(last updated: Jan 02, 2009)

The greenhouse effect is responsible for raising the average temperature of the Earth by 33
C. Without it the oceans would freeze right to the equator, and there would be no complex life on Earth. The burning of fossil fuels and other human activity is increasing the level of greenhouse gases in the atmosphere, which is leading to increasing warming. On this page, the greenhouse effect is explained starting with simple models, then advancing to more complex and scientifically accurate descriptions.

The Greenhouse and the Blanket
Basic Radiation Balance Model
More Advanced Radiation Balance Model
Greenhouse Gas Absorption Bands
Logarithmic Response to Greenhouse Gases
The Greenhouse Effect on Earth and Neighboring Planets
Converting Increased Carbon Dioxide Levels into Temperature Change


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The Greenhouse and the Blanket

The Glass Greenhouse - a poor analogy
A glass greenhouse stays warm mainly because the glass walls prevent the wind from removing heat from the enclosed area, and prevent warm air rising from inside the greenhouse to be replaced with cooler air from above. The heat trapping properties of the glass itself are relatively minor. A glass greenhouse has very little to tell us how the so-called "greenhouse effect" on Earth actually works.


The Blanket Model - a simplistic beginning
We can think of greenhouse gases as a "blanket", that allows energy from the sun to pass through it and warm the Earth, but slows down the release of energy from the Earth, similar to how a blanket keeps you warm on a cold night. If you add another "blanket" (increase greenhouse gas levels) the Earth gets a little warmer. However, a real blanket works by slowing down (insulating) the transfer of heat from your body. Insulation and convection have nothing to do with how greenhouse gases work.

A problem with this simple model arises when we realize that there is a lot more water
vapor in the atmosphere then carbon dioxide. The amount of water vapor can vary but averages around 0.4%, compared to less than 0.04% for carbon dioxide. Water vapor also absorbs energy over a wider spectrum than carbon dioxide. If our "blanket" is mostly water vapor with a few specks of carbon dioxide, and the water is the better absorber, then doubling the amount of carbon dioxide would seem to make little difference. But in fact water vapor only contributes two thirds of the greenhouse effect. That fact can only be understood by discarding the simple blanket model, and using a more scientifically sound radiation balance model.

This analogy is useful in the sense that addimg more blankets has a diminishing effect on keeping you warm. The same is true for increasing greenhouse gas levels.


A Basic Radiation Balance Model

We will begin with a world without any greenhouse gases. The Earth receives its heat as visible light from the sun. To stay in temperature balance, it must radiate the same amount of energy that it receives back into space, which it does at a longer (infrared) wavelength. If the sun increases in intensity, the surface of the Earth will warm, and it will radiate more energy back into space until the temperature comes back into balance (at a higher level than before).

Now we will add greenhouse gases, but will (for the moment) assume the entire atmosphere is the same temperature as the surface of the earth. The Earth receives light from the sun, and tries to radiate the heat (infrared radiation) back into space. Some of this infrared radiation will be absorbed by the new greenhouse gases, which will, in turn, radiate the absorbed energy into space. But because these gases are at the same temperature as the Earth's surface (averaged over a period of time), they will radiate the same amount of energy into space. The Earth will lose the same amount of energy, so the greenhouse gases will have little effect on the temperature.

What went wrong? We did not describe the atmosphere properly. Greenhouse gases are distributed throughout the atmosphere, which gets cooler with altitude. The key point is the amount of energy a greenhouse gas radiates depends on its temperature. Greenhouse gases near the surface have little effect, because they radiate at about the same temperature of as the Earth's surface [They may also transfer their energy to other molecules in the atmosphere, causing local warming]. However, higher up in the atmosphere they are cooler, so they radiate less energy. Thus the Earth as a whole radiates less energy than it would have in the absence of greenhouse gases, and this gets a little warmer. Most of the greenhouse effect takes place high in the troposphere.

Greenhouse gases like carbon dioxide and methane are "well mixed", meaning they have the same concentration throughout the troposphere. However, water vapor is different, which we observe whenever it rains or snows. Colder air holds less water vapor. Because the temperature of the atmosphere falls with altitude, the concentration of water vapor decreases with height. Near the top of the troposphere its concentration is less than that of carbon dioxide. So although there is a lot more water vapor than carbon dioxide in total, there is relatively less water vapor where it matters most. That is why water vapor only accounts for two thirds of the greenhouse effect.



