Climate Skeptics: Nasif Nahle’s Shaky Math

I’ve been thinking a lot about how to tackle the problem of misinformation in the global warming debate. Shouting matches on the internet just feed the trolls and rarely achieve anything, and people don’t want to read accurate technical, science-y things, so what can we scientists really do? We can’t attack peoples’ character even when they attack ours, because that just makes us look bad, and fuels the global warming denier image of being an “underdog” or an “outsider”. These people are not on a crusade against science, they are just concerned (and a bit paranoid).

Global warming deniers are people too.

So I’ve decided there are two ways I can actually do something about this problem.

  1. Make simplified explanations of work in climate science more widely available.
  2. Write respectful critiques of contrarian ideas.

This is an information war, but unfortunately the right answers don’t win by virtue. Warming contrarians have made huge strides in convincing people of their wild ideas because they have drowned out the correct ideas within certain audiences. The best way to combat this problem is to be more vocal. In my case, I’m going to try and get more articles like this higher up in Google search results.

The second point above is something that is severely lacking. Even I will admit to being overly crude in my criticism. This is clearly illustrated by numerous responses to the work of biologist Nasif S. Nahle, which simply try to discredit him based on his background, and not his ideas.

This is the wrong way to approach the issue.

The work of Dr. Nahle has been touted by many who would love to see the global warming issue just go away. I first heard about Dr. Nahle’s work when someone sent me this article:

Determination of the Total Emissivity of a Mixture of Gases Containing 5% of Water Vapor and 0.039% of Carbon Dioxide at Overlapping Absorption Bands.

He claims to prove that an increase in the concentration of atmospheric CO2 will result in a cooling effect on the climate system. He does this with idealized calculations of radiative properties of a mixture of gases.

Before I talk about whether his ideas are valid, I feel compelled to point out that his paper is terribly written (technically speaking). For anyone thinking that people can’t get published when they do work that goes against the current understanding, this is a good example of work that could never be published either way! I don’t buy the idea that you won’t get published if you propose something “against the grain”. But you certainly won’t get published if you are a terrible writer.

In this case, the writing is so bad, that the equations are hard to follow. Many symbols are not defined, or the symbols are switched to different ones without explanation. Being familiar with this type of derivation makes it possible to figure out what was done, but it really shouldn’t be this hard.

Now on to the real problem with Dr. Nahle’s idea

His whole conclusion hinges on the “correction” factor (Δε) where the emission spectra overlap:

He assumes a mixture of water vapor and CO2. With the equation above he calculates the emissivity of the mixture.

But then he compares this with the correction factor for a new mixture that includes oxygen:

And makes the following (slightly inaccurate) conclusion:

“The emissivity of the water vapor decreased by 0.0872 units.”

He really means to say that the emissivity of the mixture decreases, because he has assumed a fixed amount of mass and unintentionally decreased the amount of water vapor in the mixture. He partially acknowledges this issue:

“The general conclusion is that by adding any gas with total emissivity/absorptivity lower than the total emissivity/absorptivity of the main absorber/emitter in the mixture of gases makes that the total emissivity/absorptivity of the mixture of gases decreases.”

So he has essentially replaced some H2O molecules with molecules of a lower emissivity. In the case of more CO2 it make perfect sense that the emissivity of a mixture with fixed mass would decrease, since H2O is a stronger infrared absorber than CO2. But, then he makes the incorrect jump that adding CO2 must therefore cool the planet, which is a gross misrepresentation of his own results.

Increasing atmospheric CO2 will not lead to reduced H2O,
because the mass of the atmosphere is not fixed.

producing a more accurate version of his calculation is a bit difficult. The mass of CO2 in the atmosphere is small compared to other constituents, but its effect can still be quite large. The more complicated part of the problem comes with understanding the feedbacks. Water vapor is expected to increase with increasing CO2, but it’s not straightforward to build this effect into a simple calculation like the one presented by Dr. Nahle. doing this in a single equation would require many more dubious simplifications.

We have definitely not observed a decrease in H2O, but there has been an obvious increase in CO2. Below I’ve created a plot of globally averaged column water vapor from NCEP Reanalysis 2. As we can clearly see, the trend is positive (and statistically significant), consistent with the notion that water vapor increases with increasing CO2.

Globally averaged TPW (i.e. CWV)

Here’s a poor man’s legend:

  • Monthly mean
  • Annual mean
  • Linear Trend (significant at the 99% confidence level)

Hopefully this article can help show why Nasif Nahle’s ideas about global warming are erroneous and misinformed.

However, I want to stress that this is not meant to discredit or demoralize him.

28 thoughts on “Climate Skeptics: Nasif Nahle’s Shaky Math

    1. Walter Post author

      I’m not sure about this, I’ll have to dig up that code. But I would guess that it will be less than the expected 7%/K, since we are not in equilibrium.

