A physically coupled sun + anisotropic Perez sky model represented as 73 directional light sources: 72 sky elements (6 rings × 12 azimuths) with Perez-weighted power densities, plus 1 direct sun source.

• for solar position via Goudriaan's algorithm:
  • latitude
  • dayOfYear
  • hourOfDay
  • minuteOfHour
• diffuse horizontal irradiance [W m⁻²].
• direct normal irradiance [W m⁻²].

The Perez all-weather sky radiance distribution (Perez et al. 1993) is:

$$ f(θ, γ) = (1 + a·exp(b / cos θ)) · (1 + c·exp(d·γ) + e·cos²γ)$$

where $θ$ is the sky-element zenith angle and $γ$ is its angular distance from the sun. The five coefficients $(a-e)$ are selected from a lookup table indexed by the sky clearness $ε$.

The 72 directional lights are normalised so that

$$ \sum_i(powerDensity_i·sin(elevation_i)) = dhi$$

• Perez, R., Seals, R., Michalsky, J. (1993). All-weather model for sky luminance distribution. Solar Energy 50(3), 235–245.
• Perez, R. et al. (1990). Modeling daylight availability and irradiance components from direct and global irradiance. Solar Energy 44(5), 271–289.