John Eggart: Layman’s guide to the greenhouse effect

Posted: July 29, 2010 by tallbloke in climate

John Eggert, who is currently discussing some of the more technical aspects of co2 radiative physics with Nasif Nahle on another thread, has kindly sent me some of the material he has written on the greenhouse effect. This article helps us get an overview on the issues. There is also a detailed maths and physics paper for download.

An Unsettling Look at the Settled Science of Global Warming
Part 2:  Layman’s Discussion
Copyright: John Eggert P.Eng.

This is the second of three papers on the impact of Carbon Dioxide (CO2) on climate. The first paper is a method of determining the total impact of CO2 on climate. This paper provides an overview of that work in terms that people without a strong scientific background can understand. If you are interested in the details surrounding what is being discussed in this paper, please refer to Part 1.

Note that these papers only consider whether increasing CO2 will change climate. No assertions about current or future temperatures are made. No assertions about the possible effects of climate change are made. No assertions about other gases impacting climate are made.

What these papers describe is the engineering method of determining radiant heat absorption by CO2 in an atmosphere (that is, the greenhouse effect). They show that this effect is practically at a maximum at around 200 ppm CO2.

Although this is a simplified report, some technical terms need to be defined. Please note that these definitions are simplifications. Exact definitions require a level of scientific understanding that most normal people do not have. The exact definitions would also double the length of this paper.

Global Warming (GW) is a term for a change in climate. It means that the earth will get warmer.

Anthropogenic Global Warming (AGW) is a term for global warming, caused by human activity.

Greenhouse Effect is a term for an increase in the atmosphere’s temperature due to heat being held in by various gases, rather than immediately radiating into space. (Note that the heat does radiate into space. It radiates from the gas, rather than the surface of the earth. As the gas warms, due to absorbing heat energy, it also radiates more heat energy).

Greenhouse Gas is a term for a gas that absorbs radiant heat and hence warms the atmosphere, thus causing the greenhouse effect.

Electromagnetic Radiation (EMR) describes a type of energy. Visible light is a small part of this energy. Other types of EMR are X-rays, radio waves and radiant heat.

Radiant Heat is a type of EMR energy. It has the same properties as light, differing only in wavelength (and the fact that our eyes cannot see it).

Kelvin is a temperature measure, similar to Fahrenheit or Celsius. One Kelvin degree is the same size as one Celsius degree. Zero degrees Kelvin (0 K) is called absolute 0 because temperature cannot get colder than this. Zero degrees Celsius (0° C) is equal to 273.15 K. Note that in proper notation, there is no degree sign (°) in Kelvin. For most scientific purposes, the Kelvin scale is used.

The Hypothesis
The greenhouse effect can be easily visualized by an analogy. Think of the atmosphere as a pane of glass and CO2 as a black marker. Light (and radiant heat is a type of light) can travel through the clean (no CO2) glass. An initial amount of CO2 in the atmosphere is like a mark on the pane of glass from the marker. Increasing the C02 is like adding another mark. As the number of marks increases, less and less light can get through the glass (and the glass gets warmer). Similarly, with the atmosphere, as more and more CO2 is added, less and less heat can escape to outer space. With the glass and marker, there will come a point when the entire glass has marker on it. Now if you make a mark, you do not change how much light gets through. The first paper in this series shows that this is also true of the atmosphere. Sooner or later, there will come a time when increasing CO2 no longer has any effect on temperatures and hence climate.

Put another way, there is a value for the atmospheric concentration of CO2 at which increasing the concentration of CO2 will no longer result in increased temperatures. The first paper in this series makes the case that this concentration is 200 ppm; that is, beyond 200 ppm, increasing CO2 will have no impact on climate.

It has been said that the marker analogy is flawed. The alternate hypothesis is that CO2 is like a blanket. The more there is in the atmosphere, the more it holds in the heat. This would be true if absorbance of CO2 followed the type of absorbance proposed by the IPCC. The first of these papers shows why the marker analogy is better than the blanket analogy and shows how the IPCC relationship is an oversimplification.

The Science
Please note that the following greatly simplifies many concepts. This is a broad and simple overview of a complicated issue, not a science course.

Everything in the universe has some positive temperature (in degrees Kelvin). Everything radiates electromagnetic energy, with the intensity of that radiation being directly tied to the temperature. So very cold things only radiate a little bit of EMR. As things get hotter, they begin to radiate at shorter and shorter wavelengths while also emitting all of the longer wavelengths as well. This is because as wavelength decreases, the energy in the wave increases. Eventually, the EMR wavelengths get to the point where we can see them with our eyes, that is, it becomes light. You see something hot glow red. As it continues to heat, it gets white hot. If the heating continues, the new EMR becomes invisible again, but is even more energetic.

