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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 classroom...it 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, 2011 submitted)

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.  (As a side note, I hope people can bookmark the home page to that blog, which is run by a team of meteorologists, climatologists, and grad students in atmospheric science, at the University of Albany in NY, and we will be posting periodically on many different issues from ENSO to climate change to recent weather around the country).

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.

Conclusions

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 2009, 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 16 August 2011 by Chris Colose.

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Comments 1 to 50 out of 88:

  1. No matter what models are used there is a simple fact that shows one "Inconvenient Truth" that needs to be dealt with in order to justify any sort of radiation trap.

    There are two planets orbiting the Sun. Both are subject to similar solar radiation.

    The Moon's surface temperature reaches ~ 396 K during the lunar day. This temperature agrees with theoretical calculations using 0.12 albedo and ~1368 W/sq m solar radiation. The long lunar day has nothing to do with it - the temperature is reached rapidly and cannot increase above the
    "blackbody" temperature no matter how long it is illuminated.

    The Earth's surface, according to the IPCC, receives ~51% of the Solar constant during the day.

    This amount of solar energy equates to a "blackbody" temperature of 331 K or ~ 58 degrees C and this is about the highest temperature recorded on Earth. Of course there is the ~20 % absorbed by the atmosphere which also causes heating.

    This demonstrates that the atmosphere actually reduces the surface temperature - if it was being radiatively heated by "greenhouse gases" it would be much hotter.

    The Moon's daytime temperature proves it is not correct to use a quarter of the insolation to assert that there is insufficient solar energy to explain Earth's temperatures.

    If you apply this to the Moon you get a result using -

    1368 / 4 (1 - 0.12) = ~301W/sq m.

    301 W/sq m gives - via Stefan-Boltzmann - ~270 K.

    So which is right ?

    270 K calculated by one quarter of the solar radiation or 396 K which is observed and confirmed even by NASA ?

    You cannot simply dismiss this - the only difference between the 2 relevant to a discussion on radiative heating is the atmosphere and oceans.

    The Earth never approaches its "blackbody" temperature which is ~87 degrees C for an albedo of 30 %.

    The atmosphere clearly reduces the heating effect of the solar radiation.
  2. Sorry - accidently double posted when I added a sentence - delete first one if you like.
  3. Observation shows the "effective" temperature of the Earth in response to the solar radiation is ~255 K or minus 18 degrees C. Observation also shows that this temperature exists about 5 km above the Earth's surface and does not reflect in any shape or form the "surface temperature".

    No matter what arguments one can enter into a theory has to be able to explain indisputable observed facts and there is at least one that no-one can argue with - the surface heating on the Moon by the solar radiation alone and the fact that the Earth is much cooler.
  4. Rosco,

    The rotational rate is actually very import. It is only when the rotational rate is sufficiently fast that it is sensible to divide the solar radiation by 4 to get the average solar radiation.

    In the case of the moon, the day side has a temperature of 390K, which is indeed a lot higher then the black body temperature you'll get by averaging the solar radiation. This should not be surprising: since the lunar day is actually 30 days long, of course you can't assume that the incoming solar radiation of 1368W/m2 is evenly distributed on the surface, and proceed to use 301W/m^2 to calculate the equivalent temperature.

    The fact that the model doesn't give you the right temperature doesn't mean that the physics behind the model (i.e. the theory) is wrong, but rather it means you are applying it incorrectly because some simplifying assumptions doesn't hold.

    For earth the rotation is sufficiently fast that it is sensible, as a simple model, to assume the incoming solar radiation is evenly distributed on the surface. The fact that the earth never approach 87 degrees is because the earth is rotating relatively fast, and therefore no point on the surface will be exposed to 1368W/m^2 long enough for the temperature to rise to that level. Again, the discrepancy is because you are applying the model incorrectly, not because the physics is wrong.
  5. IanC

    We’ll agree on how the 255 K “effective temperature and the IR output to space of ~240 W/sq m is calculated – and it is supported by observation.

    But this does not justify reducing the solar radiation by four for any calculation OTHER than this.

    This balance calculation is erroneously offered as proof that the “effective temperature” relates to the Earth’s surface temperature caused by the solar radiation - which it does not.

