I was a bit reluctant to write this article, since it is certainly a horribly annoying issue. There are no insights to be gained here, at least not with regard to climate science. It is only about cleaning up a horrible mess. The only thing making it worthwhile is in pointing out how stupid people are. And with people I mean "experts".

You may have heard that the GHE shall violate the 2nd law of thermodynamics, since the relatively cold atmosphere is supposed to warm the warmer surface. Heat does not flow from cold to warm, you know. The discussion on it is endless and equally useless. Then there are people who deny back radiation all together, and others who "prove" the GHE by measuring back radiation in some way. On top of that there are people who find a flaw in the back radiation based GHE and claim to have falsified the GHE altogether. It is a perfect shit show!

The cause for all this mess originates from the claim that "back radiation" would cause the GHE. That is a "consensus science" claim. The German term "fremdschämen" would most accurately describe how I feel about it. It is idiocy by the power of 4. Let us straighten this out once and for all in three simple steps.

1. Radiation is a function of temperature, as the Stefan-Boltzmann law tells us. Thus "back radiation" is a function of the temperature of the atmosphere. I hope we can all agree so far.
2. The temperature of the atmosphere is a function of the surface temperature. At least the climate models have it that way. Yes there is this discussion on the "hot spot", which is a mess on its own. But obviously atmosphere- and surface temperatures are interconnected.
3. If you try to explain the surface temperature with back radiation, you eventually have gone full circle!!!

It is indeed that damn simple! It is circular reasoning par excellence. Of course in "climate science" circular reasoning is not circular reasoning, but a "feedback", which seems to be a "scientific" discipline on its own. It is certainly a gift that keeps on giving, as long as you can fool donators you were on to something. That should be enough to sort out the mess.

Just in case it is not, we can iterate the perspectives on the idiocy. What would happen with "back radiation" if temperatures were lower? Obviously it would go down. The same thing inverted if temperatures went up. Maybe you get the point now.

Just in case still not, let us point out another perspective. What if we lived on a planet where GHGs were very heavy and they would accumulate close the surface, as opposed to the rest of the atmosphere. The emission layer was just 100m above the surface, so that emission altitude was marginally higher, emission temperature and emissions were only marginally lower due to GHGs. The GHE would be tiny, almost negligible. Yet "back radition" looking up from the surface would be intense, as you would look into a gas about as emissive as the surface itself.

The same issue applies to real world Earth. "Back radition" is a lot larger than the GHE, whatever magnitude it actually has. This fact alone should be enough of a signal to understand these are separate things. Also you may look up into the atmosphere at any wavelength where it is perfectly opaque and measure the full amount of "back radiation". What you can not see is, at what altitude it will clear up. It could be just ground fog that clears up 50 meters above your head, it could be some spectral line of vapor, clearing up at 3.000m, or it could be CO2 at 15µm only clearing up at some 30.000m altitude within the stratosphere. This emission altitude and with it the emission temperature makes all the difference, but there is no way you could tell by measuring "back radiation", which even technically is no indicator of the GHE.

To make matters worse, some "experts" (and non-experts) have realized the disparity between "back radiation" and "GHE" and so they try to figure out what it means. If someone with a mediocre IQ tries himself in logical reasoning, it is like a child driving a car - the prospects are not good. They will head right for the first possible obstacle they can crash into. In this instance, since "back radiation" > "GHE", they conclude the GHE must actually be much larger!? They back check their theory by looking to the moon (seriously!) which has some arithmetic(!)¹  mean surface temperature of only ~210K and it all seems to add up. With the moon, without atmosphere, being apparently so much colder than Earth, while receiving the same solar irradience, they reason the atmosphere must heat Earth by a lot more than the erroneous 33K. On top of that, based on the "insight" the GHE was actually much larger, some come forward and argue they had falsified the GHE?! Yes, it is a perfect intellectual train wreck!

So no, "back radiation" does not cause any GHE. It has nothing to do with it. At best it is an indication of a (partially) opaque atmosphere, which is a requirement for a GHE, but that is all. The GHE is due to an elevation of the emission layer in combination with the atmospheric lapse rate. Without the specific properties of gases, which adiabatically heat up due to pressure, a GHE would not even be possible. And to be fair I will openly admit that there are quite a lot of "experts" who get this part perfectly right²³. So it should not be much of a secret.