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Joseph Postma and the greenhouse effect

What the science says...

Joseph Postma published an article criticizing a very simple model that nonetheless produces useful results.  He made several very simple errors along the way, none of which are very technical in nature.  In no way does Postma undermine the existence or necessity of the greenhouse effect.

Climate Myth...

Postma disproved the greenhouse effect

"Skeptics hope that Postma’s alternative thermal model will lead to the birth of a new climatology, one that actually follows the laws of physics and properly physical modeling techniques...Postma deftly shows how the systemically tautologous conjecture that is “back-radiative heating” just doesn't add up. We see how climatologists fudged the numbers to make it appear as if Earth actually raises its own temperature by having its own radiation fall back upon it - a conjecture contrary to fundamental physics." (John O'Sullivan)

Some recent attention has recently been going around the web concerning a new “paper” done by Joseph E. Postma (PDF here) which claims to “…physically negate the requirement for a postulation of a radiative atmospheric greenhouse effect.”  

The claims are of course extraordinary, along the lines of Gerlich and Tseuchner’s alleged falsification of the atmospheric greenhouse effectAs is often the case with these types of “skeptics,” the more extravagant the claim, the more obscure the publishing venue; in this case the host is Principia Scientific International, which according to the website “…was conceived after 22 international climate experts and authors joined forces to write the climate science bestseller, ‘Slaying the Sky Dragon: Death of the Greenhouse Gas Theory.’” Most rational people would stop here, but this is the Americanized age where we need to glorify everyone’s opinion and must provide rebuttals for everything, so here it goes:

I ask that the reader have the paper open in a new window so they can follow along with this article.

The Foundations

Most of Postma’s first 6 pages are actually correct.  He describes the greenhouse effect through the so-called layer model, which is a simple way to break up the planet into a “surface” and an “atmosphere,” with outer space overlying the top layer.  This model is described in many climate books such as Dennis Hartmann’s Global Physical Climatology, David Archer’s Understanding the Forecast, Marshall and Plumb’s Atmosphere, Ocean and Climate Dynamics, and radiation books like Grant Petty’s First Course in Atmospheric Radiation.  I will say that I do not particularly like this model as a suitable introduction to the greenhouse effect.  It is useful in many regards, but it fails to capture the physics of the greenhouse effect on account of making a good algebra lesson, and opens itself up to criticism on a number of grounds; that said, if you are going to criticize it, you need to do it right, but also be able to distinguish the difference between understood physics and simple educational tools.

The atmosphere in Postma’s paper is just a single slab, so he has two layers (atmosphere+surface), but in general you can have many atmospheric layers.  He goes on to solve for the energy balance of each layer (see equations 11-14). RealClimate derived the same result in less than a page here.

 Figure 1: Layer model is Postma's paper.  Click to Enlarge


Postma actually doesn’t get the atmospheric radiative flux right.  The emission is not σTa4, it is fσTa4, where f is the atmospheric emissivity/absorptivity (following his notation) and Ta is the atmospheric temperature.  The emissivity is a unitless factor between 0 and 1 descrbing how good of an absorber/emitter the object is relative to an ideal body.  f = 1 describes a blackbody.  By Kirchoff's law, the absorptivity of a layer must be equal to the emissivity (at the same wavelength),  Both right hand sides of equations 11 and 12 are thus wrong, but it turns out that those errors cancel each other out and he gets equation 14 right.  The factor of 2 in Equation 12 comes about because the atmosphere emits both up and down, although Postma clearly doesn't know how to derive this result formally, based on later statements he makes about this.  Toward the end of page 14 he says this is invalid since the atmosphere radiates in 3-D, not just up and down.  In fact, the quantity σT4 refers not only to the total power output of an object (the rate of energy emission), but it also refers to isotropic (equally intense in all directions) radiation.  The result σT4 is obtained if one assumes that a plane radiates uniformly over a hemisphere (for example, the domed "half sphere" field of vision that a human can see  when you stand outside, with the base of that half-sphere being the surface you sre standing on; the other hemisphere is invisible (see this image).