    Wikipedia says - http://en.wikipedia.org/wiki/Greenhouse_effect -

    “If an ideal thermally conductive blackbody was the same distance from the Sun as the Earth is, it would have a temperature of about 5.3 °C.”

    This is again based on reducing the solar radiation by the factor of four.

    My whole point about the Moon is to plainly demonstrate this is absurd logic.

    The Moon, not a perfect blackbody, reaches much higher temperatures that this method says is possible.

    The reality is there are such things as day and night and during the day the Earth is NOT subject to 170 W/sq m but most likely 4 times that on average over the illuminated disk – this flux would result in much higher temperatures than are observed and this in turn demonstrates the Earth’s atmosphere does NOT add heat during the day – rather it shields us from the solar radiation.

    This reality demonstrates a problem for the radiation trap “greenhouse effect” – if the Sun has the capability heat the Earth’s surface above observations then something is reducing the effect NOT increasing it.

    The only differences are the oceans and the atmosphere on Earth.

    I do not believe the “greenhouse effect” as postulated exists – I do not believe Fourier postulated it at all – if fact his words state it is impossible :-

    "In short, if all the strata of air of which the atmosphere is formed, preserved their density with their transparency, and lost only the mobility which is peculiar to them, this mass of air, thus become solid, on being exposed to the rays of the sun, would produce an effect the same in kind with that we have just described. The heat, coming in the state of light to the solid earth, would lose all at once, and almost entirely, its power of passing through transparent solids: it would accumulate in the lower strata of the atmosphere, which would thus acquire very high temperatures. We should observe at the same time a diminution of the degree of acquired heat, as we go from the surface of the earth."
    I see no support for a radiation trap greenhouse effect in this language – rather an acknowledgement that greenhouses work by preventing convection.
    Response: [Sph] Readers should note that Rosco's initial statement statement concerning observations is either incorrect or at best so vague as to imply an untruth.

    The surface of the earth is clearly not 255K, as supported by observation, but the observed temperature of the earth as viewed from space is 255K.

    More correctly, as well, the IR output of the surface of the earth is about 396 W/m2 (as supported by observations), and the output of the earth to space is in fact ~240 W/m2 as supported by observation.

    All of these numbers are well established, supported by observation, and also supported by theoretical models and calculations. They all match.

    It falls to the Galileos among us not only to disprove the theory, but also to provide an alternative theory that so well fits the actual observations.

    Claims that the observations don't exist, or even worse misrepresentations of the actual observations, should be a warming sign to any reader as to the intent and veracity of further claims by the commenter.
  6. I need to add:-

    1. The maximum temperature is determined by the power of the radiation.
    2. The Moon heats so quickly from ~ minus 210 degrees to about 90 degrees C that graphs of the increase are almost vertical.
    3. If the solar radiation hitting the Earth's surface is ~170 W/sq m how do experiments such as the one performed by Wood and others achieve such high temperatures inside a glass covered box where no IR backradiation can enter ?
    4. How do solar panels produce electricity at ~170 W/sq m - 100% efficiency ??
    5. "Turning our attention to the example of Langley's greenhouse experiment on Pike's Peak in Colorado (mentioned by Arrhenius, 1906b), we may be tempted to ask how it is that a greenhouse can reach such high temperatures. Qualitatively, we may attribute the difference between the 15ºC mean surface temperature and the 113ºC observed in Langley's greenhouse to the fact that noon-time radiation at the surface is three to four times as intense as the mean radiation over the whole of the earth's surface." Given that a glass greenhouse prevents IR radiation from leaving it also prevents it entering - show how did that temperature arise in the few hours it did ? It certainly did not accumulate fro a mere 170 W/sq m input.
  7. What if increased levels of CO2 actually provide another mechanism for the Earth's surface to cool.

    Obviously convection of air heated by contact is the major mechanism for the Earth's surface to cool - if radiation were the main method of cooling then reality does not exist - radiators do not heat or cool by radiation they convect.
  8. The simple model does not prove anything, it's just a way to explain the basics of energy balance applied to a planet with an atmosphere. Arrhenius already did a bit better dividing the Earth in latitudinal bands and doing the calculations for each season but retaining the uniformity over the 24 hours.

