The average amount of time that passes between when a molecule of CO2 in the atmosphere
absorbs a photon until it emits one (the relaxation time) is about 6 microseconds (values from 6 to 10 microseconds are reported) .
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Heat is conducted in the atmosphere by elastic collisions between molecules.
The average time between collisions of molecules in the atmosphere at sea level conditions is less than 0.0002 microseconds .
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Thus it is at least 6/0.0002=30,000 times more likely that a collision will occur (thermal conduction) than a photon will be emitted.
The process of a molecule absorbing the energy in a photon and conducting the energy to other molecules is thermalization.
Thermalized energy carries no identity of the molecule that absorbed it.
Thermalization explains why CO2 (or any other gas which does not condense in the atmosphere) has no significant effect on climate.
Thermalization results in the influence of CO2 on climate to be not significantly different from zero.
There simply is not enough time, by a factor of about 30,000, for the molecule to emit a photon.
Humid nights cool slower than when the air is dry, because the energy in the radiation from the surface is thermalized,
(mostly) by
water vapor warming the air.
At low altitudes, any photons that emit from the jostling molecules are thousands of times more likely to be absorbed by water vapor molecules than CO2 molecules. At extremely high altitudes, ca 30 km, the situation reverses, there are very few water vapor molecules and the time between collisions becomes the same or lower than the relaxation time so CO2 radiant emission to space dominates.