The short answer is – A lot.
If you are performing calculations of CO2 impacts, you look at how much CO2 there is in any one bit of air (concentration) and how far it is from heat source to cool thing (distance). The product of these two things determines how much radiant energy is absorbed by the CO2.
We will use ‘bar’ for pressure (1 bar = 100 kPa) and meters for length, though we will use bar cm for the product (for reasons that will become apparent).
We will start with normal air, 80% N2, 20% O2.
First, displace air with CO2 until the mixture becomes 50% CO2, 40% N2, 10% O2. Let’s all agree that a 50% atmosphere of CO2 is a lot of CO2.
4 meters of this mixture will have a “Path Length” of 200 bar cm.
Now only displace 10% of the air, so 10% CO2, 72% N2, 18% O2
20 meters of this mixture will have a “Path Length” of 200 bar cm and absorb as much radiation as 4 meters of the 50% concentration.
Now only displace 0.039% of the air. Thus about 80% N2, 20% O2, 390 ppm CO2.
5,128 meters of this mixture (at the surface of the earth) will have a “Path Length” of 200 bar cm and absorb as much radiation as 4 meters of the original mixture that was 50% CO2. So over a very long length, 390 ppm is a LOT of CO2.
The atmospheric pressure drops as elevation increases. For the total atmosphere (40 kilometers for calculation purposes), at 100 ppm CO2 throughout, the path length will be somewhere around 67 bar cm (using the ‘standard atmosphere’ equation for change in pressure with elevation). At 390 ppm, the path length is somewhere around 261 bar cm, or more than a 50% CO2 atmosphere over 4 meters. At one time, one could review Leckner’s curves for CO2 absorbance on google books. The page with the curves has been removed from the review of the reference (Bejan, Adrian; Kraus, Allan D. Heat Transfer Handbook. John Wiley &Sons., 2003 Page 618 ). If you go to that book in a library, you will see that at 200 bar cm, the emissivity is nearly identical to that at 100 bar cm and the increase to 500 bar cm is less than that from 100 to 200, over a temperature range from 0 celsius to 2,000 celsius. Beyond 500 bar cm, there is no further impact from increasing CO2. It is at about 100 bar cm that the growth begins to flatten out from the logarithmic that is used in climate models. I will be happy to provide a photocopy of the individual page to anyone who asks, as that is ‘fair use’, but will not post such a photocopy here as that might be construed as copyright violation.
Johneggert's Blog 
John,
I posted a link to your PDF on this on a solarcycle24.com. global warming discussion and got the following reply from a poster called steve, I would appreciate your comments on his reply.
” Re: Greenhouse Effect
« Reply #112 Today at 7:44pm » [Quote]
julian,
Eggert has the curious idea that the “IPCC” formula of 5.35 ln(C/Co) is in some way an input to the model. In fact this formula is an empirical fit obtained by doing the sorts of calculations on real atmosphere profiles that he is doing, but with quite a bit more detail and certainly a lot more thought!
eg. he talks about ignoring temperature differences in the atmosphere! D’Oh!
If he’d done a bit more research he would have known that this calculation comes from: Myhre et al., New estimates of radiative forcing due to well mixed greenhouse gases, Geophysical Research Letters, Vol 25, No. 14, pp 2715–2718, 1998
The temperature differences in the atmosphere are key as the increase in CO2 essentially reduces the ability of warmer lower layers to lose energy to space because more of the radiation is absorbed by more CO2 above. The increased emissivity of the higher layers cannot make up the difference because the layers are colder. “
Hi Julian:
Thank you for your question.
Short answer:
If my method is so flawed, why does it provide the same results as Myhre et al for most atmospheric levels of CO2, only begining to deviate at higher concentrations?