    Anyway, the simple model aproximates the planet as a uniform sphere with a uniform temperature. The Earth has an atmosphere and oceans which help smoothing the temperature out and this aproximation may apply to a certain extent. The moon is different and you can not use the same aproximations. What you're a demonstrating is that the simple model does not apply to slowly rotating bodies with no atmosphere, which we all know.

    If you want a better model for the moon, calculate the energy balance locally. You'll get fairly reasonable values except for the night side where the temperature drops too fast and too low.
  9. Rosco,

    Go get a course on basic physics first. Earth cools by radiating to space!! Nothing else cools the Earth from a system perspective. Radiators heat with both radiation and convection. I mean c'mon. Do we have to uber analyze everything??? G'd'mn broken education system.

    Oi!!!
  10. Rosco,

    As Riccardo said, this is a simple model, and when you consider a simple model. The advantage of a simple model it gives you a crude, easily to calculate estimation. Whether this estimation is any good depends on the assumptions.

    In this case, this simple, zero dimension radiative balance model will be good for a planet that is rotating quickly and have a high heat capacity (such as the earth), and poor for a slowly rotating, low heat capacity object such as the moon.

    This model can give poor estimations for two reason:
    1) The physics is wrong (your assertion, which is incorrect).
    2) The assumptions that enables us to calculate a numerical value is not satisfied (this is the correct explanation).

    To explain the temperature on the moon, you'll need to use a more sophisticated model, where rotation is fully taken into account, while the physics is exactly the same as the simple model. Indeed the model reproduces the diurnal temperature on the moon very well, with the maximum temperature exactly what you would expect with 1368 Wm-2 of solar radiation with 0.11 albedo.
  11. 6 Rosco:

    Response to your individual points
    1) That's only one factor. The heat capacity and the length of day will play a big role.
    2) Not sure what your point is, but as I have re-iterated, you can't apply the simple model to the moon. The fact that the simple model fails spectacularly for the moon does not mean that it is automatically meaningless for earth. Earth and the moon differ very significantly.
    3-5) No one says that the instantaneous solar radiation is 170W/m^2. It obviously varies according to the time of day, latitude, cloud cover and so on. You can probably get close to 1368w/m^2 if you are on the equator at noon on a sunny day.

    If you want a decent weather/climate model that realistically models the earth you will have to take these factors into account. However, no matter what the level of sophistication is, a model with an atmosphere will always be warmer than the same without, because it is dictated by physics.
  12. 7 Rosco:

    What if increased levels of CO2 actually provide another mechanism for the Earth's surface to cool.

    How exactly?

    Again, no ones says that convection doesn't play a role. Convection is included in all weather and climate models. Yet to explain the vertical structure of the atmosphere you need BOTH convective and radiative processes. While taking CO2 out of the atmosphere will not alter the convective process, it will definitely affect the radiative balance.
  13. 1, Rosco,

    Just noticed your first post. Sorry I'm so late to the party, but it contains several errors which invalidate the whole thing.

    Your first and most obvious error is that you are comparing the peak daytime temperature on the moon with the average temperature on earth. 396˚K is the daytime maximum on the moon. 40˚K is the nighttime minimum. The average temperature on the moon is thus 218˚K.

    This is well below the 270˚K that you computed by (properly) distributing the incoming energy over the surface of the sphere (giving 301 W/m2, average).

    Why? Because the surface of the moon reflects a large amount of the light (as proven by how bright it is when viewed from the earth at night). [I find it interesting to note that you applied the albedo to the earth, and forgot to do so to the moon.]

    For the temperature of the earth, it is clear that something is heating the earth, because with it's albedo the average temperature should be 254˚K (-19˚C), and yet it is clearly warmer. This is from 1368W/m2, divided by 4, multiplied by the albedo factor of 0.7, then applied to Stephan-Boltzmann, as you've done.

    So something is warming, not cooling the earth.

    But the greenhouse effect, left alone, would heat the earth well past the 288˚K we see today. But it doesn't! Why not?

    Because convection and evapotranspiration, as well as the complexities of the absorption and transmission of radiation through an atmosphere of continuously variable density, add additional factors that moderate the greenhouse effect.

