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Energy Business
Howard Hayden
Howard Hayden
·Posted in Energy Business
Mon, Oct 7

CO2 is Innocent! Proof is in a recent Science paper.

 

Numerous emails have come my way showing a 485-million-year graph of temperature from a recent paper in Science (Judd et al., Science 385, eadk3705 (2024) 20 September 2024), with the message that we’re in a very cool state right now:

 

 

I pretend no expertise in such measurements or the in the models used to infer the temperatures, so I shall just assume that the graph is correct.

 

However, there is some faulty logic in imputing temperature changes to CO2 concentration changes.  Let me explain.

 

It is well known that the amount of IR that goes to space (ca. 239 W/m2, according to IPCC, 2021) is less than the amount emitted by the surface (398 W/m2).  The 159 W/m2 difference is due to net absorption by atmospheric gases, and is called the greenhouse effect by the IPCC.  About 30 W/m2 of the greenhouse effect is presently due to CO2.

 

IPCC uses the term radiative forcing to represent changes in (A) the greenhouse effect; (B) solar flux; and (C) planetary albedo.  They give a formula for calculating the radiative forcing from CO2:

, where C0  is the initial CO2 concentration.  The formula is based on the IR spectral properties of CO2; van Wijngaarden and Happer used more accurate spectral data from HITRAN and get values that are a bit different.  For doubling, the IPCC formula results in 3.7W/m2; v-W & H get 3.0 W/m2.  For our purposes we will use the IPCC values.

 

The Judd paper plots temperature on the y­-axis against CO2 concentration plotted on a logarithmic scale so that the graph shows temperature versus CO2 radiative forcing. (Fig. 4, lower left in their paper; see below)

 

So far, so good.  But there are two serious omissions from the graph.  The first and most obvious is the actual radiative forcing from CO2 in W/m2.

 

The second omission is an extremely common omission when climate scientists plot temperatures along an axis: the increase in surface IR emission.  (Evidently, university Climate Science curricula do not include any reference to the Stefan-Boltzmann law.)

 

I have appended both scales to a graph from the Science paper (page 2 of the attached letter to the editor of Science).

 

The upshot is that the range of forcing is about 12 W/m2, insufficient by over a factor of 10 from being able to absorb the increase in surface radiation.

 

My letter to Science follows:

 

 

Howard C. Hayden
785 S. McCoy Drive
Pueblo West, CO 81007

September 24, 2024

Science Magazine Letters

Re:  Judd et al., Science 385, eadk3705 (2024) 20 September 2024

The 485-million-year history of Earth’s surface temperature by Judd et al neither asks nor answers some obvious causality-related questions:  Where did the CO2 come from that supposedly caused the temperature to rise, and where did it go when the decrease supposedly led to the cooling?  Which happened first: CO2 changes or temperature changes?  How does a correlation suddenly become causation?

The authors attempt to prove causality with Figure 4, which shows temperature versus radiative forcing using a logarithmic axis of CO2 concentration, but there are two serious omissions.  The x-axis graph should surely show the actual radiative forcing—the increase in the ability of CO2 to block IR from going to space. For the CO2 data in their paper, the forcing varies by about 12 thermal watts per square meter (W/m2), as calculated from a well-known logarithmic formula from the IPCC.

The second omission is a separate scale showing the increase in thermal emission from the surface alongside the temperature scale.  The temperature range of the data (ca. 24 ºC) corresponds to a change in surface IR of about 135 W/m2, as one can easily calculate from the Stefan-Boltzmann law.

How can an increase of about 12 W/m2 in the ability to block IR from going to space possibly block an additional 135 W/m2 of IR from the surface from going to space?

It can’t.

Their Figure 4 actually shows that CO2 change is a minor contributor to temperature change. There is no justification whatsoever for their descriptions of CO2 as exerting “dominant control on variations in Phanerozoic global climate.”

Howard C. Hayden

Prof. Emeritus of Physics, UConn
[email protected]