Irradiation spectrum
The solar radiation we see 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.
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 changed further
by absorption in the atmosphere and depends on the length of the light
path. It varies approximately with the inverse cosine of the latitute.
The irradiation at the equator it is called AM1 (perpendicular incidence),
in Central Europe it is AM1.5. In Earth orbit the irradiation density in
orbit is called AM0 (air mass zero). Notable absorption occurs for UV light
around 350 nm in the ozone layer of the upper athmosphere and at longer
wavelengths due to water and carbon dioxide in the denser atmosphere close
the ground.
More precicely, the is calculated from AM = 1/cos z, where z is the
agle between sun and the normal through a horizontal plane at the point
of observation. Due to the daily revoltution of the Earth the angle z changes
the day.
cos z = sin(L)*sin(D) + cos(L)*cos(D)*cos(t)
L is the geographical latitude, t is the time, counted until or from
real noon. D is the solar declination angle for a given day. 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
spectral intensity of the diffuse light is centered 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).
The calculation of the irradiation angle is important for the design
of sun-tracked systems. For a prediction of the power output of a system
the air mass classification is much too simple. The attenuation of the
light in the atmosphere depends also on temperature, pressure, pollution,
moisture and many more. If precise irradiation data are required, for example
for the calculation of the revenue for a planned system, much more elaborate
irradiation data is mandatory. Local system installers usually have access
to comercial databases.
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Additional infomation:
Fraunhofer lines
The AM1.5 spectrum
Angular dependence of insolation
Database of irradiation spectra