Sam Atwood & Janet Fang
Fall 2006, EESC W4400
The Greenhouse Effect
The greenhouse effect is the natural mechanism by which earth’s surface is warmed by the
infrared-absorbing gases in its atmosphere. Earth’s energy balance is affected by the amount of
incident sunlight, reflectivity, and the greenhouse effect. With thermal equilibrium and energy
conservation, we should expect:
EnergyIn = EnergyOut.
In the radiative transfer processes, earth is warmed through visible (incoming, solar) radiation,
and earth is cooled through infrared (outgoing, terrestrial) radiation. The Stefan-Boltzmann Law
states that the energy flux emitted by a blackbody (something that emits and/or absorbs radiation
with 100% efficiency) is related to the fourth power of the body’s absolute temperature:
F = σT4, where T is the temperature (in kelvins) and σ is a constant valuing 5.67 x 10-8
W/m2/K4.
The planetary energy balance between outgoing infrared energy and incoming solar energy is:
σTe4 = S/4(1-A), where Te is effective temperature, S is solar flux, and A represents albedo.
Given that earth’s surface temperature is about 15oC and its effective temperature is -18oC, the
magnitude of earth’s greenhouse effect is 33oC.
A secondary definition
of greenhouse effect is
the difference between
earth’s surface
temperature/radiation
and earth’s effective
temperature/radiation:
Tg = Ts – Te.
Incoming
solar radiation
Reflection
Emission from atmos.
Emission from atmos.
Transmission
Emission from surface
Suppose the
atmosphere is a singlelayer of gases, then
radiation is absorbed and reflected by the atmosphere, which then reradiates it to surface.
Greenhouse gases warm the surface by absorbing infrared radiation and reradiating some of it
back toward the surface. Atmospheric greenhouse gas concentration changes the energy
absorbed and reradiated to the surface, causing a surface temperature change. Greenhouse gases
in the atmosphere have a warming effect on surface temperatures. Important atmospheric
greenhouse gases include (in order of descending concentration): water vapor, carbon dioxide,
methane, nitrous oxide, ozone, and CFCs.
A strong absorption feature in earth’s
atmosphere is the 15-μm CO2 band;
this feature is especially important to
climate because it occurs near the
peak of earth’s outgoing radiation.
Earth’s surface emits strongly in this
particular wavelength region, but very
little of this radiation can escape
directly to space because it will be
absorbed by CO2 molecules in the
atmosphere.
CO2 levels in the past have not been
higher than 300 ppm; our CO2 levels
are now at 380 ppm.
The present planetary imbalance is large, relative to earth’s history (Hansen et al., 2005).
Greenhouse gases exist naturally in our atmosphere, and the incoming and outgoing radiation
was approximately in balance. But humans are acting to increase greenhouse gas concentrations.
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According to IPCC-TAR, “Human activities—primarily burning of fossil fuels and changes in
land cover—are modifying the concentration of atmospheric constituents or properties of the
Earth’s surface that absorb or scatter radiant energy. In particular, increases in the concentrations
of greenhouse gases (GHGs) and aerosols are strongly implicated as contributors to climatic
changes observed during the 20th century and are expected to contribute to further changes in
climate in the 21st century and beyond.”
(As with most graphs, be careful not to ignore the error bars.)
This anthropogenic increase in
greenhouse gas concentration
results in the enhanced
greenhouse effect, with global
warming implications.
The pairing of surface
temperatures with the
greenhouse effect will lead to a
strong positive feeback on any
perturbations to our present
climate (Raval & Ramanathan,
1989).
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With the enhanced greenhouse effect, climate sensitivity (the equilibrium global temperature
change due to a doubling of CO2) is between 1.5 and 4.5oC. This estimate of sensitivity is based
on the contributions of the greenhouse effect as well as numerous feedback mechanisms present
in the planetary system. Uncertainty in these numbers comes from the complex nature of these
interactions and is the best estimate of theory and projections from global general circulation
models.
Models and observations agree that humans are changing greenhouse gas concentrations, which
can lead to global warming.
