1) The atmosphere is not a perfect absorber of radiation like a blackbody, but rather a "gray body" that absorbs some but not all radiation. 2) Radiation passes through the Earth's atmosphere, with 45-50% of incident radiation reaching the ground. Some radiation is reflected and scattered by the atmosphere. 3) Shortwave radiation that enters the atmosphere is transferred to the ground through reflection, absorption, and transmission. The incoming and outgoing radiation must be in balance.

1. Riccardo Rigon
IlSole,F.Lelong,2008,ValdiSella
Solar Radiation
Absorptions crossing the Atmosphere

2. R. Rigon
Atmosphere is a gray body
• The blackbody is an ideal object that absorb all the radiative energy it receives
• Real objects (bodies, “gray bodies”) are not capable of absorbing all radiation.
• To understand the difference between a blackbody and a gray body we need to
analyse the interactions between a surface and the electromagnetic radiation
incident onto it.
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Absorption and transmission of short wave radiation

3. R. Rigon
Atmospheric absorption
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Radiation passes quite freely through the Earth’s atmosphere and it warms
the surfaces of seas and oceans. A portion of between 45% and 50% of the
incident radiation onto the Earth reaches the ground
Absorption and transmission of short wave radiation

4. R. Rigon
Radiation
transmitted
Radiation reflected
Shortwave Radiation budget
The solar radiation penetrates the
atmosphere, and it is transferred
towards the ground, after being
reflected and scattered.
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Absorption and transmission of short wave radiation

5. R. Rigon
the incoming radiation equals
the reflected one plus
the absorbed plus
the transmitted
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Shortwave Radiation budget
S It should not be forgot that
the radiation budget is an
energy budget, for which
Radiation
absorbed
Absorption and transmission of short wave radiation

6. R. Rigon
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Energy
absorbed by
atmosphere
Transmitted
radiation
Corrected Solar
constant
Solar radiation
reflected back to space
This budget can be apply to any slice of the atmosphere
Shortwave Radiation budget
Absorption and transmission of short wave radiation

7. R. Rigon
• is the reflection coefficient, said atmospheric
reflectivity (albedo)
• is the transmission coefficient, said atmospheric
transmissivity
• is the absorption coefficient, said atmospheric
absorptivity
Coefficients
The following coefficients can also be defined
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Absorption and transmission of short wave radiation

8. R. Rigon
Energy conservation:
Which is, indeed, valid for reflectivity, transmissivity and absorptivity of any other body
implies that reflectivity, transmissivity and absorptivity sum to one:
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Shortwave Radiation budget
Absorption and transmission of short wave radiation

9. R. Rigon
We just forget for a
moment this. It will be
splitted into two parts:
one depending on
diffuse radiation and
another on cloud cover
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Shortwave Radiation budget
Absorption and transmission of short wave radiation

10. R. Rigon
Atmosphere is pretty transparent: which
means that we can, as a first approximation,
neglect it (atmosphere is heated from below)
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Shortwave Radiation budget
Absorption and transmission of short wave radiation

11. R. Rigon
In any case let’s concentrate on
the transmitted radiation
This can be decomposed into two parts:
direct and diffuse solar radiation
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Shortwave Radiation budget
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Absorption and transmission of short wave radiation

12. R. Rigon
Evidently, for simmetry
is also composed by reflected and
diffuse solar radiation
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Shortwave Radiation budget
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Absorption and transmission of short wave radiation

13. R. Rigon
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Diffuse radiation comes from scattering
Incident solar radiation strikes gas molecules, dust particles, and
pollutants, ice, cloud drops and the radiation is scattered. Scattering
causes diffused radiation.
Two types of light diffusion can be distinguished:
Mie scattering
Rayleigh scattering
Absorption and transmission of short wave radiation

14. R. Rigon
Rayleigh Scattering
•The impact of radiation with air molecules smaller than λ/π causes
scattering (Rayleigh scattering) the entity of which depends on the
frequency of the incident wave according to a λ-4 type relation.
•In the atmosphere, the wavelengths corresponding to blue are scattered
more readily than others.
incident radiation
diffuse radiation
transmitted radiation
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Absorption and transmission of short wave radiation

15. R. Rigon
•When in the atmosphere there are particles with dimensions greater than 2 λ/π
(gases, smoke particles, aerosols, etc.) there is a scattering phenomenon that
does not depend on the wavelength, λ, of the incident wave (Mie scattering).
•This phenomenon can be observed, for example, in the presence of clouds.
Mie Scattering
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incident radiation
diffuse radiation
transmitted radiation
Absorption and transmission of short wave radiation

16. R. Rigon
Diffused Light
Scattering selectively eliminates the shorter visible wavelengths, leaving the
longer wavelengths to pass. When the Sun is on the horizon, the distance
travelled by a ray within the atmosphere is five or six times greater than
when the Sun is at the Zenith and the blue light has practically been
completely eliminated.
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Absorption and transmission of short wave radiation

17. R. Rigon
Tilt of the Earth’s axis
and atmospheric effects
The tilt of the earth’s axis and atmospheric effects together affect the amount of
radiation that reaches the ground.
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Absorption and transmission of short wave radiation

18. R. Rigon
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One way to take into account of absorption
Would be to run a full model of atmospheric transmission (e.g. Liou, 2002).
However hydrologists prefer to use parameterizations, and the
concept of atmospheric transmissivity.
Absorption and transmission of short wave radiation

19. R. Rigon
Solar radiation transmitted to the ground under
clear sky conditions
Finally:
Fraction of direct solar radiation
included between the considered
wavelengths
Transmittance of the
atmosphere
Correction due to
elevation of the site
Corripio,2002
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Absorption and transmission of short wave radiation

20. R. Rigon
We do not enter in the details of how
and
are determined. Please look, for
instance, at Formetta et al., 2012
Solar radiation transmitted to the
ground under clear sky conditions
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Absorption and transmission of short wave radiation