Why do you want to know this?

What we call a "radiative window" is a set of wavelengths where there is a high probability for the photon emitted by the surface to escape the Earth's atmosphere.

Why is it related to greenhouse gases? Because they absorb thermal infrared photons and an increase in their concentration "closes the window" = narrows the spectral bands where the photon can escape.

How is this related to climate change? The incoming solar radiation penetrates the atmosphere in the shortwave and warms the surface (partially, it is absorbed by atmospheric gases, but this effect is small compared to trapping the longwave radiation). The surface emits the photons in the longwave, which are either trapped by the atmosphere or escape it. Each photon carries certain amount of energy.

The lower the concentration, the broader the window, the larger the probability for the photon to escape and to carry away the energy, and the colder the climate. (and vice versa)

Hope this helps.

Thank you very much Dr. Artem for your time and beautiful notes.

Regards,

Shukra

Shukra,

The atmospheric radiative windows are better know as the infrared window. There is a description of the infrared window in Wikipedia. See https://en.wikipedia.org/wiki/Infrared_window

Alastair

If he cannot find this himself he is not worth an answer

I still like the question. I've not been entirely satisfied with the answers I've seen.

I once spent some time at a website where they said they were giving "low-level" explanations and "higher-level" explanations... The trouble was, the explanations weren't just "Less-advanced" and "more-advanced" descriptions of the same theory. They were literally different theories.

In a less-advanced version, it had to do with Beer's law, and as concentration increased, the bandwidth didn't narrow, but the concentration made the gas go from transparent to opaque..

In the medium advanced version, it was very much like the description given by Artem G. Feofilov . That is, that the bandwidths narrow as the concentration of greenhouse gasses grow in the atmosphere.

In the most advanced version, the Carbon Dioxide captured 100% of the light from the ground, but released the energy at a higher altitude, hence providing a greater insulative effect.

These different models seem mutually exclusive to me, rather than being three different "levels" of description of the same theory.

Harry ten Brink

I was wondering why you were so critical of someone for asking a question. Is it because of the unstoppable noise of global warming denialists? So many clueless people all voicing an opinion about an issue they know virtually nothing about? I can understand that difficulty. Yet, to me, the confusion about the Atmospheric Window is the SOURCE of the confusion about global warming science. Ever since the popular documentary "An Inconvenient Truth" where a well-intended, but slightly incorrect explanation for CO2 induced global warming was widely believed, a situation has been created where those desiring to figure out the real explanation are demonized, and misidentified as being on the same side as the climate science deniers.

From your answers, Harry, I conjecture you believe that Shukra Raj Paudel is trolling to drive a wedge between the scientists who defend the idea of CO2 induced global warming. Perhaps, but it's also possible he has no idea that he's stepping on the question behind the controversy at all. That controversey is there, whether he asks about it or not, and whether people are aware of it or not.

The people who all agree that CO2 induced global warming is happening may actually have completely different theories or understanding why or how CO2 causes warming. Whether you think these differences are subtle, or dramatic, the fact is they are different, and mutually exclusive.

I've already listed those three above, but I'll list them here as Version 1, 2, 3.

Version 1: Infrared Image of Ground is Visible from Space, but as concentration of CO2 gets higher the image disappears, made more and more blurry . (This was essentially the version of things as presented by Al Gore, though he added that the CO2 looked like little demons.

Version 2: Like Version 1, except the concentration of CO2 actually affects what colors (wavelengths or frequencies) of light get through the atmosphere unimpeded. This is the reason that Artem G. Feofilov gave. I am aware that differences in pressure can have some effect on the width of spectral lines. This is part of how we classify stars as OBAFGKM. However, these are large changes in pressure, and the changes in concentration of CO2 would have an incredibly small effect on the pressure of the gas in our atmosphere.

Version 3: None of the light gets through the atmosphere unimpeded, but the concentration affects either the insulative properties of the atmosphere, or the thickness of the insulation.

I am personally the most convinced of Version 3. Unfortunately this puts me at odds with anyone who has become convinced of Version 1 or Version 2, though we are all on the same side when it comes to the idea that it is urgent that CO2 emissions be reduced.

Jonathan Doolin

This is ResearchGate and one may assume that a questioneer first googles for atmospheric window

Notice: that he simply asks what is

Such a question is most often already answered in an encyclopedia

and Wikipedia is a good first aproach

When the questioner does not like the lemma or is left with a question it is a different story

And for your question: please give us/me the references for the version

Now it is not easy to grasp the essence of these

And Al Gore is not the expert I would go to to learn about IR spectroscopy line spectra line broadening and background continuum for the specific gases of which water is the most important

Dear Harry,

You give, as your reason, "IR spectroscopy line spectra line broadening " This is, what I have called, above "Version 2" I disagree that Version 2 is correct. There should be no spectral broadiening based on changes in concentration of CO2.

I do, however, agree with Version 3. There should be a change in the heat insulation properties of the atmosphere, based on changes in concentration of CO2.

To me, the concept of insulation is not really an idea so controversial that it needs much defense. However, it does need to be acknowledged.

On the other hand, your idea that the spectral lines of CO2 broaden with changes in concentration on the order of parts-per-million, should require some level of defense.

I feel that your argument does not defend your position, but seems to consist of a political attack on Al Gore, a red herring about water vapor, and behavioral principles about what sorts of questions and answers are acceptable on researchgate.

Also, you did not actually acknowledge the hypothesis, regarding insulation.

Regards,

Jonathan Doolin

Yes Jonathan,

You are correct. The scientific model of the greenhouse effect is faulty, but since it is "scientific" no scientist will accept criticism of it, as you and I have found :-(

However, line broadening does occur when CO2 concentration increases. For most of the 15um CO2 band, the lines are so broad that they overlap and result in saturation of the outgoing absorption. At the edges of the band there remains an increase in absorption as the IR window is closed, but it is a tiny effect. Thus from a practical (engineering) point of view the CO2 absorption can be regarded as saturated and an increase in atmospheric CO2 will not lead to more absorption.

The reason that the global temperature is rising as a result of increased CO2 is that increasing CO2 leads to the absorption happening closer to the Earth's surface, because of the Bouguer-Lambert-Beer law of absorption.

"If the intensity of the beam entering a layer of matter of thickness l is equal to I0, then, according to the Bouguer-Lambert-Beer law, the intensity of the beam as it leaves the layer is

I(l) = I0e-kel

where k is the specific extinction coefficient of the light calculated per unit concentration c of the substance determining the absorption; k depends on the nature and state of the substance and on the wavelength of the radiation passing through it." [ https://encyclopedia2.thefreedictionary.com/Bouguer-Lambert-Beer+Law ]

Doubling atmospheric CO2 leads to the same absorption occurring in a layer of air of half the height, and so it will be heated with twice the effect. The warm air will still convect so that effect is minimal, but adjacent to the surface of the ground where convection does not occur the air temperature will rise.

This causes the snow line to increase in altitude and latitude, with the result that the glaciers and sea ice melt causing the planetary albedo to decrease. It is the decrease in planetary albedo which is causing the global warming.

I can go on about where the science and scientist are going wrong if you would like. Interestingly, another engineer, like us, who is now a judge has spotted the flaw in the scientific model, but the scientists just ignored him!

Cheers, Alastair.

