Extraterrestrial irradiance and clearness index

Extraterrestrial irradiance

The extraterrestrial irradiance, i.e. the irradiance outside the atmosphere, is generally described as a sinusoidal function with a \(3.3\%\) amplitude over the year, to take into account the Earth's orbital ellipticity: $$ \textsf{ENI} = \mathsf{E_{sc}} \left(1 + 0.033 \cdot \cos{(\theta)} \right) $$ where \(\mathsf{E_{sc}}\) is the solar constant and \(\theta\) is the orbital angle of the Earth around the Sun measured since January 1.

Until version 8.1, the solar constant used in the software was \(\mathsf{E_{sc}} = 1367 ~ \mathsf{W/m^2}\).

From version 8.1, it was updated to \(\mathsf{E_{sc}} = 1361 ~ \mathsf{W/m^2}\), correcting calibration errors from earlier measurements¹².

To compare it to ground irradiance projected on the horizontal plane, it is useful to define EHI as: $$ \textsf{EHI} = \textsf{ENI}\cdot\sin \mathsf{HSol} $$ where HSol is the sun height in radians.

Clearness Index

The clearness index \(K_t\) is a measure of the attenuation of the irradiance due to the atmosphere. It is defined as $$ K_t = \frac{\textsf{GHI}}{\textsf{EHI}} $$ where GHI is the global horizontal irradiance on the ground.

The monthly average of \(K_t\) should usually lie between about \(K_t = 0.12\) and \(K_t = 0.82\) at any place and for any month. If these limits are exceeded (in very particular cases), you may modify them in the "Advanced parameters", topic "Size and Meteo".

Cutoff for low sun heights

PVsyst applies a cutoff for low sun heights \(\mathsf{HSol} < 2°\). In such a case, we define \(K_t = 0\).

Cloud enhancement

Cloud enhancement (CE), also referred to as overirradiance or irradiance enhancement, is a physical phenomenon where clouds act as lenses and increase the measured GHI above the EHI values, resulting in clearness index values \(K_T > 1\).

Values as high as \(\textsf{GHI}= 1832 ~ \mathsf{W/m^2}\) have been reported ³. Note, however, that cloud enhancement is limited in time, and that the magnitude of the enhancement depends on the measurement time step and on the type of sensor used.

An example of a cloud enhancement scenario from Emck and Richter ³ is shown below:

When importing custom weather data, high Kt sub-values are flagged.