Responding to the CO2 Coalition's "Fact #2" on the Effect of Increasing CO2

The CO2 Coalition claims to exist "for the purpose of educating thought leaders, policymakers, and the public about the important contribution made by carbon dioxide to our lives and the economy. The Coalition seeks to engage in an informed and dispassionate discussion of climate change, humans’ role in the climate system, the limitations of climate models, and the consequences of mandated reductions in CO2 emission." And if you think there's even a grain of truth in that, we can dispel with that right here. 

On their website, they have what they consider educational resources, including a series  of "facts" that ostensibly would help us get past media propaganda to the scientific evidence about AGW. Their second "fact" has the following title: "The warming effect of each molecule of CO2 declines as its concentration increases." As is typical in these "facts," the title is superficially true; the disinformation comes in the way it's explained. In this case, we're treated to the following graph.

And of course it is true that there's a logarithmic relationship between CO2 and temperature. It's well-documented and well-publicized that doubling CO2 causes a linear increase in radiative forcing (expressed as ΔF ≈ α*ln(rCO2) where rCO2 is C/280) and that GMST increases linearly with an increase in radiative forcing (expressed as ΔT = λ*ΔF). So far, so good, but then come the lies. After admitting that "both sides agree," they claim, "This inconvenient fact, important though it is, is kept very well hidden and is rarely mentioned, for it undermines the theory of future catastrophic climate change." But there are countless resources from the IPCC and elsewhere documenting the well-known fact that the relationship between CO2 and warming is logarithmic. The only reason why the people at the CO2 Coalition know about this logarithmic relationship is because actual climate scientists publicized it and told them.

And the lies continue from there. Anyone familiar with the evidence here might wonder about the large numbers on the Y axis of the CO2 Coalition's graph above. They quote Happer explaining why: "The vertical red lines show the decrease of flux to space caused by successive increases of the CO2 concentration C by 50 ppm increments. The increments are so small that they need to be multiplied by a factor of 100 to be clearly visible on the graph." Really? It never occurred to Happer simply to take all the numbers on the y-axis and divide them by 100? This is just a stunt - Happer said this to create the false impression that increasing CO2 can't cause much if any more warming, but that of course is a lie. As he already admitted, doubling CO2 causes a linear increase in temperature. And scientists estimate that to be about 3°C warming at equilibrium with 2xCO2.

Same Data as the CO2 Coalition's Graph Above

And there are more mistakes in Happer's quote. He says, "every doubling of CO2 concentrations decreases the radiation to space by 3 W. For example, the first red bar show that increasing C from 50 ppm to 100 ppm decreases the radiation to space by 300/100 W/m^2 = 3 W/m^2.” This comes from a fake "paper" that is actually just an unpublished manuscript Happer put on the arXiv. His 3 W/m^2 figure comes from modeling CO2 at 400 ppm and 800 ppm and subtracting one from the other. Values for the ΔF for 2xCO2 generally fall in the range of 3.7 to 4 W/m^2, and this allows us to calculate the α value in the equation I cited above. Here are estimates that appear in IPCC reports, and none overlap Happer's value of 3 W/m^2:

ΔF2xco2 ≈ α*ln(2) 

AR3: 3.71 ± 0.4 W/m^2, so α = 5.35

AR5: 3.80 ± 0.38 W/m^2, so α = 5.48

AR6: 3.93 ± 0.47 W/m^2, so α = 5.67

Happer also mispresents the logarithmic relationship between CO2 and radiative forcing: "The blue curve is almost flat for current concentrations of CO2, so the greenhouse effect is very insensitive to changes in CO2 concentrations. In the jargon of radiative transfer, the greenhouse effect is said to be 'saturated.'" We've talked about the saturation myth here before, so I don't need to repeat myself here. But I'm quite positive that Happer knows that the limit of ln (x) as x→∞ is ∞. Happer certainly knows that ln(x) never "saturates." The actual log relationship between CO2 and radiative forcing can be better and more honestly expressed in the following graph.

Using ΔF2xco2 = 3.71 W/m^2, you can see that with every doubling of CO2 above 280 ppm, less long wave radiation (LWR) escapes to space. At 1000 ppm (corresponding to concentration maximum concentration in Happer's graph), the decrease is about 7 W/m^2, and surface temperature must increase until that imbalance returns to 0. If ECS is 3°C, then that would mean an increase in temperature of about 7*3/3.71 = 5.7°C. That ΔT is about the same as the difference between the last glacial maximum and the Holocene Thermal Maximum. That's a big deal, no matter how flat a blue line looks on Happer's graph.

The IPCC's central estimate for ECS is 3 C for 2xCO2 with a range from 2.5-4°C. Since 3.25°C is the mathematical center between 2.5 and 4, above I decided to plot both how ΔF and ΔT change with increasing CO2. The blue shows the 2.5 to 4 C range for ΔT and the red shows the uncertainty range for ΔF (assuming ECS = 3.25 C). In effect what Happer did is play with the scale of the Y-axis of his graph to create the false visible impression that increasing CO2 above current concentrations doesn't change temperature; he showed a Z(C) ΔF of about 34 W/m^2 on a scale from 0 to 400 W/m^2 to make the blue line appear flat above about 200 ppm.

Conclusion

As you can see, even though the title of this "fact" is superficially true, what follows is a bunch of lies. And we can't give the CO2 Coalition the benefit of the doubt here; we can't chalk this up to someone who lacks knowledge making a mistake. This article quotes Happer saying things that he certainly knows to be false. I've been thinking about responding to each and every one of these CO2 Coalition "facts." I've already addressed their first fact multiple times here, so I didn't want to start with that one. I probably won't go in order, but after I generate a few, I'll set up a page on this blog that links to my responses so interested people can see them in the order that the CO2 Coalition numbers them.