Anything that gets in the way of EMR will absorb some of that EMR. The rest will either pass through (like light through a window) or reflect (like light off a mirror). Because we cannot create or destroy energy, the absorbed EMR energy must change into another type of energy. This is usually heat content, meaning that as something sits in light it will tend to warm up. As the thing that absorbs EMR warms up, it emits more EMR as well until a new equilibrium is reached and the temperature no longer changes.

In the case of the atmosphere, there are two sources of EMR. There is the EMR from the sun that warms things up. There is also the EMR from the earth that cools things down. Most of the EMR from the sun is very energetic and at short wavelengths. Most of the EMR from the earth is less energetic and at much longer wavelengths.

The atmosphere of the earth is sort of like a pair of coloured glasses. Some of the EMR can get through and some gets stopped by the atmosphere. In particular, most of the EMR that we can see with our eyes, that is, light, gets through. Some ‘colours’ do not get through particularly well. In particular, infrared or radiant heat, is absorbed by certain gases, such as carbon dioxide, water, methane and others. One gas, ozone, absorbs EMR in the range of ultraviolet (UV). This light causes sun burn and is linked to skin cancer (and vitamin D production, so do get a bit of sun every day!). The UV from the sun is absorbed by the ozone, stopping most of it from getting to the surface of the earth.

The amount of EMR that is absorbed by a gas depends on two things. First is the total distance the EMR goes through in the gas. Second is the concentration of the gas. This means that a short length of gas with a lot of the gas will absorb a similar amount of EMR compared to a long length of gas with a little gas. It is this product or the number you get by multiplying two numbers, which is important in determining how much EMR will be absorbed. This product is called ‘path length’. Because the atmosphere is a pretty long length (for most calculations, it is enough to consider the first 42 kilometers), it does not take much of any particular gas for that gas to begin to have a noticeable effect.

There are at least two ways to figure out how much EMR will be absorbed by the atmosphere, and hence how much it will tend to warm up. Part 1 of this paper is a detailed description of the engineering method of doing this. The second is as performed by climate scientists.

Climate scientists quoted by the various assessment reports of the Intergovernmental Panel on Climate Change (IPCC) use an equation in their models of the atmosphere to account for variation of CO2. This equation is not used in any other field, producing incorrect values for the amount of radiant heat absorbed in an atmosphere.

The Engineering
It is, in theory, possible to calculate how much radiant heat will travel through any particular path length of gas. These calculations are extremely complicated and have areas of uncertainty.  Things such as re-radiation by the gas itself, atomic structure of the gas, etc., must be taken into account. The types of calculations for this are very important in a number of fields, including, but not limited to, climate science.

Some areas that also need to perform such calculations are heating design, greenhouse design, blast furnace design, and so on. Note the repetition of the word ‘design’. This implies the application of science to come up with something that works, or more commonly – engineering. In order to be able to perform calculations for designing many different types of things that must account for radiant heat loss in the atmosphere, H. C. Hottell at MIT performed thousands of measurements of heat as it went through various concentrations of CO2 at various lengths of gas. He then generated a number of graphs that are used by engineers in designing a huge range of applications. In the 1970’s, B. Leckner further refined these curves. The premise of these papers is that these graphs and methods for determining radiant heat absorption in the atmosphere are applicable to determining radiant heat absorption in the . . . atmosphere.

The challenge in using these curves to estimate how much energy is absorbed by the atmosphere, and hence how big the greenhouse gas effect will be, is calculating the atmosphere ‘path length’. Part one of this paper details a method for doing this. Once this ‘path length’ is known for CO2, it is possible to figure out what the effect of changing CO2 will be.

This was done for concentrations from 1 ppm CO2 to 800 ppm CO2. The IPCC equation assumes a 0 for ‘forcing’ at 278 ppm CO2. Although this is entirely arbitrary and without any use, other than as an illustration, the effect can be duplicated by taking the absolute numbers generated using path length calculations and subtracting the value at 278. This was done. In addition, it is possible to reverse this process on the IPCC results and come up with an absolute value for heat absorbed. The result was: For concentrations up to about 100 ppm CO2, the prediction of the impact of CO2 on heat in the atmosphere is (within reasonable limits) equal. At somewhere between 100 to 200 ppm, the results begin to separate.  Beyond 200 ppm, the difference becomes significant. The following graph illustrates this. The source data for this graph is below the graph.

