The Impact of CO2, H2O and Other “Greenhouse Gases” on Equilibrium Earth Temperatures
By Paul Homewood
David Coe posted a draft paper here back in January on the IR absorptive characteristics of “greenhouse” gases. His paper has now been published by the IJAOS:
http://www.ijaos.org/article/298/10.11648.j.ijaos.20210502.12
More about the author:
David Coe is a physicist, having read physics at Oxford back in the sixties. His day job for the last 20+ years has been developing a range of sensors for the monitoring of gaseous emissions to atmosphere using infra-red absorption spectroscopy. He thus has not only some knowledge in this area but have access to a database of molecular absorption spectra for most common gases, particularly CO2 and H2O. He is the founding director of the company Codel International Ltd, based in Bakewell, Derbyshire.
If David is right, it would have huge implications, as a doubling of carbon dioxide emissions at current rates would take us well into the 22ndC, and the resulting half degree warming would be barely noticeable.
Comments are closed.
NOT A LOT OF PEOPLE KNOW THAT 
I believe that good, optimistic prospect accords with the publications of Ratzer and Lightfoot and the World Climate Declaration
Congratulations David. Good choice of publisher.
Now more Scientists need to publish here.
You maintain the full copyright of your paper!
Wow, I got through the Abstract, and took a glance at the full paper. One thing stands out, it is full of precise facts and figures, with actual numbers and uncertainty limits stated. Most of the doom and gloom, global warming disaster is imminent papers, are light on the mathematical detail. As Lord Kelvin said:-
I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot measure it, when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind.
So I guess the MSM will ignore the publication of the report, but I look forward to two of my favourite climate change doom mongers, Michael Mann and Bob Ward taking it apart line by line. Maybe Greta and Prince Charles could offer an opinion.
I have always wondered why the Western oil companies have never actively take on the eco loons and defended their record of bringing mankind the benefits of low cost fossil fuels. The head of BP, the aptly named, Bernard Looney is taking the company green and the share price is suffering.
Its a funny old world!
In searching for data about the Allam Cycle for CCS I found a paper by D Fernandes et al to be informative. It goes into great detail of the thermodynamics of the process but makes a bald staement that CO2 reaching 430 ppm will lead to a 2 Deg C rise in global temperatures (from the usual base). The writers are clearly people of some genius so who do I believe? I am now utterly confused by the whole issue.
As soon as you see an argument about atmospheric thermodynamic processes you can be sure that the authors are simply guessing. The atmospheric processes are extraordinarily complex and it is the attempts to calculate climate sensitivity from these processes that has lead to the previous uncertainty in this parameter. The power of this new paper lies in its simplicity. There are no assumptions about complex thermodynamic processes. In fact there are no assumptions at all. It is based upon rock solid spectral absorption data from the excellent HITRAN data base.
What, you mean no hysterical speculation at all, just measured, observed evidence?
Goodness me, that’ll never do.
Doesn’t look like a guess to me. Indeed, as David points out above, “ There are no assumptions about complex thermodynamic processes. In fact there are no assumptions at all. It is based upon rock solid spectral absorption data from the excellent HITRAN data base.”
No fudge factor needed!
The CO2 is often landed with 0.75C increase in temp thru doubling. All the other numbers are developed through feedbacks and none explain why we don’t burn up with runaway temps. Most skeptics work around the edges with clouds and thermodynamics that are used to provide the negative feedback. It’s a great paper and provides good ammo.
Thanks Paul for posting about this paper, and to David Coe for leading the effort producing and publishing it. I did a post at my blog incorporating some of the key diagrams from the paper. For example:
For anyone interested the synopsis is at:
Thank you Ron. That is a very fair summary.
Alas, there are far too many vested interests in so-called climate change and I fear that David Coe et al’s excellent paper will be sidelined and ignored, although I would hope not!
And far too many reputations staked, not just scientists but politicians, celebs, royalty etc. Mere science will never be enough to change that.
I noticed what I think must be a small, but important, error in the penultimate paragraph. It says “There is, and never can be, a tipping point”. I think it should be “There is NOT, and never can be, a tipping point”. Sorry if this seems pedantic.
It is astonishing that no matter how many times you proof read your own work you always miss that vital error! Thank you for pointing this one out.
