T8. Carbon Dioxide and Atmospheric Radiation

One of the factors that is more and more being considered in deciding how the nations of the world will, in the future, provide energy for their inhabitants relates to the amount of carbon dioxide generated as each converts various forms of fuel into energy. The simplistic explanation often given for global warming is that the increase in carbon dioxide molecules in the atmosphere reflect more of the Earth’s energy back in the same way as a “greenhouse” works, but it is actually a little more complicated than that, and so the tech talk of the day is going to be about what actually happens. I’m going to base it somewhat on the book “Climate, Present, Past and Future,” by H.H. Lamb.

If I heat a piece of iron, as the temperature of the iron goes up, it will radiate energy and we would see this by a change in the color of the light it puts out. As the iron gets hotter the light changes from red to orange and then yellow. This is a change in the wavelength of the energy being radiated. Sensibly the hotter the object gets, then the shorter the wavelength of the maximum energy transmitted. This is true for all objects that are hotter than their surroundings, including the Sun and the Earth. (This is Wien’s Law.) The energy comes to the Earth from the Sun it is in a package of wavelengths that are very short (below 4,000 nanometers or 0.000000004 meters) and about half of the energy is contained in the band that is visible light (400 to 740 nm). However the Earth is a much cooler place than the sun and so the energy that it radiates back out is in a different range, generally between 3 and 100 microns (μm) (3,000 to 100,000 nm). The difference changes the way in which the energy interacts with the atmosphere through which it passes, either going in or coming out.

Change in the wavelengths of energy coming and going through the atmosphere


The atmosphere is, itself, made up of different gases, and particles. These both absorb and reflect some of this energy. Energy reflection generally comes from the particles, dust, such as that from the recent eruption of Mt Redoubt in Alaska. These can scatter and reflect both energy coming in and going out. When there are a large number of eruptions, or one or two individually very large ones, then the dust thrown high into the atmosphere will reflect the sun’s energy before it reaches the ground, and with less sun, the globe cools. It has even been suggested that particles could be artificially placed in the stratosphere to reflect sunlight and counterbalance warming. Most of the radiation that is reflected, however, is reflected back from the tops of clouds, or from reflective surfaces once the energy hits the Earth’s surface. Thus, of the energy coming in at the top of the atmosphere only some of it makes it through to the ground.

Solar Energy through the atmosphere as a function of frequency (Source Wikimedia Commons)

The smooth curve at the top of the atmosphere has been chewed up a little by the time it reaches the ground. This is because some of the gases in the atmosphere absorb the energy in certain wavelengths. Thus, for example, the ozone layer at the top of the atmosphere, although thin will absorb the entire energy spectrum below 290 nm, so none of that gets through. In a similar way the oxygen in the air and water vapor absorb all, or a large portion, of the energy in other wavelengths within the spectrum, as shown. Note that with relatively little of the energy being in the longer wavelengths, the role of carbon dioxide on incoming energy is very limited.

When the Earth re-radiates the energy it has received, it has changed the spectrum of distribution, and it is at these longer wavelengths that the carbon dioxide and other gases play their role. The amount of CO2 is not that great (Lamb quotes it as being equivalent to a layer at the surface 2.5 to 2.8 cm thick, or just over an inch), yet it is sufficient to absorb all the radiation between 4.0 and 4.8 μm. But this is the important quote

In the absence of water vapor, the carbon dioxide at present in the atmosphere would absorb 15-20% of the total energy emitted from the Earth. Water vapor is, however, a still more effective absorber of radiation on most of the same wavelengths as CO2, and linked together they appear to absorb ALL (my caps) the terrestrial radiation greater than 14 μm. So it seems that changes in the amount of carbon dioxide in the atmosphere can only affect wavelengths in the CO2 band about 4.3 μm, and between about 12-14 μm, for which the wave length absorption by water vapor is incomplete. In the stratosphere, where the quantity of water vapor is small, absorption by carbon dioxide just over a narrow band about its maximum at 14.7 μm exceeds that by water vapor.

Lamb goes on to note

Absorption curves reproduced by Shaw in 1930 and Plass in 1954 indicate that, in the absence of water vapor, the carbon dioxide in the atmosphere would absorb ALL (my caps) the radiation between 12.5 and 17.5 μm emitted by the Earth’s surface (taken as having a mean effective, or overall mean, temperature of 288 deg A), this main absorption band alone accounts for 14% of the Earth’s emission. In fact, however, the water vapor present absorbs in the lower atmosphere almost all the radiation between those wave lengths emitted by the surface wherever temperature is over 283 deg A, and its re-radiation returns much of this to the Earth; so the influence of CO2 must be limited to the colder, drier climates and seasons, and to higher levels of the atmosphere.

The point that should be noted is that, even at the lower concentrations of CO2 in the atmosphere when the book was written, the carbon dioxide was absorbing all the radiation that was available in the frequency ranges over which it is effective. Changing the concentration of the gas in the atmosphere does not increase the amount of radiation being captured, all that can be already is. This was pointed out to by one of my colleagues who is an authority in this field a couple of years ago. The only difference that increasing the concentration makes is that it allows the energy to be absorbed that much closer to the ground, but the difference is relatively trivial.
As William Happer noted in his recent testimony before the Senate Environment and Public Works Committee

There is little argument in the scientific community that a direct effect of doubling the CO2 concentration will be a small increase of the earth’s temperature -- on the order of one degree. Additional increments of CO2 will cause relatively less direct warming because we already have so much CO2 in the atmosphere that it has blocked most of the infrared radiation that it can. It is like putting an additional ski hat on your head when you already have a nice warm one below it, but you are only wearing a windbreaker.

I will tackle the role of methane, methane hydrates and permafrost and water vapor in future notes.