Lecture 2
Global and
Zonal-mean
Energy
Balance
A zero-dimensional view of
the planet’s energy balance
RADIATIVE BALANCE
Roughly 70% of the radiation received from the
Sun at the top of Earth’s atmosphere is absorbed
by the land and ocean surfaces, and to a smaller
extent, the atmosphere. This absorbed solar
energy provides the fuel for atmospheric and
oceanic motion, and the flows of energy
determine the planet’s temperature distribution.
When averaged over a period of several years and
over all latitudes and longitudes, Earth as a whole
loses approximately as much radiant energy to
space as it gains from the sun. When this
condition is satisfied, we say the planet is in a
state of radiative balance.
Recall that objects constantly emit radiation
according to their temperature. Objects that emit
with 100% efficiency are called blackbodies, and
have a distribution of wavelengths of emitted
radiation is given by the Planck function, which
has a characteristic shape:
This curve is for an
object with a temperature
of about 5800K, the
approximate temperature
of the sun.
the distribution’s
peak wavelength...
…is inversely proportional to
the temperature of the object
(=2898/T, Wien’s law). The
hotter the object, the shorter
the typical emission
wavelengths
The total energy emitted by the object is
the area under the curve...
…and is proportional to the
fourth power of the object’s
temperature (=σT4). This
relationship is known as the
Stefan-Boltzmann law. So
the energy emitted increases
very quickly as the object’s
temperature increases.
The wavelength distributions of the radiation emitted
by the sun and the earth are very different, because
the sun is so much hotter than the earth.
The Planck functions for
temperatures characteristic
of the sun and the earth.
The peak wavelength of the
sun’s distribution is at about
0.5 microns (green light),
while the peak wavelength
for the earth’s distribution is
at about 10 microns
(infrared radiation).
Solar versus Terrestrial Radiation
For studies of Earth’s climate, we consider two parts of
the electromagnetic spectrum:
1) short-wave radiation emitted by the sun, 0.1
µm < λ < 4.0µm (ultraviolet, visible, near infrared),
often called solar radiation, and
2) long-wave radiation emitted by Earth,
4.0µm ≤ λ < 60 µm (near infrared, infrared, far
infrared), often referred to as terrestrial radiation.
The atmosphere is relatively transparent to solar
radiation, and is nearly opaque to terrestrial
radiation. This arrangement is the basis of the
planet’s greenhouse effect, and simplifies radiative
transfer calculations.
Absorption by Atmospheric
Gases
Certain trace gases absorb
electromagnetic radiation at
specific frequencies. The
absorption lines are broadened
by Doppler and Lorentz effects,
creating large swaths of the
spectrum where the clear-sky
atmosphere strongly absorbs
radiation.
(figs from Hartmann)
Absorption spectra of radiation in the
Earth’s atmosphere
(a)
(a) for the entire vertical
extent of Earth’s
atmosphere,
(b)
(b) for the portion
absorbed above the
tropopause (11 km),
and
(c)
(c) individual absorption
spectra for various
radiatively active
gases in Earth’s
atmosphere.
The greenhouse effect of Venus
From geometry, we can calculate the average solar flux
over the surface of Venus. It is approximately 661 W/m2.
Venus is very reflective of sunshine. In fact, it has a
reflectivity (or albedo) of 0.8, so the planet absorbs
approximately 661 X 0.2 = 132 W/m2.
By assuming that the incoming radiation equals the
outgoing radiation (energy balance), we can convert this
into an effective radiating temperature by invoking the
Stefan-Boltzmann law (total energy = σT4). We find that
T=220K.
But Venus’ surface has a temperature of 730K!!!
The explanation for this huge discrepancy is the planet’s
greenhouse effect.
The greenhouse effect of Earth
From geometry, we can calculate the average solar flux over
the surface of Earth. It is approximately 343 W/m2.
The earth has a much lower albedo than Venus (0.3), so the
planet absorbs approximately 343 X 0.7 = 240 W/m2.
By assuming that the incoming radiation equals the outgoing
radiation, we can convert this into an effective radiating
temperature by invoking the Stefan-Boltzmann law (total
energy = σT4). We find that T=255K.
Earth’s surface has a temperature of 288K
While much smaller than Venus’ greenhouse effect, earth’s
is crucial for the planet’s habitability.
Meridional Energy Flows
In the annual and zonal mean, the local imbalances of net heating imply that
energy must be transported from equator to the poles by the atmosphere and
oceans.
The radiative imbalances of the preceding figure can be used to calculate
the implied energy transport from equator to pole in each hemisphere.
Further calculations with atmospheric and oceanic circulation data can be
used to calculate the energy transport within the atmosphere and ocean.
RT: Top of atmosphere (TOA) radiation (from satellites)
AT: Atmospheric heat transports
OT: ocean heat transports