eggert co2 graph

IPCC Heat Length see also AR4
Atmospheric Forcing IPCC Path Absorption Forcing ΔF = αln(C/Co) IPCC q = αlnC
CO2 ΔF q Length Leckner q ΔF Co= 278 ppm CO2
ppm W/m² W/m² Bar-cm ε W/m² W/m² α= 5.35 W/m²
1 -30.11 0.00 0.67 0.033 10.42 -33.46
2 -26.40 3.71 1.3 0.045 14.20 -29.67 q=εσ(T^4) W/m²
5 -21.50 8.61 3.4 0.063 19.89 -23.99 σ= 5.67E-08 SB constant
10 -17.79 12.32 6.7 0.078 24.62 -19.25 T= 273.15 Kelvin
50 -9.18 20.93 33.5 0.116 36.62 -7.26
100 -5.47 24.64 67.0 0.130 41.03 -2.84
200 -1.76 28.35 134.0 0.138 43.56 -0.32
278 0.00 30.11 186.3 0.139 43.88 0.00 Note that in both cases, ΔF is
400 1.95 32.05 268.1 0.140 44.19 0.32 equal to q-q0 where q0 is
800 5.65 35.76 536.1 0.141 44.51 0.63 at CO2=278

Note that the “path length” method works for calculations that would duplicate massively higher levels of CO2 in the atmosphere than are likely. That is, this method is valid for amounts of CO2 far in excess of what will be caused by humans burning fossil fuels.

The IPCC curve shows a continual increase in the effect of CO2. There is an absolute and constant value for ‘forcing’ for every doubling of CO2 concentration. The path length method shows the effect flattening out, and becoming 0 at about 800 ppm. That is, from 0 ppm to about 100 ppm the path length method shows a similar value for doubling compared to the IPCC method. The table below summarizes this.

Doubling Heat Heat
Atmospheric IPCC IPCC Absorption Absorption
CO2 q Δq q Δq
ppm W/m² W/m² W/m² W/m²
1 0.00 10.41657
2 3.71 3.71 14.20442 3.79 From 1 to 2
5 8.61 19.88618
10 12.32 3.71 24.62099 4.73 From 5 to 10
50 20.93 36.61583
100 24.64 3.71 41.03498 4.42 From 50 to 100
200 28.35 3.71 43.56021 2.53 From 100 to 200
400 32.05 3.71 44.19152 0.63 From 200 to 400
800 35.76 3.71 44.50717 0.32 From 400 to 800

This table shows that at levels of CO2 above 200 ppm, the effect drops by an order of magnitude. It is approaching 0 and is, practically speaking, negligible or more simply, zero.

The path length method shows an impact due to CO2 increasing from 278 ppm to 400 ppm to be about the same as an increase from 400 ppm to 800 ppm. That is, what has happened over the last 100 years would require a doubling of CO2 for the same effect. The best estimates given to date are a change of somewhere between 1 to 3 degrees Celsius over the past 100 years, assuming the data as reported by the IPCC is representative of the actual ‘global mean temperature’. Note that this is a highly controversial assumption at this time.

The Copenhagen consensus discussed a change of no more than 2 degrees Celsius. Thus it is clear that no action on reducing CO2 is required to meet the Copenhagen consensus.

What It Means

The short summary of what it means is: CO2 increases will not increase the greenhouse effect. Full stop.  That is it. CO2 is not a pollutant, it will not change the weather or climate. There is no basis whatsoever for trying to control the amount of CO2 in the atmosphere.

The IPCC equation assumes a “logarithmic” or log relation between forcing and CO2. The path length curve more closely resembles a ‘log log’ relation between forcing and CO2. That is the IPCC model is an oversimplification that results in overestimating the impact of CO2 at higher concentrations. The IPCC reports discuss the impact on forcing of doubling CO2. This is because they believe the relation is logarithmic. Indeed for most of the range of CO2 concentrations, it does resemble this.

The doubling table above shows that there is a strong case to be made that this doubling does not continue for all concentrations of gas. This effect is not seen in other fields that calculate radiant heat loss in the atmosphere. It is a precept of science that the laws of science that hold in one area are the same everywhere. Thus, radiant heat absorption in climate science will behave the same way as radiant heat in engineering. Utilizing the climate science model for calculating radiant heat absorption results in inaccurate values for radiant heat absorption at higher levels of CO2. As atmospheric CO2 increases, this error increases as well.


“The Green House effect violates the second law of thermodynamics”.

The second law of thermodynamics states that net heat flow can only move from hot to cold. All bodies radiate energy. If there is a warm body next to a cooler body, both radiate heat. The warm body will radiate more heat than the cooler body, hence there will be a net flow from warm to cold, hence there is no violation of the second law. As it can be shown that all bodies radiate heat, were it true that this fact violated the second law of thermodynamics, then the second law would be wrong, not the (provable) fact that all bodies radiate heat. Seeing as no one is contesting the validity of the second law, it is safe to say there is no violation.

“There is too little CO2 in the atmosphere to impact climate”.