  1. Stephen

    Nahle hasn’t changed water vapour for oxygen as you have claimed about the two equations as you have claimed. The two figures changed are at the right hand sides of the equations and in turn refer to CO2 and Oxygen alone.

    1. Walter Post author

      I don’t understand your point. The right hand side of the equations do not refer to CO2 and O2 alone. The key value that has changed is the “correction factor” that asserts to describe the effect of overlapping spectral bands. My main criticism is that Nahle assumes a fixed mass, which explains why he comes to the wrong conclusion that increased CO2 can be a cooling agent.

      1. Stephen

        And I don’t understand why you think he should change the mass to make his point. What is the percentage change of the total atmospheric mass by raising CO2 levels from 0.028% to 0.056% (the dreaded doubling of industrial levels phophesising the apocalypse) for example? It is too negligible to factor in, especially as nature is constantly varying the total mass naturally. You make assumptions of water vapour feedbacks to make more significant changes in mass, but this assumes that CO2 causes warming in the first place, which the calculation shows is not the case. So you use the very same assumption that Nahle’s calculation falsifies to try and falsify his calculation! Talk about a straw man!

        1. Walter Post author

          We cannot assume that the effect is negligible just because the change in mass is small. The total emissivity of a mixture should increase as CO2 is added. And even though the increase is small, the end result of higher atmospheric emissivity in the climate system will reduce the efficiency of surface cooling, as well as a host of feedbacks (I will admit some are not well constrained, but that’s another discussion). The smallness of the effect is consistent with the long timescale of the problem, which is only detectable with statistical significance after several decades of data has been collected. The anthropogenic signal is very slow, but still significant, as thousands of legitimate studies have shown.

          Dr. Nahle has found a little trick to make the emissivity dramatically smaller when a large amount of oxygen is added (replacing water vapor) and then extrapolated to how the emissivity will change when a small amount of CO2 is added. This is not good science. I am not an expert in radiative transfer, but I suspect that Nahle’s “correction factor” formula is incorrectly used. He mentions that his formulas came from a list of textbooks, but does not lay out the details of how this formula was derived. His carelessness in this area is another issue that obfuscates the paper.

        2. Walter Post author

          I just thought of another way to think about this. Let’s say we have a realistic mixture of air (i.e. mostly nitrogen) and then increased the mass of CO2 while keeping the overall mass the same, like Dr. Nahle does in his paper. If the CO2 replaces either oxygen or nitrogen (or both), the emissivity will obviously increase since CO2 is a better IR absorber. This makes the conclusions of the paper misleading. Nahle essentially argues that the overall emissivity goes down when H2O molecules are replaced by molecules with less emissivity, without acknowledging the sensitivity of this result to other replacement scenarios. This omission tricked him into mistakenly thinking he can broadly apply his result to the real climate system.

    1. Walter Post author

      The notion of disproving the existence of “backradiation” and the approach of using day and night measurements reveals a fundamental misunderstanding of what this term means. It’s better to think of “backradiation” as “reduced cooling”. The atmosphere doesn’t warm the surface, but it can slow the surface cooling rate. It’s also important to understand that the “backradiation” in the famous Trenberth diagram is meant to represent how the atmosphere works when averaged over a long time, so the impacts of daily and yearly fluctuations are averaged out. Thus trying to find “backradiation” in radiometer measurements doesn’t make any sense. I only skimmed the article, but I suspect that a more careful reading would reveal that he has neglected terms of the atmosphere and surface energy budgets. The approach of analyzing the atmospheric energy budget, as opposed to the surface or top of atmosphere budgets is a very interesting topic that has only recently been explored. There is more about this topic in this recent paper:

      1. Mike

        I think one of the things that raises suspicions is that the energy flows between the surface and atmosphere in the Trenberth diagram appear to be double the value of the input solar radiation. I suspect this is an apples and oranges comparison, but would appreciate any clarification you could offer.

        Thinking of global warming as a process my simple analogy is a pot of water on a hob that will happily simmer with the lid on, but will not reach boiling point with it off at the same heat setting. Is that a fair comparison?

        Thanks and Happy New Year


        1. Walter Post author

          I agree the Trenberth diagram can be confusing. An important thing to keep in mind is that half the planet is in the dark all the time, and most of the are that is lit by the sun is receiving indirect sunlight, so this strongly affects the globally averaged value of solar energy absorbed at the surface. On the other hand, the processes behind the “back-radiation” are relatively well homogenized across the globe and are still emitting radiation downward on the dark side of the planet. So, I think the root of the confusion comes from thinking too narrowly about the solar term. Peter Ward always talks about how warm you feel standing in direct sunlight, which is not an appropriate illustration when talking about a globally averaged process.

