If you are here looking at this it may be that you saw my avatar at a Wordpress blog where I made a comment. Thanks to Gravatar I get to pick my own avatar, the graphic that appears by my name. When you hover over it you will see a link pointing here promising to tell you about that little blue marble. I will do that. But first let me give you a bit of context...

One of my pet peeves is when one or another "climate skeptic" pretends that the only reason why climatologists expect rising levels of carbon dioxide (CO2) to warm the Earth's climate system is that there exists a correlation between levels of carbon dioxide and global temperature, either in the paleoclimate record or in the instrumental record.

It isn't. And I get a certain satisfaction from being able to remind them otherwise.

The Absorption of Thermal Radiation by CO2

We have known since 1859 that carbon dioxide absorbs thermal radiation. You can actually see it in the video on the left. Iain Stewart places a candle on one end of a tube and a thermal camera on the other end, then gradually puts more carbon dioxide into the tube. The tube remains transparent in visible light. You can still see right through it. But the candle as viewed by the infrared camera gradually fades away.

Now someone could of course point out that Stewart is putting a great deal more carbon dioxide into that tube than what you would normally find in that much air in the atmosphere. Quite right. However what matters isn't so much the amount of carbon dioxide per volume but the amount of carbon dioxide per area cross section of atmopheric column. If you imagine the same volume of carbon dioxide added to a tube of the same width but stretching from the ground to the edge of space he really hasn't added that much carbon dioxide, has he?

We know the absorption spectra of carbon dioxide. Experiments have been performed in laboratories that measure the spectra at different wavelengths, pressures and temperatures. We are virtually able to derive the absorption spectra of carbon dioxide from the first principles of quantum mechanics. And we understand that when you increase carbon dioxide concentrations in the atmosphere you increase the average height where radiation that is absorbed and then emitted by carbon dioxide is emitted for the last time prior to escaping into space.

In the troposphere temperature falls roughly as a linear function of altitude. The rate at which it falls with altitude is what is known as the lapse rate. So when you raise the altitude from which radiation escapes you lower the temperature. Lowering the temperature means that you reduce the brightness of the radiation that gets emitted -- as brightness is proportional to the absolute temperature raised to the fourth power.

  


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The carbon dioxide molecule in its ground state...

In 1859 experiments by John Tyndall showed that carbon dioxide and water vapor absorb infrared radiation. He published his results in:

Tyndall, John, 1861. On the Absorption and Radiation of Heat by Gases and Vapours, and on the Physical Connection of Radiation, Absorption, and Conduction. 'Philosophical Magazine ser. 4, vol. 22, 169-94, 273-85. (PDF Available at the National Science Digital Library's NSDL Wiki.)

... and also posited that humans might change the climate through our emissions of greenhouse gases.

A better view of my avatar...

The Atmospheric InfraRed Sounder

My avatar is of course a satellite image. It was made possible by the Aqua satellite [archive] launched in 2002. The data comes from one of its six instruments [archive]: the Atmospheric InfraRed Sounder (AIRS) [archive]. AIRS is capable of viewing 2,378 different infrared channels -- and when it sees the brightness drop in one channel or another this indicates absorption. Given a few channels one is able to make a spectral "fingerprint" identification of the gas that is responsible.

To measure CO2 concentrations in the mid-troposphere the sounder looks at the band around 15 millionths of a meter (15 μm or wavenumber of 667 cm-1). That particular band of absorption is due to the bending mode of the CO2 molecule. This is the mode of vibration that is almost entirely responsible for the enhanced greenhouse effect, at least under Earth conditions. In its ground state CO2 consists of a linear molecule with a carbon atom at the center two oxygen atoms at the end. The molecular bonds give the oxygen atoms a negative charge and the carbon a positive one. Thus the electrical part of the electromagnetic field at the appropriate frequency is able to interact with the CO2 molecule, causing it to enter a state of excitation in which it bends about the middle.

Infrared photons will be absorbed by CO2 in that band. The greater the concentration the greater the absorption. The energy is quickly lost in collisions, mostly with nitrogen and oxygen. In a nitrogen or oxygen pair both atoms have the same net charge and neither are capable of absorbing or emitting the radiation and are invisible to it. But with absorption by greenhouse gasses the atmosphere warms just as food in a microwave oven -- given the absorption of microwave radiation by water molecules.