As this series of papers illustrates, the level of CO2 in the atmosphere, though seemingly small, is enough that further additions of CO2 no longer impact on climate. That is, from a climate point of view, there is a lot of CO2 in the atmosphere. The irony of this misconception is that if there were indeed “too little” CO2 in the atmosphere, small changes would have a drastic effect. This is why methane is such an important greenhouse gas (but that is a topic for another paper).

“The effect of water is so large that the effect of CO2 cannot be noticed”.

While water is the main reason that there are noticeable differences in day to day greenhouse effects, the impact of CO2 is additive. The massive effect of water on the greenhouse effect is seen by everyone on a humid summer night when the temperature hardly drops after the sun sets. Or on a very dry summer night when it starts to get cool even before sunset. The effect of CO2 adds to this, but CO2 does not vary as much as water does. The impact of CO2 is also less, but by no means trivial. If there were no CO2 in the atmosphere, the planet would be colder. At low levels of CO2 (lower than any the earth has likely ever seen), increases in CO2 would have a very noticeable effect on temperature, no matter how much water was present.

Copyright John Eggert 2009

The following supporting material is also copyright. People wishing to reproduce this work should contact John directly.

An Unsettling Look at the Settled Science of Global Warming
Part 1: Details

An Unsettling Look at the Settled Science of Global Warming
Part 2:  Layman’s Discussion

An Unsettling Look at the Settled Science of Global Warming
Part 3:  Summary for policymakers

  1. Nasif Nahle says:

    Dear John,

    You say in your article:

    That is, from a climate point of view, there is a lot of CO2 in the atmosphere. The irony of this misconception is that if there were indeed “too little” CO2 in the atmosphere, small changes would have a drastic effect. This is why methane is such an important greenhouse gas (but that is a topic for another paper).

    Would you mean if we talk a bit about the mean free path of photons in the atmosphere without colliding with a molecule of carbon dioxide at its current mass fraction?

  2. John Eggert says:


    Yes, in a manner of speaking. The path length approximation is not a quantum physics method however, so speaking of individual photons would seem to confuse the issue. The method looks at how much of the incident radiant energy is absorbed by the intervening gas. At some point of concentration of CO2, increasing the concentration of CO2 no longer increases the amount of incident radiation absorbed by the intervening gas.

  3. DirkH says:

    Thanks, i didn’t know about Leckner’s experiments. Will bookmark this page and show it to my warmist friends here in Germany.

    My prediction is that Der Spiegel will find out about this approx. Jan 2011. They have a time lag of 6 months against the blogosphere.

  4. GabrielHBAY says:

    I am not sure how to articulate this, but let me try. In a free and unconfined body of gas like the atmosphere: Do we or do we not know if there is dynamic interaction between the different greenhouse gasses in terms of concentration? In other words, can a forced increase in concentration of the one ‘crowd out’ the concentration of the others? Could an increase in concentration of CO2, for example, have a contrary effect on the concentration of H2O, thereby affecting an increase in effect of the CO2 but a balancing decrease in effect of the H2O? Seems to me the real world situation is too complicated to even be sure that the effect of one of the several greenhouse gasses can be evaluated as if it stands alone. I instinctively suspect that no theory that does not handle the entire atmosphere as a ‘system’ will work.

  5. tallbloke says:

    Hi Gabriel and welcome. I think you may be articulating the basis of Ferenc Miscolczi’s paper on the subject. You can find links to it on this thread:

  6. GabrielHBAY says:

    Thanks. Will have a look and hope I can understand it! LOL Not my field, but I find it very interesting.

  7. John Eggert says:

    Tallbloke has requested that I provide an e-mail address if anyone wishes to contact me directly. Use jgefromtheinternet at hotmail dot com


    [reply] No compulsion, just thinking ahead that you might get asked for permission to reprint etc. I can put that email address on the pdf’s available for download, or not, as you wish. Let me know. -Rog.

  8. GabrielHBAY says:

    Ok… Skimmed the gist of it, and this does seem to be just what makes intuitive sense to me. Would explain so much! Is any weight being given to this view in the broader community of scientists working in this field? That is, outside the community of those hell-bent on demonizing CO2…

  9. The funny thing of all this discussion is that without CO2 there would not be any glucose synthesis by plants, no cellulose, then no jeans, no pants, no underwear, and last but not least NO YOU. 🙂

  10. DirkH says:

    GabrielHBAY says:
    July 29, 2010 at 2:37 pm
    “Ok… Skimmed the gist of it, and this does seem to be just what makes intuitive sense to me. Would explain so much! Is any weight being given to this view in the broader community of scientists working in this field?”