So far, it is simple textbook stuff with not much promise.

Geometry of the Global Energy Budget

Postma then goes on to describe fictitious “boundary conditions.”  In particular, he seems to have serious objections to the averaging of the solar radiative flux over the Earth.  In essence, he would prefer we had one sun delivering 1370 W/m2 of energy to the planet, with a day side and a night side, noon and twilight, etc. instead of the simple model where we average 1370/4=342.5 W/m2 over the planet (so that the whole Earth is receiving the appropriate "average" solar radiation).  The number becomes ~240 W/m2 when you account for the planetary albedo (or reflectivity). 

The factor of 4 is the ratio of the surface area to the cross section of the planet, and is the shadow cast by a spherical Earth.  It is therefore a geometrical re-distribution factor; it remains “4” if all the starlight is distributed evenly over the sphere; it is “2” if the light is uniformly distributed over the starlit hemisphere alone; with no re-distribution, the denominator would be 1/cosine(zenith angle) for the local solar flux.

In simple textbook models, we like to prefer explanations that get a point across, and then build in complexity from there (see Smith 2008 for descriptions on a rotating Earth).  Of course, students who use this model are probably educated to the point where they know that day and night exist, and certainly GCMs have a diurnal cycle.  The radiative calculations are done explicitly by accounting for the temperature distribution and absorber amount that is encountered at each grid box.  Postma is simply tackling a non-issue, just as how people criticize the term “greenhouse effect” for not working like a glass greenhouse. Postma objects to teaching this simple model because it is not real.   All that is done, however, is to use a brilliant and sophisticated technique, taught only to the geniuses among us, called averaging! And of course, simple models are used in any is how we learn.

But, in actuality, the globally averaged solar re-distribution approximation is not bad when we use it to describe the temperature for planets like Earth or Venus.  These planets have an atmosphere or ocean that transport heat effectively, especially Venus with virtually no day-to-night or pole-to-equator temperature gradient.  The atmosphere and/or ocean help smooth the diurnal temperature difference very well.  Therefore, when coming up with a temperature estimate, it is a great first approximation.  If you want the local equilibrium temperature for an airless body like Mercury or the Moon (that does not transport heat), then you want to use the no-redistribution or hemisphere only solar factor.  This is well-known (see e.g., Selsis et al 2007).  On Mercury, there is no heat distribution and very little thermal inertia; before the sunrise the temperature on the surface is somewhere near 100 K (-173 °C) and by noon the temperature on the surface of Mercury rises to about 700 K (427 °C).  This may also be relevant for tide-locked planets (very slow rotation since one side is always facing the host star, the other in perpetual darkness).  Earth does not experience any such changes of the sort.  On Venus, the variability is even less, and most of the planet is at around 735 K.

Summary so far...

To summarize so far, Joseph E. Postma did not like a simple model of Earth’s radiative balance where we approximate the Earth as a sphere with uniform solar absorption.  Of course, this is never done in climate modeling or in more detailed analyses appropriate for scholarly literature, so it is more an exercise in complaining about undergraduate education than an attempt to correct what he calls a “paradigm” in climatology.  Nonetheless, the 0-D energy balance model is a useful approximation on Earth when coming up with an average emission temperature (~255 K), since air circulations and oceans tend to even out the diurnal temperature gradient on Earth, in addition to the thermal inertia provided by the system.

Venus is More Optically Thick Than a One Layer Model Can Give You

Postma starts by using Venus as a template for where the greenhouse model he is using breaks down.  And indeed, he is right.  His argument is that f (the emissivity) cannot possibly be greater than 1 (which is correct), and yet it must be in order to produce the Venus surface temperature in his Equation 29)  Based on this, he then states that the standard greenhouse model does not work in general.  The problem is that his Equation 29 assumes a one-layer atmosphere, which is an absurd assumption when you approach the extremely high optical thickness of Venus. Venus has a 90 bar atmosphere that has well over 90% carbon dioxide, some water vapor, and a greenhouse effect generated by suluric acid droplets and SO2.  The radiative transfer on Venus works much differently than on Earth, owing in part to intense collisional broadening of CO2 molecules.  A photon has an extremely difficult time escaping Venus, unable to do so until it reaches the very outer parts of its atmosphere.

