<p>To answer the original question about CO<sub>2</sub> saturation, I'll describe spectral absorption.  Each gas in the atmosphere absorbs light at specific wavelengths, and some wavelengths are absorbed more than others.  The spectral absorption of CO<sub>2</sub> is shaped like a V.  With no CO<sub>2</sub>, the radiative spectrum of Earth would resemble a black-body.  When CO<sub>2</sub> is added, this 'V' is pushed into the black-body spectrum, making a notch.  At present concentrations, the bottom of this notch is 'saturated', meaning it hits the bottom.  As more CO<sub>2</sub> is added, the V is pushed further down into the radiative spectrum.  The bottom certainly remains saturated, but the edges of the notch continue to erode.</p>
<p>There are other problems with this paper.</p>
<p>Figure 6 in the paper shows that doubling the atmospheric concentrations of CO<sub>2</sub>, N<sub>2</sub>O, and CH<sub>4</sub> would cause increases in radiative forcing.  They claim these increases are negligible, but they are not.  Their own data show that doubling CO<sub>2</sub> would cause an additional increase of 3.74 W/m<sup>2</sup>.  To put this in perspective, all radiative forcing to date, referenced to the start of industrial times in 1750, is 3.4 W/m<sup>2</sup>.  Doubling N2O would cause an additional 1.99 W/m<sup>2</sup>.  Doubling CH<sub>4</sub> would cause an additional 1.12 W/m<sup>2</sup>.  These numbers are not &quot;negligible&quot;.</p>
<p>Figure 15 in the paper presents their model's results, side-by-side with satellite measurements.  To the naked eye, they look good.  However, when they are plotted against each other, they do not match.  As their model is meant to study spectral absorption, you might think their model would match the satellite data in the &quot;spectral window&quot; where no absorption occurs.  It does not.  Their model must be scaled by +5.6%, -3.9%, and -12.5% for the Sahara, Mediterranean, and Antarctic datasets, respectively.  Even after adjusting the model to match the satellite data, the model overestimates the amount of outgoing radiation.  This infers that the Earth is staying cool, when in fact it is retaining heat.  The discrepancy is on the order of 3-5% globally, which is quite large.</p>
<p>In answering this question, I have used the data presented in the paper itself.  As the authors did not provide the raw data, I used software to digitize the graphical data.  My results may be off by a decimal place, but they are in the ballpark.</p>

CC BY-SA 4.0
2023-09-09T22:14:14.733Z
It would be helpful if the answer could include a sentence on how close models generally are expected to match reality in this field. In my personal work experience in other fields (which is admittedly dated by now), a particular predictive model matching to within 10% of the current reality on a particular metric can be acceptable, and matching to within 5% would be excellent. As a consequence, one may look towards the use of ensemble modelling.
njuffa
CC BY-SA 4.0
2024-01-05T17:02:49.483Z
It is not true that "their own data show that doubling CO2 would cause an additional increase of 3.74 W/m²." Per their Table 2 (p.19), they show an additional 3.0 W/m² (not 3.74) from a doubling of CO2, an additional 1.1 W/m² (not 1.99) from a doubling N2O, and an additional 0.7 W/m² (not 1.12) from a doubling of CH4. Whether you consider those numbers negligible or not is a matter of perspective, but they certainly are not worrisome. We've already had about log2(420/280) = 58% of a doubling from CO2, plus about half that from other GHGs, yet only 1.15±0.13 °C of warming from it.
Dave Burton
CC BY-SA 4.0
2023-06-22T22:24:23.687Z
2023-06-23T02:40:29.513Z
2023-06-23T02:40:29.513Z
Zim Sherman
<p>The abstract of the paper says it is based on the assumption absorption bands are not saturated.  This is true only at low levels of CO2, much lower than at present.  See NASA Technical Memorandum 103957, Appendix E, which shows that zero IR energy gets to space in the 14-16micron band.  That is, the band is salready saturated</p>

