Vincent J. Curtis
14 Oct 23
Chemists are steeped in the Beer-Lambert Law (some would say stewed!) because it is the basis for analytical spectroscopy, of which there is a lot these days. My first job out of university was as an analytical chemist for a large steelmaker, and one of my tasks was to measure the Zn content of wastewater. For this we used a Varian AA6 atomic absorption spectrophotometer. The calibration range was from 0 to 7 ppm Zn; 8 ppm deviated noticeably to the right of the straight absorption line from 0 to 7; and by 9 ppm the absorption line from 8 was so flat the instrument could not reliably detect differences in concentration; they were lost in the noise.
When I saw the presentation of the Will & Bill paper[1] at the Heartland 2021 conference, and saw that there was no change in the CO2 absorption peak from about 50 and certainly from 100 ppm to 800, I recognized the complete flattening of the absorption curve. Quantitatively measurable absorption much beyond 100 ppm is going to be unreliable and lost in signal noise. In my view, the IR absorption by CO2 is maxxed out by 100 ppm; and line broadening absorption is of no significance. Whatever there might be is, for practical purposes, lost in noise, and isn’t that just what we’re seeing when actually trying to measure global temperatures and emission spectra from space?
Getting back to Beer-Lambert, my calculation in Part 1 of this series showed that 99.4% of radiation at 667 cm-1 is absorbed within 10 m of the ground, and that all of this is thermalized (within the limits of Maxwell-Boltzmann distribution). Adding more CO2 just shortens the distance in which complete absorption occurs.
Other examples of the mis-education of chemists are the beliefs that there has to be a difference in temperature for heat to flow, and that heat flows from the higher to the lower temperature: Fourier’s Law, or some such. On this basis, the illustration in the IPCC heat balance[2] of 398 W/m2 flowing into the atmosphere means the warm ground is heating the cool air above it; but that 342 W/m2 flowing from the air into the ground would mean the ground was colder than the air, contradicting the assumption of the 398. Now, I’ll accept that net 56 is what the ground puts into the air, but then what to make of the rest? You get 80+82+21+56 = 239 put into the troposphere from all sources, which is precisely what is radiated to space; and 82+21+56 = 159, the GHE number as determined by Howard Hayden, Ph.D.; and 159 + 0.7 = 160, the amount of heat absorbed by the ground from the sun’s rays. The figures are suggestive, and the role of CO2, if any, is obvious nowhere. (All IR absorption is found in the 80 and the 56.)
A net heat flow of 56 from the ground into the atmosphere would mean that if the atmosphere is at 288K, then the ground must be 299K.
Pardon me if I continue to think out loud.
The IPCC model is a steady-state, meaning the heat equation boils down to the Laplace equation.
If adding CO2 to the lower atmosphere results in a higher temperature, then that would seem to violate the law of conservation of energy: where is this extra energy to heat the lower atmosphere going to come from? Is the ground going to start pumping more than 56 into the lower atmosphere, and if so, where is that energy going to come from within the model? The ground receives 160 from the sun’s rays, and puts it all back into the troposphere 82+21+56 = 159 (within model error of 0.7.) It’s all accounted for, already.
If you conceived the troposphere as an insulator, Fourier’s Law in 1-D would have the near ground level at 288K and 230K (159 W/m2 radiative power) at the other side of the insulating wall, that being the top of the troposphere.
What you put in at one end, you have to take out at the other in a steady state, and 398 is too much; but, if you take the lower troposphere as that needing to lose heat, then there’s your 239: (82+80+21+56), with the ground effectively at 299K, not 288K; the satellites couldn’t tell the difference. And you still don’t have to make theories about greenhouse effects. What greenhouse effect there is, is that absorption of IR and thermalization within the first 10 m of the ground, an effect already maxxed out; the effects of line broadening are lost in noise. Any more energy put into the lower troposphere by the ground would appear to violate the law of conservation of energy. (There’s also IR absorption and thermalization within the inbound 80.)
