Weather file

Method

The global horizontal, diffuse horizontal and direct normal irradiance of every timestep come from the uploaded file. When the file has no direct normal column, the tool derives it from the global and diffuse values and the sun height (1). When the file has global and direct normal columns but no diffuse column, the diffuse part is the global minus the direct normal times the sine of the sun height, with the same 5° floor. When the file has only global irradiance, the tool splits it with the model chosen at upload (Weather tab, API form field decomposition). If none is chosen: the Erbs correlation, which gives the diffuse fraction as a function of the clearness index (2, 3), with the direct normal irradiance then derived by (1). The other choice is DIRINT (Perez and co-workers 1992): Maxwell's DISC model gives a direct normal irradiance from the clearness index and the air mass (4, 5), and DIRINT multiplies it by a coefficient from the published table, chosen by bins of the zenith-independent clearness index (6), of its change from the neighbouring timesteps (7), of the zenith angle and of the precipitable water from the dew point (8). The diffuse part is then the global minus the direct normal times the cosine of the zenith (9). Values DIRINT fills in or derives: the station pressure is the file's pressure column, or the standard atmosphere's pressure at the site elevation when the file has none; the dew point comes from the file's temperature and relative humidity by the Magnus formula (10), and without a humidity column the table's column for unknown precipitable water is used; the day of year is the local standard day of the timestep. The parse report names the model used and, for DIRINT, when the water was not known.

The math

1. Direct normal irradiance
2. Diffuse part by the Erbs correlation
3. Clearness index
4. DIRINT: DISC clearness index and air mass
5. DIRINT: DISC direct normal irradiance
6. DIRINT: zenith-independent clearness index
7. DIRINT: stability index
8. DIRINT: direct normal irradiance
9. DIRINT: diffuse part
10. Dew point (Magnus)

$$\text{DNI} = \frac{G_h - D}{\max(\sin 5°,\ \sin\alpha)} \tag{1}$$ $$D = k_d\,G_h,\qquad k_d = \begin{cases} 1 - 0.09\,k_t & k_t \le 0.22 \\ 0.9511 - 0.1604\,k_t + 4.388\,k_t^2 - 16.638\,k_t^3 + 12.336\,k_t^4 & 0.22 < k_t \le 0.80 \\ 0.165 & k_t > 0.80 \end{cases} \tag{2}$$ $$k_t = \frac{G_h}{E_0\,\max(\sin 5°,\ \sin\alpha)},\qquad E_0 = 1361\left(1 + 0.033\cos\frac{2\pi t}{8760}\right) \tag{3}$$ $$k_t = \min\!\left(1, \frac{G_h}{E_{0,S}\,\max(0.065, \cos\theta_z)}\right),\quad E_{0,S} = 1370\,(1.00011 + 0.034221\cos B_d + 0.00128\sin B_d + 0.000719\cos 2B_d + 0.000077\sin 2B_d),\quad B_d = \frac{2\pi(n - 1)}{365},\quad \text{AM}_a = \min\!\left(12, \frac{p}{101325}\cdot\frac{1}{\cos\theta_z + 0.15\,(93.885 - \theta_z)^{-1.253}}\right) \tag{4}$$ $$\text{DNI}_{DISC} = E_{0,S}\left(K_{nc} - (a_M + b_M\,e^{c_M\,\text{AM}_a})\right),\qquad K_{nc} = 0.866 - 0.122\,\text{AM}_a + 0.0121\,\text{AM}_a^2 - 0.000653\,\text{AM}_a^3 + 0.000014\,\text{AM}_a^4 \tag{5}$$ $$k_t' = \min\!\left(1, \frac{k_t}{1.031\,e^{-1.4/(0.9 + 9.4/\text{AM}_a)} + 0.1}\right) \tag{6}$$ $$\Delta k_t' = \text{mean}\left(|k_t' - k'_{t,prev}|,\ |k_t' - k'_{t,next}|\right) \tag{7}$$ $$\text{DNI} = \text{DNI}_{DISC}\cdot X_P(k_t', \theta_z, \Delta k_t', P_w),\qquad P_w = e^{0.07\,T_d - 0.075} \tag{8}$$ $$D = \min\!\left(G_h, \max(0, G_h - \text{DNI}\,\max(\cos 85°, \cos\theta_z))\right) \tag{9}$$ $$T_d = \frac{243.04\,\gamma_M}{17.625 - \gamma_M},\qquad \gamma_M = \ln\frac{RH}{100} + \frac{17.625\,T_{amb}}{243.04 + T_{amb}} \tag{10}$$

where

Symbol	Meaning	Unit
$\text{DNI}$	the direct normal irradiance	W/m²
$G_h$	the global horizontal irradiance	W/m²
$D$	the diffuse horizontal irradiance, from the file or estimated by (2)	W/m²
$\alpha$	the elevation of the sun above the horizon	degrees
$k_d$	the diffuse fraction of the global horizontal irradiance	—
$k_t$	the clearness index	—
$E_0$	the extraterrestrial normal irradiance	W/m²
$t$	the time from 1 January 00:00 to the middle of the timestep	hours
$E_{0,S}$	the extraterrestrial normal irradiance by Spencer	W/m²
$n$	the day of the year	—
$\theta_z$	the zenith angle of the sun, 90° minus its elevation	degrees
$p$	the station pressure	Pa
$\text{AM}_a$	the absolute air mass, Kasten 1966, at most 12	—
$a_M, b_M, c_M$	Maxwell's cubic polynomials in $k_t$, one set for $k_t \le 0.6$ and one above	—
$K_{nc}$	the clear-sky direct beam transmittance	—
$k_t'$	the zenith-independent clearness index	—
$\Delta k_t'$	the stability index; one neighbour alone at the ends of a sunlit run	—
$X_P$	the coefficient of Perez's table for the bins of $k_t'$ (6), $\theta_z$ (6), $\Delta k_t'$ (6) and $P_w$ (4, plus a bin for unknown water)	—
$P_w$	the precipitable water	cm
$T_d$	the dew point	°C
$RH$	the relative humidity	%
$T_{amb}$	the ambient temperature	°C

References

1. Erbs, Klein & Duffie 1982, Estimation of the diffuse radiation fraction for hourly, daily and monthly-average global radiation, Solar Energy 28(4) 293–302
2. Perez, Ineichen, Maxwell, Seals & Zelenka 1992, Dynamic Global-to-Direct Irradiance Conversion Models, ASHRAE Transactions 98(1) 354–369
3. Maxwell 1987, A Quasi-Physical Model for Converting Hourly Global Horizontal to Direct Normal Insolation, Solar Energy Research Institute, SERI/TR-215-3087
4. Alduchov & Eskridge 1996, Improved Magnus form approximation of saturation vapor pressure, Journal of Applied Meteorology 35(4) 601–609
5. pvlib-python 0.16.1 source code (github.com/pvlib/pvlib-python), reference implementation: pvlib/irradiance.py, disc() and dirint()

API

weather = {…} or {"id": "met_…"}; POST /api/parse-weather form field decomposition = erbs | dirint

Symbols follow the symbol registry.