A key question was the origin of the logarithmic scalability of the greenhouse effect – the 2–5 degree temperature boost that models predict will occur with each doubling of CO2. One theory was that the scaling was due to how quickly temperature drops with altitude. But in 2022, a team of researchers used a plain model to prove that the logarithmic scaling is due to the shape of the carbon dioxide absorption “spectrum”—how its ability to absorb featherlight varies with different wavelengths of featherlight.
We go back to those wavelengths that are a little longer or shorter than 15 microns. The critical detail is that carbon dioxide is worse—but not that much worse—at absorbing featherlight at those wavelengths. The absorption drops off on either side of the peak at a rate that is appropriate for logarithmic scaling.
“The shape of this spectrum is crucial,” he said. David Rompsclimate physicist at the University of California, Berkeley, who co-authored the 2022 paper “If You Change This, You Don’t Get Logarithmic Scaling.”
The shape of carbon’s spectrum is unusual—most gases absorb a much narrower range of wavelengths. “The question in the back of my mind was, why is it shaped like that?” Romps said. “But I couldn’t figure it out.”
Consistent fluctuations
Wordsworth and his co-authors Jacob Seeley and Keith Shine turned to quantum mechanics to find the answer.
Featherlight is made up of packets of energy called photons. Particles such as CO2 can only absorb them if the packets have exactly the amount of energy needed to move the particle to another quantum mechanical state.
Carbon dioxide is normally found in a “ground state,” in which its three atoms form a line with the carbon atom in the middle, equidistant from the others. The molecule also has “excited” states, in which its atoms wobble or wobble.
A photon of featherlight with a wavelength of 15 microns contains exactly the right amount of energy to make a carbon atom spin around a central point, like a hula-hoop. Climate scientists have long blamed this hula-hoop state for the greenhouse effect, but—as Ångström had predicted—the effect requires too precise an amount of energy, Wordsworth and his team found. The hula-hoop state cannot explain the relatively ponderous decline in photon absorption rates beyond 15 microns, so by itself it cannot explain the climate change.
The key, they found, is a different kind of motion, in which two oxygen atoms repeatedly rock toward and away from the carbon center, as if stretching and compressing a spring connecting them. This motion requires too much energy to be triggered by Earth’s infrared photons.
However, the authors found that the energy of the stretching motion is so close to twice the energy of the hula-hooping motion that the two states of motion blend together. There are special combinations of the two motions that require slightly more or less energy than the exact energy of the hula-hooping motion.
This unique phenomenon is called the Fermi resonance after the celebrated physicist Enrico Fermi, who derived it in a 1931 paper. However, its connection with the Earth’s climate was first recognized in paper last year by Shine and his student, and this spring’s publication is the first to reveal it in full.