Using the layer model, you would need many atmospheric layers to produce something close to Venus; with enough layers you would find that you could produce the surface temperature of Venus without violating conservation of energy.  With just one perfect absorbing atmospheric layer, the surface temperature cannot exceed 21/4 times the emission temperature (Te=~230 K on Venus).  But with two perfectly absorbing atmospheric layers, it can rise to 31/4Te.  With three layers, the maximum temperature is 41/4Te, and so on.  The reason the surface temperature is capped in this way is because the atmosphere itself must be emitting radiation and heats up when it absorbs photons from the surface, which in turn increases emission.  If the atmospheric layer were instead a good infrared reflector (i.e., it has a high thermal albedo), then you could delay heat loss to space that way and increase the surface temperature well beyond this value.  This could happen with CO2 clouds instead of H2O clouds, the latter are much more effective IR absorbers than IR scatterers, whereas the former could raise the IR albedo.

In essence, Postma stretches a simplified model to areas that it was never designed to go to, and then declares that its failure to work means the whole paradigm of the greenhouse effect is wrong.  The incompetence is overwhelming.  Postma is not done though, and decides to dig in further.  His next argument is amusing, but perhaps a bit strange to follow, so I will try to explain.

Lapse Rate Confusion

He claims that observations of the atmospheric lapse rate (the rate at which temperature declines with height) disallow the greenhouse effect.  His reasoning is that the atmosphere is at a fixed height.  When greenhouse gases warm the surface, and cool the upper atmosphere, that height still remains fixed, but obviously the temperature difference between the bottom and top of the atmosphere must increase.  Postma then claims that this necessarily implies that the lapse rate must have a greater slope than the theoretical value that he derived of about -10 K per kilometer (which is about right for a dry air parcel ascending).  That is, if the atmospheric height remains fixed, and the temperature difference between bottom and top is increased, then the rate at which air cools with height must increase.  Since this is not observed, then we have a problem, right?

In actuality, the atmospheric height is a distraction.  The adiabatic lapse rate does not extend beyond the point where convection breaks down, which is the tropopause.  The whole point of the greenhouse effect is that increasing atmospheric greenhouse gases does increase the “average” height at which emission to space takes place (and the tropopause increases in height too), so one IS allowed to extrapolate further down the adiabat to reach a higher surface temperature.  On Venus, the optical thickness forces the tropopause to some 60 km altitude. Additionally, it is worth pointing out that greenhouse gases warm the upper troposphere, not cool it, but they do cool the stratosphere.


Figure 1: Qualitative schematic of the old (blue) and new (e.g., after CO2 increase) temperature with height in a dry atmosphere.  Moisture tends to enhance the tropical upper atmosphere warming relative to surface.  Temperature increases to the right. 

TOA vs. Surface

Perhaps just as crucial to all of this, Postma cannot get around the surface energy budget fallacy, which says that increased CO2 causes surface warming by just increasing the downward infrared flux to the surface.  This problem is described in standard treatments of the greenhouse effect, which he does not seem to know exist, such as in Ray Pierrehumbert’s recent textbook. The primacy of the top of the atmosphere budget, rather than the surface energy budget, has been known at least since the work of Manabe in the 1960s (see also Miller 2012)

In reality, the top of the atmosphere budget controls the surface temperature even more than the surface forcing, because the atmosphere itself is adjusting its outgoing radiation to space (and much of the radiation to space is originating in the upper atmosphere, owing to its IR opacity). Where the atmosphere is well-stirred by convection, the adjustment in temperature at this layer is communicated to the surface.  I described this in more detail here. 

Postma runs into this mistake again when he claims that the low water vapor in hot deserts is a problem for greenhouse theory, but this is largely due to the lack of evaporation cooling, which is just one component of the surface energy budget, and nearly absent in a desert.  This is one scenario where a detailed consideration of the surface budget is critical, as well as in other weakly coupled regimes.