CC BY-SA 4.0
2023-09-09T16:13:23.177Z
This does not provide an answer to the question. Once you have sufficient [reputation](https://earthscience.stackexchange.com/help/whats-reputation) you will be able to [comment on any post](https://earthscience.stackexchange.com/help/privileges/comment); instead, [provide answers that don't require clarification from the asker](https://meta.stackexchange.com/questions/214173/why-do-i-need-50-reputation-to-comment-what-can-i-do-instead). - [From Review](/review/late-answers/18506)
Peter Jansson
CC BY-SA 4.0
2023-10-25T06:40:44.033Z
Where's this abstract at?
JeopardyTempest
CC BY-SA 4.0
2023-10-28T00:31:39.700Z
Being saturated just means all the outgoing IR is caught within the atmosphere, where it re-radiates equally in all directions, ie half going back down. More CO2, the lower down it gets absorbed and re-radiated as well as the higher up it must re-radiate to escape to space. More energy is retained within the atmosphere. Almost the textbook definition of global warming.
Ken Fabian
CC BY-SA 4.0
2024-01-05T17:15:03.317Z
NASA Technical Memorandum 103957 Appendix E is "Transmittance at sea-level." The fact that it is zero between 14 & 16 µm (pp. 114-116) does not mean that "zero IR energy gets to space" in that band. Rather, it means that all of the radiation from the surface in that band is absorbed in the atmosphere. However, the CO2 in the atmosphere doesn't just absorb radiation, it also emits it, so quite a bit of radiation in that band does reach space. van Wijngaarden and Happer report that a doubling of CO2 would reduce the amount of that escaping radiation by a globally averaged value of 3.0 W/m².
Dave Burton
CC BY-SA 4.0
2023-09-08T17:58:49.203Z
2023-09-08T17:58:49.203Z
Robert Hisey
<p>With respect to the peer reviewed status, peer review is broken, even Nature recognizes that. The insistence on peer review is generally by those who are unable to assess a paper for themselves or are looking for an excuse not to consider it. Try watching <a href="https://climatethemovie.net/" rel="nofollow noreferrer">Climate the movie</a> and see what Happer has to say for himself.</p>
<p>The photon path length for CO2 at 15 microns is 20cm, for water at 7.6 microns is 4mm (temperate latitudes) ~ 1mm in tropics. For methane it is 250m
Path length is the average distance traveled by a photo before striking a GHG.
That means that by a metre or two above the surface all radiation that can be absorbed by GHGs has been absorbed. This is what saturation looks like.
Increasing CO2 does not cause any more absorption in the main bands, the only increase comes from the wings due to band broadening. For water, band broadening means that its spectral lines become effectively joined to approximate a black body. This is how it absorbs all the radiation that methane might otherwise have absorbed. However note above that the path length of a photon at 7.65 to hit a methane is 250m but only 4mm to hit a water molecule. That is why methane is irrelevant.
With respect to the variation between W&amp;H and the satellite, It must also be remembered that the calculation are based on clear air - no cloud. Cloud substantially reduces the radiation to space, But what do the satellites deem as clear air ? I have been in the tropics and in the Mediterranean where there is no cloud but moisture/pollution make the air very hazy. I suspect this would impact significantly on the satellite data.</p>

CC BY-SA 4.0
2024-05-18T16:10:52.377Z
2024-05-18T16:10:52.377Z
Peter
<p>The paper by W.A. van Wijngaarden &amp; W. Happer has not been published. Only a preprint has been uploaded by the Authors in arXiv.
Preprints and early-stage research uploaded in arXiv have not been peer reviewed.
I guess the paper was rejected when submitted to scientific journals. We don't know why the paper did not pass the peer-review process, i.e., the scientific reasons behind its possible rejection.
However, I wish to remind that a paper by D. Schilknecht, entitled &quot;Saturation of the infrared absorption by carbon dioxide in the atmosphere&quot; was published in 2020 in a scientific journal (International Journal of Modern Physics B, see <a href="https://www.worldscientific.com/doi/abs/10.1142/S0217979220502938" rel="nofollow noreferrer">https://www.worldscientific.com/doi/abs/10.1142/S0217979220502938</a>).
The peer-reviewed paper by Prof. Schilknecht leads to similar conclusions, i.e., upon doubling the CO2 concentration, a 0.5 °C increase of the surface temperature should be expected. The paper clearly states (pag. 15) that &quot;This conclusion is in strong contrast to the values of 1.5-4.5 °C quoted in the 2013 IPCC report&quot;.</p>