Alastair Bain McDonald

Thanks,

First let's make a distinction, because earlier, I said Beer's Law was in Version 1, and Insulation was version 3.I also said, in a later post, " the concept of insulation is not really an idea so controversial that it needs much defense. However, it does need to be acknowledged. "

Now, you have presented an equation

(Intensity_{far surface}}/(Intensity_{near surface}) = Exp(-kel)

I couldn't parse what kel stood for from the link, but

Wikipedia's current article on Beer-Lambert Law offers

(Intensity_{far surface}}/(Intensity_{near surface}) = Exp(tau)

where the transmittance, tau=Sum over N gasses [attenuation cross section of each gas * integral over height (number-density of each molecule at each height)]

So that's what I would call Version 1, Beer's Law. So tell me this: for Carbon Dioxide at 400 parts per million in the atmosphere, and light of the relevant frequency for CO2's bending mode, 667/cm, what is the value of tau? What is the value of tau above the rainforests? What is tau above the oceans? What is tau above the deserts? What is tau above the ice-caps?

I have heard that rain forests will actually, suck up huge amounts of Carbon Dioxide, and then breathe it out again, over the course of the day, or the year. But how does that affect "tau" the transmittance?

For CO2, Is tau a number that tends to hover between -1 and -3, or is tau a number that hovers between -20 and -30?

Earlier, I claimed that Beer's Law and Insulation were different models for what's going on... Let's revisit that and consider what is expected from insulation. From Wikipeda's article on "Thermal Insulation" I find an equation:

P/A = k*Delta T/d

Is there a way to show that the Thermal Insulation equation is equivalent to Beer's Law when tau is a large number? (One would need to give an additional integral to tau as given at Wikipedia, because the attenuation cross section of Carbon Dioxide would also be a function of the light-color-frequency, and the insulation equation has no frequency dependence.)

If so, then I may have actually somewhat incorrect in making the distinction between Beer's Law and Insulation, but what I'd still like to see done well, is a description to prove that the insulation equation could be derived from conditions where tau is high for all frequencies of light.

But let me ask another question here... At what value of transmittance is the underlying image obscured? i.e., Does Beer-Lambert's Law go continuously from a clear image to an obscured image? At or about what transmittance could you say the image through the substance is clear? At or about what transmittance would you say the image is entirely blurred?

And another issue... The insulation equation is not designed for predicting the temperature difference between a radiant source and the vacuum of space. It's designed to put a material between two heat-sinks and determine how fast the heat flows between them. However, I think there ought to be a way to consider the thermal conductive properties of carbon dioxide to get a function.

Harry ten Brink : " Now it is not easy to grasp the essence of these "

I see now, somewhat of the issue Harry was having. The insulation idea is not quite so easy in essence. My claim just now was "the concept of insulation is not really an idea so controversial that it needs much defense. However, it does need to be acknowledged. " Such an idea may need more defense than I thought--in the form of better definition, e.g. nailing it down, understanding it with as much clarity and precision as we can.

Carbon Dioxide absorbs light in a significant bandwidth around 667 /cm, where water vapor is transparent. In that range, it acts according to Beer's Law, but it also acts as a frequency-dependent heat insulator. The trouble is, Beer's Law does not give a function of temperature. The insulation equation gives a formula where the difference of temperature is already known. What is needed then, is a form for the insulation equation that gives us the maximum possible transfer of heat, when one side is exposed to radiation, and the other side is freely radiating heat into the vacuum of space.

Regards,

Jonathan Doolin

@Jonathan Doolin,

I am not sure what you mean by “insulation” as it is not a recognised technical term, but I suspect that it could mean absorbance, which is described by Beer's Law here:

A = ebc,

Where A is absorbance (no units, since A = log10 P0 / P ) e is the molar absorbtivity with units of L mol-1 cm-1 b is the path length of the sample - that is, the path length of the cuvette in which the sample is contained. We will express this measurement in centimetres c is the concentration of the compound in solution, expressed in mol L-1

https://teaching.shu.ac.uk/hwb/chemistry/tutorials/molspec/beers1.htm

So if the concentration doubles then the path length will half for the same absorbance. In other words the same amount of energy will be absorbed in half the amount of gas.

The molar absorbtivity varies with frequency, and at low concentrations and path lengths, it forms lines of absorption. This can be seen here: http://rabett.blogspot.com/2017/05/co2-atmospheric-absorption-is-not.html

If you look at the final two spectra you will see that for a doubling of CO2 there is very little change in the absorption with both showing 100% between 600 and 750 cm-1. NB Professor Halbern, the author of the blog, concludes by denying that the absorption is saturated. As far as I am concerned it is as good as, making the accepted scheme where outgoing long wave radiation adjusts to match incoming radiation impossible.

What actually happens is that the surface warms and there in more evaporation from the oceans and clouds produce a negative feedback by reflecting short wave radiation, which limits the warming, just as is now happening with the runaway warming on Venus.

Tau varies with altitude, i.e. path length, but on the two spectra I discussed the transmittance is given as 0.32 and 0.29 for path lengths of 10 km. The energy absorbed is then 68% and 71% of the radiation emitted by a black body at the temperature of the Earth's surface over the spectral region described. At longer wave lengths the radiation is absorbed by water vapour.

Hope this helps,

Cheers, Alastair.

Alastair Bain McDonald

Perhaps this is not a question of either one or the other, but of both. I am suggesting that the predominant phenomenon is probably insulation. You're suggesting that the predominant phenomenon is spectral broadening.

You've given me a link to this website http://rabett.blogspot.com/2017/05/co2-atmospheric-absorption-is-not.html "

where they have used a program called Spectral Calc to find the "transmittance" of air, through 1m, 100 m, 1000m, and 10000m. At 10 kilometers, you find that "Spectral Calc" gives you zero transmittance for a wide range of frequencies.

I can't tell from your comments, for sure, whether you agree with Professor Halbern; ELIRABETT's conclusion. It seems fairly conclusive, now that I look at it, that 10km of CO2 at 400 ppm has transmittance at 32% between 500 to 900 /cm. And at 560ppm has transmittance at only 29%.

What the Spectral Calc program does not do, however, is account for the radiation of heat at the cold side of the tube. If it did, the graph might resemble this: https://web.archive.org/web/20120317051121/http://ishmael.altervista.org/fig2.jpg (from https://www.skepticalscience.com/saturated-co2-effect-advanced.htm)

Here you see an effect of insulation.

The high part of the curve represents the light that came through the transparentness of the atmospheric window, unaffected.by the presence of the carbon-dioxide. The low part of the curve represents a thermal spectrum coming from the upper surface of the troposphere, where the boundary of the troposphere radiates it's limited bandwidth Planck Spectrum freely into space,

The difference in temperature between the lower layer (high curve) and the upper layer (low curve) represents the Delta T you would use in calculating the R-Value of the troposphere.

One should expect that as the Carbon Dioxide in the atmosphere increases, the high curve representing the temperature on the ground will get higher, while the low curve, representing the temperature of the top of the troposphere, should get lower.

Regards,

Jonathan Doolin

P.S.

I was trying to put Wien's Law into cm^-1 form,

(Calculated from 1/lambda=5.879x10^10 Hz /3x10^8 (1m/100 cm)

Wien's Law in these variables is f_peak=(1.96 cm^-1 K^-1) T, so the temperature with peak-wave-number 667/cm is 340 Kelvin.

I thought that sounded awful hot, so I started doing an image search for Planck spectrum in wavenumber units... Seem to be rare, but I came across this website: https://wattsupwiththat.com/2011/03/10/visualizing-the-greenhouse-effect-emission-spectra/

It, similarly, shows graphs where the top of the atmosphere and the bottom of the atmosphere seem to be two distinct curves, but these seem to be from satellite spectroscopy data.

Hi again @Jonathan Doolin,

Eli Rabbet is saying that CO2 is not saturated; I am saying it nearly is! It is not a matter of a glass half empty or half full. It is a matter of a glass nearly full, with Eli, and everyone else, saying that it is not full because the water has not reached the brim.