The way CO2-induced warming really works in a well mixed atmosphere is by reducing the rate of infrared radiation loss to space.  Virtually all of the surface fluxes, not just the radiative ones, should change in a warming climate, and act to keep the surface and overlying air temperature relatively similar.  The back-radiation will indeed increase in part because of more CO2 and water vapor, but also simply because the atmosphere is now at a higher temperature. But if the lower atmosphere was already filled with water vapor or clouds to the point where it emitted like a blackbody (at its temperature), increasing CO2 would not directly increase downward emission before temperature adjustment, but would nonetheless warm the planet by throwing the TOA energy budget out of whack.


In summary, Joseph Postma published an article criticizing a very simple model that nonetheless produces useful results.  He made several very simple errors along the way, none of which are very technical in nature.  More sophisticated models are obviously designed to handle the uneven distribution of solar heating (which is why we have weather!); nonetheless, the educational tools are useful for their purpose, and in no way does Postma undermine the existence or necessity of the greenhouse effect.  Without a greenhouse effect, multiple studies have shown that the Earth collapses into a frozen iceball (Pierrehumbert et al., 2007; Voigt and Marotzke 2010, Lacis et al 2010) and indeed, after an ice-albedo feedback, plummets below the modern effective temperature of 255 K.  This work makes extraordinary claims and yet no effort was made to put it in a real climate science journal, since it was never intended to educate climate scientists or improve the field; it is a sham, intended only to confuse casual readers and provide a citation on blogs.  The author should be ashamed.

Last updated on 1 January 2015 by Chris Colose. View Archives

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Comments 26 to 50 out of 99:

  1. YOGI "With an albedo of 0.12, we actually receive more IR than visible from the Moon." Could you please elaborate a bit? I'm really missing the logic.
  2. KR The daylight figure for the Moon is the same as near Earth space maximum temp` at 121 degC, while the Lunar night figure is affected by warmth from the Lunar surface so is higher at the equator and lowest at the poles. The maximum temp is just a direct sunshine figure that you can take on the Moon or in near Earth space, so it`s apples and oranges. What temperature does 396 W/m^2 correspond to ?
  3. YOGI - It would correspond to a uniform temperature of 17.4C; see the Stefan-Boltzmann law. The average temperature (~15C) of the Earth surface radiates a bit more effectively due to variations - given positive and negative variations, and the T^4 relationship for radiative power, any variations will increase the energy radiated. Please read the OP, including the reference to Selsis 2007 for airless bodies with slow rotation rates like the Moon or Mercury. This is very unlike the more quickly rotating Earth with oceans and atmosphere to distribute heat far more evenly. You are continuing to compare apples to, well, coconuts. I would strongly suggest that you read up a bit on IR absorption and the lapse rate, and how they together cause a much lower emission of IR energy to space than would occur if we did not have greenhouse gases in the atmosphere. Postma's nonsense will, IMO, not be helpful to your understanding.
  4. YOGI @27, the mean global surface temperature is 288 degrees K, corresponding to a black body radiation of 390 W/m^2. The temperature required to match the Sun's 1368 W/m^2 TSI at noon, with the sun vertically overhead, and ignoring albedo and assuming zero specific heat would be 394 degrees K. However, the sun is not always vertically overhead everywhere. So if we ignore albedo and specific heat, the temperature everywhere else on Earth would be less than the point where the Sun is vertically overhead. Indeed, ignoring albedo and specific heat, the entire night side of the globe would be at approximately 2.7 K (the temperature of the cosmic background radiation) Any location within approx 2000 Km of the dawn or dusk but in full daylight would have a temperature less than 288 K. Most importantly, even if we assume all areas in full daylight are at 394 K, while all night areas are at 3 K, the Global Mean Surface Temperature would be 198.5 K. That is 90 degrees K less than the current GMST, and over 50 K less than the GMST of the ideal black body with perfect conduction which is used in simplified calculations of the Earth's effective temperature for radiative equilibrium. In other words, while the atmosphere (and ocean, and thermal capacity of rocks and soil) clearly do mitigate the peaks in daylight temperature, in doing so it also minimizes the minimums in night time temperatures. What is more, the overall effect is to increase the Global Mean Surface Temperature. So your assumption is wrong.
  5. #29 "the entire night side of the globe would be at approximately 2.7 K (the temperature of the cosmic background radiation)" Why are you throwing such wildly incorrect figures around ? Even the Moon`s night time does not get that cold. Even in the coldest place in our solar system, which is in craters of the S pole of the Moon it does not get that cold.
  6. Moderator, why are you deleting my comments ?