Good to see but Nothing new here…..Physics and Geological history support each other. This only reinforces the work of Scotese (1999) and Berner (2001) confirmed by the work of W Jackson Davis in 2017 entitled “The Relationship between Atmospheric Carbon Dioxide Concentration and Global Temperature for the Last 425 Million Years
Climate 2017, 5, 76; doi:10.3390/cli5040076 There is NO relationship between CO2 concentration and temperature…..none whatsoever.
Does that vital finding clash in any way with Clutz’s Fig 14 above?
I see it swept through “peer review” in 9 days. Not bad for a revolutionary hypothesis!
Another guess at ECS is just what we needed !
The prior 673 guesses were not enough.
I too fear that we will be ignored, but will go down fighting. I have recently been informed that there is the following IPCC protocol.
IPCC Protocol for Addressing Possible Errors in IPCC Assessment Reports, Synthesis Reports, Special Reports and Methodology Reports (“the Protocol”), as adopted by the Panel at the 33rd Session in Abu Dhabi (10-13 May 2011) and as amended at the 37th Session in Batumi (14-18 October 2013), of a significant error underlying all IPCC reports.
Dr Patrick Frank and Christopher Monkton have both filed notices of errors in the past couple of months. I have been advised to do the same, which of course I will do. I doubt that Dr Frank and Viscount Monckton will take no for an answer. Neither will I!
Richard Green. If you think that this is a guess, please point out which part of the paper is based upon guesswork. After all that is what constructive criticism is supposed to be about.
David – it is an excellent paper. What you didn’t address (and stated that you couldn’t address it) is the effect of the increased H2O vapour (from amplification of the CO2 increase) on the cloudiness. It’s a pretty fair bet that increased water-vapour would lead to increased cloudiness, that would thus reflect a bit more of the incoming radiation and thus produce a negative feedback. This would likely reduce the overall temperature rise since 1850 from CO2 somewhat below 0.24K. Quantifying this from a WAG into an actual prediction is not going to be easy. We really don’t know clouds that well (apologies to Joni).
I’d also note that you assigned the whole 140ppm rise (from 280ppm to 420ppm) to human-generated CO2 emissions, and since the temperature rise after the LIA started around 1700 and we’d expect a warmer ocean to outgas CO2, that (presumably natural) rise in temperature should have moved some of the CO2 from the ocean into the atmosphere after sufficient delays for the ocean currents to move.
Overall, though, that 0.24K looks distinctly non-scary. Anyone looking at the graphs of temperature versus CO2 over the last 300 years should be able to see that whatever effect CO2 has it can’t be very large because we can’t see it in the data. Thus though people have calculated a large effect based on theory, it isn’t there in practice, so those theories must be wrong (or be missing some other effect).
As Mark Twain said, it’s easier to fool people than to persuade them that they’ve been fooled.
I hope you have good luck with persuading the IPCC that they’ve got it wrong. Unfortunately, their salaries depend on them not understanding you, and not accepting your calculations.
Simon. Thank you for your comments. We have been very careful not to drift into speculation, particularly about clouds, when writing this paper. We have tried to base every statement on known facts and basic physics. As for the source of the CO2 rise I believe it is caused mainly by anthropogenic emissions, but not in the way described by the IPCC. To suggest that half the emissions are retained by the atmosphere is total rubbish. Why a half and not a quarter or three quarters. That is never explained. This will be the topic of the next paper we are preparing.
Simon
Agreed I think Ed Berry,s new paper clearly demonstrates that most of the increase in CO2 is natural. It also appears that Happer and Wijngaarden,s latest spectral analysis lines up very well with David,s findings.
We have hundreds of “calculations” of ECS.and TCS.
We have hundreds of confident scientists making those calculations.
The right answer for ECS and TCS is “we don’t know”.
There are a few recent studies I consider reasonable.
Happer is one.
Coe is another.
But the actual ECS does not matter much.
Because it appears to be low enough to be harmless
There are too many variables that can cause climate change,
both natural and man made, to know exactly what CO2 does.
We can easily make a worst case guess,
by assuming ONLY CO2 causes global warming,
and using the results of lab spectroscopy experiments.
That worst case guess is that CO2 causes mild harmless warming.
And we have had mild harmless warming in the past 45 years.
