Shakespeare was a pretty good communicator. I do a good job with my audience, fishermen. When it gets to academic communication, I need a Redneck to geek translator.
I say frame of reference is the first consideration in thermodynamics, the geeks think I am miss applying the meaning of frame of reference. WTF?
I say increasing the thermal conductivity of air changes the rate of heat flow, I get blank stares.
I say you have to recognize the boundary layers before you can formulate a solution and all I hear is chuckles.
That is the nature of a complex problem, some easy solutions appear masking the more complex relationships.
Radiant forcing is an easy solution. Different molecules respond to different wavelengths or photon energies producing an impact, obvious in the radiant transfer of energy. The not so obvious is the interactions of the change in energy flux or flow with other molecules and other methods of energy transfer. There are critical points where the interactions need to be understood.
Saturation is a critical point in radiant heat interaction. Since molecules are limited in the spectrum or range of photon energies they can absorb and emit, as they approach a saturation point, where all energy levels are occupied, reactions and interactions have to change. The changes depend on the environment where saturation occurs, temperature, pressure, composition of molecules, relative velocity of molecules and relative energies of molecules, to name a few.
Two that appear to be more important than considered are the relative velocities and energies. When a radiant spectrum range reaches saturation, it not long can change the relative velocities or energies with the addition of more absorbent molecules in that spectral window. For there to be a change in impact there has be be a change in one or more of the other variables, temperature, pressure or composition. Adding more of just the same molecule in the saturated spectrum produce interesting changes.
At perfect saturation, all the interactions are at a maximum. The average relative velocities and energies are maximized for maximum interaction with the condition it that environment. Adding more molecules in that radiant spectrum reduces the distance between the similar molecules which changes the average relative velocity and energy of the photon exchange. This increases the probability that the photons involved in the interaction can match the energy and wavelength of other molecules with a different radiant spectrum. This would cause a broadening of the overall radiant spectrum of the environment. This is the effect found useful in laser technology. Energized photons in a chamber designed to reflect photons above or below a desired wavelength bounce back and forth until their relative velocity and energies match that of another molecule in the desired emission spectrum.
For a CO2 laser, the peak energy wavelength is close to but not exactly equal a nitrogen spectral peak. With the right chamber dimensions and the right excitation, the relative velocities and energies of the two molecules match closely enough for the nitrogen molecule to emit the absorbed radiant energy at the wavelength the discharge mirror is tuned to release. Nitrogen lases.
Since most molecules have emission spectra inclusive of a number of wavelengths, without the tuning of the discharge mirror, other lasing wavelengths which can also be excited are contain in the lasing chamber. All of these other wavelengths are less energetic than the desired peak wave length. Contained in the chamber, they can either climb up, step by step toward the peak wavelength or down to a weak energy wavelength. Nitrogen is a good lasing gas, because its peak energy wavelength is relatively isolated from weaker wavelengths.
In a mixed gas environment, the number of weaker energy wavelength increases. Once the maximum energy wavelength is saturated, the probability of weaker wavelength excitation increases, effectively stepping down the peak absorption and spreading the energy more uniformly across the entire spectrum of the environment. Wavelengths, where there is an easier path to de-excite or emit the energy will allow photons to leave the local environment freeing that wavelength for excitation yet again.
If we continue to add molecules in an open environment, the molecules will diffuse uniformly through the environment within the limits of their physical properties based on temperature, pressure and the limits of gravitation and magnetic/electric field constraints. As the environment of the individual molecules change, the path of least resistance for emission changes. Spectral broadening in one environment leads to increased excitation in the weaker spectral energies increasing rate of photons finding an unoccupied transmission frequency/wavelength. Due to the force of gravity, free emission windows increase with the reduction of gravity which reduces the density of molecules and in our atmosphere, the average temperature/energy of the radiant spectrum. Increasing the concentration of one type of molecule increases the average height of the effective maximum radiant layer of that molecule's spectrum relative to the surface.
Below this average maximum energy layer, the average relative velocity and energy decreases. At lower energies, the conductive properties of the environment are enhanced. Some molecules, water vapor for example, have nearly constant thermal conductivity. Other molecules, carbon dioxide for example, have nonlinear thermal conductivities. Once radiantly saturated, the thermal conductivity of both of these molecules are enhanced. The enhancement is greatest from water vapor where the concentration of water vapor is the greatest. The enhancement of carbon dioxide is greatest where the concentration of water vapor is the least. Both molecules are in competition for the available energy.
So I find, that the change in forcing is equal to 5.35ln(Cfinal/Cinitial) a bit simplistic. I am rather surprised that so few seem to agree.