Both Eli's spectra and your Fig 2 show the same part of the spectrum, but what I have not mentioned is that John Tyndall discovered that greenhouse gases not only absorb radiation they also emit it. Emission is not included in Eli's spectra from SpectralCalc, but can be seen in your Fig 2 as emission at 220 K. It seems that it is assumed by SpectralCalc that the emission can be deducted from the abdsorption to form a net absorption, but that is untrue. The emission is a function of air temperature, not solely absorbed radiation.

That means in the CO2 band, the terrestrial OLR (outgoing long wave radiation) at the top of the atmosphere in the CO2 667 cm-1 band does not depend on the surface temperature. This can be seen in Fig 6 from Hanel et al (1971) which I have attached.

So increasing the amount of CO2 only has a small effect on the amount of long wave (terrestrial) radiation at the top of the atmosphere. Moreover, if you increase the concentration of CO2 the amount of radiation it emits to space could increase and cause cooling!

So what I am saying is that increased CO2 causes the Earth's surface to warm. This melts snow and ice leading to less reflected solar OSR (outgoing short wave radiation) which causes global warming.

The radiation balance at the top of the atmosphere consists of three components: solar incoming short wave radiation (ISR), reflected outgoing short wave radiation (OSR), and terrestrial outgoing long wave radiation (OLR). When the ice melts than the OSR decreases and the Earth warms until the surface temperature (of the oceans) has increased enough to produce enough clouds to restore the OSR to its previous value. It is the OSR which adjust to maintain the balance not the OLR.

Does that make sense?

Cheers, Alastair.

Alastair Bain McDonald

" Eli Rabbet is saying that CO2 is not saturated; I am saying it nearly is "

Yes. The numbers were 32% at 400 ppm, 29% at 560ppm. And the trouble was, the article didn't make plain the question "percent of what?" exactly. I assumed that it was the percentage of energy that passed through the bandwidth plotted in the graphs. http://rabett.blogspot.com/2017/05/co2-atmospheric-absorption-is-not.html " I said above " It seems fairly conclusive, now that I look at it " but I agree that "being conclusive" and "explaining lhe entire cause of CO2 induced global warming" are not the same thing.

We are both now pointing at another phenomena, which we are describing with different words, but I think is the same phenomenon.

The phenomenon I am descrribing as "insulation" and the phenomenon you are describing as " greenhouse gases not only absorb radiation they also emit it... The emission is a function of air temperature, not solely absorbed radiation."

Then, once realizing that we are talking about the same thing, then it's appropriate to check carefully that our intuition and/or math about this phenomenon is the same.

ABMcD: " Moreover, if you increase the concentration of CO2 the amount of radiation it emits to space could increase and cause cooling! "

This seems subtly wrong to me. When you increase the concentration of CO2, the equilibrium condition (Heat In) = (Heat Out) is where we should start, at high level. My initial intuition is that the CO2 emissions in the bandwidth wher CO2 is opaque should be reduced--indicating a cooler top-surface of the troposphere. And that the radiation signature from the earth's surface would be slightly increased, (because it is warmer).

I see you have made abbreviations for the following:

ISR: Incoming Short-wave Radiation

OSR: Outgowing Short-Wave Radiation

OLR: Outgoing Long-Wave Radiation.

I think, though, that OSR is affected by the albedo of the planet... That is, the OSR consists almost entirely of reflected waves in the visible spectrum. With desertification and ice-caps melting, this reduces the OSR, increasing the amount of heat absorbed by the ground, thus increasing the OLR.

The OLR, though, should be classified twice, as OTWLR, and OOWLR.

The Outgoing Transparent Window Long-Wave Radiation, and Outgoing Opaque Window Long-Wave Radiation.

ABMcD: " When the ice melts than the OSR decreases and the Earth warms until the surface temperature (of the oceans) has increased enough to produce enough clouds to restore the OSR to its previous value. It is the OSR which adjust to maintain the balance not the OLR. "

Yes, that phenomenon is there, of course. For instance, it's been rather difficult for amateur astronomers in the past few years because the telescopes simply don't get a clear view of the skies like they used to, because of all the water vapor in the air, these days.

But more relevant to the actual CO2 induced global warming is that the OTWLR (Outgoing Transparent-Window Long-Wave Radiation) should be increasing due to the ground temperature heating up becaue of the radiation energy captured by OOWLR (Outgoing Opaque Window Long-wave Radiation).

Thanks,

Jonathan Doolin

Some remarks

1. CO2 is a trace component in the atmosphere and does hence not count in the heat capacity of the atmosphere

2. The terrestrial IR energy absorbed by the CO2 is transferred to the air molecules within milliseconds

3. The saturation effect has been described ad nausea in the third IPCC report, because deniers used it to deny any effect of increased CO2

here a summary. https://www.ipcc.ch/ipccreports/tar/wg1/044.htm

paragraph above effect of AEROSOLS

Here is what one of the "deniers" makes of it; mid you he has gone thru the whole greenhouse effect:

http://clivebest.com/blog/?p=1169

PS. Clive Best is a denier of the large water feed-back NOT of the increased warming by CO2

"1. CO2 is a trace component in the atmosphere and does hence not count in the heat capacity of the atmosphere"

True. Consider this, though. What is the R-value of 1 inch thick air, vs the R-value of 1 inch thick fiberglass? Then compare, likewise the heat capacity of fiberglass vs. air. I'm leaving this as an exercise for now. My guess would be that the insulation capabilities are very different because the fiberglass will block a lot of infrared radiation that the air would not have blocked. But the heat capacity per unit volume is probably about the same.

"2. The terrestrial IR energy absorbed by the CO2 is transferred to the air molecules within milliseconds"

That may be accurate--I was going to give the "equilibrium state" anywhere from hours to days to adjust to new concentrations of Carbon Dioxide, but regardless of how quick the response is, as I put in my last response, "the equilibrium condition (Heat In) = (Heat Out) is where we should start, at high level. "

3. The saturation effect has been described ad nausea in the third IPCC report, because deniers used it to deny any effect of increased CO2

here a summary. https://www.ipcc.ch/ipccreports/tar/wg1/044.htm

paragraph above effect of AEROSOLS

The trouble is, you're offering an ad nauseam explanation, where we should be getting a clear one. The link you have, there, states, "It has been suggested that the absorption by CO2 is already saturated so that an increase would have no effect. This, however, is not the case. Carbon dioxide absorbs infrared radiation in the middle of its 15 mm band to the extent that radiation in the middle of this band cannot escape unimpeded: this absorption is saturated. This, however, is not the case for the band's wings.: It is because of these effects of partial saturation that the radiative forcing is not proportional to the increase in the carbon dioxide concentration but shows a logarithmic dependence. Every further doubling adds an additional 4 Wm-2 to the radiative forcing. "

Assuming, by mm, they meant to say μm, this is relevant to the conversation Alastair Bain McDonald and I, were having about the 667/cm band which would be, in wavelength, the 15 micro-meter band.

The effect, mathematically, is 2^Δ(P/A)=(c_f/c_i) where c_i=the initial concentration, and c_f is the final concentration. In logarithmic form, this gives Δ(P/A)=ln(c_f/c_i)/ln(2) **Correction - Should be Δ(P/A)=4*ln(c_f/c_i)/ln(2) **

I think we have assented that The numbers were 32% at 400 ppm, 29% at 560ppm... So it would correspond, according to Δ(P/A)=ln(560/400)/ln(2)=0.485 Watts/meter^2 **Correction - Should be 1.94 W/m^2t**

And then you can go into Stefan Boltzmann's Law and figure out how that .485 Watt's/meter^2 affects, for instance, a temperature around 273 Kelvin.

