Upload
riccardo-rigon
View
115
Download
0
Embed Size (px)
Citation preview
R. Rigon
3
Earth “is” a gray body
Having a temperature emits radiation
A. A
dam
s -
Par
t of
the
snak
e ri
ver
pic
ture
Long wave radiation
R. Rigon
Gray Bodies
• Plank’s Law for gray bodies:
• The Stefan-Boltzmann equation for gray bodies:
W� = ✏�2⇡c2h��5
ech
�KT � 1[Wcm�2µm�1]
W = ✏�T 4[Wcm�2]
4
where ε is the average emissivity calculated over the entire electromagnetic
spectrum.
Long wave radiation
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
5
Long wave radiation
R. Rigon
Comparison of blackbody and gray body
6
In reality emissivity depends, at least, on wavelength. Earth should be probably defined a selective radiator
Long wave radiation
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.
7
Long wave radiation
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.
9
Long wave radiation
R. Rigon
The atmosphere is warmed from below
Therefore the temperature is higher at ground level than it is at higher altitudes.
10
Long wave radiation
R. Rigon
Greenhouse Effect
In the absence of atmospheric absorption the average temperature of the Earth’s surface would be about -170C.
11
Long wave radiation
R. Rigon
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
R. Rigon
But now concentrate on the surroundings of a point
14
Aft
er H
elb
ig, 2
00
9
Any point being at a certain temperature emits long wave radiation
which must be accounted for
Long wave radiation
R. Rigon
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.
16
All the contributions
Long wave radiation
R. Rigon
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
17
Long wave radiation
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.
18
R. Rigon
The real process:
The hydrological parameterisation:
Long-wave radiation
19
Long wave radiation
Global emissivity of the atmosphere
Temperature at 2 m from ground
R. Rigon
The hydrological parameterisation:
€
εatm = εBrutsaert (1− N6) + 0.979N 4 Brutsaert (1975) + Pirazzini et al. (2000)
€
εatm = εBrutsaert (1+ 0.26N)
€
εatm = εIdso(1− N6) + 0.979N 4
€
εatm = εIdso,corr(1− N6) + 0.979N 4
Brutsaert (1975) + Jacobs (1978)
Idso (1981) + Pirazzini et al. (2000)
Hodges et al. (1983) + Pirazzini et al. (2000)
Parameterisation of Long-wave radiation
20
Long wave radiation
where N is the fraction of sky covered by clouds