D$	the diffuse horizontal irradiance of the weather file	W/m²
$A_i$	the anisotropy index	—
$\theta$	the angle between the sun and the perpendicular to the module plane	degrees
$\theta_z$	the zenith angle of the sun, 90° minus its elevation	degrees
$\beta$	the tilt of the module plane from the horizontal	degrees
$\text{DNI}$	the direct normal irradiance	W/m²
$E_0$	the extraterrestrial normal irradiance: 1367 W/m² times the correction for the Earth–Sun distance, $1 + 0.033\cos(2\pi t/8760)$ with $t$ the hours from 1 January 00:00	W/m²

References

1. Hay & Davies 1980, Calculation of the solar radiation incident on an inclined surface, Proceedings of the First Canadian Solar Radiation Data Workshop, 59–72

API

array.transposition_model = hay_davies

Symbols follow the symbol registry.