Δ(P/A)= σ(T^4-273^4)=.485

T=(.485/5.67x10^-8+273^4)^.25

T=273.1 **Correction Should be 273.4 Kelvin**

The trouble is, we're already seeing temperatures rise far more that 0.1 (correction: 0.4) degrees Celsius, and if I've done this calculation correctly, (please check!) the 4 Watts/meter^2 for doubling CO2 does not explain it. ALSO, the radiative forcing IS NOT the greenhouse effect. The greenhouse effect, caused by glass in a greenhouse is not an effect caused by the fact that two layers of glass blocks more light than one layer of glass. It is due to the fact that the thicker the glass, the greater the temperature difference between the two sides of the glass can be.

"Here is what one of the "deniers" makes of it; mid you he has gone thru the whole greenhouse effect: http://clivebest.com/blog/?p=1169

PS. Clive Best is a denier of the large water feed-back NOT of the increased warming by CO2"

There in that article, Clive mentions "the temperature profile of the atmosphere is called the (adiabatic) lapse rate and is approximately -7 degrees per km falling to -4 degrees per km in the tropics. "

A thought on inuslation, then, is how to explain this difference in the lapse rate? It seems to me, a "good" insulator is one with a high lapse rate of temperature, while a "bad" insulator would be one with a low lapse rate of temperature.

Harry,

Thanks for posting that.

They say "It has been suggested that the absorption by CO2 is already saturated so that an increase would have no effect. This, however, is not the case. Carbon dioxide absorbs infrared radiation in the middle of its 15 mm band to the extent that radiation in the middle of this band cannot escape unimpeded: this absorption is saturated. This, however, is not the case for the band's wings. It is because of these effects of partial saturation that the radiative forcing is not proportional to the increase in the carbon dioxide concentration but shows a logarithmic dependence. Every further doubling adds an additional 4 Wm-2 to the radiative forcing."

What they don't say is how that 4 Wm-2 is calculated, nor do they say that in 2018, 17 years later it is still not agreed what the value of climate sensitivity is. Nor do they point out that absorption can only increase on one wing, that adjacent to the IR window. The absorption on the other wing is already saturated by water vapour.

They also say "The increased concentration of greenhouse gases in the atmosphere enhances the absorption and emission of infrared radiation. The atmosphere''s opacity increases so that the altitude from which the Earth's radiation is effectively emitted into space becomes higher. Because the temperature is lower at higher altitudes, less energy is emitted, causing a positive radiative forcing."

This flaw in that argument is more difficult to see. It is that it is a circular argument. Why will the altitude of the effective radiation increase? If it does, then it will be at a height where the OLR matches the ISR, so there is no need for the surface to warm.

To put it another way, if the absorption of radiation is saturated then the emission of radiation at the top of the atmosphere will also be saturated. So increasing the amount of CO2 will not affect the outgoing radiation.

I can't say that I am convinced by my own argument here, but I am heartened by Clive Best's post http://clivebest.com/blog/?p=1169 which comes to the same conclusion as me, that the IPCC argument is circular.

Jonathan Doolin

I have a bit of new information that is very old!

The greenhouse effect was discovered by H-B de Saussure, (H-B de S) working on an idea by Pierre Bouguer, not by Joseph Fourier as is generally believed.

I have translated the relevant chapter of de Saussure's book here: Working Paper "Travels in the Alps" Volume 2, Chapter 35 by H-B de Saussur...

At the time Saussure was writing heat was believed to be a fluid called caloric, and in the first part of the chapter Saussure describes two schemes that try to explain the cold on the mountains by considering caloric. I have greyed out those descriptions as they are not relevant, or well translated.

What Saussure did was to use a hot-box to measure the solar energy on a mountain and the valley below and show that solar radiation is not absorbed by the atmosphere. He also reflected the radiation from a how cannon ball showing the existence of IR radiation which had be proposed by Lambert. Saussure then argues that the air is heated by IR radiation from the ground, not by solar radiation (which heats the ground.)

Fourier cites Saussure, but claims that the hot box is a model of the atmosphere and hence the greenhouse effect. But that is not what Saussure was arguing. He was arguing that the air near the surface is heated by terrestrial radiation.

Fourier developed his analysis to explain heat conduction, and claimed that although absorption was happening, that some conduction of heat through the atmosphere would occur, in other words your insulation effect, but that is not what Saussure had found.

Saussure's work was never translated into English, but Fourier's was and his became the dominant paradigm although it is wrong!

Alastair Bain McDonald

That is an impressive amount of effort that you have devoted to translating this entire book from French to English. For now, though, let's look at your summary.

(1) What Saussure did was to use a hot-box to measure the solar energy on a mountain and the valley below and show that solar radiation is not absorbed by the atmosphere.

(2) He also reflected the radiation from a how cannon ball showing the existence of IR radiation which had be proposed by Lambert.

(3) Saussure then argues that the air is heated by IR radiation from the ground, not by solar radiation (which heats the ground.)

1,2,3 seem in good agreement with all models I know.

(4) Fourier cites Saussure, but claims that the hot box is a model of the atmosphere and hence the greenhouse effect.

(5) But that is not what Saussure was arguing. He was arguing that the air near the surface is heated by terrestrial radiation.

Can you give any more technical explanation of the difference between Fourier's model and Saussere's model? For instance, can you compare and contrast the two models with anything I said in my last post?

Thanks,

Jonathan Doolin

Jonathan

A first answer

The lapse rate in the atmosphere derives from cooling by expansion of rising air

it is one degree for dry and 0.65 for humid air because of condensation in clouds and associated heat release

In case of increasing CO2 the average height at which the terrestrial heat is emitted becomes higher. This implies a temperature profile change towards higher atmospheric temperatures up to that level and thus at surface level.

The brilliant atmospheric physicist has a summary in the first part of attached publication

Alistair

Clive Best mistakes the 4 Wm-2 from CO2 doubling with the historical trend line of temperature

The 4 would give 1 C with doubling while with water feed back there is a multiplier that indeed is still the central issue

For a much better and more recent "popular" description I like to suggest (part of a long series of entries)

http://scienceofdoom.com/2009/11/28/co2-an-insignificant-trace-gas-part-one/

Jonathan Doolin

I've not translated the whole book which consists of four volumes. I have only translated one chapter, some other bits and pieces, plus the letter to the Journal de Paris mentioned in that chapter. I have very little knowledge of the French language and used automated translations to help me. I had to translate the whole chapter to be sure that I was not missing anything, and the parts greyed out have received less attention than the rest.

I have now corrected the link to the translation of Saussure's letter to the Journal de Paris, which describes how he invented the hotbox which he then used as helio-thermometer.

The letter is interesting because in it he describes how he showed it was not heating was not produced by the absorption of glass, but rather by the prevention of convection. This was also the conclusion of Professor RW Wood, but not of Eli Rabett. Remember him?

Harry ten Brink

Thanks for posting the Twomey paper.

It makes it easier to see where the IPCC went wrong when they wrote:

"The increased concentration of greenhouse gases in the atmosphere enhances the absorption and emission of infrared radiation. The atmosphere''s opacity increases so that the altitude from which the Earth's radiation is effectively emitted into space becomes higher. Because the temperature is lower at higher altitudes, less energy is emitted, causing a positive radiative forcing."

The main error is to claim that the radiation is emitted from an effective height based on its distance from the surface. The radiation to space will be from the top of the atmosphere not from the bottom. So to find the effective temperature you have to work down to a place where the air is at the effective temperature, not work upwards.

