I recently (Spring 2018) ran into someone who denied carbon dioxide's
greenhouse effect in the atmosphere; which I have simply known for years, but
had never examined in detail. So I googled, in the course of which I found a
paper by a climate denialist claiming that, since the carbon dioxide re-emits
the light it absorbs, absorbing it doesn't make any difference. This is wrong
in so many ways. The paper also gave one graph of black-body radiation
which was just one big long curve over a broad range of frequencies, with no
indication that the actual shape varies with the temperature of the black body
doing the emitting. This is rather important.
So first let's look at re-emission. When a molecule (or atom – there are some) in the air absorbs radiation, most of the absorbed photon's engergy goes into exciting the internal modes of the molecule. At higher frequencies, i.e. energies, this may knock an electron out of an atom's ground state pattern of orbitals into one of the orbitals that's normally vacant; at lower energies, the molecule's geometry can wiggle (e.g. in a CO2 molecule, with each oxygen double-bonded to the carbon O=C=O, the angle between bonds from carbon to the two oxygens can vary, allowing oscillations in this angle, for example) in various ways. The details aren't crucial: the molecule has internal states that support many possible energy levels and will absorb a photon that kicks it from the state its in into some other state. When that happens, it puts the molecule into an unstable state, from which it can decay back to its ground state by emitting the sae photon it absorbed.
However, the molecule can typically also decay back to the ground state via various intermediate states, in which case it'll emit a succession of photons, of lower energies than the one it absorbed. In the case of a high-energy photon knocking an electron out from an inner orbital to a normally vacant one, for example, that electron could drop back to where it was, emitting a photon of the same frequency as knocked it out; however, other electrons of the same atom, that were in filled orbitals further out than the one that now has a vacancy, may get round to dropping down into that slot first, moving the vacancy further out; and the escaped electron may drop back via any vacant energy levels there may be in between. There are thus far more ways for the atom to re-emit the energy it received than just in the form it arrived – unless the electron knocked out was in its outer-most occupied orbital and was knocked to the immediately next orbital out, which leaves no smaller step by which to return. Likewise, for the more geometric internal modes at lower energy, the energy absorbed from one photon can commonly be emitted in several.
So the spectrum of light coming off a gas that's absorbed some tends to be blurred and at lower energies than the spectrum absorbed. There are more ways for gas in the atmosphere to absorb lower-energy photons, so this tends to make the energy more apt to be re-absorbed again – and, thus, again and again. Furthermore, at each absorption and re-emission, the emission's direction is independent of that of the absorbed light, so the energy gets a chance to be routed back down to the Earth's surface rather than escaping.
In any case, even if the re-emitted photon was of the same frequency as the absorbed one, simply because the energy is being repeatedly absorbed and re-emitted, its journey through the atmosphere isn't a nice straight line at the speed of light, like the incoming visible light from the sun; it's a random-walk with delays (between absorption and re-emission) through the depth of the atmosphere. The size of the steps in that walk depends on the optical density of the atmosphere at the photon's frequency: if that frequency is within the absorption spectrum of carbon dioxide, increases in the carbon dioxide concentration will shorten the length of the steps in the walk, causing those photons that do escape to take longer about it – they take more steps, each of which involves a delay between emission and re-absorption. As each step also randomly changes the direction, more steps means more chance to end up headed back towards the ground. So, even when emission hasppens at the same frequency as absorption, the energy – carried by photons at a frequency in the absorption spectrum of a constituent of the atmosphere – only diffuses slowly out of the atmosphere, in contrast to sunlight's express arrival by the shortest path.
Meanwhile, each time a molecule absorbs or emits a photon, that photon has momentum, which changes the momentum of the molecule. Some of the time, this will slow the molecule, some of the time it'll speed it up; usually it will change the direction in which it's moving, either way. The (magnitude of the) momentum of the molecule determines its kinetic energy, which is its contribution to the thermal energy of the gas of which it's a part. So those changes in momentum can move energy between light and the gas that's absorbing and emitting it. The fine detail of which way energy flows on average need a lot of trouble to work out; but, fortunately, we don't need to. The second law of thermodynamics says that, on average, heat flows from warmer to colder in so far as there's thermal contact; and the coupling between light and molecules does indeed ensure thermal contact. The light is black-body radiation at the temperature of the Earth's surface; the gas is the atmosphere above it. In the troposphere (the thick gooey part of the atmosphere where most of its mass is), temperaature drops off with altitude, so the upper troposphere gets warmed by the Earth's black-body radiation on its way out; and the rate (hence the extent) at which it is so warmed increases with the number of times that black-body radiation's photons get absorbed and re-emitted on their way out, which increases with the concentration of any gas whose absorption spectrum has a significant peak in the range of frequencies near to the black body radiation's peak (where the greater proportion of its power is carried).
So re-emission doesn't prevent atmospheric carbon dioxide from reducing the rate at which Earth radiates away energy; indeed, absorption and re-emission are an integral part of the process by which escaping energy is delayed in its escape, causing there to be more warmth in the atmosphere than there would be with less carbon dioxide.
Now, all of the above actually also applies to the infra-red component of the Sun's in-bound radiation; however, the sun's in-bound radiation has its peak energy content in the visible and near-visible frequency range; so slowing the arrival of energy in the infra-red (and giving it a greater chance to be radiated back away from Earth, before it arrives) makes little difference to the rate at which the Sun warms the Earth. The black-body radiation The Earth (which is rather cooler than The Sun) radiates is at lower frequencies; and a larger proportion of it is in the frequency-ranges where carbon dioxide has strong absorption. So the carbon dioxide makes a bigger difference to the rate at which Earth loses heat than to the rate at which it gains heat; and this will cause Earth to warm, on average.
Written by Eddy.