CC BY-SA 4.0
2024-05-16T15:21:39.327Z
Does his paper offer any explanation of why the temperature has already gone up by over 1 °C , when we're about halfway to doubling the CO2 concentration?
Mark
CC BY-SA 4.0
2024-05-18T08:58:31.830Z
Read it (it's open access) and you'll know. Anyway, very briefly, it depends on the logarithmic nature of the Beer-Lambert law.
Riccardo
CC BY-SA 4.0
2024-05-18T22:48:14.720Z
You reference a paper that says "upon doubling the CO2 concentration, a 0.5 °C increase of the surface temperature should be expected." We haven't even doubled  yet, but the temperature has already gone up over a degree.  You're claiming that's because of the logarithmic nature of the Beer-Lambert law.  I'll suggest it's because the referenced paper is clearly wrong.
Mark
CC BY-SA 4.0
2024-05-19T15:45:13.633Z
I'm not claiming anything. I tried to summarize the rationale behind the paper published by Schilknecht in an International scientific journal. If you have solid arguments against it, send a specific comment to the same scientific journal. This is the way science works. I wonder if you have ever seen a plot of y = log(x). Do you know the concept of derivative? do you know the derivative of log(x) ???
Riccardo
CC BY-SA 4.0
2024-05-16T10:30:53.083Z
2024-05-16T10:30:53.083Z
Riccardo
<p>The paper, <a href="https://arxiv.org/pdf/2006.03098.pdf" rel="noreferrer"><em>Dependence of Earth’s Thermal Radiation on Five Most
Abundant Greenhouse Gases</em></a><sup>1</sup>, has been reportedly rejected from several major journals.  By analysing absorption spectra of greenhouse gases in more detail than has been done previously, it claims to show that CO2 is now effectively saturated (with respect to radiative forcing) and any further increase in atmospheric concentrations will lead to negligible temperature change at the surface.  Their numerical results agree with previous literature on the subject.  The authors are known climate emergency sceptics.  While noting that it is obvious that if the result is correct there would be enormous political ramifications, my question is not concerned with those.</p>
<p>Presuming the article is not being published because it's so incorrect it doesn't merit peer review, <strong>I would like to know <em>precisely and technically</em> why the paper is wrong</strong>.  The authors are physicists so I would like to understand its flaws from the perspective of climate science if possible.</p>
<p>I am specifically <em>not</em> interested in hearing arguments along the lines of &quot;the IPCC is right and this is incompatible with that so it must be wrong&quot; - again I am looking for a precise and technical rebuttal.</p>
<p>Thanks!</p>
<hr />
<p>[1] W. A. van Wijngaarden and W. Happer, <a href="https://arxiv.org/pdf/2006.03098.pdf" rel="noreferrer">“Dependence of Earth’s Thermal Radiation on Five Most Abundant Greenhouse Gases.”</a> arXiv, 2020. doi: 10.48550/ARXIV.2006.03098.</p>

CC BY-SA 4.0
2023-05-31T09:15:11.813Z
I've seen the basic argument before, and the model would seem to fail to explain the climate of Venus.
gerrit
CC BY-SA 4.0
2023-05-31T09:17:00.733Z
The paper does not say that further increase in CO2 will cause 'negligible' temperature rises. In fact its conclusions about the direct forcing of a doubling in CO2 are in line with values commonly quoted as you note. Adding in feedbacks you arrive at the range of forcing commonly accepted and backed up by observation.  Only expert reviewers will know why the paper is (if it has been?)  rejected., but it certainly doesn't  overturn basic climate science.
Andy M
CC BY-SA 4.0
2023-05-31T09:22:53.963Z
From the conclusions on Page 34, *Doubling the CO₂ concentration (...) surface warming (...) result of 2.3 K*, that is not consistent with "any further increase in atmospheric concentrations will lead to negligible temperature change at the surface". Their estimate is well below the range of estimates by other models, but 2.3 K is not negligible.
gerrit
CC BY-SA 4.0
2023-06-01T10:49:00.613Z
@gerrit The sensitivity to CO2 doubling (including feedbacks) has been debated for quite some time, resulting in a wide range of 1.5 to 4.5 K. The three key problems with this paper are (a) The authors think they've done something new, a line-by-line analysis. This is not new. (b) The authors repeatedly use the word "saturated" so as to downplay the effects. All atmosphere scientists worth their salt know this. It's why the effect of adding CO2 is logarithmic rather than linear. (c) The authors appear to have ignored feedbacks. They lament the lack of water vapor data. These data do exist.
David Hammen
CC BY-SA 4.0
2023-08-15T11:02:52.290Z
Nothing is wrong with this paper. Attempts to defame the authors will not change that. Scientific objections? Write a scientific paper.
Prof. dr. C.A. de Lange.
Prof. dr. Cornelis A. de Lange
CC BY-SA 4.0
2023-08-15T23:59:30.207Z
Outgoing IR (from ground in one direction) being absorbed within the atmosphere, then reradiated in all directions (half up, half down) before it reaches space - halving how much (of the portion absorbed is going spacewards - is how the greenhouse effect works, If 'saturation" means all is absorbed and none makes it all the way to space in one go, it just means it is absorbed and re-radiated lower in the atmosphere, which retains more heat - and that is the very definition of enhanced greenhouse effect.
Ken Fabian
<climate-change><geophysics><climate-models><atmospheric-radiation>
What is technically wrong with Wijngaarden & Happer's paper claiming to show that CO2's contribution to surface warming is saturated?
SLD
# What is technically wrong with Wijngaarden & Happer's paper claiming to show that CO2's contribution to surface warming is saturated?

