Irradiation spectrum

Sunlight is emitted by the so called photoshpere and corresponds approximately to the radiation of a black body at 5800 K. Compared to the ideal spectrum of Plancks law the intensity in some regions of the spectrum is reduced due to absorption in colder regions outside the photosphere. Many elements in the atmosphere of the sun are identified by their indvidual absorption lines (Fraunhofer lines). Most prominent are those of hydrogen, calcium and iron around 400 nm. The intensity of the light emitted by the sun at different wavelengths is called AM0 spectrum.

Figure1: Comparison of spectral irradiation densities: black body radiation (black) at 5800 K, AM0 irradiation in earth orbit (red), AM1.5 irradiation in Central Europe (green).

On the surface of the earth the irradiation spectrum is different from AM0 due to changes by absorption in the atmosphere. The amount of change is approximately desribed by the inverse cosine of the latitude because it depends on the length of the light path through the atmosphere. Notable absorption occurs for UV light around 350 nm in the ozone layer of the upper atmosphere and at longer wavelengths due to water and carbon dioxide in the denser atmosphere close the ground. The changes in the illumination spectrum are usually classified by the Air Mass (AM) which is calculated from AM = 1/cos z, where z is the angle between sun and the normal through a horizontal plane at the point of observation.

There are standard tables for AM0 which means conditions in earh orbit without the atmosphere, and for AM1.5 which corresponds roughly to conditions in Central Europe and North America. At the equator the spectrum would be called AM1 (Air Mass 1 for perpendicular incidence).

Due to the movement of the sun the Air Mass is subject to seasonal and daily changes. It is possible to account for these changes by replacing the cos z term.

cos z = sin(L)*sin(D) + cos(L)*cos(D)*cos(t)

L is the geographical latitude of the observer, t is the time counted until or from real noon. Additionally, D, the solar declination angle, changes throughout the year. It is -23.5° at winter solstice, 0° at equinox, and +23.5° at summer solstice.

Finally, in addition to the direct illumination from the sun there is also a contribution of the diffuse background. Due to the frequency dependence of Rayleigh scattering (~w⁴) the spectrum of the diffuse light shows an enhanced intensity in the blue region which is also the reason for the blue colour of the sky.

Figure 2: Comparison of typical irraditation spectra (recorded at noon on March, 28 1987 in Golden, Colorado): Direct normal (black), global horizontal (red), and diffuse (green). The red curve is composed of the direct irradiance (black curve corrected for the incident angle) and the diffuse background (green curve).

Solar cells and modules are rated with respect to their power output at given Air Mass, AM0 for space solar cells, AM1.5 for terrestrial application. For a rating of a system or even power plant this is far too simple. The attenuation of illumination in the atmosphere depends on temperature, pressure, pollution, moisture and many more variables. If precise irradiation values are required, for example for planning a system, much more elaborate irradiation data is mandatory. Local system installers usually have access to comercial databases for this purpose.

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Additional infomation:

Fraunhofer lines
Angular dependence of insolation
Database of irradiation spectra