There are as many theories as there are mechanisms in climate science. So the debate will never end. I would be nice to have a starting point to, at least work from, so I may be able to better understand some of the more exotic theories.
I start with a ball in space with a surface temperature of 288K degrees and see what happens. Not much to work with here so there should be little to debate. Space has a temperature of about 3K degrees. The tropopause has a temperature of about 213K degrees. If you consider that the average minimum temperature is less than the starting temperature, there is an average rate of cooling by all thermodynamic means. The average minimum surface temperature of the Earth is... it doesn't exist.
It has been used by botanists to determine change in plant growth with global warming. It is not a big glossy iconic banner of climate science doomsayers though. Nocturnal global average temperature is rising greater than the average global temperature is rising. How much doesn't seem to be all that important to some, but it is the strongest "signature" of radiant impacts on surface temperature. Global average maximum temperature is not rising at the same rate. That would be the strongest "signature" of the Earth's response to radiate enhanced global warming. We only get to see the average, not the average of the averages. this is an interesting omission due to the complexity of determining just the average. Not a simple problem it seems.
A way around that, not great but somewhat informative, is to use the average cooling rates. This is tricky since the exact rates are complex, but we do have estimates from before NASA got kicked out of the Earth Energy Budget business thanks to currently not so trust worthy alarmists. NASA had a budget that indicated that conductive (a combination of conductive and convective) was 7%, the Latent (possibly missing the sensible portion of latent cooling) was 23%, and radiant total was 21%, of all of the energy absorbed by the surface from solar. Assuming these are reasonable proportions of the nocturnal emission, then 13.7% for conduction, 45.1% for latent and 41.1% for radiant. These values were for a surface temperature at the time of 288K degrees producing 390Wm-2 of outgoing long wave radiation, which should be approximately the total energy leaving the surface, on average. Then as nocturnal flux, 53.3Wm-2 for conduction, 175.9 for latent and 160.9 for radiant. If you look at it this way you see that all three play a significant role in surface cooling.
The temperature of the tropopause being approximately 213K or -60C degrees, radiates 117Wm-2 by the S-B equation anyone reading this should know and love. So if we subtract that from 390Wm-2 we would have 273Wm-2, the amount of surface energy that interacts with the atmosphere up to the tropopause. 117Wm-2 would be the amount that could be considered the "tropopause greenhouse emission rate". This is a value just for determining the magnitude of the individual out going fluxes on the troposphere.
The big question is the radiant part of this puzzle, so the greenhouse effect of the tropopause only to nocturnal outgoing long wave radiation would be 117/160.9=0.727,or an emissivity of 0.727. Yes, there are other impact in the atmosphere, but we live on the surface.
Typically, the top of the atmosphere emissivity is use to determine the impact of a 3.7Wm-2 increase in forcing for a doubling of CO2. I personally believe that is happy horse hockey. But the math used is a series that reduces to F(surface)=1/(1-emissivity), which would yield, 1/(1-0.727)=3.66 or that the 3.7Wm-2 would be felt as 3.66*3.7=13.56Wm-2 at the surface, for my Tropopause greenhouse effect estimate.
So my estimate indicates more impact of forcing at the surface would be caused. But there is one other thing to consider, as the portion of the outgoing radiation reflected increases, the other fluxes, conductive, latent and the non-interactive radiant would increase. Energy will find its path of least resistance.
NASA kindly included the percentage of outgoing that interacts, 15% which using the ratio as before indicates that 29.4% of the outgoing would interact with the atmosphere, the remainder would be atmospheric window spectra. Some of this interaction is likely above the tropopause, but this is an estimate.
Latent and the atmospheric window fluxes should be unarguably cooling at the surface. NASA indicates that 6% of the 51% emitted from the surface is atmospheric window radiation which would become 11.8% of the surface flux, 46Wm-2, in my example. If the surface flux were to increase by 13.56Wm-2 due to the doubling, or 13.56/390=0.035 or 3.5%, then latent and atmosphere radiation would increase by 3.5%, (175.9+46)=221.9Wm-2, would increase to 229.7 or by 7.7Wm-2. The net warming due to the doubling would be 13.56-7.7=5.86Wm-2. This is just an estimate, don't go crazy yet.
The surface temperature at 395.86Wm-2 would be 289.06K or 1.06C degrees of warming felt at the surface. So how does that compare to the actual measurement since the preindustrial period? Since it is assumed that the impact is a natural log function solely of the change in concentration of CO2, we are now at 390PPm versus the assumed 280PPM initially or ln(390/280)= 0.33 or the ln(2)=0.69 for 0.33/0.69=0.48 or 48% of the way home. 48% of 1.06 is 0.51 degrees. This is a little less that the current warming by about .2 degrees depending on the time period you assume provides the average for the preindustrial period.
There are a lot of assumptions in this example, as there are a lot of assumptions in all the theories. CO2 does have a radiant impact, the question is how much of a radiant impact it has on the surface, globally. I contend that this is just as reasonable an estimate as any other given the complexity, even using the basic methods used to estimate the much greater impact some suggest, only the tropopause is considered as a thermodynamic boundary.
What this does do much better, is give a reasonable perspective of the negative feedbacks that should be expected, all things being equal of course. There are a lot of things I could have done to make this appear to be a more valid estimate. Those would be futile given the uncertainty involved, there is only so much a turd can be polished.
Oh, By the way, the tropopause gets little respect, it is a major thermodynamic boundary that is not changing as estimated. While there a lot of things that are complex, this is one that would seem to be the most critical to understand.