Moreover, the OLR is not just from the CO2. It also originates from the other greenhouse gases and the IR window. Since the CO2 is mainly saturated, the only change to the OLR will be in the wings of the CO2 band. So the effect of increasing the CO2 will be minimal.

Moreover, it is claimed that the imbalance at the top of the atmosphere (TOA) will cause the Earth's surface to warm, but no mechanism is described that would make that happen. Only the Mesosphere has to warm for the TOA balance to be restored, and the surface temperature would remain unchanged.

It is a nice theory if you believe that the OLR in the CO2 band travels from the surface out to space, but is not realistic.

@Jonathan Doolin, do you agree?

Harry ten Brink , Alastair Bain McDonald

Thanks for the reference to S. Twomey's paper. I will for now, just offer this critique of equation (1) from his paper, because I think a clear explanation of the greenhouse effect probably needs a distinction of effective and actual temperature.

Twomey offers $$(1)\;\; \sigma T_e^4 = (1-A)S_0$$

Here, $S_0$ is the incoming intensity $$S_0=\frac{P\subText{incoming}}{A\subText{cross-section}}$$ from the sun, about 1000 Watts per square meter if the sun is straight overhead. (An unfamiliar experience for people outside the tropics)

$\sigma=5.67\times 10^{-8} \UnitUnitPerUnitSquared{Watt}{Kelvin$^4$}{meter}$

Albedo, $A$ is a unitless number in the domain [0,1]. It is a function of the incoming frequency distribution, and the properties of the surface. Albedo could increase with greater ice-coverage, or decrease due to desertification and paving. The incoming frequency distribution is a thermal Planck Spectrum from the sun at near constant 5778 Kelvin.

$T_e$ is the “effective” temperature of the ground.

Equation 1 is making certain assumptions

\begin{enumerate}[1.]

\item all of the energy that is not reflected by the surface is absorbed by the body

\item the body achieves thermal equilibrium

\item thermal equilibrium is maintained by emitting light over the same surface as came in

\item The emissivity of the object is 1 over all frequencies

\end{enumerate}

How well are these criteria met?

Well, there are some issues... For one, the rotation of the earth and the position of the sun means that the surface area of emission is essentially 4 times the surface area of absorption. This is the ratio of the area of a disk of radius R, compared to the area of a sphere of radius R.

On average, we can probably assume that the earth is roughly in thermal equilibrium over a long enough period.

And we can probably assume that the SURFACE of the earth has emissivity of approximately 1 in the Infrared Frequencies of light that make up the thermal spectrum. However, let’s think for a moment about what would be the case if this were NOT true.

If the emissivity were less than 1 over the relevant spectrum, then the body would heat up higher than its effective temperature, so as to release sufficient radiation in the available bandwidths of emission.

As an example, consider a surface that absorbs visible light, but cannot emit in the radio spectrum. It would continue to absorb visible light, thus gaining temperature, until it rose to a temperature high enough to emit in the infrared spectrum. So though the effective temperature would be a temperature that would yield a radio spectrum, the actual temperature would be a temperature sufficient to put out an infrared spectrum.

I think there could be a better way to express this as

$$(2)\;\; \sigma T\subText{eff}^4=e\subText{missivity} \sigma T\subText{actual}^4=\frac{(1-A\subText{lbedo})S_0}{4}$$

Where $e\in[0,1]$ is going to be a measure of what the proportion of the Planck Spectrum of $T\subText{actual}$ gets out.

Notice this does not conflict materially with Twomey’s equation (1). The divide-by-4 on the right-hand side is describing a particular scenario where the incoming and outgoing surfaces are not the same. The “effective temperature” is still in place, but with additional clarification about what the “actual temperature” might be, if the body does not have a Planck emission spectrum.

I'm not a fast reader, but in case someone hasn't got my problem, I do write too much.

Alastair Bain McDonald "The main error is to claim that the radiation is emitted from an effective height based on its distance from the surface."

I made a comment on this in my response... I wouldn't so much say that the word is in error, any more than the "effective temperature" is. The trouble is with what I call "ironic language". The ironic language would be okay if they contrasted what the mean by "effective" with what most people would mean by the "actual" value of things.

I came to think of "effective height" as "the number of layers of Carbon Dioxide" the beam has to go through. But that is increased by adding to the concentration of CO2 rather than actually increasing the height of the troposphere.

" Moreover, it is claimed that the imbalance at the top of the atmosphere (TOA) will cause the Earth's surface to warm, but no mechanism is described that would make that happen "

I don't think that Twomey is claiming an imbalance at the top of the atmosphere. Rather, he's claiming that the effective height rises, keeping the effective temperature gradient the same, resulting in a hotter lower surface. My complaint is that the words should be more like The Actual height stays the same, while the actual temperature gradient increases, causing the hotter lower surface.

That being said, I'm still only on page 1.

Effective height is the hypothetical level at which the temperature equals that of a globe without atmosphere of -33 C. With CO2 and other greenhouse gases increasing this occurs at a higher level in case of ajustment

Using the forcing idea it means that at the original level more radiation is emitted outward and thus at the top of the atmosphere at an increased CO2 column burden. Thus before the vertical Temperature profile has adjusted

This assumes the lapse rate in the atmosphere to be constant like Twomey argues

To go a step further I refer to "scienceofdoom"

I was on vacation and I missed this vivid discussion :)

My two cents: when I write "the spectral window becomes narrower" I do not mean the spectral line width (which is sensitive to temperature and pressure but not to CO2 concentration changes). What I'm talking about is the spectral dependence of the column optical depth. Let's consider the window described by five points with the following optical depths: 100, 3, 1, 3, 100 and let's increase the concentration so that the optical depths become 200, 6, 2, 6, 200. Not only the total energy escaping through the second window will be smaller than that for the first one, but also the spectral halfwidth of the second window will be narrower: http://puu.sh/Bhhlv/cef0afbdd6.png

(dashed curve is normalized to solid one to compare the halfwidths).

Of course, all these distributions depend on the actual optical depths and after some threshold in concentration there will be almost no windows left, so that all the photons emitted in the infrared CO2 band will be trapped. This is what is meant when one speaks of the saturation with respect to CO2.

Harry ten Brink "Effective height is the hypothetical level at which the temperature equals that of a globe without atmosphere of -33 C "

I don't understand this definition. I have come up with one possible interpretation, but I don't think it is likely to be what you mean.

P/A=P/(4 π (r_s + h_e)^2) = σT^4 = σ(273.15-33)^4

I am imagining a blackbody of radius $r_s$ with surface temperature unknown, surrounded by a vacuum. The intensity of radiation off the surface is measured at height h_e above the surface, and found to be σ(273.15 Kelvin -33 Celsius)^4.

If that were the case, though, Carbon Dioxide concentration would not affect this quantity at all.

Artem G. Feofilov : spectral line width (which is sensitive to temperature and pressure but not to CO2 concentration changes).

Could you comment on equations 5 and 6 of my work-in-progress at https://www.researchgate.net/profile/Jonathan_Doolin/post/What_is_atmospheric_radiative_windows/attachment/5b79d626cfe4a7f7ca5b6193/AS%3A661441430421505%401534711334390/download/TwomeyResponse.pdf

I was trying to get across that in my intuition here, it was the number-density of the Carbon-Dioxide molecules that was the main linear factor of concern. It seems to me, the quantities, temperature, pressure, affect the density of the gas, then the concentration*density of the gas will affect the number density of the Carbon Dioxide molecules.

But in the end, what is the spectral line width is a comparison of what is blocked out by the lower layers, compared to what is re-emitted by the upper layers.