A More Scientific Description of the Radiation Balance Model


The greenhouse effect is governed by the following physical laws:
(1) Wien's Law - The wavelength of energy emitted from a body increases with decreasing temperature.
(2) Stefan-Boltzmann - A body in space radiates an amount of energy proportional to the fourth power of its temperature. The warmer the body, the more energy is lost.
(3) Conservation of Energy - The Earth must emit the same amount of energy that it receives for its temperature to stay constant.
(4) Lapse Rate - The temperature of the atmosphere decreases with altitude.
(5) Clausius Clapeyron - The maximum possible concentration of water vapor (absolute humitidy) decreases exponentially with falling temperature and pressure, and thus with altitude in the atmosphere. Relative humidity, the fraction of water vapor compared to the maximum possible at a given temperature, also declines with altitude. In the lower troposphere, saturation vapor pressure increases by 7% for each degree K.  [ref]
(6) Logarithmic Response - The radiative forcing of a greenhouse gas is proportional to the logarithm of its concentration, for any concentration that is likely to occur on Earth.
(7) Kirchhoff's Law - Objects that absorb radiation strongly at a given wavelength will emit strongly at the same wavelength.


The Emission Spectrum of the Sun and the Earth

All matter with a temperature above absolute zero emits radiation. The hotter the substance, the more radiation it emits and the shorter the average wavelength of the radiation emitted. Being a hot body, most of the Sun's radiation has a short wavelength, around the visible light part of the electromagnetic spectrum (Law 1). This energy heats the Earth. In order to maintain a temperature balance, the Earth must radiate as much energy as it receives (Law 3). Being cooler than the Sun, this energy is in the form of longer wave infrared radiation (Law 1). The emission spectrum rises quickly and falls slowly, but appears as the shape of a bell curve on the logarithmic scale of the graph below.

Emission_Spectrum_Sun_Earth.png



Absorption of Longwave Radiation by Greenhouse Gases

The greenhouse effect is caused by the fact that the atmosphere is mostly transparent to incoming shortwave solar radiation, but some gases absorb part of the longwave energy radiated back to space. Over 99% of the atmosphere consists of nitrogen and oxygen, both two-atom molecules with no ability to absorb infrared radiation. The remaining fraction of a percent consists of more complex molecules such as water vapor, carbon dioxide, methane and others, which are responsible for the greenhouse effect.

Molecules with more than two atoms have more than one chemical bond. Vibrations in a gas molecule are like vibrations of a piano string in that they are sensitive to frequency. This is because, like a piano string, a gas molecule will only vibrate at its “ringing” frequency. All of their bonds ring together rather than each bond ringing with its own characteristic frequency.

Water is a molecule that is bent when in its lowest energy state. Hydrogen atoms hold their electrons more loosely than oxygen atoms, and so each hydrogen has a slightly positive charge (marked using the lowercase greek letter delta, as δ+). The oxygen end of the molecule has a slight negative charge. A rotating an H2O molecule would oscillate the electric field and generate light. There are several modes of vibration of the water molecule, including a symmetric stretch and a bend. These modes are also infrared active.
Greenhouse_RadiationAbsorption_WaterVapor.png

The CO2 molecule is shaped in a straight line with carbon in the middle. It is a symmetric molecule; the oxygen atom on one end pulls the electrons just as tightly as the other oxygen on the other end. Therefore rotating the molecule at rest has no effect on the electric field. The symmetric stretch also has no effect. However, there are two modes of vibration which do generate an asymmetry in the electric field. One is an asymmetric stretch, and the other is a bend. The bend is the most climatically important one. [ref]
Greenhouse_RadiationAbsorption_CO2.png


Greenhouse Gases Raise the Altitude from which the Earth Radiates

The presence of greenhouse gases means that instead of radiating energy from its surface, the Earth radiates energy back into space from higher up in the atmosphere. Convection is always lifting air from the ground to high altitudes in the troposphere, causing the air to cool by expansion as it rises. This is the basic reason that temperature goes down with height in the troposphere (Law 4). As a result, the infrared radiation that escapes to space comes more from the higher, colder parts of the atmosphere. Since the emission rate of infrared radiation increases to the fourth power of temperature (Law 2), the radiation from these layers is much feebler than the radiation that would escape from the ground. If the concentration of greenhouse gases is increased, the average radiation occurs from a higher altitude, so less energy is lost and more is retained (Law 3).

