OK. let's put it as simply as possible. Is there a mathematical/theoretical basis for assessing the likelihood of a IR photon from the surface running into a CO2 molecule in its journey through the atmosphere?

I am aware of the modtran/hitran data sets but I kinda assumed they were all empirical and designed to answer USAF/USN requirements for missile and IR detection purposes. Correct me if I have that wrong.

Bonus points for matching the theory and the measurements!

Are you sure ppmv is the right measure? Not partial pressure, which would at least give an equivalent to density where ppmv does not?

And if all CO2 molecule are hit, we still don't know how many photons get clean away.

Yes Dung, but i'm trying to get there by a logical sequence. Although satellite measurements have recorded a change in absorption in the CO2 bands. One of the bands is (possibly) still changing, the other not. This is on the Harries et al paper which promised much but failed to deliver for whatever reason. Still no link between theory and measurement on the GHE is apparent. I wonder why.

I understood modtran and hitran to be based originally on measurements then translated to models. I see now there is no such claim in the current editions, so models it is. I see that there is an ongoing effort in the apectroscopic community to refine the models in the light of new measurement techniques. All to be commended, and I suppose we should accept them as mostly right most of the time.

I think everything will radiate IR at night until it reaches 2.75K or morning comes. You can it seems produce ice in the desert by radiative methods if the sky is clear.