    My prediction stands. We’re just ahead of the curve and it’ll take 6 months to trickle down to the mainstream. ATM the entire blogosphere is abuzz with reconsidering back-radiation. It will take 6 months until the media will have to take notice. Then we will see the first headlines like “Biggest climate swindle ever.”

    tallbloke, you can put that on your predictions page. Jan 2011.

    [reply] Done!

  11. bushy says:

    Tallbloke, this makes all sorts of sense but I have a question. First of all I do not accept that the increased CO2 has any appreciable effect on or climate but one thing bugs me. The CO2 molecule absorbs the shortwave infrared and then re-emits but at what wavelength? The wavelength emmited depends on temperature i would presume and if so does this emmited radiation then fall outside of the band absorbed by subsequent co2 molecules. Makes sense to me anyhow.

    [reply] Wait for one of our experts to answer, I don’t know.

  12. Nasif Nahle says:


    Indeed, talking on photons mean free path would complicate this issue, although it would shed light on why the carbon dioxide cannot be an efficient absorber-emitter gas.

    Regarding the calculations of the total emissivity of the carbon dioxide, I put special attention to every detail of the algorithm and find that the total emissivity of the CO2 doesn’t change with the path length. This fact was observed also by Hottel and Sarofim, Leckner and others. I applied the following formula:

    ECO2 = 1-[(a-1 * 1-PE / a + b – (1 + PE)) * e [-c (Log10 (paL) m / paL)^2]] * (ECO2)0

    That formula was taken from Modest’s book on radiative heat transfer. The mathematical process that I applied and the data were reviewed by several colleagues in physics of three universities.

    The correction factor (ECO2) was taken from the tables on total emissivity of the carbon dioxide recorded by Hottel, Leckner and other authors from experimentation. From those charts, I read that the total emissivity of the carbon dioxide at pCO2 = 0.05, a pabs of 1 bar cm, and a T of 300 K the total emissivity of the carbon dioxide is 0.008, although it was the outcome of experimentation. Therefore, I calculated the emissivity of the CO2 at the same physical conditions and found the ciphers given by those authors were correct.

    Nevertheless, we are not talking about the actual current pCO2 in the atmosphere, but a pCO2 (0.05 bar cm) which is ~132 times higher than the actual pCO2 in the atmosphere.

    Therefore, I applied the following formula for knowing the correction factor (ECO2) by which I had to multiply the observed total emissivity of the carbon dioxide:

    ECO2 = [e ((|√ Log10 (290 K * T∞)| / (- c * 1 K)] * [pCO2 * 100 / 5 (pabs)]

    This gave a magnitude for the total emissivity of the carbon dioxide of 0.0017.

    This figure must be multiplied by the correction factor obtained from the first side of the formula, that is, by 1-[(a-1 * 1-PE / a + b – (1 + PE)) * e [-c (Log10 (paL) m / paL)^2]] , which is 0.999948. Therefore, the total emissivity of the carbon dioxide at its current mass fraction in the atmosphere is 0.999948 * 0.0017 = 0.001699. or 0.0017 by rounding up the cipher.

    The formula you subscribe in your post, delta F=5.35 * ln[CO2/CO2o] is incomplete because the figure 5.35 has units W/m^2, so the magnitude F would have units W/m^2. Nevertheless, the concept F must have units °C / W m^-2 if F is referring to Tsens of the carbon dioxide.

    The same problem appears in the formula ΔT = 5.35 W/m^2 * LN [CO2/CO2] because the outcome would be in W/m^2, not in K or in °C.

    On the other hand, if we apply the radiative forcing given by the IPCC into the formula for deducing ΔT, the final conclusion is that the CO2 is quite insignificant in the effect of warming of the Earth:

    ΔT = [5.35 W/m^2 (LN (CO2act / CO2std))] / 4 (σ) (T)^3

    Introducing known values:

    ΔT = [5.35 W/m^2 (LN (385 ppmV / 278 ppmV))] / 4 (5.6697 x 10^-10 W/m2 K^4) (255 K)^3 = 0.46 K

    However, the change of temperature is 290 [K -(255 K – 273 K)] – 273 K = 35 K above the temperature the Earth would have without the redistribution of thermal energy by convection. Therefore, the explanation is not in the carbon dioxide, but in water vapor:

    ΔT = [7.24 W/m^2 (LN (H2Og f/ H20g i))] / 4 (σ) (T)^3

    Introducing known magnitudes:

    ΔT = [7.24 W/m^2 (LN (50000 ppmV/ 1000 ppmV))] / 4 (5.6697 x 10^-10 W/m2 K^4) (255 K)^3 = 7.53 K

    The theoretical conclusion is that the main mechanism of heat transfer from the surface to the atmosphere and into the atmosphere is not radiation, but conduction-convection at the boundary layer.