          The pot of boiling water analogy is actually not accurate. Adding the lid to the pot actually does more to block convection, rather than enhance the downward radiation. The same can be said about the ubiquitous “blanket” analogy. However, I have yet to think of a better way to illustrate the process. There’s a recent paper that talks about better “mental models” here:

  2. mike

    Thanks for the reply. I’m hoping Stephen will join this discussion, as he is convinced that it is some kind of perpetual motion/energy scam.

    Thanks for the comments on the pot. I had realised it was convection, but thought it was close enough as an analogy.

    1. Walter Post author

      I guess the pot analogy is ok since you are still reducing the efficiency of energy loss from the system and causing the pot to heat up and reach a new equilibrium. I wish there was an analogous example that worked on radiative processes, but without creating a vacuum convection will always dominate the heat fluxes.

  3. Gordon Lehman

    The full column emissivity of CO2 is very low by all counts. Hottel measured .14 in the 50’s. Staley and Jurica (1972) get about .19. Nassif calculates .002 by two different methods.

    We can safely say that CO2 is a lousy blackbody in it’s fundamental bend. Having absorbed a photon at WN 667.4, there is somewhere between a .002 and a .2 chance it will remit the photon; and between a .998 and a .8 chance it is going to use the energy to kinetically agitate neighboring molecules instead.

    This material property has important consequences for notions of radiative transfer. CO2 transfers radiation poorly, yet its absorbance is .98 in one meter at 400ppm. Basically, “the photon stops here”.

    This is why radiative transfer models can only successfully model the surface boundary layer.

    1. Walter Post author

      A lot of what you’re saying doesn’t make sense from a technical stand point, but I think I understand what you mean. However, it’s important to realize that the IR band is what is important for understanding global warming. There is no such thing as a “fundamental band” in the context of molecules. It’s not accurate to think of a molecule like you would a mechanical resonator.

      The emissivity of CO2 in the far IR part of the spectrum is in fact close to 1. So the statement that “CO2 transfers radiation poorly” is misleading. You mention a wavenumber of 667.4, but this is out in the microwave part of the spectrum, so it isn’t relevant to the discussion. Also, IR wavelengths are much larger than a molecule, so thinking about a single molecule absorbing a single photon is also technically inaccurate and misleading.

      Radiative transfer is perhaps one of the best understood parts of the climate system, and can successfully model much more than the surface boundary layer. The main limitation of radiative transfer models is that they are very computationally expensive, and thus we are forced to make compromises. But these compromises don’t change the conclusion that CO2 is an excellent absorber and emitter of IR radiation.

  4. Richie

    As I understand his argument, it is revolutionary: that CO2 cools the planet by quantum-transforming IR to radio wave frequencies which don’t “heat” the atmosphere. In other words, CO2 reduces available “heat.” If this precis accurately reflects his thinking, it’s nonsense, is it not?

    And while I have got you, I’d appreciate some physics viz-a-viz the idea that solar energy in the bands available to CO2 is finite, and that beyond a certain PPM, it won’t matter how much CO2 is in the atmosphere because all the available solar energy will have been absorbed.

    1. Walter Post author

      I think his argument is much simpler than what you are saying. His argument is more about how to “properly” calculate emissivity of a mixture when the composition changes. It’s not about energy moving between frequencies.

      As for your other question, I don’t quite get what you’re asking. There is a “saturation” effect of high CO2 because of the natural negative feedback provided by the Stefan–Boltzmann law, but CO2 doesn’t absorb much solar radiation.

  5. Richie

    Thank you, sir, for attempting to make sense of my unscientific question.

    Nahle wrote:
    “The wavelength of the dispersed quantum/waves has been elongated up to 14.8 µm
    (redshift); this elongation puts the IR quantum/wave out of the range of absorptivity of carbon
    dioxide by the specificity and sensitivity of absorption and emission potentials; consequently,
    the energy of these quantum/waves cannot be reabsorbed by molecules of carbon dioxide.”

    My first question concerns the above mechanism. He seems to be saying IR is transformed into non-absorbed quanta. Or something like that.

    My second question goes to the idea I saw somewhere (not in Nahle) that above a certain PPM concentration — I think it was 600 ppm — all available IR has been “captured,” for lack of the correct term, so no further heating augmentation can occur regardless of how much CO2 is emitted into the atmosphere: sounds like Big Oil disinfo.