The many decades of IPCC predictions of rapid, dangerous warming,
based on The Charney Report in the 1970s,
are just noise (actually climate propaganda)
You give the impression that you believe the IPCC
wants to make accurate climate predictions, and might give
your work a fair trial. If so, you are a dreamer.
The IPCC was created to predict scary, man made climate change,
and that’s why the climate computer games are so inaccurate —
they are not intended to be accurate !
-They are only intended to support
the coming climate crisis predictions,
which are intended to scare people.
When people are scared, they tend to
turn toward their government and demand
that something be done. And that is EXACTLY
what leftists politicians want to hear.
The IPCC Summary says the same thing every year:
Assuming all climate change
is man made, and dangerous,
we blame climate change on humans,
and declare that is is dangerous !
Change date, repeat the next year.
Like the Groundhog Day movie
Coe — that was a joke !
Either you need a better sense of humor,
or I need better jokes !
Of course your ECS is a guess.
There are too many variables that can cause climate change,
both natural and man made, to know exactly what CO2 does.
Based on actual temperature measurements since 1979,
the ECS is not very high — probably below the last IPCC
huige range of +1.5 to +4.5 degrees C.
So your calculations make a lot more sense
than the IPCC’s. But you are trying to calculate
the correct ECS number, while the iPCC is trying to scare people.
And they are doing a good job of scaring people.
Let’s not pretend that anyone actually KNOWS
exactly what ECS is.
Of course we need to know ECS to four decimal places.
That’s real science.
Three decimal places is malarkey.
Sorry. I had a momentary sense of humour lapse.
Sorry if I got you riled up, Coe !
Not intended.
I paid $1 for that joke.
No problem. We’re on the same side
Can anyone point to the equilibrium average global temperature and show that prior to any significant man-made CO2, the planet kept pretty close to that temperature?
Since the average global temperature has never been a constant then it is surely obvious that it is not remotely suitable for measuring energy changes in the system? It is an utterly simplistic metric wholly inappropriate for what it being used for.
Exactly Phoenix, our climate system is far more complex than the reductionists with their incomplete theories and wonky mathematics can fathom.
Again I’ll show the explained (proxy) variations in temperature & CO2
Where an upper panel shows the air temperature at the summit of the Greenland Ice Sheet, reconstructed by Alley (2000) from GISP2 ice core data. The time scale shows years before modern time. The rapid temperature rise to the left indicate the final part of the even more pronounced temperature increase following the last ice age. The temperature scale at the right hand side of the upper panel suggests a very approximate comparison with the global average temperature (see comment below). The GISP2 record ends around 1854, and the two graphs therefore ends here. There has since been an temperature increase to about the same level as during the Medieval Warm Period and to about 395 ppm for CO2. The small reddish bar in the lower right indicate the extension of the longest global temperature record (since 1850), based on meteorological observations (HadCRUT3). The lower panel shows the past atmospheric CO2 content, as found from the EPICA Dome C Ice Core in the Antarctic (Monnin et al. 2004). The Dome C atmospheric CO2 record ends in the year 1777.
There is no equilibrium glonal average temperature.
Because our planet is not in thermodynamic equilibrium.
The climate is always changing.
I believe the climate today is the best climate
for humans, animals and plants since the late 1600s.
But that’s just my personbal opinion.
According to the IPCC, however, the global climate was perfect
on June 6, 1750, at 3:26 pm — any change from that temperature,
in either direction, is a climate emergemcy
… which can only be prevented
by spending a huge amount of money
and building lots of windmills.
Well said Richard Greene!
Our planet does not need and doesn’t show any equilibrium global that makes sense between average.global CO2 levels and global temperature.
Historically atmospheric CO2 levels risen and fallen while temperatures have done what the earth does — commanded by the sun.
Within the range I predicted: 0 to 0.89 degrees C per doubling.
Global temperatures have never been constant. That big orange thing in the sky and our distance from it keep varying. What we refute is that CO2 plays any significant role in mean temperatures.
