This page presents a simple physical model of the greenhouse effect that demonstrates how the blanketing effect of greenhouse gases in the atmosphere can elevate the surface temperature of a planet. The model is an instructional "toy model," meaning it strips the process down to its essential elements so that the basic ideas are easy to convey. Models that are used to make predictions by climate experts are substantially more sophisticated, but at root the physics are similar to what is described below.

* The first key idea is that
hot objects lose heat faster than cold objects. * This
is obvious from everyday experience (you can feel the heat
coming from a fire). Detailed observations show that the rate
of heat loss is * very sensitive* to temperature -- specifically,
if the temperature is doubled (on an absolute scale), the rate
of heat loss is not twice as high -- it is * sixteen times*
as high.

*The second key idea is that planets are near an equilibrium where
heat lost to space almost exactly equals sunlight gained.*
Because hot objects lose heat rapidly, they tend to cool off if
they have no energy source to maintain their temperature. On
the other hand, because cold objects only lose heat slowly, they
tend to warm up in the presence of energy sources. In both
cases, the objects converge toward a condition where they lose heat
at exactly the same rate that it is supplied by energy sources.
In the case of planets, the energy source is sunlight.

Let's see how this works for a planet with no atmosphere. At
the position of Earth, the absorbed sunlight is
240 Watts/meter^{2}. In equilibrium, this means that
the planet would lose heat to space -- as infrared radiation --
also at a rate 240 Watts/meter^{2}. How can we calculate the
temperature from this? Detailed measurements show that,
mathematically, the relationship between heat loss and temperature
can be described by
the equation F = &sigma T^{4}, where F is the rate of heat
loss (the "heat flux") and
&sigma is a fundamental physical
constant (called the Stephan-Boltzmann constant) with a value
of 5.67 x 10^{-8} Watts/meter^{2} Kelvin^{4}.
We can rearrange this equation to state that, for a planet with
no atmosphere,

T = (F/&sigma)^{1/4}.

Plugging in F=240 Watts/meter^{2} and &sigma=5.67 x 10^{-8}
Watts/meter^{2} Kelvin^{4}, we find that T=255 K, which
corresponds to a temperature of -18^{o}C or 0^{o}F.

Thus, if Earth had no greenhouse effect, the average surface temperature
would be 0^{o}F -- far below the freezing temperature! The
oceans would be totally frozen and life would not exist on Earth.

** How does having an atmosphere with greenhouse gases affect this
situation?** * The greenhouse effect only works if
the atmosphere is transparent to sunlight but opaque to infrared (heat)
wavelengths.* Many gases -- CO2, water vapor, methane -- behave
just this way. These are the __ greenhouse gases.__

In this case, the Earth still gains 240 Watts/meter^{2} from
the sun. It still loses 240 Watts/meter^{2} to space. However,
because the atmosphere is opaque to infrared light, the surface
cannot radiate directly to space as it can on a planet without
greenhouse gases. Instead, this radiation to space comes from
the atmosphere.

However, atmospheres radiate both up and down (just like a fire
radiates heat in all directions). So although the
atmosphere radiates 240 Watts/meter^{2} to space, it
also radiates 240 Watts/meter^{2} toward the ground!
Therefore, the surface receives *more energy* than it
would without an atmosphere: it gets 240 Watts/meter^{2}
from sunlight and it gets *another*
240 Watts/meter^{2} from the atmosphere -- for a total
of 480 Watts/meter^{2} in this simple model.

Now like the atmosphere, the Earth's surface is near an equilibrium
where it gains and loses energy at almost the same rate. Because
the surface gains 480 Watts/meter^{2} (half from sunlight
and half from the atmosphere), it also must radiate
480 Watts/meter^{2}. Unlike the atmosphere, however, the
ground can only radiate in one direction -- upward. Thus,
the surface radiates 480 Watts/meter^{2} upward, and
because the atmosphere is opaque to this infrared light, it is
absorbed by the atmosphere rather than escaping to space.
Notice that the atmosphere, the surface, and the planet as a whole
each gain energy at exactly the same rate it is lost.

We can again use the simple expression T = (F/&sigma)^{1/4}
to calculate the temperature of the surface. Using
F = 480 Watts/meter^{2} and &sigma=5.67 x 10^{-8}
Watts/meter^{2} Kelvin^{4}, we find that T=303 K,
which corresponds to 30^{o}C or 86^{o}F.

__Key points__:

&diams Without greenhouse gases, we calculated that the surface temperature
would be 255 K (0^{o}F),
whereas with greenhouse gases we calculated the
surface temperature would be 303 K (86^{o}F).
Therefore, the blanketing effect of atmospheric greenhouse gases
has caused an elevation of the surface temperature. *
This is the greenhouse effect!*

&diams The greenhouse effect is *NOT* a situation where
"heat is trapped and can't escape." The above calculation makes
clear that the opposite is true: the greenhouse effect
is how the atmosphere adjusts so that it *CAN* lose heat
when greenhouse gases are present in the atmosphere. About the
same amount of heat escapes to space regardless of whether
a greenhouse effect exists.

&diams In our simple model, we predicted an
elevation in surface temperature of
48^{o}C (86^{o}F). This is an overestimate. On
the real Earth, the current average surface temperature is 288 K
(59^{o}F), not 303 K, so the actual greenhouse effect causes a warming
of only 33^{o}C (59^{o}F) relative to an atmosphere
without a greenhouse effect. Thus, the crude model presented here
overestimates the strength of the greenhouse effect by 50%.
This discrepancy is caused by several
factors that we neglected. For example, some sunlight is absorbed
in the atmosphere rather than at the surface, and some infrared
radiation from Earth's surface can escape to space rather than
being absorbed in the atmosphere. These effects are all included
in real climate models. Properly taking these effects into
account would lead to a predicted temperature much closer to the
actual temperature.

&diams An increase in the abundance of CO_{2}, water vapor, methane,
and other greenhouse gases causes a decrease in the fraction of infrared
radiation from the surface that can escape to space. This forces
the surface temperature to increase as the Earth strives to reach
the new equilibrium.
*More greenhouse gases mean a stronger greenhouse effect and a
hotter planet.*

&diams When the greenhouse gas abundance is increased, it takes time
for the system to warm to the new equilibrium temperature.
During these times, the Earth absorbs slightly
more sunlight than it loses heat, which is what allows the warming.
Thus, during these times, the Earth is slightly out of equilibrium.
What this means is that * even if the abundances of greenhouse gases
became constant right now, the Earth would continue to warm by
another 0.5-1 ^{o}C (1-2^{o}F) over the next 50-100 years
as it reached the new equilibrium temperature.*
This delayed warming has already been caused and is unavoidable.
Of course, additional warming will occur if greenhouse gas abundances
continue to increase.