(Asked by: username_0 on 2023-05-29)

The paper, [*Dependence of Earth’s Thermal Radiation on Five Most
Abundant Greenhouse Gases*](https://arxiv.org/pdf/2006.03098.pdf)1, has been reportedly rejected from several major journals. By analysing absorption spectra of greenhouse gases in more detail than has been done previously, it claims to show that CO2 is now effectively saturated (with respect to radiative forcing) and any further increase in atmospheric concentrations will lead to negligible temperature change at the surface. Their numerical results agree with previous literature on the subject. The authors are known climate emergency sceptics. While noting that it is obvious that if the result is correct there would be enormous political ramifications, my question is not concerned with those.

Presuming the article is not being published because it's so incorrect it doesn't merit peer review, **I would like to know *precisely and technically* why the paper is wrong**. The authors are physicists so I would like to understand its flaws from the perspective of climate science if possible.

I am specifically *not* interested in hearing arguments along the lines of "the IPCC is right and this is incompatible with that so it must be wrong" - again I am looking for a precise and technical rebuttal.

Thanks!

---

[1] W. A. van Wijngaarden and W. Happer, [“Dependence of Earth’s Thermal Radiation on Five Most Abundant Greenhouse Gases.”](https://arxiv.org/pdf/2006.03098.pdf) arXiv, 2020. doi: 10.48550/ARXIV.2006.03098.

**Tags:** climate-change, geophysics, climate-models, atmospheric-radiation

> **Comments:**
> **username_1**: I've seen the basic argument before, and the model would seem to fail to explain the climate of Venus.  
> **username_2**: The paper does not say that further increase in CO2 will cause 'negligible' temperature rises. In fact its conclusions about the direct forcing of a doubling in CO2 are in line with values commonly quoted as you note. Adding in feedbacks you arrive at the range of forcing commonly accepted and backed up by observation.  Only expert reviewers will know why the paper is (if it has been?)  rejected., but it certainly doesn't  overturn basic climate science.  
> **username_1**: From the conclusions on Page 34, *Doubling the CO₂ concentration (...) surface warming (...) result of 2.3 K*, that is not consistent with "any further increase in atmospheric concentrations will lead to negligible temperature change at the surface". Their estimate is well below the range of estimates by other models, but 2.3 K is not negligible.  
> **username_3**: @username_1 The sensitivity to CO2 doubling (including feedbacks) has been debated for quite some time, resulting in a wide range of 1.5 to 4.5 K. The three key problems with this paper are (a) The authors think they've done something new, a line-by-line analysis. This is not new. (b) The authors repeatedly use the word "saturated" so as to downplay the effects. All atmosphere scientists worth their salt know this. It's why the effect of adding CO2 is logarithmic rather than linear. (c) The authors appear to have ignored feedbacks. They lament the lack of water vapor data. These data do exist.  
> **username_4**: Nothing is wrong with this paper. Attempts to defame the authors will not change that. Scientific objections? Write a scientific paper. Prof. dr. C.A. de username_4.  
> **username_5**: Outgoing IR (from ground in one direction) being absorbed within the atmosphere, then reradiated in all directions (half up, half down) before it reaches space - halving how much (of the portion absorbed is going spacewards - is how the greenhouse effect works, If 'saturation" means all is absorbed and none makes it all the way to space in one go, it just means it is absorbed and re-radiated lower in the atmosphere, which retains more heat - and that is the very definition of enhanced greenhouse effect.  

