I understood what you were trying to do Samwik, and I could at least follow your argument, I could just see the simplification wouldn't work as I think you have now worked out.
The problem is that "greenhouse effect" is not a simple thing to understand and indeed the greenhouse effect on earth as a planet doesn't even work the same way as the greenhouse after which it is named. I would argue the name of the effect should actually should be changed which would help layman. It took months of arguing to get wikipedia to actually accept the analogy was faulty and the article still contains some errors.
As the process is very complicated and then you get the next problem you correctly identified in this quote
It’s become apparent, in discussing the greenhouse effect with Paul on the climate-science forum, (as you may notice on this forum) that he doesn’t correctly or completely enough, understand the actual processes or mechanisms by which physical reality operates; and yet he uses his misconceptions as proof …to disprove the validity of the physical sciences needed to understand climate.
That is true of every layman discussion I have ever seen on the subject, it's just the how out of depth that varies.
As you probably guessed my background is hard sciences and I care little about the result and politics, what I care about is that people don't butcher the physics.
The problem with the photon story is that a photon in the range of 4-100um has the mean free path of about 25 meters here at around sea level. You guys didn't even discuss and I suggest even know what that means. It basically mans an IR photon emitted off the earth as such won't make it 25m before it is absorbed by the atmosphere. Do you see the problem with the bouncing photon you are trying to tell me its going to climb up thru a couple of km of atmosphere 25 meters at a time. That isn't remotely what happens.
The story is the same as a garden hose or an electron in a wire you can't follow the movement of an individual electron or molecule of water.
A related question we sometimes get asked is how fast does an electron move thru a wire. That we we can answer and it's called drift velocity and it has simple mathematics.
http://resources.schoolscience.co.uk/cda/16plus/copelech2pg3.htmlIt's funny Layman imagine electrons flying thru wires at some incredible speed the reality is like in the worked example 5 amps in 0.5mm area cross section wire the electron moves at a slow tenth of a mm per second. The same situation exists for H2O molecule in a hose.
The movement of the IR energy thru the atmosphere looks much more like the hose or wire situation and I can always tell peoples understanding of the physics in how they discuss it. One of my concerns with climate scientists is many don't themselves understand the movement of the energy.
For example the roll of Nitrogen (which makes up 78% of the atmosphere as N2) is important. It shares a resonant frequency with CO2 and the two can easily kinetically exchange energy. The N2 can not emit the energy as a photon (its a Homonuclear molecule) and it stays in the N2 a long time ... hint it might move a fair way in that time in the atmosphere before it bumps into another CO2 molecule and gives the energy back.
There are in fact hundreds of these pathways and they do not all change the same with changing CO2 levels.
The reason the Earth doesn't rapidly change between -180 and 300 deg C is also telling you the energy isn't just transparently moving thru the atmosphere. The atmosphere itself must be holding onto some of the energy so it has the thermal equivalent of inertia. That is also obvious in that the temperature profile thru the height of the atmosphere.
The lesson here is the free mean path of an IR photon in the atmosphere is small and the photon bounce story thru the atmosphere as some fully transparent media is fanciful.
