Solar turbidity factors – Linke turbidity coefficient

The weakening of the solar energy that reaches the solar panel therefore depends on the state of the sky, the density and shape of the clouds, the composition of the gases in the atmosphere, and the humidity of the air. Permanent atmospheric factors also weaken solar irradiation. This attenuation has nothing to do with local atmospheric conditions, but includes ozone and moisture concentration. But that’s not all. Two other important factors, water vapor and aerosols, known as atmospheric haze, affect the attenuation of sunlight reaching the solar panel.

This further means that some solar panel installers consider standard testing conditions *STC* as a realistic situation.

In order to assess the atmospheric situation, annual data for the location are required: Climate and climatic factors (severe winters with or without snow, length of spring and autumn with estimation of precipitation)
Distribution and speed of winds during the year (wind is a good purifier of the atmosphere)

• Amount of precipitation from rain and snow, rate of evaporation, retention of snow cover.
• Mean monthly air temperature
• Atmosphere pressure
• Mean relative humidity

Hence, all these data are impractical to observe, so solar panel installers often avoid unnecessary complications.

There are several turbidity factors, but Linke’s, which is marked with TL, is the most commonly used.
In 1922, Linke defined this factor as the number of clean and dry atmospheres required to produce the same effect on direct radiation as a clean atmosphere. This factor is dependent on the optical depth of the clean and dry atmosphere, which is determined by the air mass, which in turn depends on the altitude angle. This factor describes the optical depth of the atmosphere due to the sun’s ray scattering process. Ozone, water vapor, and carbon dioxide contribute to this scattering.
Linke’s coefficient ranges from 1 to 10. For instance, Linke’s coefficient is 1 for a clean atmosphere, 2 for a clean, warm summer day, and 3 for humid, warm air. For humid, warm air, this coefficient is in the range of 4 to 6. In a polluted city atmosphere, it is 8.

and we have:

• A – flux of extraterrestrial radiation entering the atmosphere
  A = 1160 + 75 * sin ( 360/365 * (n – 275))
  where n is the regular day of the year
• I_BH – direct irradiation in a horizontal surface
• β – altitude angle
• σ – Integral Rayleigh optical thickness due to scattering in the atmosphere
• m – air mass coefficient : m = 1/sin(β)

The formula for optical thickness can be calculated in several ways, the Kasten formula is most often used :
.. for m <= 20, in other cases :

The calculation of the direct component IBH requires knowledge of the direct component of horizontal radiation I_H. Liu Jordan’s formula for the decomposition of total horizontal radiation is used for this to the direct and diffuse component using the brightness index

I_DH - diffuse component of horizontal irradiation
The clearness index is defined as the mean ratio of horizontal insolation to mean horizontal extraterrestrial insolation on the earth’s surface.

and we have:

• SC: Solar Constant = 1377 W/m2
• Hsr: hour angle Hsr = arccos(-tan(L) * tan(σ))

and in this formula we have :

• L: latitude
• σ: solar declination = 23.45 * sin(360/365 * (n-81))

All these formulas are applied in the SPAC application algorithm, so it was important to mention them.

If the Linke coefficient is low, it means the sky is clear and the air is clean. When looking at the Linke turbidity coefficient for a place with a moderately continental climate, numbers between 1.8 and 4.5 will be found. Small amounts of straight horizontal irradiation that show up during the day are high-value effects.

Summer precipitation can cause humidity and increase the coefficient. Precipitation (snow and rain) as well as wind are good air purifiers. On the other hand, evaporation after rain can cause humidity, which is not favorable.

More about Linke's coefficient