    Your effort at disproving the greenhouse effect through the simplest of math is a non-starter, because you included many logical mistakes in your calculations.

    Hint: A lot of really, really smart people have been thinking about this for over a hundred and eight-five years. If it were as simple to untangle as you'd like it to be (i.e. encapsulated in a short blog comment), we wouldn't be having any discussions about it.
  14. Sphaerica, the Moon has an albedo of 0.136, slightly less than half of that of Earth. Therefore high albedo is not the cause of its lower mean surface temperature. Rather, that is the consequence of its uneven energy distribution. Because radiation to space increases with the fourth power of temperature, a body with very high and very low surface temperatures at different locations radiates energy to space far more efficiently than one with a constant surface temperature. Consequently its mean surface temperature will be lower, even though it radiates the same energy to space.

    This means that, given Earth's albedo, 255 K is the maximum Global Mean Surface Temperature for the Earth if we ignore the greenhouse effect. Because the temperature of the Earth's surface is not uniform, in practice it would be lower than that. The often quoted 33 degrees C increase in the GMST as a result of the greenhouse effect is, therefore, an underestimate.


    Of course, these facts in no way help Rosco's case. Rather they undermine it. They show why comparisons between the Earth and the Moon are misleading if not carefully done, viz, the Earth has a very even surface temperature, while the Moon has a very uneven surface temperature. They highlight his cherry picking by quoting daylight temperatures for the moon instead of the Mean Surface Temperature. And they highlight is stunning inability to comprehend the meaning of the word "average", as in "Total Solar Insolation averaged over the surface of the Earth", or the "average surface temperature".
  15. 14, Tom,

    Interesting! I never knew or considered that (the fact that a day/night "average" must be done more carefully by considering radiation and Stephan-Boltzmann, not by mere add and divide)!

    I can make use of that in a blog-post-project I've been working on... if life ever allows me to return to it.
  16. Dikran,

    Postma's paper, in the end, waters down to two things.

    First, he misuses the term "thermodynamics" repeated, treating it more as an incantation to ward off evil spirits than as an actual, applicable argument. He doesn't reference real thermodynamic "laws." He just throws the word around whenever and however he pleases.

    So after throwing around the word thermodynamics as many times as he can, then acting as if he has proven something and so can dismiss radiative effects, he gets to the real heart of his argument, which is that lapse rate is entirely defined by gravity, and explains the temperature of the surface of the earth.

    But here is the real gem of his smoke and mirrors act. What he does now is to do a basic, wikipedia derivation of lapse rate proportional to gravity, which of course gives the wrong answer. He then instead substitutes in the environmental lapse rate, which is the observed lapse rate. He picks a point in the atmosphere which is really arbitrary (he justifies it by saying it's the point where the atmosphere radiates at 255˚K, but that's the nifty legerdemain, because it doesn't actually matter where he started, he'll still get the same answer). Then he works down, and lo and behold, the surface temperature of the earth comes out correct!

    So... he dismisses radiative theory by using the word "thermodynamics" as many times as he can, couched in a lot of gibberish which is nothing more than a (poor) restatement of basic atmospheric physics, and then he goes on to introduce a superior theory, which he proves by getting the right answer... except he constructed his equation from observations, so he had to get the right answer!

    What he actually proves is that temperatures computed from lapse rate observations match observed temperatures.

    Interestingly, he does not address the elephant in the room. What happens to the energy that is radiated from the surface of the earth at 288˚K? Where does it go? Why does it not escape into space, to be seen by passing alien spaceships that can then remark "wow, that place is nice and toasty, we should visit some day, don't you think?"

    Postma establishes that the surface of the earth is 288˚K because of gravity and pressure, and everyone knows that PV=nRT. But he stops there and fails to explain how the atmosphere avoids then cooling from that point on, because it must be radiating at 288˚K!
  17. Cheers Sphaerica. I noticed that Postmas paper lapsed into all the lapse rate nonsense.

