There is nothing exciting here to be revealed, just a few notable details to round up our understanding of the physics. If you should ever look up the GHE of CO2 you would need to be very lucky to find any consistent answer. For instance wikipedia¹ will tell you CO2 contributes 9-26% to the GHE, as.. “It is not possible to assign a specific percentage to each gas because the absorption and emission bands of the gases overlap.. Clouds also absorb and emit infrared radiation and thus affect the radiative properties of the atmosphere”

Yes, both are true statements and regrettably it does not seem to resonate otherwise in climate science. Yet it is no reason to give such vague numbers. It is not too hard to pin down pretty exact values for the CO2 GHE, both overlapped (gross, or “single factor addition) and non-overlapped (net, or “single factor removal)². Indeed the relation between both terms is highly significant for ECS estimates, climate modelling and so on, as we are going to see in upcoming articles.

For now what we need to know is that there is a main absorption band of CO2 in the 13.1 to 17.2µm range. Beyond it CO2 is absorbing over about half the emission spectrum, though at such low intensities, that with current (and future) concentrations this will only play a negligible role. Accordingly we can concentrate on this main absorption band.

A black body at 288K will emit 390W/m2, as we all know by now. Of these 390W/m2 18.9%, or 73.7W/m2 are within the named range. With CO2 @400ppm however emissions in this range are substantially lower, only about 40W/m2. The rest is simple math, as we can conclude CO2 reduces emissions by 33.7W/m2. Relative to a (erroneous) total GHE of 150W/m2 that would be 22%, which makes me wonder how one could get to 26%? Probably it is based on an equally erroneous GHGE (greenhouse gas effect, excluding clouds) of some 130W/m2, while the low end 9% reads as “how much does CO2 reduce emissions”, meaning some 390W/m2 as a base. These are pretty useless numbers quoted out of context, as so often in “climate science”. I digress..

Now this approach, as simple as it is, already contains a little flaw. Even ignoring the overlapping issues with vapor and clouds, CO2 will not block the emissions of a perfectly emitting surface. As I have pointed out, the spectral hemispheric emissivity of water is about 0.91, which largely predetermines that of the surface as a whole. However within the specific range of 13.1 to 17.2µm, the hemispheric emissivity of water is even lower, namely 0.895. And since we have no, or only very poor data for land, especially in this range, we will have to stick to it as a best approximation.

So other than a perfect black body, the real surface will only emit 66W/m2 (=73.7x0.895) within the CO2 band, meaning CO2 reduces emissions only by 26W/m2. It is an interesting detail only revealed once you have exact figures on the emissivity of water, something “climate science” finds too hard to do. Me however, since I have the data, I can just look it up.

Eventually we are left with the question what the net GHE of CO2 is, with other GHGs and clouds given. We can ask modtran³, but it is not going to give us a perfect answer right away. The problem is, you can fine tune all the parameters to give you a good enough approximation of average global conditions. What you can do however, is to look up all the different options there are and then simply infer the rest.

The closest fit with the uchicago version is certainly the “1976 U.S. Standard Atmosphere” with “Stratus CU … Top 2.0km” (CRE 24.9W/m2), which gives a non overlapped value of 21.9W/m2. By comparison, with a reasonable CRE, the tropical scenario gives 26W/m2, marking the high end, and some 15W/m2 for high latitude winter marking the low end. Then the US scenario runs a bit high in emissions with 242.9W/m2. Adding a stronger CRE (“Cumulus Cloud Base .. Top 2.7km, 39W/m2 CRE) drops emissions to 228.9W/m2, which is way too low. The non overlapped CO2 effect in this instance would be 18.2W/m2. With linear regression we can infer, that with a proper CRE of 30W/m2 and total emissions in the 239-240W/m2 range, CO2 will add about 21W/m2 to the GHE, at least according to modtran. The figure is yet in good accordance with the 21.7W/m2 Schmidt et al (2010) name (in their paper it is 14% of 155W/m2 GHE)⁴.

Regrettably we are not quite done yet. While Schmidt et al assume a perfectly emitting surface, we will allow for realistic conditions. The CRE we can add in modtran is simply one opaque cloud layer at low altitude, which stands in stark contrast to the complexity and diversity of cloud types and altitudes. It would not necessarily matter, since it is about the average quantitative effect, how ever it is caused in detail. The problem is rather that with such a model eventually all surface emissions will be blocked anyhow and accordingly surface emissivity, or the lack of surface emission respectively, is completely irrelevant. But since in reality there is an abundance of (partially) clear skies, surface emissivity will matter after all.

Accordingly we will have to take the 7.7W/m2 difference between a perfect emitter and real surface emissions into account, but a) only to the extent of clear sky conditions and b) as far as vapor is transparent to these surface emissions. And that is about where my wisdom ends, as I can only guess what fraction that will be, also given that modtran will not be all too precise on those edges of its scope. A fair guess might be 2 or 3W/m2, which would bring the net CO2 effect to 18-19W/m2. I can only call for improvements to this estimate and further research on the subject. Being conservative and just to have something to work with, I will stick with the 19W/m2 figure.

The question may be up, what all this is good for. First of all, combined with the theoretical framework provided on this site, it tells us CO2 is indeed a very important GHG. I have concluded the net total GHGE to be only about 35W/m2, so that CO2 will be responsible for over half it, given the 19W/m2 figure is roughly accurate. Equally 26W/m2 relative to a total gross GHGE of 85W/m2 is quite powerful. The often quoted idea CO2 would only be minor potent relative to vapor is not quite true. Then considering the circumstances, that is latent heat, lapse rate and so on, which I dealt with here, CO2 actually IS a GHG, which is not really true for vapor.

The really important and delicate part however goes like this. Assuming the surface was a perfect emitter, ignoring the overlapping issues, “climate science” presumes a CO2 GHE of about 34W/m2. When estimating the effect of doubling CO2, that figure will serve as a base magnitude. If you doubled CO2 from 400 to 800ppm, this figure would indeed grow by about 4W/m2 to 38W/m2.

But in reality things go a bit different. Not just the 34W/m2 figure is wrong, as a good part of the assumed surface emissions “blocked” by CO2 do not exist in the first place, but CO2 will only add some net 19W/m2 to the GHE. This quotient of 19/34 will not just be true for the first 400ppm, but also for any additional 400ppm of CO2. It is one of the main reasons why climate models and ECS estimates run far too hot, though certainly not the only one. Those issues however go a bit beyond “basic greenhouse defects” and so we will deal with them in a new, separate category.

PS. I might want to add, though it certainly deserves a more explicit discussion, that as the water emissivity chart shows, average weighted hemispheric emissivity in the far IR range (beyond 17.2µm) is only 0.875. Incidentally this far-IR range is the main, though not only, absorption range of vapor. It is a detail having mighty implications on the inferred GHE of vapor, far more severe than those discussed with regard to CO2. Also it is one of the reasons why vapor is so extremely overrated.

¹https://en.wikipedia.org/wiki/Greenhouse_effect

²https://pubs.giss.nasa.gov/docs/2010/2010_Schmidt_sc05400j.pdf

³http://climatemodels.uchicago.edu/modtran/