Bad vibrations

Bad vibrations? A brief explanation of the heat trapping properties of CO₂

I'm pickin' up good vibrations
She's giving me the excitations
Brian Wilson / Mike Love / The Beach Boys

Basic mechanism for the absorption of radiation

When radiation (visible light, infra red, ultra violet …) impacts an atom or a molecule, if the frequency of that radiation matches the natural resonant frequency of the molecule energy it is momentarily absorbed, 'exciting' the molecule into a higher energy state. After a short time the same amount of energy is re-radiated and the molecule returns to its normal or 'ground' state. Although the radiation is only 'borrowed' this capture/release is nevertheless an absorption mechanism, because the re-radiation occurs in a random direction so in the simplified 1-dimensional case there would be a 50% probability the radiation were sent back in the direction it came from. It can be readily understood that for a sufficiently deep and concentrated layer of molecules, this scattering and attenuation could amount to absorption

The three main component gases of earth's atmosphere (diatomic Nitrogen and Oxygen, monatomic Argon) are transparent to heat (infrared) radiation. Or, in terms of the explanation in the previous paragraph, these molecules' bonds are too rigid, too 'highly strung' to respond or resonate to frequencies in the infra-red

Molecules with three (or more) atoms are different. Additional bonds provide more ways to twist and bend the molecule and in the same way it takes much less energy to bend a ruler than to stretch it, these vibrational modes match specific infra red wavelengths / frequencies. All the 'greenhouse gases' (Carbon dioxide CO₂, Water vapour H₂O, Methane CH₄, CFCs etc.) are molecules with three or more atoms

Relevance to the 'Greenhouse' Effect

Presence of the above mentioned gases in the atmosphere contribute to the Earth being warmer than it would otherwise be. In fact without any greenhouse gases in the atmosphere Earth would be frozen solid with sub-zero temperatures across the globe.

The analogy is drawn between a warmer-than-expected Earth and a greenhouse which allows tropical plants to grow in a temperate climate. The mechanisms for both are:

• Solar energy in the visible light portion of the spectrum shines straight through the atmosphere / glass panels, which are transparent to light
• Earth / greenhouse plants warm and re-radiate energy as infra red radiation - invisible to human eyes
• Heat radiation increases with absolute temperature to the fourth power, so (°C + 273)⁴. A 0.1% increase in temperature results in a 0.4% increase re-radiated heat
• If the air / glass panels were completely transparent to infra red (heat) radiation the temperature would increase until an equilibrium were reached where energy in = energy out
• Given the air / glass panels are partially opaque to infra red, the heat has to 'try harder' to escape - as the system is temporarily in a non-equilibrium state, temperature rises until a new equilibrium point is established

Specific absorption characteristic of CO₂

The CO₂ molecule can stretch asymmetrically, stretch symmetrically and bend parallel or perpendicular to the double bond O=C=O. The wave numbers for these four modes are 2349 cm^-1, 1340 cm^-1, 667 cm^-1 and 667 cm^-1

The second, symmetric stretching mode is IR inactive (does not absorb heat radiation) because:

"there is no change in the net molecular dipole"

an explanation for this - and the additional absorption at wave number range 3600-3800 cm^-1 is beyond the scope of this page

Nevertheless the salient features of the interaction between infra-red radiation and CO₂ are the absorption peaks (or transmittance 'notches'):

• Asymmetric stretching at wave number 2349 cm^-1
• Bending (both modes) at wave number 667 cm^-1

These bending modes are illustrated below along with a graph of infrared transmittance (scale 0=opaque to 100=transparent) versus wave number related to CO₂ levels at the present day

It is also instructive to see the effect of increasing CO₂ levels on transmittance. While increasingly high concentrations will, eventually completely block infra red radiation at the relevant wave number transmittance cannot drop below zero. At other wave numbers / lengths frequencies the atmosphere remains transparent to IR. The numerical value inset in the animation below refers to ppm CO₂

In conclusion

FLUKE is not counselling complacency about rises in CO₂ levels in the atmosphere, merely observing:

• CO₂ blocks SOME frequencies of IR radiation. Once they're blocked, they're blocked - and further rises have little additional effect
• Temperature rise results in a non-linear (fourth power) increase in IR relation
• Ice will undoubtedly melt, sea levels will rise, extreme weather become more common. The Earth won't catch fire