Does CO2 content play a role in the “insulation” constant of the troposphere? Well, no. Maxwell-Boltzmann distribution effects matter in the upper atmosphere, not in the lower, where the excited state would be thermally quenched before radiation, and the thermal diffusivity of CO2 isn’t that different from other atmospheric gases, never mind the insignificant concentration.
What if other IR active molecules were added to the atmosphere, such as CFCs? Assuming their only effect is IR absorption and subsequent thermalization, this heat appearance would be deducted from the atmospheric window incorporated into the 239. If it meant that, effectively, more heat is being put into in the lower atmosphere by the ground, then, as we have seen, that appears to violate conservation of energy; besides, that 239 total would have to be made up elsewhere, by processes neglected in the model.
A higher temperature; and higher difference in temperature between the lower and upper troposphere would mean an off-setting faster rate of heat transport to the upper atmosphere, an example of Le Chatelier’s Principle. (whom the chemists claim as one of their own.)
If a climate model claims that the temperature in the lower troposphere is going to rise by so many degrees by 2100, you have to ask how? It can’t be just more CO2, or CO2 and water vapor and more IR absorption and thermalization. If the sun heats the atmosphere directly by more than 80, then there’s that much less than 160 striking the ground; and if the ground is cooler and the atmosphere warmer, then the heat transfer from the ground to the air is less than 56. Putting more water vapor into the air means less energy for sensitive heat, and/or cools the ground (taking away from the 56). Line broadening, I claim, is of no significance and lost in noise (aside from requiring the conservation of energy be violated somewhere). And if you heat the lower troposphere somehow, that will warm the upper troposphere by convection eventually, raising the rate at which Maxwell-Boltzmann effects convert that heat into IR radiation to space, another example of Le Chatelier’s Principle.
It seems that all the models require more heating by closing the atmospheric window, (by thermalization of IR not mentioned in the IPCC budget) in violation of conservation of energy. Recall the ground is receiving 160 from the sun, and putting into the troposphere 82+21+56+0.7 = 160, accounting for all the surface receives, and must put back.
The upshot is that theories of CO2 induced greenhouse effects are unnecessary, and, frankly, invisible, in the IPCC heat flow diagram, once you get rid of the unphysical 342 going from a cooler air into the warmer ground. They would seem in violation of the conservation of energy also. The lower troposphere has 239 from all sources to get rid of, and that’s what leaves to space; a computed GHE forcing number of 159 appears at the top of the troposphere as well as being that which strikes the ground, and a near ground level temperature of 288 is sustainable if the ground is effectively 299K. Where IR absorption plays a role in the model is in the sun heating the air directly i.e. the 80, and in the 56, which is completely absorbed within a few meters of the ground emitting it. (I can already hear Willie Soon saying “I told you so!)
If you want to heat the earth, you have to
make the albedo smaller.
-30-
Let me acknowledge that the inspiration for this article came from an on-line back-and-forth with Howard Hayden, Ph.D. I am responsible for all the content of the piece. Dr. Hayden also provided me with the IPCC AR6 energy budget, which I will attach to the tweet announcing publication of this piece on my blog.
For reference, the IPCC AR6 energy flow goes more or less as follows:
All values are are in Wm-2
340 incoming from the sun
100 reflect back into space (albedo)
80 absorbed by the atmosphere incoming
160 absorbed by the surface of the earth
82 used by the earth’s surface to evaporate
water
21 sensible heat from the earth’s surface
56 net radiated from earth’s surface (the
difference between 398 up and 342 down)
239 thermal outgoing to space, of which an indeterminate
amount is through a thermal window
0.7 imbalance
[1] W.A. van Wijngaarden,
W. Happer “Dependence of the Earth’s Thermal Radiation on the Five Most
Abundant Greenhouse Gases.” June 8, 2020.
[2] IPCC AR6 Radiation
Budget.
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