At a given temperature collisions will also maintain a certain percentage of molecules in an excited state at any given time, thus over a given period a certain number will undergo spontaneous decay, falling back into the ground state and emitting photons in the process. The warmer the atmosphere the higher the rate of emission -- for the same reason a hot iron will glow more brightly the hotter it gets. The main difference is that with a greenhouse gas like CO2 matter is able to emits only in a few bands.

Reduced luminosity at a given wavelength implies a cooler temperature. Since temperature falls with altitude, this implies that photons at that frequency escape only higher up. Thus given the difference in brightness we might try to crudely estimate the small variations in CO2 concentration that are responsible for the variation in the altitude and consequently temperature at which radiation in that wavelength finally escapes.

However, AIRS has thirteen wavelengths in the band around 15 μm that it regularly uses for detecting CO2 where each channel gives it a slightly different perspective on the gas -- a bit like what we get with two eyes. Now when you look at things with only one eye you can't tell how far away something is just by looking at it. But when you have both eyes open your brain is capable of combining the two views to give you a three-dimensional perception of the world. Objects which are closer stand out from the more distant background -- due to the brain's use of triangulation.

In much the same way AIRS' access to so many different channels makes available to it a much richer world than would be possible with just one channel. Using the appropriate weighting function AIRS is able to combine the information from the different channels and estimate CO2 levels at a given altitude in the mid-troposphere independently of temperature. Please see for example M.T. Chahine, et al. (2008) Satellite remote sounding of mid-tropospheric CO2, Geophysical Research Letters, Vol. 35, L1707,doi:10.1029/2008GL035022.

Alternatively, if one were to assume that CO2 is "well-mixed" with a distribution estimated according to a model, one might then try to estimate temperature using lines in the CO2 spectra. This approach has actually been used before. However, AIRS is able to estimate temperature indepedently of assumptions regarding the homogeneity gas concentrations through the use of a weighting function employing eight different spectral channels. (Please see: M. Chahine (March 7-10, 2006) AIRS CO2 Retrievals Using the Method of Vanishing Partial Derivatives (VPD), AIRS Science Team Meeting, Caltch-Pasadena, CA.) Undoubtedly a good thing, because while the variation is slight, AIRS has shown that there is greater variation in CO2 concentration than one would expect simply on the basis of model calculations.

Satellite measurements differ considerably in how they are done from the more traditional airborne flask measurements. Among other things a flask is only able to sample air from a specific location, but the analysis can be done in the lab, whereas a satellite image has to peer through the upper layers of the atmosphere if it is to view a specific layer deep within, but it is capable of simultaneously observing a large part of the Earth. Nevertheless, these satellite measurements show close agreement with airborne, better than 2 ppm. (ibid., Chahine, et al. (2008))

In this case the two large regions of dark red represent high concentrations of CO2 coming off of the densely populated, industrialized US coasts at about 8 km. Plumes rising up from our larger cities, already beginning to be whipped around the globe by the jet stream. Another much smaller region of dark red is below them in the shadow. CO2 being released by plant decay in the South American winter prior to being taken up during the growth season of their Spring.

The image is based off of monthly data from July 2003. Deep blue represents about 360 ppm by volume -- but you will see that only around Antarctica, cyan is about 375 ppm, yellow 377, and deep red about 380 ppm. In July of 2003 just about the only places you would see that over large areas were around the coasts of the United States. But by 2010 virtually the whole globe would be deep red -- if you didn't slide the key forward with the general rise in CO2 concentrations. You can read more about the data this image is based off of here: NASA: Aqua/AIRS Global Carbon Dioxide. (2003.07) [archive]

The satellite image demonstrates that just as increasing the levels of CO2 in a tube within a laboratory reduces the amount thermal radiation that is able to make it from one end of the tube to the other, increasing the levels of CO2 in the atmosphere reduces the rate at which radiation escapes to space. Now if you reduce the rate at which radiation escapes to space but keep the rate at which radiation enters the system the same then energy must accumulate in the climate system. This follows from the principle of the conservation of energy, and this is what raises the average temperature of the globe. And the temperature will keep on rising until the increased infrared luminosity compensates for the increased concentrations of CO2 in the atmosphere -- so that the rate at which energy leaves the system is equal to the rate at which energy enters the system.