NASA used to say that the Sun was the most important source of climate forcing:
“The Sun is the primary forcing of Earth’s climate system. Sunlight warms our world. Sunlight drives atmospheric and oceanic circulation patterns. Sunlight powers the process of photosynthesis that plants need to grow. Sunlight causes convection which carries warmth and water vapor up into the sky where clouds form and bring rain. In short, the Sun drives almost every aspect of our world’s climate system and makes possible life as we know it. ”
But you have to hunt in the internet archive to find it now:
https://web.archive.org/web/20100416015231/https://science.nasa.gov/earth-science/big-questions/what-are-the-primary-causes-of-the-earth-system-variability/
Please post you paper and conclusions to as many places as possible so that at least some readers will see that the CO2 role is not significant.
The first100ppm of Co2 is claimed to have a significant grteenhouse effect.
I would say that is significant.
Richard Greene
Nitpicers of America
Excellent paper. It should be sent to Greta, Attenborough and XR for a proper scientific review.
And by the way – all the best things come from Derbyshire
A ‘scientific view’ from Greta, XR and Attenborough? You’re ‘avin’ a laff!!
The battle over 20th century temperature rises is over, sceptics lost, the next battle may be over the 21st century Pause/Slowdown. The massive propaganda effort over “extreme” weather will continue, and will intensify if the current temperature stasis continues. UAH satellite data is crucial, I hope that Dr. Roy is nowhere near retirement. GHCN data continues its rapid decline, for many countries there is now insufficient temperature data to allow reliable detection of non-climatic perturbations.
A terrific paper which at long last sets a scientific basis for ECS and atmospheric transmittivity.
The IPCC have always fudged this by combining the emissive properties of a range of gases, volatiles and dust then “agreeing” the errors and averaging of these to create both the ECS and the infamous “Radiative Fiddle Factor” that is the driver for the overheating mathematical models (varying from 2 to 8.5 W/m2 in various models).
The IPCC and their tame peers were never called to task to justify these figures which are the basis for the world-wide waste of money to save the planet from carbon.
As a technical query, when evaluating high temperature gaseous radiation of CO2 / H2O mixtures (as in hot gases in furnaces) the transmittivity of the mixture is slightly less than that of the two separate gases. Can this be a non-ideal gas effect that might impact HITRAN?
Thanks for the comments Jack. When dealing with high temperatures in furnaces you have to be aware that the radiated energy is at much lower wavelengths than earth temperatures and you are using a different section of the spectrum. the absorption characteristics are then quite different. Hitran is effective in these situations.
This kind of article is so sick because it totally fails to understand Planck’s Radiation Law and its implications. Without that, the wildest errors are unstoppable.
To put it in simplest terms, a black body (Planck) radiator at temperature T attempts to cool by emitting a characteristic spectrum of radiation that peaks at the Wien wavelength, which is inversely proportional to T. This means that the torrent of emitted photons has a temperature of T because when absorbed by another object it can’t raise its temperature higher than T. This is how thermal equilibrium is achieved via radiation.
But the U.N. IPCC octopus has totally falsified this simple physics with the claim that any radiation of any wavelength if emitted in enough quantity can raise the temperature of an absorbing object by any amount. Hence, radiation from CO2 is capable of raising global temperatures by several C, indeed, already has, because the “vacuum” temperature of the Earth sans atmosphere is 252K, while the observed temperature is 288K, which supposedly proves the heating power of CO2 without really proving anything. If you look into where the 252K figure came from, you will find a beehive of lies and a pure fairy story that works backward to make the numbers come out.
Zonk! CO2’s radiation absorption/emission wavelength of 15 microns has a Planck radiation temperature of -80C, which can’t melt an ice cube and can’t raise the temperature of anything higher than -80C, which is colder than dry ice. Thus the whole edifice of CO2 global warming and all its fancy calculations is revealed to be a gigantic fake physics hoax designed by hardcore global Marxists to frame CO2 as evil in order to scare people into bowing to their demands to shut down the fossil fuel industry, not realizing they will be destroying their own happy wealthy comfortable lifestyles. After that, global Marxism can’t be stopped.
This basic thermal physics is the iceberg that will sink the IPCC ship given enough time, despite their desperate sprint for the cash combined with their power to shadow-ban all critics. They have politicized science big time, threatening the future of the world. But too bad for them, physics trumps politics, and the truth will win in the end.
