Extraterrestrial & Global Irradiance Simulation

Predicting photovoltaic energy output requires bridging top-of-atmosphere solar dynamics with ground-level atmospheric transmission. This simulation synthesizes multiple critical solar engineering parameters: dynamic extraterrestrial normal irradiance (\(G_{0n}\)), solar declination (\(\delta\)), local zenith angle (\(\theta_z\)), air mass optical path length (\(AM\)), horizontal extraterrestrial flux (\(G_0\)), direct beam horizontal irradiance (\(G_b\)), and global horizontal irradiance (\(G_{GHI}\)).

Comprehensive Mathematical Model

The complete simulation pipeline couples Earth's orbital geometry with broadband atmospheric extinction formulations:

1. \(G_{0n} = 1367 \left[1 + 0.033 \cos\left(\frac{2\pi d}{365}\right)\right]\) | 2. \(\delta = 23.5 \sin\left(\frac{360(284+d)}{365}\right)^\circ\) | 3. \(\theta_z = |\Phi - \delta|\)

4. \(AM = \frac{1}{\cos(\theta_z)}\) | 5. \(G_0 = G_{0n} \cos(\theta_z)\) | 6. \(G_b = G_0 \times 0.7^{AM^{0.678}}\) | 7. \(G_{GHI} = 1.1 \times G_b\)

Parameter Breakdown:

\(G_{0n}\): Extraterrestrial irradiance normal to the solar beam (\(\text{W/m}^2\)).
\(\delta\): Solar declination angle governing seasonal altitude variations.
\(\Phi\): Site geographic latitude angle in degrees.
\(\theta_z\): Solar zenith angle at solar noon.
\(AM\): Relative optical air mass path length.
\(G_0\): Extraterrestrial irradiance incident on a horizontal surface.
\(G_b\) & \(G_{GHI}\): Direct beam and global horizontal irradiance accounting for clear-sky atmospheric attenuation.

Interactive Simulation Panel

Configure the site latitude and select any day of the year to evaluate instantaneous solar geometry, air mass, and clear-sky irradiance metrics at solar noon.

Latitude Angle (\(\Phi\), in degrees):

Day of the Year (\(d\)): 276 (October 3)

Extraterrestrial Normal (\(G_{0n}\))

1392.3 W/m²

Declination Angle (\(\delta\))

-4.25°

Zenith Angle (\(\theta_z\))

48.75°

Air Mass (\(AM\))

1.520

Extraterrestrial Horizontal (\(G_0\))

917.4 W/m²

Beam Horizontal (\(G_b\))

579.5 W/m²

Global Irradiance (\(G_{GHI}\))

637.5 W/m²

Annual Comparison Curve at Solar Noon

The comparative annual profile below illustrates the gap between top-of-atmosphere horizontal irradiance (\(G_0\)) and ground-level global horizontal irradiance (\(G_{GHI}\)) across all 365 days at the specified latitude, highlighting seasonal atmospheric losses.

Extraterrestrial & Global Horizontal Irradiance Simulation

Comprehensive Mathematical Model

Interactive Simulation Panel

Annual Comparison Curve at Solar Noon