If atmosphere had a constant density with a discrete top, its temperature at the top would be the same as at the bottom. It would radiate at the same temperature no matter how much of it was greenhouse gas. The greenhouse effect only takes place because of the atmosphere's temperature gradient.



Carbon Dioxide is Relatively More Abundant where the Greenhouse Effect Actually Takes Place

Given that water vapor is about 1% of the atmosphere as compared to 0.037% for carbon dioxide, one might think that the relative difference made by carbon dioxide is small. This is made worse by the fact that on a per-molecule basis water vapor is 3.3 [need a reference for this] times as effective as carbon dioxide. But water vapor has one critical distinction - it is a liquid at a moderate temperature and pressure. Because it precipitates out of the atmosphere, its concentration is not constant. Instead, the atmosphere cools with altitude (Law 4), and the ability to hold water decreases rapidly with temperature (Law 5), so water vapor concentration decreases rapidly with altitude. At the top of the troposphere, where most of the greenhouse effect takes place, there is less water vapor than carbon dioxide. It turns out that water vapor is responsible for about 65% of the greenhouse effect, while carbon dioxide and other greenhouse gases are responsible for the rest. See also this discussion.


A Cartoon Summary of the Greenhouse Effect

Greenhouse Effect
  1. Shortwave radiation (mostly visible light) from the sun reaches the Earth and warms it, unaffected by passing through the oxygen and carbon dioxide molecules in the atmosphere [A carbon dioxide molecule is straight, not bent].
  2. The Earth radiates longer wave (infrared) radiation back to space. The oxygen molecule on the left is transparent to this radiation, but the carbon dioxide molecule on the right absorbs radiation that is at a specific wavelength.
  3. The carbon dioxide molecule re-radiates the energy at a random angle. Kirchhoff's Law [Law 7] tells us it will most likely emit at the same wavelength it absorbed from. Some of them will radiate the energy into space. Its altitude (thus temperature) will determine the amount of energy it radiates.
  4. In the right panel, the concentration of carbon dioxide and water vapor has increased. This does not result in a proportional increase in the greenhouse effect because not all molecules will have the opportunity to absorb radiation. The molecules that radiate into space are only slightly higher than before. Effectively, the average altitude at which the Earth radiates from has been raised. Therefore the warming only increases logarithmically with greenhouse gas concentration. That means each doubling has the same impact as the previous one.
  5. Radiation escapes into space from the upper troposphere. The atmosphere is thinner and cooler, so the radiating temperature is lower. Carbon dioxide has the same concentration throughout the troposphere, but water vapor concentration decreases with altitude. So while there is much more water vapor near the surface, there is relatively less higher up, so carbon dioxide makes a much larger contribution to the greenhouse effect than its average concentration would suggest.


Measuring the Greenhouse Effect

The picture below shows actual measurements of longwave radiation reaching the surface of the Earth due to the greenhouse effect.
DownwellingLongwaveRadiation_GlobalSurface.png
Geographical distribution of model downwelling longwave flux (DLF), at the surface for January and July, averaged over 1984–1993. [ref]



Greenhouse Gas Absorption Bands

A greenhouse gas does not absorb all thermal radiation, it absorbs only certain wavelengths. When the absorbing wavelengths of different greenhouse gases overlap, the effectiveness of each gas is reduced.

From here:
Carbon dioxide has three absorption bands at wavelengths of 4.26, 7.52, and 14.99 micrometers (microns). The Earth's emission spectrum, treated as a black body (no atmospheric absorption), peaks at between 15 and 20 microns, and falls off rapidly with decreasing wavelength. As a result, the carbon dioxide absorption bands at 4.26 and 7.52 microns contribute little to the absorption of thermal radiation compared to the band at 14.99 microns. Natural concentrations of carbon dioxide are great enough that the atmosphere is opaque even over short distances in the center of the 14.99 micron band. As a result, at this wavelength, the radiation reaching the tropopause from above and below the tropopause is such that the net flux is close to zero.