Too bad, there is vast ignorance about thermal physics, but I’ve been providing a free online course that covers all the basics and brings you up to speed to see through IPCC lies. Expect to spend thousands of hours to master it, but when you do you’ll agree it was the most valuable time you ever spent.
https://www.quora.com/What-specific-chemical-properties-of-carbon-dioxide-causes-the-greenhouse-effect-Why-chemically-is-carbon-more-reflective-than-other-gases/answer/TL-Winslow
I don’t understand this, because the only parameter you can sizeably tweak is the albedo (little scope to vary solar temperature/Earth-Sun distance). Please enlighten me. (My rough calculation for the no-GHG Earth temp gave me 257 K, a little high.)
TL Winslow – the Planck radiation temperature of a microwave oven is around 0.042K if I got the calculation correct, so it can’t heat up my bowl of beans, either.
When a photon is produced, the point where it will be absorbed is beyond its event horizon, so it can’t tell whether the temperature of that body is higher or lower than where it is emitted. Similarly, in flight that photon emission location is beyond its event horizon, so it can know the temperature of neither its source nor destination. Thus for radiation, the temperatures of source and destination have no effect on the photon path.
When it reaches a body, the photon will either be absorbed or not. If not, then the heat in that body will not change. If absorbed, then it adds to the heat energy in the body, whether it comes from a colder or hotter body. If it was otherwise, then causality would be violated and the body emitting the photon would need to be able to predict the future for possibly 13.8 billion years.
A body above absolute zero radiates energy according to S-B. It makes no difference what body absorbs that photon, or indeed whether it will ever be absorbed.
For a receiving body, if it absorbs the photon its energy goes up by that quantum. Thus the CO2 radiation at 15 microns will warm the ground, and the microwave oven heats my beans.
As far as I know, causality is totally inviolable.
Figure that if the body at -80C wasn’t there, then you’d be exposed to open space at less than 4K or -269C. I think you’d cool faster exposed to the 4K.
CO2 is not heating anything.
It is disripting the ability of our planet to cool itself.
The greenhouse gasses are a partial barrier
between Earth’s surface and the infinite heat sink of space.
Without that greenhouse, outdoor plants would die at night
because it would get so cold.
Oh dear Mr Winslow. You do climate scepticism a huge disservice claiming to be the only expert in town, when in fact your knowledge is wafer thin.
Well said, David.
When I read: (Winslow) ‘This kind of article is so sick…’, I knew I was not going to read any kind of science. Except….Winslow seems well-read: it’s his conclusions that are too dogmatic to give time to.
Personally, Harry, may I suggest Winslow is barking mad!
Winslow has a number of good points mixed into a very verbose and often unclear article. I would recommend the Flanders & Swann song “The First and Second Laws of Thermodynamics” to him, (and anyone else who hasn’t heard it): “Heat can’t flow from a cooler to a hotter ‘cos the heat in the cooler will get hotter as a rule(r)”; it also explains entropy well.
I’ll not discuss whether Winslow is mad or not, but his comment misses the context for the study done by Coe et al. They take the fundamental radiative supposition of IPCC and prove how little CO2 can warm earth’s surface even so.
I cmmented above that the wide differences between so-called scientific explanations leaves me confused and I am a qualified engineer. How are the politicians with their History and PPE degrees supposed to understand it? I think I tend to fall back on old fashioned common sense – minute variations in tiny amounts of CO2 in the atmosphere can’t possibly cause hurricanes in Louisiana and floods in Bangla Desh. But then the naggy side of my mind says that it is indisputable that we are are pumping out billions of tons of CO2 into the atmosphere – isn’t it having any impact? Are the Muna Loa measurements all they are cracked up to be?
Vernon
Admittedly they are only cheap devices but the outside measurements I have been taking for the last six months on the south coast of England regularly show a range of 520 to 580ppm, never ever as low as the current official 420ppm
Similar devices in France and Australia show pretty similar results.
The official figure from mauna loa and cape grim etc rely on the air being used by the measuring device to be artificially dried and thereby create conditions that don’t exist anywhere in the real world.
There are also frequent spikes of co2 to 650ppm which further complicates matters.
