Published settings

Method

The Perez equations run in their published form, with the inputs and constants below. The solar constant is 1367 W/m². The direct normal irradiance is the file's direct normal column, and it enters the sky clearness without a cap. The sky brightness uses the Kasten and Young 1989 air mass with no altitude factor. The circumsolar coefficient is floored at zero, as in the 1990 paper. The circumsolar part is counted at every sun elevation above the horizon; the 5° floor in its denominator keeps it finite when the sun is low.

Settings

Setting	Value
Solar constant $S$	1367 W/m²
Eccentricity factor $e_t$	$1 + 0.033\cos\frac{2\pi t}{8760}$, with $t$ in hours
Direct normal irradiance $\text{DNI}_{used}$	the file's direct normal column
Cap on the direct part of the clearness $c_\varepsilon$, as a fraction of $E_0$	none
Air mass $\text{AM}$	Kasten and Young 1989
Altitude factor $f_z$	1
Floor of the circumsolar coefficient $F_{1,min}$	0
Circumsolar cutoff elevation $\alpha_c$	none
Coefficient table	Perez 1990, all-sites composite, 8 clearness bins

The math

1. Extraterrestrial irradiance
2. Direct sunlight
3. Sky clearness
4. Sky brightness
5. Circumsolar and horizon-band coefficients
6. Uniform part
7. Circumsolar part
8. Horizon-band part
9. Diffuse sky light on the plane

$$E_0 = 1367\,\left(1 + 0.033\cos\frac{2\pi t}{8760}\right) \tag{1}$$ $$\text{DNI}_{used} = \text{DNI},\qquad B = \text{DNI}_{used}\,\max(0,\ \cos\theta) \tag{2}$$ $$\varepsilon = \frac{(D + \text{DNI}_\varepsilon)/D + 1.041\,\theta_z^3}{1 + 1.041\,\theta_z^3},\qquad \text{DNI}_\varepsilon = \text{DNI}_{used} \tag{3}$$ $$\Delta = \frac{D\,\text{AM}\,f_z}{E_0},\qquad \text{AM} = \frac{1}{\sin\alpha + 0.50572\,(\alpha + 6.07995)^{-1.6364}},\qquad f_z = 1 \tag{4}$$ $$F_1 = \max\!\left(0,\ f_{11} + f_{12}\,\Delta + f_{13}\,\theta_z\right),\qquad F_2 = f_{21} + f_{22}\,\Delta + f_{23}\,\theta_z \tag{5}$$ $$D_{iso} = D\,(1 - F_1)\,\frac{1 + \cos\beta}{2} \tag{6}$$ $$D_{circ} = D\,F_1\,\dfrac{\max(0,\ \cos\theta)}{\max(\sin 5°,\ \sin\alpha)} \tag{7}$$ $$D_{hb} = D\,F_2\sin\beta \tag{8}$$ $$D_{plane} = D_{iso} + D_{circ} + D_{hb} \tag{9}$$

where

Symbol	Meaning	Unit
$E_0$	the extraterrestrial normal irradiance at time $t$	W/m²
$t$	the time from 1 January 00:00	hours
$\text{DNI}_{used}$	the direct normal irradiance the model uses	W/m²
$\text{DNI}$	the direct normal irradiance of the weather file	W/m²
$B$	the direct sunlight on the module plane	W/m²
$\theta$	the angle between the sun and the perpendicular to the module plane	degrees
$\varepsilon$	the sky clearness, which selects the row of the coefficient table	—
$D$	the diffuse horizontal irradiance of the weather file	W/m²
$\text{DNI}_\varepsilon$	the direct normal irradiance that enters the sky clearness	W/m²
$\theta_z$	the zenith angle of the sun, 90° minus $\alpha$	radians
$\Delta$	the sky brightness	—
$\text{AM}$	the relative air mass of Kasten and Young 1989	—
$f_z$	the altitude factor of the sky brightness	—
$\alpha$	the elevation of the sun above the horizon	degrees
$F_1$	the circumsolar coefficient	—
$F_2$	the horizon-band coefficient	—
$f_{11} \ldots f_{23}$	the six coefficients of the clearness row, from the published table	—
$D_{iso}$	the uniform part of the diffuse light on the plane	W/m²
$\beta$	the tilt of the module plane from the horizontal	degrees
$D_{circ}$	the circumsolar part of the diffuse light on the plane	W/m²
$D_{hb}$	the horizon-band part of the diffuse light on the plane	W/m²
$D_{plane}$	the diffuse sky light on the module plane	W/m²

References

1. Perez, Ineichen, Seals, Michalsky & Stewart 1990, Modeling daylight availability and irradiance components from direct and global irradiance, Solar Energy 44(5) 271–289
2. Kasten & Young 1989, Revised optical air mass tables and approximation formula, Applied Optics 28(22) 4735–4738

API

array.perez_settings = published

Symbols follow the symbol registry.