Commenting on a Comment by Happer and Lindzen

Recently I came across a document reportedly written by William Happer and Richard Lindzen (HL) entitled Comment and Declaration on the SEC’s Proposed Rule “The Enhancement and Standardization of Climate-Related Disclosures for Investors,” File No. S7-10-22, 87 Fed. Reg. 21334 (April 11,2022).[1] As I read through the science-related material in the document, it became quickly apparent to me that his document is utter garbage. It's so bad, I wonder to what extent either of them actually wrote it. Rather than go through the document section by section, I want to just analyze the section on climate sensitivity. What we'll see here is that the paper is inconsistent with itself, it contradicts the other published works of the authors, and of course, it's demonstrably false.

Internal Inconsistencies

The section I'd like to discuss primarily is section II.M, with the brief title, "The Logarithmic Forcing from CO2 Means that Its Contributions to Global Warming is Heavily Saturated, Instantaneously Doubling CO2 Concentrations from 400 ppm to 800 ppm, a 100% Increase, Would Only Diminish the Thermal Radiation to Space by About 1.1%, Thus Confirming There is No Reliable Scientific Evidence Supporting the Proposed Rule.' This section begins by introducing the following graph made by Gregory Wrightstone of CO2 Coalition.

There's nothing wrong with this graph for what it is. It shows the amount of additional warming for increasing CO2 concentrations in 50 ppm increments prior to feedbacks. It does this using the standard formula for calculating the increase in radiative forcing for a change in CO2 - RF = 5.35*ln(C/C0) combined with the Planck feedback = 3.2 W/m^2/C. From this formula we can learn that doubling CO2 would cause a 3.71 W/m^2 increase in radiative forcing (5.35*ln(2)) and 1.15 C of warming prior to feedbacks. None of this is controversial, and I would agree with this. From here they eloquently conclude, 

This means that from now on our emissions from burning fossil fuels could have little impact on global warming. There is no climate emergency. No threat at all. We could emit as much CO2 as we like, with little warming effect.

This is what we call a non sequitur, of course, because these calculations do not include warming from feedbacks. As I've described in other posts, the central estimate for ECS in the scientific literature is about 3 C for doubling CO2. Feedbacks roughly triple warming from CO2 alone. But let's come back to that. There are some internal consistency issues coming up here that we first have to deal with.

HL say that effective temperature of the earth without greenhouse gases is 16 F (or 264 K) while the current temperature of the earth is 60 F (289K). Most sources I've read use 255 K and 288 K, but for now we'll need to stick to their numbers. The difference between the two is 25 C. They claim that greenhouse gases has caused decrease from 394 W/m^2 to 277 W/m^2, so that a change of -117 W/m^2. This implies a normalized greenhouse effect (g) of 117/394 = 0.3, and that would mean that the Planck Feedback would be (g-1)*4𝜎𝑇^3 = -0.7*4𝜎*289^3 = - 3.83 W/m^2/C. So it takes 3.83 W/m^2 to raise temperatures 1 C. But in the graph above, they used a Plank feedback of 3.2 W/m^2/C. They aren't being consistent. 

HL introduce the Planck curve for the earth at 289 K and shows that the difference between the the curve at 400 ppm CO2 and his model for 800 ppm CO2.[2] HL write, the difference is hardly noticeable, a decrease of radiation to space of about 3 W/m2." So here doubling CO2 causes only a 3 W/m^2 increase in radiative forcing. But did we not just show from the formula above that it causes 3.71 W/m^2 increase in radiative forcing? We absolutely did. If you want doubling CO2 to cause 3 W/m^2 change in RF, then the 5.35 in the formula in the above graph should be 4.33, but then doubling CO2 would cause 3/3.2 = 0.94 C warming instead of 1.15 C warming. That's more internal inconsistencies in this document.

But there's more. They decided to calculate pre-feedback CO2 sensitivity again. Why are they calculating again what they just finished calculating? I really don't know. After calculating that the 3 W/m^2 is 1.1% of the 277 W/m^2 radiated to space, they write, "to increase the flux by 1.1% and bring solar heating back into balance with radiative cooling, a temperature increase of dT/T, of ¼*1.1% = 0.28%. is needed. Since the absolute temperature of the Earth is approximately T = 300 K, (60° F), the required temperature increment is dT = 0.0028 x 300 K = 0.84 K = 0.84°C." So now HL have lowered the value they had calculated to be 1.15 C to a new value 0.84 C. But there's also a mistake here. They say the temperature of the Earth is 300 K (60 F) but 60 F is actually 289 K (300K is 80 F). So this is a mistake. To do this calculation properly we need to do use 289 K: dT = 0.0028 x 289 K = 0.81 K = 0.81°C. So what we see here is that HL's calculations are not even remotely consistent internally because they're frequently assuming different values for the same things, and sometimes even converting units improperly. His initial calculation sensitivity was essentially correct at 1.15 C.  But that value flatly disagrees with the (corrected) value of 0.81 C or even the stated (uncorrected) value of 0.84 C.