" What I'm talking about is the spectral dependence of the column optical depth. Let's consider the window described by five points with the following optical depths: 100, 3, 1, 3, 100 and let's increase the concentration so that the optical depths become 200, 6, 2, 6, 200. "

Okay, what would a doubling of the concentration of Carbon Dioxide actually do? It would have an effect of ∛2 on the linear density in each direction, so that the photons have to go through ∛2 more layers of carbon dioxide, and each layer has Area density ∛2 ·∛2 times as dense. Wouldn't those combined effects contribute to the effective optical depth?

" Not only the total energy escaping through the second window will be smaller than that for the first one, but also the spectral halfwidth of the second window will be narrower: "

Okay, I think you mean that the second window will allow a smaller bandwidth of radiant energy to escape, but I may be confused because it seems to me that you've put this "Not only P, but also Q" where I would have said "Q implies P".

" after some threshold in concentration there will be almost no windows left, so that all the photons emitted in the infrared CO2 band will be trapped. "

Let's describe the scenario with your five-point notation as optical depths of 0,∞,∞,∞,0, so literally there is NO window left. The effective depth becomes infinite, meaning there is no way a photon from the ground in the relevant frequencies can escape into space.

There are two questions to ask here, (1) does our actual environment pretty much resemble the scenario described by 0,∞,∞,∞,0? and (2) does the increase in concentration of Carbon Dioxide still affect the warming of ground temperatures.

Though I may be proven wrong, my inclination is to answer YES, and YES to these two questions. For instance, it seems pretty well agreed that a doubling of concentration actually does prevent an additional 4W/m^2 from escape, by narrowing the escape window. If accurate, and that is a lot, then my answers would be NO and YES.

The reason is that the actual global warming phenomenon has less to do with the width of that optical window, and more do with an entirely different phenomenon, which is just the insulative properties which still increases even when the effective optical depth is infinite.

Jonathan Doolin, I believe, we should agree on what we call a spectral line and its width. I speak in terms of a classical radiative transfer in an infinitely thin atmospheric layer. If we consider an optical transition between two rotational-vibrational levels of a given atmospheric molecule then the probability of the transition will follow the Voigt lineshape https://en.wikipedia.org/wiki/Voigt_profile , which represents a convolution of two broadening mechanisms, namely, Doppler broadening and pressure broadening (Lorenzian).

What you mean is the effective lineshape in optical thicknesses (or in an outgoing spectrum), which might be way different from Voigt or any other simple profile because each point of this shape represents an integral of absorption coefficient over height. I had to explain this so that the readers are not misled by similarity of terms.

Answering your questions - if the CO2 windows are closed then the photons can still escape the troposphere because the CO2 does not absorb everywhere in the infrared - finally, some molecule or object will emit the photon in the transparent part of the spectrum and the photon will escape. However, if the CO2 window is closed, further increase of CO2 concentration should not affect that much the warming because the system is already "saturated" with respect to CO2. But, there are other greenhous gases like CH4 - if we increase their concentrations, we'll close the remaining infrared windows.

I never tried to estimate the remaining transparency of the windows, so I can't prove or disprove the 4W/m2 value you give, but it doesn't seem to be unreasonable.

The eqs.5 and 6 of your manuscript are correct, but their usage in the estimates of the radiative transfer requires some thinking. The problem is that the CO2 absorption and emission spectrum is complex and the line overlapping/mixing in the lower atmosphere does not make it simpler. For each given wavength, we can estimate the effect of CO2 doubling, but to get the total energetic effect one has to calculate the absorption spectrum with high spectral resolution at each height and make a convolution. Otherwise, the non-linearity will affect the result (absorption in a bunch of lines cannot be substituted with an absorption in the band without special tricks).

Jonathan

In the absence of an atmosphere with absorbing gases the temperature at the surface would be according to the balance between absorbed energy and outgoing terrestrial energy: t=-33 C

equation 1 in every report on energy balance and thus also in Twomey

Because of absorption by greenhouse gases and down emission of radiation the surface is at a higher temperature and via lapse rate the level of -33 is at about 5 km

This one-dimensional picture is the simplest to understand the greenhouse effect and the enhanced GH effect

There is a simple explanation of the effective temperture of a planet in McGuffie and Henderson-Sellers. They write:

"… climate can be simulated by considering the radiation balance. The total energy received from the Sun per unit time is πR2S [because the Earth presents a disk of radius R to the solar radiation] where R is the radius of the Earth. The total area of the [surface of the[ Earth is, however, 4πR2. Therefore, the time-averaged energy input is S/4 over the whole Earth. Hence,

(1 - α)S/4 = σTe4 (3.1)

where α is the planetary or system albedo, S is the solar constant (1370 W m-2), and σ is the Stefan-Boltzmann constant. If the atmosphere of the planet contains gases which absorb thermal radiation, then the surface temperature, Ts, will be greater than the effective temperature, Te. The increment ∆T is known as the greenhouse increment and depends upon the efficiency of the infrared absorption. Thus the surface temperature can be calculated if ∆T is known, since

Ts = Te + ∆T (3.2)

For the earth, the greenhouse increment due to the present atmosphere is about ∆T = 33 K, and hence combining equations (3.1) and (3.2) give, for α = 0.3, Te = 288K.”

McGuffie, K. and Henderson-Sellers, A. (2001) A Climate Modelling Primer, Research and Developments in Climate and Climatology, 2nd (Paperback), Wiley-Blackwell.

So Te is the hypothetical temperature of the surface of a planet with no greenhouse gases. On the other hand, the effective height Ze is the height where the atmosphere is at the effective temperature, and from where it is assumed that the outgoing radiation is emitted.

My first objection to that scheme is that the greenhouse gases are not black-bodies, not is the emission from the Earth that of a black-body. It is a series of bands which depend strength of the greenhouse gases creating them.

Artem G. Feofilov "Jonathan Doolin, I believe, we should agree on what we call a spectral line and its width. I speak in terms of a classical radiative transfer in an infinitely thin atmospheric layer. If we consider an optical transition between two rotational-vibrational levels of a given atmospheric molecule then the probability of the transition will follow the Voigt lineshape https://en.wikipedia.org/wiki/Voigt_profile , which represents a convolution of two broadening mechanisms, namely, Doppler broadening and pressure broadening (Lorenzian)."

I had not heard of the Voight Profile, but the wikipedia page describes

G(x;σ)=Normal (Gauss) Distribution with mean 0, and standard deviation σ L(z;γ)=Cauchy Distribution giving Resonance behavior, with mean 0, and deviation-parameter γ

You're proposing (introducing the idea to me the idea) that a single layer of Carbon Dioxide ("infinitely thin") will have two phenomena that broaden the absorption profile...

Doppler Broadening, I feel familiar with. This would be associated with the Gaussian distribution of velocities due to the temperature of the gas.

Pressure Broadening--I am not sure of. Is this something to do with the pressures that occur when the molecules collide with one another?

AGF: "What you mean is the effective lineshape in optical thicknesses (or in an outgoing spectrum), which might be way different from Voigt or any other simple profile because each point of this shape represents an integral of absorption coefficient over height. I had to explain this so that the readers are not misled by similarity of terms."

Thank you for the distinction Artem. I think, your description of what I mean seems fair. Certainly, where I suggested 0,∞,∞,∞,0 for a lineshape, each point was meant to represent an integral of absorption coefficient over height.

In light of your Voight distribution model, such a thing may seem impossible, because both the Gauss and Lorentz distribution have infinite tails. Hence passing through an infinite optical depth would block all radiation. But if we assume that energy is quantized, and photons come in discrete energies, I think it may be reasonable to assume there is some effective cutoff where we can say that greenhouse gasses are fully transparent, even with infinite optical depths...