    The result of natural convection at the boundary layer surface-atmosphere gives a load of thermal energy of 172.53 J, satisfactorily high as for keeping the atmosphere warm.

    Tallbloke… Sorry for the extension of this post.

    [reply] No problem Nasif, thanks for taking the time to contribute!

  13. Leonard Weinstein says:

    Are there any more recent absorption and re radiation measurements for CO2 with the actual radiated wavelengths from Earth? Also are there measurements for Methane at the levels of interest for Earth? I would like some references if possible. I also would be interested in levels like on Venus. I have been in a discussion with the Science of Doom on why Venus has a hot surface, and could use some help.

  14. John Eggert says:


    Venus is substantially closer to the sun and has a very high SO2 component to the atmosphere. SO2 absorbs much more energetic EMR, hence the atmosphere is heated from above as much as from below. It is a different soup there. The interesting thing about SO2 is everyone talks about aerosols. SO2 itself is a very white gas. I believe that SO2 itself, in addition to the aerosols is responsible for absorption of EMR. I have seen no credible argument that this is not the case.

    As with my CO2 graphs, where 50% of the impact of CO2 occurs in the first 10 ppm, other gases also have substantial effects at the very lowest concentrations. This means that possibly immeasurably small levels of a gas could impact climate. Of course with methane (for instance) we would need to know the relative number of ungulates today versus 200 years ago. How many buffalo where there on the great plains? Do they fart more or less than cows. Not something I’ve seen modelled!

    No time for much more right now, I’m off for a vacation.


  15. tallbloke says:

    Have a great holiday John, and be sure to check in when you return. I wouldn’t be surprised if there are a couple of posts awaiting replies. Thanks again for your contribution.

  16. John Eggert says:


    Your statement:

    algorithm and find that the total emissivity of the CO2 doesn’t change with the path length.

    is wrong.

    It is relatively constant, but each path length curve varies with temperature and hence emissivity.

    Not sure about who has been reviewing your work. I’ve taken an advanced heat transfer course at university where we were trained in the correct method of using Hottel’s curves. I’ve also tutored a number of people in the course.

    The equation you are quoting is the equation for the path length curves. The reason one uses the curves, rather than those equations is they are somewhat onerous. If you look at the graphs of emissivity versus temperature for various path lengths, you should see your results on the curves. This may actually occur.

    That being said, what value are you using for path length (paL in your equation)? This is the only thing I have issue with. You may be calculating emissivity correctly, but before you can determine emissivity, you must determine the path length. You have a great deal of information regarding the use of path length, but nothing on how you calculated path length.

    How are you determining the path length of a column of atmosphere?



  17. Nasif Nahle says:


    Only for answering your question, the reviewers are physicists from three different universities.

    No it’s not wrong. It’s the same method used by Manrique, Modest and Serway and other authors. I have read their examples and all of them coincide with the method I applied. What’s your algorithm?

    I would like you consider the left section of the algorithm, which is only a correction factor. Actually, the most importan subject is the emissivity obtained by the second formula that I provided:

    ECO2 = [e ((|√ Log10 (290 K * T∞)| / (- c * 1 K)] * [pCO2 * 100 / 5 (pabs)]

    The results are the same than those obtained by Hottel and after Leckner and other authors by experimentation, therefore, the algorithms are correct.

    Regarding the determination of the length of a column of air, I apply another algorithm which takes into account the dispersion of the carbon dioxide in the atmosphere with altitude, which I suppose you know quite well given that you work on that.

    I invite you to make the calculations introducing any path length you wish for you can see that the change of Total Emissivity is really insignificant.

  18. Alan McIntire says:

    This is a fascinating thread.
    What happens when you apply those CO2 figures to Venus? I realize that a
    significant fraction of the warming on Venus must be due to those clouds. Does
    spectrum broadening account for the difference between the limited effect on earth
    and the atmosphere of Venus with about 250,000 times as much CO2 as we have?

    I know nothing about the specific absorption spectrum of
    CO2, but I was familiar with this model for an n layer atmosphere,

    and realized that by assuming that gases absorbed in all frequencies rather than only
    in a fraction, the greenhouse effect was overestimated. I worked out the
    following just to clarify to myself my understanding.

    The general equation where the atosphere absorbs a fraction p of radiation

    atmosphere absorbs p, reradiates both earthward and sunward
    Sun—–> 1- 1/2 P 1/2 p 1/2 p <—- p Earth
    1-p <—–
    <—- 1-p Earth

    The top of the atmosphere is in balance, receiving 1- 1/2p from the sun, getting 1/2 p from the atmosphere,
    1-p from earth, for total of 1 – 1/2p.

    The atmosphere is in balance, receiving p from earth, radiating 1/2 p to space, 1/2 p to earth.