Contradicting Published Works

To continue, let's just consider their (incorrectly calculated) value of sensitivity of 0.84 C. They conclude that "this estimate, 0.84°C, is four times smaller than the 3° C "most likely" warming claimed by the IPCC for a doubling of CO2." Actually no. The IPCC's value for sensitivity prior to feedbacks is about 1.15 C, consistent with the formula in the graph above and a Planck feedback of 3.2 W/m^2/C. HL then acknowledge that the IPCC gets their value of 3°C through positive feedbacks, like water vapor, which roughly triple sensitivity of CO2 alone. HL offer no evidence-based rebuttal, though, only a few assertions. They say for instance, that "large positive feedbacks are unusual in nature" and most are negative, so they argue that the IPCC violates "LeChatelier’s Principle." They conclude, "basic physics shows that doubling CO2 would result in a temperature increase of less than 1°C."

But that's rather interesting because in 2020, Happer wrote a paper that calculated ECS to be 2.3 C after accounting for the positive feedback from water vapor. "Doubling CO2 concentrations with water vapor feedback increases the surface temperature warming to ∆θo = 2.3 K from ∆θo = 1.4 K, or by a factor of 1.6." His value of 1.4 C was assuming constant absolute humidity and his value of 2.3 C was assuming constant relative humidity. Here his value of 2.3 C was almost 3 times greater than the value reported in this HL paper. And it's not like Happer didn't know about his own paper. It's even cited in this section of the paper.

Similarly, Richard Lindzen wrote a paper for the CO2 Coalition that concluded, "Analysis of the temperature data leads to the conclusion that if anthropogenic contributions are the cause of warming since the end of the Little Ice Age, and if aerosols are limited to a contribution of 1 Watt per square meter, then climate sensitivity in excess 1.5°C is precluded."  So here Lindzen is explicitly saying that sensitivities as much as nearly 2 times higher than their estimate can't be precluded, given assumptions of the paper.

Neither of these papers are peer-reviewed, but the HL paper clearly contradicts what they have previously said about climate sensitivity. This paper doesn't acknowledge those contradictions or explain why their positions have changed. They simply assert that sensitivity is 0.84°C on the basis of bad calculations that aren't even consistent with other calculations in the same section of his paper. 

Let me be clear - if Happer and Lindzen really want to go on record scientifically that their best estimate for ECS is ~0.84 C and on the basis of their best scientific judgment, write the comment sent to the SEC, I have no objection to that. I disagree, of course, but that's what the free interchange of ideas in the public sphere should allow. But this report appears to be contradicting the best scientific judgment that its authors have published while at the same time using the scientific credentials of the authors to lend credibility to the political aims of the document. And the paper is a garbled mess.

It's Demonstrably False

There are numerous problems with this section of the paper, and I saw many other issues in other sections, but I figured the blog post would be too long if I tackled them all. There are some real problems with their portrayal of paleoclimate and their relationship to sensitivity. HL seem to have done no research on this; they're just repeating stuff that shows up on blogs and political websites like the CO2 Coalition. But a sensitivity of 0.84 C is objectively absurd.  Just using round numbers there has been 2.1 W/m^2 increase in RF from CO2, while other GHGs and aerosols have nearly canceled each other out. The total net RF from GHGs and aerosols is probably about 2.2 W/m^2. If ECS = 0.84 C that means temperature increases at a rate of 0.84/3.71 = 0.23 C/W/m^2, so anthropogenic forcings are responsible for 2.2*0.23 = 0.51 C warming. But we've had 1.2 C warming and the energy imbalance has increased to 0.8 W/m^2. So of the 1.2 C warming, 0.69 C was caused by something other than GHGs and aerosols. If ECS is 0.84 C, then that 0.69 C is equivalent to 0.69/.23 = 3 W/m^2. Add that to the current energy imbalance and you have 3.8 W/m^2 that is completely unaccounted for by HL. It can't be accounted for by the Sun; solar variability is small, only about 0.2 W/m^2 in radiative forcing. Volcanoes cause short-term cooling that lasts only a couple years. Where did this 3.8 W/m^2 come from? Nobody knows, and HL don't even try to explain it in their paper.

References:

[1] William Happer and Richard Lindzen. Comment and Declaration on the SEC’s Proposed Rule “The Enhancement and Standardization of Climate-Related Disclosures for Investors,” File No. S7-10-22, 87 Fed. Reg. 21334 (April 11,2022).
https://www.sec.gov/comments/s7-10-22/s71022-20132171-302668.pdf

[2] W. A. van Wijngaarden and W. Happer. Dependence of Earth’s Thermal Radiation on Five Most Abundant Greenhouse Gases. 2020 Unpublished paper. https://arxiv.org/pdf/2006.03098.pdf

[3] Richard Lindzen, On Climate Sensitivity. https://co2coalition.org/publications/on-climate-sensitivity/