    1. Walter Post author

      yea, I don’t quite understand his reasoning here. He seems to be putting a lot of faith in the conduction process to disperse the vibrational energy of molecules, but I’m not aware of studies showing this. I think that even if this were true it wouldn’t support his conclusion about global warming since the atmosphere is still absorbing more energy and warming up, but I’ll have to think about this more.
      On your second comment, I don’t think there’s a limit of energy absorption. If a molecule is vibrating/rotating, there’s nothing that says it can’t absorb more energy and vibrate/rotate faster. Weird things might happen at really high temperatures, but in the context of the Earth’s atmosphere this isn’t relevant. re-reading your question I guess you’re asking something different. If you think about greenhouse gases making the atmosphere opaque in the IR band, then you could imagine a state where the atmosphere absorbs 100% of the upwelling IR radiation. In this extreme state there is still IR emission to space since molecules emit radiation in all directions. The planet would look much different when viewed from space because you wouldn’t be able to make out any surface features in the IR band. In other words, the atmosphere would become extremely “hazy” and diffuse in the IR band. I’m pretty sure that even if you added more greenhouse gases to this state you could further warm the planet by further slowing the eventual emission to space, which is what really causes the warming in the first place. Therefore, I don’t think there is such a limit, unless you consider other feedbacks like I mentioned in my other comment.

  6. Duncan Winn

    “Global warming deniers are people too.”

    This illustrates the most damaging aspect of the argument for man-caused climate change. It’s like calling someone a heritic or Christ denier. It does nothing to bolster your scientific argument to put it in terms of a religious argument.

    1. Walter Post author

      I’m not sure I get your point. Are you saying the fact that I use the term “denier” discredits the field of atmospheric science?

      If someone categorically dismisses a mountain of scientific evidence from thousands of scientists over many decades with an argument that doesn’t stand up to reason, I think it’s fair to say they are “in denial”.

  7. David Ringsmuth

    The emissivity of CO2 and other anthropogenic gases is important in the climate discussion. But it is not the silver bullet. In another article Nasif Nahle demonstrates the emissivity of CO2, without regard to H2O, or any other gasses:

    Here you make a claim that the long wave IR absorbency of CO2 is nearly 1, or nearly a black-body, without offering any support. Of course the bigger discussion is not just limited to LWIR. Why don’t you show your work? Let’s see the calculation you use to determine the total emissivity of CO2 in our atmosphere. We’ll give that to someone trained in radiative heat transfer and get back you. If you can’t do that, please demonstrably falsify this:

    Secondly, if you can, please explain the historical record for both short and long-term correlation between temperature and CO2 where CO2 lags, follows temperature, not leads it. If CO2 correlates positively, following temperature in the historical record, why aren’t climate models firstly validated against the historical record before they try to extrapolate the future? If the model does not validate the historical record, it’s not valid.

    Thirdly, let’s put up a challenge to create a back-tested climate model that reflects total atmospheric emissivity, solar variability, and atmospheric convective influence. For inspiration look here:
    If the concepts in this simple test are true, then the conclusions are extremely important.

    Here is a model based on two layers in the sun, back-tested 32 years, 97% accurate:

    If anthropogenic influence models are failing, and they are failing, it makes sense to gain perspective.

    1. Walter Post author

      I hate long comments like this. Am I supposed to reply to all of it and write a novel? Or do I only reply to one and make it seem like I’m avoiding the other questions? Why do people do this? It makes so much more sense to have separate threads for separate comments!

      Anyway, to stay on the topic of Dr. Nahle I’ll just address the first part about his paper about the “Total Emissivity” of CO2. This is another example of his sloppy work, where he changes symbols without warning and doesn’t adequately label and describe things. If I wrote like this I’d never get published. Also, this paper has the same conceptual problem as I describe above, because he talks about increasing the partial pressure of CO2 but doesn’t acknowledge what other gas that co2 is replacing. If it is effectively replacing water vapor, then the decrease in emissivity is no surprise, and it doesn’t say anything about our understanding of global warming.

      However, the bigger problem with that piece of writing is that he never once uses the word “wavelength” or “frequency” or “spectrum”. If you look at the plot of below (that I got from here), which shows the absorption across the spectrum (related to emissivity), you’ll notice that CO2 absorbs strongly in the IR band where the Earth emits a lot of energy. This is what we care about! Nahle’s idea of “total emissivity” is worthless if you ignore the dependence on wavelength. If the “total emissivity” represents the average emissivity across all wavelengths then it will definitely be small and also not relevant to the mechanism behind anthropogenic global warming.

      Absorption spectra

      Hopefully you can see how Nahle’s work in this area is lacking and misleading.

    1. Walter Post author

      The point is that emissivity of a substance is not a single number, because it depends on wavelength. Sometimes it does boil down to a single number when you are comparing isulation materials for example, but in the context of the greenhouse effect it gets a bit more complicated. In some bands the emissivity of CO2 is zero, and in part of the IR band it is close to 1. I don’t have a table of exact values to share, but I don’t need those values to show the problems with Dr. Nahle’s work here.


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