    Earth's surface is in balance, receiving 1- 1/2p from sun, 1/2 p from atmosphere, and
    radiating out p to atmpsphere, 1-p to space, for a total of 1.

    Again take a planet
    with no greenhouse atmosphere. Add 1 "standard greenhouse
    atmosphere" of a gas that absorbs radiation
    from 1/10 of the total outgoing spectrum, and is transparent in the
    rest. What will the warming effect be?

    You can compute this using the "harmonic mean".

    For the general formula,break the atmosphere into ranges, p0, p1,
    p2…pn. p0+ p1 + …pn had better add up to 1. Take say 3 gases, with
    effective ranges of atmospheric absorption = p1, p2, p3.
    Throw in p0, the value for no absorption.
    p1 has an effective "standard greenhouse atmosphere" of a1, p2 has a
    "standard greenhouse atmosphere of a2, etc.

    The total greenhouse effect will be


    p0/1 + p1/(a1+1) + p2/(a2+1) + p3/(a3+1)

    For a concrete example, let p0 =0.3
    and of course a0=0, let p1 = 0.6 and a1 = 1 ( maybe that's water
    let p2 = 0.1 and a2 = 10 (maybe that's CO2).

    Then, total watt flux will be

    _______________________________ = 1/0.609 = 1.642
    0.3/1 + 0.6/(1+1) + 0.1/(10+1)

    The ground temperature will be (1.642)^1/4 = 1.132 times top of
    atmosphere flux, with a top of
    atmosphere flux of 255 K, surface temperature will be 255* 1.132 =
    288.66 K.

    Let's double the amount of CO2. Assuming everything else stays
    constant, the new temperature flux will be

    ___________________ = 1/0.605 = 1.653

    0.3 + 0.3 + 0.1/(20+1)

    The temperature at Earth's surface will increase to (1.653)^1/4 * 255
    = 289.14 K. Now
    increase the level of CO2 by another factor of 10. Again, assuming
    everything else stays constant,
    the new temperature flux will be 1.665.

    255 * (1.665)^0.25 = 289.66 so increasing CO2 by a factor of 10
    only increased temperature by 0.52 K.
    There is a limit here of 1.666….. No matter how much CO2 is
    increased, forcing in watts can't go past that level.

    Caveats: The temperature assumes the earth is a black body. In
    actuality, it approximates a gray body
    with an average emmissivity of about 0.95. That implies that if the
    effective temperature is 288 K,
    watts radiated per square meter of surface will not be 390.7 but
    0.95*390.7 =371.165 watts

    The model is assuming classical theory rather than quantum theory.
    Once quantum theory is
    taken into consideration, temperature magnification can go higher.

    The combined broadening from a normal speed distribution of
    and the broadening due to the uncertainty
    principle is addressed in the Voigt temperature profile.

    I understand the normal distribution part, but I have no idea of the theory behind the Cauchy distribution part.

  19. Alan McIntire says:

    Sorry, I messed up on my copy and paste, making my first post incomprehensible

    [reply] I’ve tidied up -I think. Let me know. – Rog

  20. Derek B says:

    I wonder if it’s safe to ignore convection here. If somehow it could be inhibited, by inserting transparent horizontal baffles every few metres through the atmosphere say, it would be a lot hotter at ground level. So in practice the temperature down here is capped by a combination of the ALR and whatever the temperature can reach higher up.
    Extra greenhouse gases above 5km, say, would have a significant effect on trapping heat below 5km (the emissivity from there up would be by no means saturated yet). That would raise the upper limit of surface temperature by the same amount.
    So I don’t find this analysis convincing yet.

  21. Nasif Nahle says:

    @Derek B…

    It is because you, Derek, believe that if Derek walks along a road, let’s say 1 meter, Derek stopps being Derek and Derek is Derek no more, but another very different thing. This reasoning is not correct. Convection is a means for the thermal energy is distributed worldwide, not a means of warming effect. What warms the Earth’s surface is the Sun, not the atmosphere. It is the surface what warms up the atmosphere, and the atmosphere, by means of convection, takes the thermal energy from one parcel and carries it on to another parcel.

    My experiment, Derek, demonstrates scientifically that such “trapping” of thermal energy by GHG does not exist. Here the evidence:

    Click to access Experiment_on_Greenhouse_Effect.pdf

    Eggert’s paper was written before I corroborated the experiment of Prof. Wood, so it is comprehensible that he is still talking about “heat” trapped by GHG…


  22. tallbloke says:

    Hi Nasif; nice to see you dropping by. Can you tell us anything about the effect of back radiation on the ocean surface? How quickly is it re-emitted for example?