---

## 4 answers

### Answer by username_6 on 2023-06-22. Score: 14

To answer the original question about CO2 saturation, I'll describe spectral absorption. Each gas in the atmosphere absorbs light at specific wavelengths, and some wavelengths are absorbed more than others. The spectral absorption of CO2 is shaped like a V. With no CO2, the radiative spectrum of Earth would resemble a black-body. When CO2 is added, this 'V' is pushed into the black-body spectrum, making a notch. At present concentrations, the bottom of this notch is 'saturated', meaning it hits the bottom. As more CO2 is added, the V is pushed further down into the radiative spectrum. The bottom certainly remains saturated, but the edges of the notch continue to erode.

There are other problems with this paper.

Figure 6 in the paper shows that doubling the atmospheric concentrations of CO2, N2O, and CH4 would cause increases in radiative forcing. They claim these increases are negligible, but they are not. Their own data show that doubling CO2 would cause an additional increase of 3.74 W/m2. To put this in perspective, all radiative forcing to date, referenced to the start of industrial times in 1750, is 3.4 W/m2. Doubling N2O would cause an additional 1.99 W/m2. Doubling CH4 would cause an additional 1.12 W/m2. These numbers are not "negligible".

Figure 15 in the paper presents their model's results, side-by-side with satellite measurements. To the naked eye, they look good. However, when they are plotted against each other, they do not match. As their model is meant to study spectral absorption, you might think their model would match the satellite data in the "spectral window" where no absorption occurs. It does not. Their model must be scaled by +5.6%, -3.9%, and -12.5% for the Sahara, Mediterranean, and Antarctic datasets, respectively. Even after adjusting the model to match the satellite data, the model overestimates the amount of outgoing radiation. This infers that the Earth is staying cool, when in fact it is retaining heat. The discrepancy is on the order of 3-5% globally, which is quite large.

In answering this question, I have used the data presented in the paper itself. As the authors did not provide the raw data, I used software to digitize the graphical data. My results may be off by a decimal place, but they are in the ballpark.

> **Comments:**
> **username_7**: It would be helpful if the answer could include a sentence on how close models generally are expected to match reality in this field. In my personal work experience in other fields (which is admittedly dated by now), a particular predictive model matching to within 10% of the current reality on a particular metric can be acceptable, and matching to within 5% would be excellent. As a consequence, one may look towards the use of ensemble modelling.  
> **username_8**: It is not true that "their own data show that doubling CO2 would cause an additional increase of 3.74 W/m²." Per their Table 2 (p.19), they show an additional 3.0 W/m² (not 3.74) from a doubling of CO2, an additional 1.1 W/m² (not 1.99) from a doubling N2O, and an additional 0.7 W/m² (not 1.12) from a doubling of CH4. Whether you consider those numbers negligible or not is a matter of perspective, but they certainly are not worrisome. We've already had about log2(420/280) = 58% of a doubling from CO2, plus about half that from other GHGs, yet only 1.15±0.13 °C of warming from it.  

---

### Answer by username_9 on 2023-09-08. Score: -1

The abstract of the paper says it is based on the assumption absorption bands are not saturated. This is true only at low levels of CO2, much lower than at present. See NASA Technical Memorandum 103957, Appendix E, which shows that zero IR energy gets to space in the 14-16micron band. That is, the band is salready saturated