If this were the whole story, adding more carbon dioxide to the atmosphere would contribute nothing to the greenhouse effect and consequently could not cause a rise in the Earth's temperature. However, additional carbon dioxide does have an influence at the edges of the 14.99 micron band. Because of this marginal effect, the change in forcing due to a change in carbon dioxide concentration is proportional to the natural logarithm of the fractional change in concentration of this gas. Specifically, [IPCC 6.3.5] gives

dF = 5.35 ln (C/Co) W/m2

where dF is the change in forcing, and Co and C are the initial and final carbon dioxide concentrations. This approximation breaks down for very low concentrations (around 1 ppm) and for concentrations greater than 5% (50,000 ppm), but is valid in the range of practical interest. The Earth's temperature is therefore relatively insensitive to changes in carbon dioxide concentrations, a doubling leading to a dF of only 3.7 W/m2.

Earth's Black-Body Radiation and Greenhouse Gas Absorption Curves


Absorption Bands

There is some overlap between carbon dioxide and water vapor in the 15 micron portion of the spectrum where the Earth's infrared radiation is at is peak. But note that the overlap of the water vapor and carbon dioxide bands only occur in the lower atmosphere, because increased atmospheric  pressure causes the absorption specturm of longwave radiation by water vapor to broaden. Higher in the atmosphere, where there is little water vapor, there is no overlap of the absorption bands, as can be seen in the above chart for 11 km above the surface at 15 microns.

Greenhouse_Water_CO2_Overlap.png

Carbon dioxide is the most frequently mentioned greenhouse gas, but water vapor absorbs infrared (heat) radiation much more strongly. Carbon dioxide is significant because it closes a “window” that would otherwise allow certain infrared wavelengths to escape the Earth’s water vapor blanket. The graph at left shows the percentage of energy absorbed in a clear tropical sky by water vapor (green) and carbon dioxide (brown). (Graph by Robert Simmon, based on model data from the NASA GSFC Laboratory for Atmospheres) [ref]



Absorption of Radiation in the Earth’s Atmosphere
Various atmospheric constituents absorb electromagnetic radiation. The important absorbing gases and their absorption efficiency as a function of wavelength is shown on the right.

Note the strong oxygen absorption in the UV part of the spectrum and that of water vapor, which absorb effectively in large sections of the IR wavelength range.

CO2 absorption band overlaps a gap in the water vapor band (referred to a “window”) hence its importance.

[The horizontal wavelength scale on this graph is clearly incorrect. The second carbon dioxide peak, aligned with the gap in water vapor, shoud be at 15 microns.]

From this lecture on the Physics and Chemistry of the Earth’s Climate System
Absorption of Radiation



The Logarithmic Response to Increasing Greenhouse Gas Levels

From the IPCC Climate Change 2001 Report:

If the amount of carbon dioxide were doubled instantaneously, with everything else remaining the same, the outgoing infrared radiation would be reduced by about 4 W/m2. In other words, the radiative forcing corresponding to a doubling of the CO2 concentration would be 4 W/m2. To counteract this imbalance, the temperature of the surface-troposphere system would have to increase by 1.2C (with an accuracy of 10%), in the absence of other changes. In reality, due to feedbacks, the response of the climate system is much more complex. It is believed that the overall effect of the feedbacks amplifies the temperature increase to 1.5 to 4.5C. A significant part of this uncertainty range arises from our limited knowledge of clouds and their interactions with radiation. To appreciate the magnitude of this temperature increase, it should be compared with the global mean temperature difference of perhaps 5 or 6C from the middle of the last Ice Age to the present interglacial.
 ...
Carbon dioxide absorbs infrared radiation in the middle of its 15 mm band to the extent that radiation in the middle of this band cannot escape unimpeded: this absorption is saturated. This, however, is not the case for the band’s wings. It is because of these effects of partial saturation that the radiative forcing is not proportional to the increase in the carbon dioxide concentration but shows a logarithmic dependence. Every further doubling adds an additional 4 W/m2 to the radiative forcing.

The Range of Carbon Dioxide Concentration for which there is a Logarithmic Response

The logarithmic behavior of CO2 in Earth's atmosphere applies between 1 ppm to around 5% (50,000 ppm). At very low concentrations (say, around 1 ppm) bands are unsaturated and Outgoing Longwave Radiation becomes more sensitive to CO2 than in the logarithmic range. At sufficiently high concentrations the absorption starts to be dominated by weak bands that have a different probability distribution than the bands that dominate in the present climate.

