Solar Radiation in the Atmosphere - Short-Wave Solar Radiation in the Earth's Atmosphere - page 2

Fig. 1.1. To the definitionof the intensity and to thefluxof radiation (radiance and irradiance)

spectral region will be called total radiation . Meanwhile, it should be noted
that further definitions of the radiative characteristics are not linked within
this limitation and could be used either for heat or for microwave ranges.
The notion of a monochromatic parallel beam (the plane electromagnetic
wave of one concrete wavelength and one strict direction) is widely used in
optics for the theoretical description of different processes (Sivukhin 1980).
Usually solar radiation is set just in that form to describe its interactions with
different objects. The principle of an independency of the monochromatic
beams under their superposition is postulated, i. e. the interaction of the ra-
diation beams coming from different directions with the object is considered
as a sum of independent interactions along all directions. The physical base of
the independency principle is an incoherence of the natural radiation sources 1
(Sivukhin 1980).
This standard operation is naturally used for the radiation field, i. e. the
consideration of it as a sum of non-interacted parallel monochromatic beams.
Furthermore, radiation energy can't be attributed to a single beam, because
if energy were finite in the wavelength and direction intervals, it would be
infinitesimal for the single wavelength and for the single direction. For char-
acterizing radiation, it is necessary to pass from energy to its distribution over
spectrum and directions.
Consider an emitting object (Fig. 1.1) implying not only the radiation source
but also an object reflecting or scattering external radiation. Pick out a surface
element dS , encircle the solid angle d Ω around the normal r to the surface.

Then radiation energy would be proportional to the area dS , the solid angle d

Ω

,

λ λ λ as well as to the wavelength ranges [ ]andthetimeinterval[ t , t + dt ].

The factor of the proportionality of radiation energy to the values dS , d

, + d

Ω λ , d

and dt would be specified an intensity of the radiation or radiance I ( r , t )atthe

λ

λ wavelength to the direction r at the moment t according to (Sobolev 1972;

1 It should be noted that monochromatic radiation is impossible in principle. It follows from the
mathematical properties of the Fourier transformation: a spectrum consisting of one frequency is
possible only with the time-infinite signal. Furthermore, the principle of the independency is not
valid for the monochromatic beams because they always interfere. It is possible to remove both these
contradictions if we consider monochromatic radiation not as a physical but as a mathematical object,
i. e. as a real radiation expansion into a sum (integral Fourier) of the harmonic terms. The separate
item of this expansion is interpreted as monochromatic radiation.