> **Comments:**
> **username_10**: This does not provide an answer to the question. Once you have sufficient [reputation](https://earthscience.stackexchange.com/help/whats-reputation) you will be able to [comment on any post](https://earthscience.stackexchange.com/help/privileges/comment); instead, [provide answers that don't require clarification from the asker](https://meta.stackexchange.com/questions/214173/why-do-i-need-50-reputation-to-comment-what-can-i-do-instead). - [From Review](/review/late-answers/18506)  
> **username_11**: Where's this abstract at?  
> **username_5**: Being saturated just means all the outgoing IR is caught within the atmosphere, where it re-radiates equally in all directions, ie half going back down. More CO2, the lower down it gets absorbed and re-radiated as well as the higher up it must re-radiate to escape to space. More energy is retained within the atmosphere. Almost the textbook definition of global warming.  
> **username_8**: NASA Technical Memorandum 103957 Appendix E is "Transmittance at sea-level." The fact that it is zero between 14 & 16 µm (pp. 114-116) does not mean that "zero IR energy gets to space" in that band. Rather, it means that all of the radiation from the surface in that band is absorbed in the atmosphere. However, the CO2 in the atmosphere doesn't just absorb radiation, it also emits it, so quite a bit of radiation in that band does reach space. van Wijngaarden and Happer report that a doubling of CO2 would reduce the amount of that escaping radiation by a globally averaged value of 3.0 W/m².  

---

### Answer by username_12 on 2024-05-18. Score: -2

With respect to the peer reviewed status, peer review is broken, even Nature recognizes that. The insistence on peer review is generally by those who are unable to assess a paper for themselves or are looking for an excuse not to consider it. Try watching [Climate the movie](https://climatethemovie.net/) and see what Happer has to say for himself.

The photon path length for CO2 at 15 microns is 20cm, for water at 7.6 microns is 4mm (temperate latitudes) ~ 1mm in tropics. For methane it is 250m
Path length is the average distance traveled by a photo before striking a GHG.
That means that by a metre or two above the surface all radiation that can be absorbed by GHGs has been absorbed. This is what saturation looks like.
Increasing CO2 does not cause any more absorption in the main bands, the only increase comes from the wings due to band broadening. For water, band broadening means that its spectral lines become effectively joined to approximate a black body. This is how it absorbs all the radiation that methane might otherwise have absorbed. However note above that the path length of a photon at 7.65 to hit a methane is 250m but only 4mm to hit a water molecule. That is why methane is irrelevant.
With respect to the variation between W&H and the satellite, It must also be remembered that the calculation are based on clear air - no cloud. Cloud substantially reduces the radiation to space, But what do the satellites deem as clear air ? I have been in the tropics and in the Mediterranean where there is no cloud but moisture/pollution make the air very hazy. I suspect this would impact significantly on the satellite data.


---

### Answer by username_13 on 2024-05-16. Score: -3

The paper by W.A. van Wijngaarden & W. Happer has not been published. Only a preprint has been uploaded by the Authors in arXiv.
Preprints and early-stage research uploaded in arXiv have not been peer reviewed.
I guess the paper was rejected when submitted to scientific journals. We don't know why the paper did not pass the peer-review process, i.e., the scientific reasons behind its possible rejection.
However, I wish to remind that a paper by D. Schilknecht, entitled "Saturation of the infrared absorption by carbon dioxide in the atmosphere" was published in 2020 in a scientific journal (International Journal of Modern Physics B, see <https://www.worldscientific.com/doi/abs/10.1142/S0217979220502938>).
The peer-reviewed paper by Prof. Schilknecht leads to similar conclusions, i.e., upon doubling the CO2 concentration, a 0.5 °C increase of the surface temperature should be expected. The paper clearly states (pag. 15) that "This conclusion is in strong contrast to the values of 1.5-4.5 °C quoted in the 2013 IPCC report".

> **Comments:**
> **username_14**: Does his paper offer any explanation of why the temperature has already gone up by over 1 °C , when we're about halfway to doubling the CO2 concentration?  
> **username_13**: Read it (it's open access) and you'll know. Anyway, very briefly, it depends on the logarithmic nature of the Beer-Lambert law.  
> **username_14**: You reference a paper that says "upon doubling the CO2 concentration, a 0.5 °C increase of the surface temperature should be expected." We haven't even doubled  yet, but the temperature has already gone up over a degree.  You're claiming that's because of the logarithmic nature of the Beer-Lambert law.  I'll suggest it's because the referenced paper is clearly wrong.  
> **username_13**: I'm not claiming anything. I tried to summarize the rationale behind the paper published by Schilknecht in an International scientific journal. If you have solid arguments against it, send a specific comment to the same scientific journal. This is the way science works. I wonder if you have ever seen a plot of y = log(x). Do you know the concept of derivative? do you know the derivative of log(x) ???  

---