    The idea that there is gravitational heating seems like nonsense to me. If gravitational heating were true, then it should be heating the surface even if the sun were to stop shining. My intuition here would be that it wouldn't, the Earth would cool and the atmosphere with it, until it eventually condensed out as ice on the surface and we would have no atmosphere at all. It is only the heat we recieve from the sun that holds the atmopshere up by providing the thermal energy that causes it to have pressure due to the movement of the molecules. It seems to me that Postma has got it completely the wrong way round.
  18. The "gravitational heating" meme is one I've seen over and over. I would suggest it as a topic for a SkS thread, except that it's so ridiculous I feel it a waste of time.

    Gravitational collapse can release energy - once per collapse. Once that happens, the energy is free to radiate away as per the Stefan-Boltzmann law, and it's quite clear that over the 4.5 billion years of Earth's existence all of the excess energy from the atmospheric collapse would be long gone.

    But such collapse cannot provide a continuing flow of energy.
  19. KR, nice explanation; the difference in clarity between your answer and mine is why I tend to keep to statistical issues! ;o)
  20. Nonsense, Dikran - your posts contain (ahem) significantly more content :)
  21. It's actually a nice, convoluted little bait and switch they pull, and what's really, really, really funny about it is they have to violate the 1st law of thermodynamics for it all to work... while all the time screeching that GHG theory violates the 2nd law of thermodynamics.

    You see, pressure is determined by density is determined by gravity, which is determined by distance from the center of the earth, so closer to the surface the pressure is higher. Who can argue with that?

    And any high school chemistry student learned that for an (ideal) gas, PV=nRT.

    So... temperature is proportional to pressure. So if the sun heats the planet to 255˚K with constant sunshine, then... clearly as the pressure gets greater nearer the surface, the temperature must rise above that!

    It's all so simple. Who needs that radiative greenhouse mumbo-jumbo anyway?
  22. Rosco is correct (roughly). The maximum temperature measured in near Earth space is 121°C, that is what is being measured on the Moon, not the Moon`s actual temperature, which is in it`s soil, not in the vacuum of space above the surface. Clearly, when maximum daytime temp is measured on Earth in direct sunshine, the atmosphere is impeding warming, not amplifying it.
  23. Yogi,

    Please forgive me if I don't take anything you say at all seriously.
  24. Sphaerica
    "..the surface of the moon reflects a large amount of the light (as proven by how bright it is when viewed from the earth at night)"

    With an albedo of 0.12, we actually receive more IR than visible from the Moon.
  25. YOGI - The average temperature on Earth is ~288K. The average temperature on the Moon is ~218K. Averages reflect the total incoming energy and radiative effects, not peak or nadir temperatures. Note the difference between the averages?

    The amount of energy radiated from the top of our atmosphere is ~240 W/m^2, corresponding to a temperature of ~255K for a blackbody. This is due to the greenhouse effect, to greenhouse gases radiating from the top of the atmosphere, and to the atmospheric lapse rate which requires a much warmer surface (radiating ~396 W/m^2) to radiate the incoming solar energy back to space at TOA.

    Rosco was completely incorrect - Postma's work is nonsense. I suggest you do some more reading.
  26. 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.
  27. 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 ?
  28. 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.
  29. 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.
  30. #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.
  31. Moderator, why are you deleting my comments ?
    Response:

    [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.

  32. 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.
  33. 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).

  34. 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.
  35. scaddenp
    The Lunar Thermal Environment
    http://diviner.ucla.edu/science.shtml
    Apollo soil temp` measurements at 35cm deep give an equatorial average of 255K with a diurnal variation of +/- 70K.
  36. Addendum to my last post:

    * Earth with ~240 W/m^2 average insolation, 0.98 emissivity: ~ -18C temperature.
  37. So what happens to all the IR back-radiation the hits the ocean surface ?
  38. 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.
  39. "[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 ?
  40. 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?
  41. 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.
  42. 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.
    http://diviner.ucla.edu/science.shtml

    You should have read on further....
  43. 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.
  44. 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.
    Response:

    [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.

  45. 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.
  46. 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.
  47. KR@46:
    What YOGI is proposing will never be proven as he ignores basic physics.
  48. 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.
  49. Camburn - Agreed; without basic physics (or at least a willingness to learn), no progress will be made.
  50. 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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