  23. Derek B says:

    Your reproduction of the Wood experiment is utterly irrelevant. It only proves what was already well known and widely accepted – that the “greenhouse effect” ascribed to the atmosphere is not actually how greenhouses work. So it’s a poor name. Big deal. I don’t know how you have the gall to keep pretending it matters. Sorry, but your constantly dragging up this furphy gets annoying.

    To explain better the point I was making above, consider this crude model:
    Take some arbitrary altitude, 5km say. Suppose the greenhouse effect is fully saturated below that, but nowhere near saturated above. There would be strong convection up to 5km, so the ALR would cap (and effectively fix) the temperature difference between the ground and that height.
    Now suppose we a little more greenhouse gas everywhere.
    Below 5km it makes no difference to the heat transfer, so the temperature difference would be maintained. But above 5km is has a significant effect on the radiative balance, trapping more heat and increasing the temperature at the 5km mark. The ground level temperature would increase by the same amount.
    Now, that’s a very crude model, and it would be much better to consider many layers with both convection and radiation at all levels, but it does prove that convection cannot be ignored when predicting how temperatures will change with increasing CO2.

    But that’s all for John Eggert’s benefit. If you do not accept his analysis you have nothing to contribute to this part of the conversation.

  24. Nasif Nahle says:

    @Tallbloke… Thank you very much for your words of welcome!

    Of course, I am tracking your excellent blog and taking note of every article posted here. BTW, the blog has become extremely interesting through the last months as you are dealing with the Sun’s issue. Very interesting and congratulations! 🙂

  25. Nasif Nahle says:

    @Derek… “If you do not accept his analysis you have nothing to contribute to this part of the conversation.”

    Then what are you doing here, talking nonsense on my experiment and the scientific method?

    What I am testing is the physics of the greenhouse effect itself which can perfectly reproduced and tested through experimentation; I do not need the whole atmosphere to test it. Consequently, your arguments are sophistry.

    Tallbloke, I apologize for this distraction.

  26. tallbloke says:

    No problem Nasif, a good old fashioned ‘greenhouse effect’ punch up is always fun. I miss SoD.
    Have you already met Derek elsewhere?

  27. Derek B says:


    I accept John’s analysis (for now) in the limited context of ignoring convection. My question is whether it is safe to do so when deducing the climate sensitivity. You, it seems to me, do not even agree with his emissivity calculation, coming up with a much lower value.

  28. Nasif Nahle says:

    Thanks again, Tallbloke.

    Yes, I met Derek at

    However, the discussion with him has reached to a dead point because Derek insists that bar cm is not units of pressure by length.

  29. Nasif Nahle says:


    It is not a matter of acceptance of Eggert’s emissivity calculation or not. It is just that he followed different procedures to calculate it. Mine is lower, yes, but in accordance to the algorithm I used. Anyway, whether you take Eggert’s number or not, the absorptance/emittance of the carbon dioxide is too low as to attribute to it any potential of warming. Carbon dioxide potential to emit radiation is quite low, as well as its absorptance; consequently, it cannot be taken seriously as a modifier of climate.

  30. tallbloke says:

    Seems to me that with the approximately logrithmic effect of co2 that even if we accept that the first 60ppm makes any contribution to the surface T of Earth, then once we are up around 270ppm increasing to 390ppm we’re not going to get much of an effect. So if, for the sake of argument, we allowed that co2 caused a 0.3C rise over the C20th, the increase from 400ppm to 530 ppm would produce a lot less.


  31. Derek B says:

    Just to keep Nasif honest, I have throughout asserted that paL is a pressure path length, it has dimension pressure * length, and is a suitable unit for it. Nasif, whether inadvertently through imperfect facility with the English language or otherwise, repeatedly said paL was a partial pressure, sometimes qualified with the meaningless “in one cm”.

    Turning to the question of the overall effect of CO2 (tallbloke), I’m not disputing that the purely radiative effect of CO2 is logarithmic (or even log log perhaps, as Eggert claims). But for the actual consequences for temperature at the earth’s surface you have to look at the whole picture, and that includes convection. According to my simple thought experiment above, it may be the increase in CO2 pressure path length above 5km (say) that’s crucial, not the path all the way from the surface.

  32. Roger Andrews says:


    Re your comment of 9.34 pm:

    The generally-accepted formula for calculating the increase in watts/sq m TOA radiative forcing caused by an increase in atmospheric CO2 is 5.35 x ln(C2/C1), so an increase from 270 to 390 ppm generates 1.97 watts/sq m of forcing. To convert this number into surface warming all you then have to do is multiply it by the climate sensitivity of your choice.

    For a zero-to 60 ppm CO2 increase, however, the formula gives a TOA forcing increase of infinity, which extinguishes life on Earth regardless of what the climate sensitivity of your choice happens to be.

    Hope this helps.