(In fact, that is my own personal hypothesis of where all the missing dark-matter in the universe is--an overlooked homogeneous distribution of diatomic hydrogen. See https://www.researchgate.net/post/Where_can_I_find_the_emission_and_absorption_spectra_of_diatomic_hydrogen_gas )

AGF: "Answering your questions - if the CO2 windows are closed then the photons can still escape the troposphere because the CO2 does not absorb everywhere in the infrared - finally, some molecule or object will emit the photon in the transparent part of the spectrum and the photon will escape. "

I don't think that's the case... Rather, a photon may continue to bounce around until it gets re-absorbed by a surface feature, raising the temperature of the surface, until a higher energy photon is produced, with high enough frequency to be in the transparent part of the greenhouse-gas absorption.

AGF: "However, if the CO2 window is closed, further increase of CO2 concentration should not affect that much the warming because the system is already "saturated" with respect to CO2. But, there are other greenhous gases like CH4 - if we increase their concentrations, we'll close the remaining infrared windows."

Agreed.

AGF: "I never tried to estimate the remaining transparency of the windows, so I can't prove or disprove the 4W/m2 value you give, but it doesn't seem to be unreasonable."

It seems to have been the concluseion of the IPCC. I was thinking the number is probably associated with my comment above: "Yes. The numbers were 32% at 400 ppm, 29% at 560ppm. And the trouble was, the article didn't make plain the question "percent of what?" exactly. I assumed that it was the percentage of energy that passed through the bandwidth plotted in the graphs. http://rabett.blogspot.com/2017/05/co2-atmospheric-absorption-is-not.html " I said above " It seems fairly conclusive, now that I look at it " but I agree that "being conclusive" and "explaining lhe entire cause of CO2 induced global warming" are not the same thing."

AGF: "The eqs.5 and 6 of your manuscript are correct, but their usage in the estimates of the radiative transfer requires some thinking. The problem is that the CO2 absorption and emission spectrum is complex and the line overlapping/mixing in the lower atmosphere does not make it simpler. For each given wavength, we can estimate the effect of CO2 doubling, but to get the total energetic effect one has to calculate the absorption spectrum with high spectral resolution at each height and make a convolution. Otherwise, the non-linearity will affect the result (absorption in a bunch of lines cannot be substituted with an absorption in the band without special tricks).

It seems to me, as we go from bottom-to-top of the troposphere, that both Pressure Broadening and Doppler Broadening will probably change by orders of magnitude as a function of height, in accordance with Temperature and Pressure. However, the concentration of Carbon Dioxide will have negligible effect on either Temperature or Pressure at any actual height.

That being said, increasing the concentration will put more layers of Carbon Dioxide at every actual height.

Thanks again,

Jonathan Doolin

Shukra Raj Paudel,

You asked "What is atmospheric radiative windows?" but it is not clear if what you want to know is "what are atmospheric windows (plural)", or if you want to know "what is the atmospheric radiative window (singular)".

The answer to the first question is given in Wikipedia in the page "Visible spectrum" https://en.wikipedia.org/wiki/Visible_spectrum

They write " Visible wavelengths pass largely unattenuated through the Earth's atmosphere via the "optical window" region of the electromagnetic spectrum. ... The optical window is also referred to as the "visible window" because it overlaps the human visible response spectrum. The near infrared (NIR) window lies just out of the human vision, as well as the Medium Wavelength IR (MWIR) window, and the Long Wavelength or Far Infrared (LWIR or FIR) window, ..."

So a radiative window is a region of the electromagnetic spectrum through which radiation passes without being absorbed.

This is true for most of the solar spectrum, which means that the air is not heated by the Sun. The solar radiation passes through the atmosphere and heats the surface of the Earth. The Earth emits far infrared radiation which is absorbed by the atmosphere, and that is what causes the air temperature to rise during the day when the Sun is shinning.

The answer to the second question is that the atmospheric radiative window is what Wikipedia call the Far Infrared window. This window falls withing the spectrum of black-body radiation emitted from the Earth's surface. When CO2 increases, the CO2 band becomes wider, and the IR window becomes narrower allowing less radiation to escape to space, and causing global warming.

just by chance, the following article caught my eye. I skimmed through it and found it interesting:

Vigasin, A. A., & Mokhov, I. I. (2017). Greenhouse effect in planetary atmospheres caused by molecular symmetry breaking in intermolecular interactions. Izvestiya, Atmospheric and Oceanic Physics, 53(2), 164–173. doi:10.1134/s0001433817020116

ABMcD: "(1 - α)S/4 = σT_e^4 (3.1)"

My trouble with equation 3.1 is that it does not actually make any reference to the temperature that is changed by global warming.

I gave 3.1 as part of equation 2 in my paper https://www.researchgate.net/profile/Jonathan_Doolin/post/What_is_are_atmospheric_radiative_window_s/attachment/5b782e3ccfe4a7f7ca5b2d21/AS%3A660986256183296%401534602812202/download/TwomeyResponse2018-08-18.pdf But I also included that it was equal to

\sigma T_{actual}^4 * emissivity

Where the emissivity is

emissivity = OutputWattage_{this-object at T_actual}/OutputWattage_{blackbody at T_actual}

ABMcD: (from Henderson-Sellers eq. 3.2) The increment ∆T is known as the greenhouse increment and depends upon the efficiency of the infrared absorption. Thus the surface temperature can be calculated if ∆T is known, since

Ts = Te + ∆T (3.2)"

That differs from my proposal in that, I believe that the increment ∆T depends not only upon the efficiency of the infrared absorption, but upon thermal insulative effects even where the efficiency of the infrared absorption is 100%.

ABMcD: My first objection to that scheme is that the greenhouse gases are not black-bodies, not is the emission from the Earth that of a black-body. It is a series of bands which depend strength of the greenhouse gases creating them.

I agree, and that is why I make the distinction between T_actual, and T_effective. Regarding these two quantities, the idea distinguishing a blackbody (emissivity=1) and a non-blackbody (0

The equation is that for incoming solar energy versus outgoing terrestrial radiation

Incoming solar radiation does not change by "global warming": constant

The equation expresses that (1-a) is absorbed of that radiation

At equilibrium the Earth has to emit radiation into space irrespective from where

This meass that looking from space the equation remains valid and that the equilibrium average radiation temperature is according to equation 1

The issue is that greenhouse gases absorb outgoing radiation (from the surface)

and this leads to warming of the atmosphere close to the surface and that is what we surface dwellers experience

An analogy is that of clouds during the night. These trap IR-energy and lead to an increase in temperature in the atmosphere. Also clouds emit IR radiation downwards which enhances the blanketing

Extra greenhouse gases means IR is trapped up to a larger height and IR is finally emitted into space at a higher level.

Assuming a lapse rate in the atmosphere that does not change by this extra amount of greenhouse gases (merely trace gases not affecting the thermal properties) this implies a higher temperature of the atmosphere at the surface= temperature as measured and experienced by us

HtB: "The equation is that for incoming solar energy versus outgoing terrestrial radiation. Incoming solar radiation does not change by "global warming": constant. The equation expresses that (1-a) is absorbed of that radiation."

Yes, that's all correct. You're talking about equation 1 from the Twomey paper, of course. "a" represents the albedo, which is the proportion of the sunlight that gets reflected off without getting absorbed. I confirmed that in both equation (1) and equation (2) of the Twomey Response versions.

"At equilibrium the Earth has to emit radiation into space irrespective from where"

Again, that seems correct. If Earth is at thermal equilibrium, it means that heat in = heat out. Since conduction and convection are unavailable to transfer heat through space, the only available process is radiation.

