Geoscience Reference
In-Depth Information
RADIATIVE PROCESSES
IN THE CLIMATE SYSTEM
The absorption of solar radiation is the primary energy source of the earth
system. Other sources are geothermal energy, tidal energy, and waste heat from
the burning of fossil fuels, which together contribute less than 0.03% to the
total energy flux into the climate system. So it is appropriate that our discus-
sion of the physical processes important for climate dynamics starts with a
consideration of radiative processes. We begin with a review of some basic
physical principles.
4.1 BLACKBODY THEORY
A
blackbody
is a theoretical object that absorbs all radiation incident onto its
surface and reradiates all that energy. The total amount of energy emitted from
a unit area of a blackbody each second (i.e., the power) is given by the Stefan-
Boltzmann law:
σ= , (4.1)
where s 5.67 10
-8
J/(m
2
s K
4
) is the Stefan-Boltzmann constant. In Eq.
4.1,
T
is the temperature of the blackbody, which is assumed to be isothermal.
This relationship was first developed experimentally (by Josef Stefan) and later
derived theoretically (by Ludwig Boltzmann).
Some materials in the real world obey the Stefan-Boltzmann law quite
closely, while others do not. Thermal emission from these materials is gener-
ally proportional to the fourth power of their temperature, but the amount of
energy emitted is generally lower than that of a perfect blackbody. A better
approximation for the energy radiated by real materials results by introducing
the blackbody
emissivity
, , defined as the fraction of the incident energy that
is reemitted. (The dependence of emissivity on wavelength is neglected here.) If
we take emissivity into account, the energy emitted by a
“gray body”
is
E
4
E
4
=
εσ
.
(4.2)
Emissivity values for substances relevant to climate are generally close to 1 (see
Blackbody radiation emission is distributed across wavelength, l, according
to the Planck formula:
2
hc
2
,
BT
()
=
(4.3)
λ
5
λ
[
exp
hc kT
/
λ
−
1
]
^
h