If David is reading this perhaps he can confirm if the official co2 readings are a fair reflection of the atmosphere or are they too artificially derived to be of any scientific meaning
Localised levels of CO2 can vary by hundreds of ppm. There are many and varied CO2 fluxes apart from the one we hear most about – fossil fuel emissions. For example biospheric photosynthesis by plants and trees remove massive amounts of CO2 from the atmosphere. You should have noticed that your CO2 levels during the night will be rising. Photosynthesis does not work in the dark! Also animal respiration introduces large amounts of CO2. Each human being on average releases 0.3 tons of CO2 per year. Imagine what the rest of the animal kingdom and insects can do. Animals, birds and insects are mobile hydrocarbon combustors, not to mention all the fish in the sea. I believe the Mona Loa data, recorded on the top of a dormant volcano in the middle of the pacific, is as good as any source of data.
Mauna Loa is far from dormant…
‘The latest eruption of Mauna Loa— the last before its longest period of quiet in recorded history— began in March 1984. In dramatic fashion, lava descended to the doorstep of Hilo, the island’s population center.’
https://www.nps.gov/havo/learn/nature/mauna-loa-1984.htm
Vernon
I would like to introduce you to Ed Berry and his analysis of how much our emissions do for the atmospheric content. https://edberry.com/blog/climate/climate-physics/preprint3/
The 33K figure for atmospheric warming looks problematic if the Moon’s average temperature from the Diviner data is just below 200K, suggesting 90K is nearer the mark.
Some interesting responses but I can’t help feeling that we are still in the realm of angels and heads of pins. Until the ice ages and warm periods are fully understood we won’t know the effects of greenhouse gases. The only plausible explanation I can visualise is that the distance from the sun varies. Maybe we shoulsd be studying orbital behaviours rather than greenhouse effects?
Thank you for this.
It is obvious from analysis of global temperature trends for the last 100 or so years that there is no discernible signature of any “slow but steady” man-made CO2 global warming as postulated by the climate alarmists. All we can discern are short term trends of cooling and warming in step with natural phenomena like the AMO (~60 year cycle) and higher frequency ENSO events. This new paper of 0.5°C CO2 climate sensitivity could even be an exaggeration. For a layman analysis see https://edmhdotme.wordpress.com/uk-temperature-analysis-from-1659-to-2019/.
Unfortunately, this paper commits a major mathematical mistake, which basically amounts to curve-fitting an arbitrary formula to a single data point. The trick of this paper lies in equation 2. They claim that the temperature of the earth can be determined by a formula involving the product of the no-reemission atmospheric absorption (a), with some empirical “energy retention factor” n. Then they use the current temperature and current value of a with this formula to calculate n. Finally, they claim n is a constant. Great! Now they have a formula to calculate the earth’s temperature when a changes. Just multiply a*n and plug it into the formula.
Unfortunately this reasoning is completely wrong. There is no reason at all to believe that n is a constant with no influence from other variables. Their reasoning is no better than the following:
I postulate a formula that the mean global temperature is equal to the number of pirates p, times the temperature per pirate x. The current number of pirates on earth is 200 and the mean temperature is ~290 K, so x=1.44. We assume x is a constant. Therefore, if the number of pirates increases to 300, the temperature will increase to 300*1.44=432 K.
Just like theirs, my formula is right, at least currently. The mean temperature really is 1.44 times the number of pirates, right now. The problem is assuming this formula will still hold true as conditions change. In particular, you can’t assume x is a constant.
There is some correct physics in this paper: namely the connection between total radiation absorbed by the surface, and surface temperature. Unfortunately, the formula for total radiation absorbed by the surface is completely empirical, with no physics in its derivation.
Other papers like Happer’s perform a rigorous, physical derivation of the climate sensitivity. They get an answer more than double the one in this paper (even before feedbacks). That calculation should be trusted over this one.
There is no “major mathematical mistake”‘ The issue is how the radiation absorption by greenhouse gases, particularly CO2, will effect the earth temperature. The Hitran data base, also used by Happer, provides an accurate assessment of atmospheric absorption, both for each gas and in total. Some of that absorbed energy will be retransmitted through to space. The question is how much. We can answer that by using the current atmospheric make up and the current mean earth temperature. Does that fraction of retained energy change? The answer has to be currently NO otherwise we would not have the stable conditions that we enjoy. It is atmospheric absorption by greenhouse gases and nothing else other than the sun that determines our current average temperatures. Moreover it is abundantly clear that the temperature “control knob” is H2O not CO2 and of course atmospheric H2O levels are dependent solely on temperature and pressure and not the activities of mankind.