HtB: "This meass that looking from space the equation remains valid and that the equilibrium average radiation temperature is according to equation 1"

What do you mean "the equilibrium average radiation temperature"? We have defined "effective temperature" to mean that quantity which is solved for by applying equation (1). That is not the temperature of the surface which is radiating, and I feel this is the point that should be stressed. You seem to be going the other way, and adding additional words that further reinforce a misconception that the effective temperature is the actual temperature of the surface.

HtB: "The issue is that greenhouse gases absorb outgoing radiation (from the surface). and this leads to warming of the atmosphere close to the surface and that is what we surface dwellers experience. An analogy is that of clouds during the night. These trap IR-energy and lead to an increase in temperature in the atmosphere. Also clouds emit IR radiation downwards which enhances the blanketing."

That seems correct.

HtB: "Extra greenhouse gases means IR is trapped up to a larger height and IR is finally emitted into space at a higher level. Assuming a lapse rate in the atmosphere that does not change by this extra amount of greenhouse gases (merely trace gases not affecting the thermal properties) this implies a higher temperature of the atmosphere at the surface= temperature as measured and experienced by us."

Let me introduce a visual so that I can describe the difference between our two descriptions. For a visual, look at the first diagram here: http://www.weather-climate.org.uk/02.php

Note the squiggly line in the diagram is straight in the troposphere layer. My description of the situation says that as carbon-dioxide levels increase, the point (h_tpause,T_tpause) where the tropopause intersects the temperature line remains fixed (same height, same temperature), and the point (h_surf,T_surf) where the earth-surface intersects the temperature line moves to the right (same height, greater temperature). The slope of the height-vs-temperature line becomes more horizontal, meaning the lapse rate of temperature per unit height increases.

What you seem to be saying, though, is that the (h_tpause,T_tpause) moves upward, and (h_surf,T_surf) moves to the right, while the slope of the height-vs-temperature line slope (lapse rate) stays the same.

Harry,

You wrote "Extra greenhouse gases means IR is trapped up to a larger height and IR is finally emitted into space at a higher level."

That is only true if the radiation is not saturated. Where it is saturated, over most of the 667 cm-1 band, it will actually be trapped at a lower height.

The IPCC/Twomey scheme is non-physical. Moreover, if that was the way the atmosphere operated, then the Earth's temperature would continue to rise, just as happened on Venus, because there is no mechanism to prevent it rising. Equilibrium is not inevitable without a negative feedback, which does not exist in this case.

Jonathan,

You wrote:

--

ABMcD: "(1 - α)S/4 = σT_e^4 (3.1)"

My trouble with equation 3.1 is that it does not actually make any reference to the temperature that is changed by global warming.

--

That is because Te, the effective temperature, is the temperature assuming that there is no greenhouse effect. [Not really that an apperopriate name!]

Global warming is not being caused by greenhouse gases, rather by the increase in greenhouse gases, which is called the enhanced greenhouse effect.

So there are three temperatures: Te, the effective temperature with no greenhouse gases , Ts, the the surface temperature before the Industrial Revolution, and Ta, your actual surface temperature that is happening now and will happen in the future.

You argued that

Te = Ta4 * emissivity

but of course that should be

Te4 = Ta4 * emissivity.

I am arguing that emissivity does not change because the absorption is saturated. Therefore we need to find another mechanism which is causing global warming. I propose it is the change in albedo, σ, caused by the increase in insulation raising the temperature of the surface so melting snow and ice cover.

Alastair

The trapping refers to the radiation emitted out to space

This is analogue to the situation in a cloud that fully traps the upgoing surface radiation . There the emission is from the top of the cloud

and a cloud that extends to a higher altitude the emission is from a greater height

Jonathan

The surface temperature is governed by a series of processes

Incoming solar energy

Outgoing IR

Outgoing heat transferred to the atmosphere

Evaporation

Emission by clouds and greenhouse gases towards the surface

This energy is all redistributed in the atmosphere and according to the lapse rate the average temperature of the atmosphere is given

Looking from space the temperature of the Earth is 255 K with respect to the IR emission. This corresponds to a level in the atmosphere of around 5 km

This can be deduced from an average lapse rate of 06. - 0.7 K per 100 m rise in altitude

Alastair Bain McDonald

ABMcD: "You argued that Te = Ta4 * emissivity but of course that should be Te4 = Ta4 * emissivity."

I did not argue that.

Look again, at equation 2 from https://www.researchgate.net/profile/Jonathan_Doolin/post/What_is_are_atmospheric_radiative_window_s/attachment/5b79d626cfe4a7f7ca5b6193/AS%3A661441430421505%401534711334390/download/TwomeyResponse.pdf

There are two equal signs here. One of them gives

\sigma T_e^4 = \sigma T_a^4 * emissivity

The other part gives

\sigma T_e^4 = \sigma T_a^4 * emissivity = (1-A) S_0/4

ABMcD: " I am arguing that emissivity does not change because the absorption is saturated. Therefore we need to find another mechanism which is causing global warming. I propose it is the change in albedo, σ, caused by the increase in insulation raising the temperature of the surface so melting snow and ice cover. "

What you are missing here is that the emissivity actually does change because it is not just a function of the absorption spectrum, but emissivity is a function of the ACTUAL temperature of the source. As the ACTUAL temperature rises, so that the "Wein's Displacement Law" peak of the thermal spectrum due to that temperature moves toward the center of the absorbed spectrum the emissivity increases.

Think this way. you have a light where 90% of it's spectrum is released from 640-650 cm^-1. Then very little light is blocked by CO2's 667 /cm line, and emissivity is near 1, and actual temperature is close to effective temperature. But you increase the temperature of that light until 90% of it's spectrum is released between 660-670 /cm. Now almost all of it's spectrum is blocked by CO2, and emissivity drops a lot, and actual temperature is greater than effective temperature.

Jonathan,

You made an interesting point when you wrote:

"What you are missing here is that the emissivity actually does change because it is not just a function of the absorption spectrum, but emissivity is a function of the ACTUAL temperature of the source. As the ACTUAL temperature rises, so that the "Wein's Displacement Law" peak of the thermal spectrum due to that temperature moves toward the center of the absorbed spectrum the emissivity increases."

That is true for black-bodies, but greenhouse gases are not black-bodies. If the temperature of CO2 rises then the centre of its absorption and emission spectrum does not change.

Moreover, for a black-body absorption equals emission (Kirchhoff's Law), but absorption by a greenhouse gas far exceeds its emission, other wise it would not heat the atmosphere.

I try to make this distinction about emissivity in section 6 here:

Preprint Emissivity-and-Albedo

The blackbody surface has emissivity(300 Kelvin) of around 1. The layer of air around it has absorption=emissivity(300 Kelvin) of 0.2, and the whole body, which emits at 1 then has 0.2 blocked has emissivity(300 K) of about 0.8.

Meanwhile, for the incoming radiation, the layer of air has emissivity(6000 Kelvin) around 0. I think, one could say for the surface, emissivity(6000 Kelvin) is (1-Albedo(6000 Kelvin)) but since that absorbed radiation is converted into heat, the Earth's emissivity(6000 Kelvin) isn't used in the output radiation.

ABMcD: " If the temperature of CO2 rises then the centre of its absorption and emission spectrum does not change. "

Have a look at figure 1 and figure 2from the linked document, and see my calculations of the change in that resulting emissivity, and the change in the resulting radiant absorption.

Jonathon,

a greenhouse gas is not a blackbody surface, and its emission does not equal its absorption. The greenhouse effect is the result of a net absorption where the absorption exceeds the emission..

In your figures 1 & 2 the frequency at which absorption takes place, shown in solid black, does not change,