    [DB] Your two moderated comments were merely repetitions of unsupported assertions you made earlier, here.  Supporting the earlier assertion with links to peer-reviewed studies appearing in reputable journals would be an example of adding to this discussion.  Merely repeating yourself, such as you did, detracts from the discussion and begs intervention by the moderation staff.

  7. Okay, 35-44K for minimum temperature because the moon is heated and does have thermal mass. Doesn't exactly change the argument. Average temp would be 217K. Your assumption is still wrong.
  8. YOGI @30, if you are going to think scientifically, you need to be able to follow the implications of assumptions made. Specifically, for the 2.7 K, the assumption was made of no specific heat, ie, that temperatures will move to radiative equilibrium with no delay. On the Moon, the night time temperature is around 90 K because of the specific heat of the Lunar rocks which prevents instantaneous changes in temperature. In crater floors in polar regions that drops to about 40 K because of heat transfer by conduction. However, if you want to use the Moon as an example, its mean temperature at the equator is 220 K, with its overall mean being lower. It has this low mean temperature despite a lower albedo than Earth's. Once again, the point is clear that the Earth's atmosphere reduces maximum daytime temperatures but increases the Global Mean Surface Temperature (even before you consider the greenhouse effect).
  9. YOGI * Flat 1m^2 object, with perfectly insulating back, pure blackbody absorption/emission: 120.5C * With 0.98 IR emissivity (as per surface of Earth): 122.5C * With 0.612 IR emissivity (as per Earth surface as seen through the atmosphere): 171.9C * Conductive blackbody plate, two sides radiating: 57C And: * Earth (spherical object with larger surface area, 0.3-0.35 albedo in visible, 0.612 emissivity in IR): ~15C --- Details matter.
  10. scaddenp The Lunar Thermal Environment Apollo soil temp` measurements at 35cm deep give an equatorial average of 255K with a diurnal variation of +/- 70K.
  11. Addendum to my last post: * Earth with ~240 W/m^2 average insolation, 0.98 emissivity: ~ -18C temperature.
  12. So what happens to all the IR back-radiation the hits the ocean surface ?
  13. YOGI - What do you think happens to back-radiation impinging on the ocean surface? Rather than presenting red-herrings and open questions, what assertions are you making about the behavior of the climate? You have thrown, quite frankly, a lot of open-ended questions about. Unless and until you bring forth a testable assertion, or a question relevant to the topic (i.e., with some explanation of how it supports/undermines a particular hypothesis), you are (IMO) just generating static.
  14. "[DB] Your two moderated comments were merely repetitions of unsupported assertions you made earlier.." Want do you require ? evidence that near Earth space temperature measurements give 121C maximum?, i.e. the same as Lunar daytime maximum. Or evidence of peak daytime temperature measurements on Earth being much less ?
  15. 35cm deep gives a lot of thermal mass. Hardly comparable to measurement of GMST. IR hitting the ocean - change of topic again? Your point? By any chance is it misunderstandings with dealt with here?
  16. YOGI @35, your source gives the equatorial mean temperature at 207 K. It specifies the relationship of surface to subsurface temperatures taken at two different sites at times which where far from the zenith hour for the Sun (as shown by the shadows). As such the sub surface temperatures would represent something close to the average for their respective latitudes, but surface temperatures may have been well below that average. Your supposition that the average subsurface temperature was 40 degrees greater than the average surface temperature is not supported by your linked site, and is contrary to the laws of thermodynamics.
  17. Tom Curtis "Your supposition that the average subsurface temperature was 40 degrees greater than the average surface temperature is not supported by your linked site, and is contrary to the laws of thermodynamics." Subsurface Temperatures Heat flow measurements made during the Apollo 15 and 17 missions (Langseth et al. 1973) revealed that the top 1-2 cm of lunar regolith has extremely low thermal conductivity. The mean temperature measured 35cm below the surface of the Apollo sites was 40-45K warmer than the surface. At a depth of 80cm the day/night temperature variation experienced at the surface was imperceptible. This implies that habitations in the lunar subsurface exist that are not subject to the harsh temperature extremes prevalent on the surface. You should have read on further....
  18. Tom Curtis "In crater floors in polar regions that drops to about 40 K because of heat transfer by conduction." Its because they never get any sunlight.
  19. scaddenp at 10:58 AM on 28 February, 2012 "Okay, 35-44K for minimum temperature because the moon is heated and does have thermal mass. Doesn't exactly change the argument. Average temp would be 217K. Your assumption is still wrong." From the NASA data, it looks like you are wrong at every step.