CO2 opacity for the present Earth is dominated by the 15 micron band group. The envelope of the absorption strength in this group tails off roughly exponentially from the center of the group, once the lines are broad enough to overlap significantly within each sub-band of the interval, and the resulting probability distribution of absorption can be shown to give rise to the logarithmic behavior. However, the exponential envelope is only approximate, and only extends a certain distance out from 15 microns, so once you put in enough CO2 you get out of the logarithmic range. [ref]



Comparing the Greenhouse Effect on the Earth and its Neighbors

It is instructive to compare the Earth with some other planets that have an atmosphere, to get a large scale perspective on the significance of the greenhouse effect.

The non-greenhouse temperature (T) of a planet is a function of its distance (d) from the sun (in astronomical units) and how much of that energy it absorbs (1 - albedo), as shown by the equation
T = 279 K [ (1 - albedo)/d2) ]1/4

The greenhouse temperature can also be calculated by multiplying the Atmospheric Lapse Rate (how fast the atmosphere gets colder with altitude) by the mean Emission Altitude (the average height from which energy is radiated into space), according to the equation

Greenhouse Difference = Lapse Rate * Emission Altitude

The table below illustrates the greenhouse effect on the Earth and some of its neighbors in space. The solar constant is the amount of energy reaching the planet. Albedo is how much light is reflected.

The Greenhouse Effect on the Inner Planets
Planet or
Satellite
Solar
Constant
Albedo CO2 Factor No Greenhouse
Temperature
Actual Average
Temperature
Greenhouse
Difference
Atmospheric
Lapse Rate
Emission
Altitude
Venus 2643 W/m2 72% 180,000 -43 C 470 C 513 C 7 C / km 70 km
Moon 1370 W/m2 7% 0 0 C 0 C 0 C - -
Earth 1370 W/m2 30% * 1 -18 C 15 C 33 C 5.5 C / km 6 km
Mars 593 W/m2 25% 1.27 -63 C -59 C 4 C 5 C / km 1 km

* The value of  33 C of greenhouse warming for Earth (cited everywhere) is based on today's albedo.  But much of that albedo comes from clouds, which would not exist if there was no water vapor, and which also have an insulating effect that is not taken into account.  So if water did not exist on the Earth, the albedo would be lower, and its temperature larger than -18 C.  But water does exist, so the 33 C is a realistic value for today's conditions.

Venus has a thick carbon dioxide atmosphere and a huge greenhouse effect. The logarithmic relationship between CO2 and radiative forcing only holds for low concentrations, less than 20% of the Earth's atmosphere. Carbon dioxide absorption bands expand with increased atmospheric pressure (collisional broadening) and higher temperatures (doppler broadening). A lot of weak bands that are inconsequential on Earth become dominant in determining the changes in Outgoing Longwave Radiation [ref]. Note that because of its reflective clouds, its no-greenhouse temperature is actually lower than that of the Earth despite receiving twice the sunlight. Clouds on Venus are composed mainly of sulfurinc acid, which (unike water vapor clouds) has no greenhouse effect. They do reflect infrared radiaion, so they also contribute to temperature by their insulating effect. For more on Venus, see [ref].

The atmosphere of Mars is 96% CO2, about 254 times the proportion on Earth. Its atmospheric mass is 2.5 x 1019 g, compared to Earth's 5.1 x 1021 g, or 1/200 as much, so Mars has 1.27 times more CO2 than Earth. Mars has one quarter the surface area of Earth, so it effectively has five times the level of greenhouse gas. It receives less than half the solar energy, and gets 4 C of extra warming.


Planetary Temperature Calculator:  T = 280 K [ (1 - albedo)/d2) ]1/4

Albedo (fraction) Distance from Sun (AU)
Planetary Temperature  C



Converting Carbon Dioxide Increase into Temperature Change

The direct increase in radiative forcing (dE) caused by an increase in carbon dioxide levels, in watts per square meter, can be found by the equation

dE = 5.35 ln (C/Co)  W/m2

where C is the new carbon dioxide level (in parts per million, or ppm) and Co is the starting carbon dioxide level.   For example, CO2 concentration has risen from 270 to 370 ppm, so the equation gives 5.35 x ln(370/270) = 1.7 W/m2 raw forcing.


Radiative Forcing Calculator

Initial CO2 (ppm) Final CO2 (ppm) Climate Sensitivity
5.35 ln (C/Co) = W/m2 direct forcing,  or C
Total warming using climate sensitivity =   C



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