Because of the saturation of absorption bands, increasing CO2 levels will have minimal impact upon temperatures. There is no conflict between this paper and Happer’s. We have derived figures for climate sensitivity which are both well below those quoted by IPCC. The difference is that we have chosen the simple way to do it. If you have tried to read the Happer paper you will understand why.
If you believe that the retention factor “n” changes, please explain how and why. I am always willing to learn.
David, thanks for your response. The retention factor “n” is indeed not a constant, as I hope to show. The first thing I’ll note is that your variable “a” is calculated as the fraction of radiation emitted by the surface that is absorbed by the atmosphere. Of course, the atmosphere itself emits radiation, and thus radiation is absorbed and re-emitted at all levels throughout the atmosphere — the final radiation that is emitted to space vs returned to the surface is the sum of all of this relatively complicated behavior. You claim to capture all of this physics in a single constant factor “n”, which raises my doubt right off the bat.
The best way to evaluate the validity of your formula is to compare it directly to an exact calculation like Happer’s ( https://arxiv.org/pdf/2006.03098.pdf ). In Table 5 Happer obtains a feedback-free climate sensitivity of 1.4 K, more than three times your value of 0.45 K. Accounting for water vapor feedback, Happer obtains 2.3 K, almost five times your value of 0.5 K. This is a major disagreement which points to some problem in your formula. I have no doubt that you have calculated “a” correctly given your expertise, so clearly the formula itself, or the assumption of a constant “n,” is at fault.
I can also make a simple argument that shows the crux of the issue. Again, “a” is the amount of surface radiation which is absorbed after leaving the surface. Suppose we surrounded the earth with a black absorbing sheet 1 meter above the ground. Then all radiation leaving the surface would be absorbed, and “a” would equal exactly 1. No amount of adding or removing greenhouse gases would change “a” anymore. If “n” were also a constant, then your formula implies adding or removing greenhouse gases would then have zero effect on the surface temperature. But this clearly cannot be the case.
The bottom line is that “a”, the absorption without accounting for re-emission, just doesn’t give enough information to calculate the climate sensitivity. It matters how high in the atmosphere the radiation is absorbed, and where the re-emission occurs, and which gas concentrations fall off at different heights. I understand the desire to produce a simple derivation, but you have to consider all of these factors, as Happer did, to get the correct result.
One more thing: since you have already done all of these calculations with HITRAN, I would think you are well on your way to doing a full calculation like Happer’s. You would have to account for re-emission and integrate the radiative transfer over the full height of the atmosphere, but it seems much of the work has already been done. It would be cool to see how your answer differs when you account for these effects.
It doesn’t matter how you manipulate the absorption data it tells you nothing about the complex thermodynamic processes in the atmosphere which determine what happens to the absorbed energy. How much is reradiated back to earth, how much is utilised in the creation of “weather” for example. Ultimately the only thing that affects average earth temperatures is how much long wavelength radiated energy is finally transmitted to space. I would suggest that you are not going to find the answer to that in quantum mechanics. For far too long climate science has complicated the issues to the extent that no-one has been able to determine who is right and who is wrong. Our paper is an honest attempt to simply the issues by calculating how much warming can be attributed to each individual greenhouse gas to maintain the current average earth temperature.
You raise valid points and I am admitting that I know next to nothing about atmospheric thermodynamics. The worrying thing is that I doubt that anyone knows very much more.
Richard Green, in an earlier comment, actually summarised the situation when he joked that this was another in the line of 672 previous “guesses” about climate sensitivity. Except we have used current earth conditions to dramatically limit the range of guesses.
This is a great paper which should generate some reaction from the warmists (although they will doubtless try to pretend it doesn’t exist). The calculations are all transparent and logical and therefore it’s easy for anyone with a reasonable grasp of science and maths to understand.
I have a couple of questions though about the assumption of an average relative humidity of 80%. I would like to understand (a) where this figure came from; and (b) if the actual average were lower (or higher) how this would affect the calculations of ECS for the other greenhouse gases.
Thankyou for your comments. The figure of 80% RH is the figure generally accepted by the climate community. Yes it is a guess. Fortunately as figure 15 in the paper shows atmospheric absorption varies very slowly with RH due to the saturation of H2O absorption bands.If we were to choose a different value for RH, say 60%, the overall result concerning the impact of CO2 would be much the same.