    [DB] "From the NASA data, it looks like you are wrong at every step."

    This is insufficient in a science-based forum and amounts to you being argumentative for form's sake.  If you disagree, it is incumbent upon you to do the maths (show your work) or to provide supportive links with an appropriate measure of explanatory context as to what you understand the link to show and why it is pertinent to the discussion.

  20. KR at 11:18 AM on 28 February, 2012 That is interesting as 171.9C * 0.7 (albedo) / 8 = 15.04C. But if I argue that daytime albedo is cancelled out by night time insulation of clouds etc, and disregard the atmospheric emissivity too, then 120.5C / 8 = 15.0625C. Or if I include Earth`s surface emissivity: 15.06C * 0.98 = 14.76125C.
  21. YOGI - You cannot divide the temperature by 8 to get an answer, as the SB equation is: Power = SB Constant * Emissivity * Area * Temp(K)^4 SB constant is 5.670373*10^-8 You need to consider the average incoming insolation, and work through the equation to get the temperature. Also - "But if I argue that daytime albedo is cancelled out by night time insulation of clouds etc, and disregard the atmospheric emissivity too..." - Then you are ignoring the details. You're more than welcome to make up your own math, your own physics - but everyone else is therefore more than justified to ignore it.
  22. KR@46: What YOGI is proposing will never be proven as he ignores basic physics.
  23. If you are going to use soil temperatures to talk about temperature on the moon cf temperature on the earth, then make sure you talk about soil temperatures on earth. However, comparison is much more difficult since earth soils are mostly wet with the due effects on thermal properties. Deviner saw night range from 35-90K. Does that change the argument.
  24. Camburn - Agreed; without basic physics (or at least a willingness to learn), no progress will be made.
  25. Just as a reminder, YOGI was challenged to hang his/her hat on some particular issue, and chose a particular paper by Postma. Now it seems to me that YOGI needs to defend Postma's paper, where a fundamental error has been identified (on page 6 - thanks Tom and Riccardo for confirming my intuition), relating to the second law of thermodynamics: "No here's the clincher: imagine that you take a mirror which reflects infrared light, and you reflect some of the infrared light the blackbody is emitting back onto itself. What happens to the temperature of the blackbody? One might think that because the blackbody is now absorbing more light, even if it is its own infrared light, it should warm up. But in fact it does not warm up; its temperature remains exactly the same [because it is in radiative thermal equilibrium with the light source]" To remain at the same temperature, it would have to be radiating energy at the same rate that it is absorbed (Kirchoff's law). If you increase the amount absorbed using the mirror, the amount emitted must increase as well. However the Stefan-Boltzman law says that the rate at which a blackbody radiates energy is proportional to the fourth power of its temperature, so it can't increase emissions without an increase in temperature. Thus Postma is wrong on the fundamental application of the laws of thermodynamics. So YOGI, the challenge is for you to explain why Postma is correct and why his example doesn't violate Kirchoff's law or the Stefan-Boltzman law.

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