1. The document discusses long wave radiation emitted by the Earth's surface and atmosphere. It describes the Earth as a gray body that emits radiation in the infrared band given its average surface temperature of 288K. 2. It explains that the atmosphere absorbs and re-emits long wave radiation from the Earth's surface, and without this greenhouse effect the average surface temperature would be around -17C instead of 15C. 3. It provides equations to calculate long wave radiation from a surface based on the surface temperature and the atmospheric emissivity and temperature, noting that multiple parameterizations exist to estimate the atmospheric emissivity.

1. Riccardo Rigon
IlSole,F.Lelong,2008,ValdiSella
Solar Radiation
Long wave radiation

2. R. Rigon
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Or is used for photosynthesis
or other chemical reactions
Spectral response

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Earth “is” a gray body
Having a temperature emits radiation
A.Adams-Partofthesnakeriverpicture
Long wave radiation

4. R. Rigon
Gray Bodies
• Plank’s Law for gray bodies:
• The Stefan-Boltzmann equation for gray bodies:
W = ✏
2⇡c2
h 5
e
ch
KT 1
[Wcm 2
µm 1
]
W = ✏ T4
[Wcm 2
]
4
where ε is the average emissivity calculated over the entire electromagnetic
spectrum.
Long wave radiation

5. R. Rigon
Gray Bodies
The behavior of a real (gray) body is related to that of a black body by
means of the quantity ελ, known as the emission coefficient or
emissivity, which is defined as:
Kirchhoff (1860) demonstrated that a good “radiator” is also a good
“absorber”, that is to say:
✏ =
W (real body)
W (black body)
↵ = ✏ ⇢ + ⌧ + ✏ = 1
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Long wave radiation

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Comparison of blackbody and gray body
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In reality emissivity depends, at least, on wavelength. Earth should be
probably defined a selective radiator
Long wave radiation

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See the Earth as gray body
a n d g i v e n t h a t t h e
temperature of the Earth’s
surface is, on average,
about 288 K, it obviously
e m i t s a s p e c t r u m o f
radiation in the infrared
band.
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Long wave radiation

8. R. Rigon
Radiation emitted by the Sun and the Earth
Yochanan Kushnir
8
Long wave radiation

9. R. Rigon
See the Earth as gray body
a n d g i v e n t h a t t h e
temperature of the Earth’s
surface is, on average,
about 288 K, it obviously
e m i t s a s p e c t r u m o f
radiation in the infrared
band.
A t m o s p h e r e i s n o t
anymore transparent to at
these wavelengths.
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Long wave radiation

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The atmosphere is
warmed from below
Therefore the temperature is
higher at ground level than it
is at higher altitudes.
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Long wave radiation

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Greenhouse Effect
In the absence of atmospheric absorption the average temperature of the Earth’s
surface would be about -170C.
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Long wave radiation

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Instead the average temperature is about 15 0C
Greenhouse Effect
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Long wave radiation

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Radiative heating
is completed by convective heat transfer, and by water vapor fluxes (latent and
sensible heat).
13But this you can see better on the energy budget slides.
Long wave radiation

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But now concentrate on the surroundings of a point
14
AfterHelbig,2009
Any point being at a certain temperature emits long wave radiation
which must be accounted for
Long wave radiation

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The atmosphere emits infrared itself
bacause of its temperature
Long wave radiation

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Long-wave radiation is given by the
balance of incident radiation from
the atmosphere and the radiation
emitted by the ground. Both values
are calculated with the Stefan-
Boltzmann law.
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All the contributions
Long wave radiation

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Longwave radiation
coming from
surrounding
Radiation losses
by the area under
exam
Longwave radiation
coming from sky
Longwave (infrared) radiation
Topographic effects: angle of view
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Long wave radiation

18. R. Rigon
Long-wave radiation
The first component should be
calculated by integrating the formula
over the entire atmosphere, but,
given how complex this process is,
typically an empirical formula is
used that uses the value of air
temperature as measured near
ground level (2m) and a value of the
atmospheric emissivity based on
specific humidity, temperature, and
cloudiness. The second component,
on the other hand, is function of the
s u r f a c e t e m p e r a t u r e a n d i t s
emissivity.
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The real process:
The hydrological parameterisation:
Long-wave radiation
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Long wave radiation
Global emissivity of the
atmosphere
Temperature at 2 m
from ground

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The hydrological parameterisation:
εatm = εBrutsaert (1− N6
) + 0.979N4
Brutsaert (1975) + Pirazzini et al. (2000)
εatm = εBrutsaert (1+ 0.26N)
εatm = εIdso(1− N6
) + 0.979N4
εatm = εIdso,corr (1− N6
) + 0.979N4
Brutsaert (1975) + Jacobs (1978)
Idso (1981) + Pirazzini et al. (2000)
Hodges et al. (1983) + Pirazzini et al.
(2000)
Parameterisation of Long-wave radiation
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Long wave radiation
where N is the fraction of sky covered by clouds

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Net Radiation
The sum of longwave and shortwave ratio
is called net radiation

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1Thank you for your attention !
G.Ulrici-2000?