# Atmospheric Attenuation of Solar Radiation

Solar radiation received at the surface of the earth in a clear sky day is subject to variations due to change in the extraterrestrial radiation and to two additional and more significant phenomena:

• Atmospheric scattering by air molecules, water and dust
• Atmospheric absorption by O3, H2O and CO2

Scattering of radiation as it passes through the atmosphere is caused by interaction of the radiation with air molecules, water as vapor and droplets, and dust. Scattered photons (mostly at short wavelengths) produce the diffuse sky radiation. The degree to wich scattering occurs is a function of the number of particles through which the radiation must pass and the size of the particles relative to the wavelength of the radiation. The pathlength of the radiation through air molecules is described by the air mass.

Absorption of radiation in the atmosphere in the solar energy spectrum is due largely to ozone in the ultraviolet and to water vapor and carbon dioxide in bands in the infrared. There is almost complete absorption of short-wave radiation by ozone in the upper atmosphere at wavelengths below 290 nm and water vapor absorbs strongly in bands in the infrared part of the solar spectrum, with strong absorbtion bands centered at 1000, 1400 and 1800 nm. Beyond 2500 nm, the transmission of the atmosphere is very low due to absorption by H2O and CO2.

The remaining unabsorbed and unscattered photons, constitute the direct beam radiation. The total radiation flux on a horizontal surface in the presence of diffuse and beam radiation is called “global” radiation.

Figure: Normally incident solar spectrum at sea level on a clear day. The dotted curve shows the extrarrestrial spectrum.

# Solar radiation spectrum and spectral response of thermopile

Most of the energy that it is emitted from the Sun is in form of electromagnetic radiation with a specific spectrum given by the temperature of his external layer. The little part of this energy that arrive to earth is our source of life and energy.

The radiation that arrives to the external layer of the earth to a normal plane, before been filtered by the atmosphere is called Extraterrestrial Radiation and can be approximately calculated by :

$\mbox{E}_{ext}\; =\; \mbox{E}_{sc}\; \cdot \; \left( 1+0.033412\cdot \cos \; \left( 2\pi \frac{dn-3}{365} \right) \right)$

been

$\mbox{E}_{sc}$ =  Solar constant, 1367 [watt/m2]
dn = day number of year (1 … 365)

Then the radiation is filtered by the gases presents in the atmosfere like H2O, CO2, O3 and O2, and reflected by the clouds. The radiation that finally arrives to the lands and oceans it’s in part absorbed and part reflected.

The absorbed radiation is transformed in heat and emitted back to the space like infrared radiation.

Image from Kipp & Zonen

To measure the solar radiation that arrives on Earth requires an instrument with a thermopile, if this is design to measure infrared wavelength the instruments it’s call Pyrgeometer but if is design to measure the visible spectrum It’s call Pyranometer. A good thermopile must have a flat response to the whole spectrum that is measuring.

Image from Kipp & Zonen