This warming which occurs as a result of a change in the greenhouse gas concentration will
not occur immediately. The planet has considerable thermal inertia, which describes the process
by which the Earth system transitions between one state of equilibrium and another. An
equilibrium state in this context describes a situation which satisfies the planetary energy
balance, namely, that energy flux into the planet equals energy flux out of the planet. If this is
not the case, the earth is not in equilibrium and according to the Stefan-Boltzmann Law, its
temperature must change to compensate. When the temperature changes to the point where the
outgoing flux equals the incoming flux, the system is in balance and another equilibrium point is
reached.
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The shift from one equilibrium point to another takes time in a real world situation. This is due to
the process which must occur before the temperature of an object emitting radiation can change.
When the incident flux on an object increases, its temperature does not change immediately, as it
first begins to store energy. The heat capacity of this object is the measure of how much energy it
can absorb from this increased flux for a given change in temperature. If its heat capacity is high,
a lot of energy is required to change the temperature. In order to return to an equilibrium state,
the object must increase in temperature (thereby emitting more radiation), to the point at which
the outgoing flux is equal to the incoming flux. Since the flux (Watts [energy per time period] /
square meter) describes how much energy enters the object (here, of constant area) over a period
of time, the increase in the flux and heat capacity of the object will determine how long it takes
to transition to this new state of equilibrium.
In the case of the Earth, the increase in greenhouse gases has led to an increase in the forcing
(flux) for the surface of the earth. The oceans take up the majority of area over the surface of the
earth and are comprised of water, which has a high heat capacity. Thus the surface and upper
layers of the ocean act as a reservoir which can absorb large amounts of energy before changing
temperatures. In other words, the Earth is described as having a large thermal inertia. Using
current estimates of climate sensitivity (0.75 C +/- 0.25 C per W/m2) and knowledge of the
ocean’s size, layers and heat capacity, models suggest that it will take between 25 and 50 years
for the earth to reach 60% of the transition between equilibrium states (Hansen et al., 2005). This
means that once a change in the carbon dioxide in the atmosphere takes place, only 60% of the
resulting temperature change will take place in the first 25 to 50 years. The IPCC TAR’s
estimate of the impact of carbon dioxide emissions on temperature through time is shown below.
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FINAL TAKE HOME POINTS
(1) Greenhouse gases in the atmosphere have a warming effect on surface
temperatures. The greenhouse effect is a natural mechanism that warms our planet to its
inhabitable temperature, but anthropogenic emissions are creating an enhanced
greenhouse effect.
(2) Rapid changes in greenhouse gases take time to alter surface temperatures. The
oceans must absorb large amounts of energy before they change in temperature. This
“thermal inertia” means that the rapid change in greenhouse gases over the 20th Century
will not raise temperatures immediately. It will take 25 to 50 years for 60% of the
temperature change to take place as the climate transitions between equilibrium states.
(3) Humans are changing greenhouse gas concentrations, which can lead to global
warming. Previous CO2 levels (since 400,000 years before present) have not averaged
over 300 ppm. CO2 levels began its exponential incline during the Industrial Revolution
of the 19th Century. Our current level is approximately 380 ppm, and while it is hoped
that we will stabilize at 500 ppm, more realistic projections suggestion 700 ppm.
References and Sources for Further Information
Tim P. Barnett et al. (2005) Penetration of Human-Induced Warming into the World’s Oceans.
Science 309:284-287.
James Hansen et at. (2005) Earth’s Energy Imbalance: Confirmation and Implications. Science
308:1431-1435.
Lee R. Kump, James F. Kasting, and Robert G. Crane (2004) The Earth System, 2nd Edition.
Pearson Prentice-Hall, Upper Saddle River, New Jersey.
A. Raval and V. Ramanathan (1989) Observational determination of the greenhouse effect.
Nature 342:758-761.
IPCC Third Assessment Report, accessed at http://www.grida.no/climate/ipcc%5Ftar/.
Wikipedia’s entry on Greenhouse Gases, accessed at
http://en.wikipedia.org/wiki/Greenhouse_gasses.
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