As Steve McIntyre is constantly pointing out, the defence of the ‘science’ of global warming is generally dependant on misdirection. I am aware of the source (and purpose) of the equation. Ignoring temperature differences is not that serious, in my opinion, but yes, that is the major weakness of the paper, though not for the reason given. If the relation between emissivity and concentration is fairly constant from 0 celsius to 2,000 celsius, I think it is not entirely unrealistic to ignore it, though if the person is willing to provide the adjustment required and the resultant emissivities, I’d be happy to incorporate them. Also, there is always a temperature gradient when examining systems. If there were no temperature gradient, there would be no heat transfer. The last paragraph shows an ignorance of the path length approximation (and radiative heat transfer in general). This heating of layers thing MUST be accounted for in all methods. The layer of atmosphere closest to the heat source always heats the next layer, and so on and so on (radiatively, convectively and by conduction, though GHG effects only require an examination of radiative). This is true for a blast furnace as much as climate. As I said, without a gradient, there is no net heat transfer. There is no Xeno’s paradox here. Scienceofdoom and I had a long back and forth about this. His only complaint with my method was the fact that the Leckner work did not extend to the temperatures of the upper troposphere. As I said, this is the weakness of the paper as the curves stop at 0 celsius. There would have to be a HUGE deviation form the shape from 0 to 2000 for there to be a significant impact, different from what I predict. This difference would have to begin to be apparent only at higher concentrations of CO2.
The primary point of the article is: In all other areas where radiant heat transfer in the atmosphere is examined, there comes a time when further increases in CO2 no longer result in further increases in heat absorption. Climate models assert that there is NO point where the logarithmic plot deviates from linearity. That is a strong assertion.
John,
The planet has been falsifying your conjecture for the past sixteen years. Further, Dr Ferenc Miskolczi shows pretty convincingly that the effect of 2xCO2 is 0.0ºC. He certainly knows more than I do about the subject. Do you know more than he does?
Explain why, with the very substantial rise in CO2, there has been no statistically significant global warming over the past decade and a half. Something is wrong or missing from your conjecture.
Finally, there has been no acceleration of global warming since the Little Ice Age. The long term rising temperature trend is not accelerating, despite a ≈40% rise in CO2. Thus, CO2 has not made any measurable difference, whether the CO2 concentration was low or high. The long term trend remains the same irregardless of CO2 levels. I think you need to re-think your premise. The real world is not in agreement.
Hey Smokey!
Thanks for your comment. Not sure who Dr. Miskolczi is. The material for this post came from a nice text book I have. “Bejan, Adrian; Kraus, Allan D. Heat Transfer Handbook. John Wiley & Sons”.
It was also taught in the university course I took on the subject. The text for that course was “Schumann, Reinhardt, Metallurgical Engineering, Volume 1, Addison-Wesley”. Since that time I have been successfully designing various things that involve heat transfer. So if Dr. Miskolczi asserts that doubling CO2 has no impact on radiative transfer (which must be the case if there is no temperature impact) then he is in direct disagreement with every person who teaches these things to engineering students around the world. Most of those guys are doctors too. Regarding the question about a rise in CO2 not causing a significant global warming, I direct you to the post “the path length approximation”. There you will see that at around 300 ppm the impact of increasing CO2 starts to flatten out. Going from 278 to 300 will have about the same impact as going from 300 to 800. And that isn’t much.
My “premise” is not mine. It is taught in engineering schools around the world. The real world is in agreement with everything I’ve said. And everything you’ve said (except about Dr.Miskolczi). Our planet is warmer because of CO2. Adding more will not greatly change that though because the effect has reached a maximum.
John,
I guess we are not far apart in our views. The “carbon” scare is based on money, not science. I have never asserted that CO2 has no effect, only that the effects of “carbon” are wildly overstated.
There is no grant money in telling people that the resulting warming will be small, and will occur mainly at night, and will raise the low temperatures, not the high temperatures, and will affect the higher latitudes, where it will be entirely welcome. No, the money is in the scare. So they wildly exaggerate; they lie for money. And the lies will only get ratcheted up, until they are able to tax the air we breathe. The ultimate dream/fantasy of conniving politicians.
Dr. Miskolczi has a particular point of view:
1. He is in agreement (with climate science) on the calculation of CO2’s impact on Outgoing Longwave Radiation (OLR), as his work involves calculating the changes in transmissivity of the atmosphere due to increases in various “greenhouse” gases. See “The greenhouse effect and the spectral decomposition of the clear-sky terrestrial radiation” from 2004.
This is mainstream (as far as I can tell from what I read).
2. He believes that the feedback exactly cancels out the increases in “greenhouse” gases – “the Earth maintains a constant optical thickness” in his 2007 paper “Greenhouse effect in semi-transparent planetary atmospheres”.
This viewpoint is critiqued in detail in the Six Part Series on Miskolczi which includes articles like Part Five – Equation Soufflé – explaining why the “theory” in the 2007 paper is a complete dog’s breakfast.