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The greenhouse effect and the 2nd law of thermodynamics

What the science says...

Select a level... Basic Intermediate

The 2nd law of thermodynamics is consistent with the greenhouse effect which is directly observed.

Climate Myth...

2nd law of thermodynamics contradicts greenhouse theory

 

"The atmospheric greenhouse effect, an idea that many authors trace back to the traditional works of Fourier 1824, Tyndall 1861, and Arrhenius 1896, and which is still supported in global climatology, essentially describes a fictitious mechanism, in which a planetary atmosphere acts as a heat pump driven by an environment that is radiatively interacting with but radiatively equilibrated to the atmospheric system. According to the second law of thermodynamics such a planetary machine can never exist." (Gerhard Gerlich)

 

Skeptics sometimes claim that the explanation for global warming contradicts the second law of thermodynamics. But does it? To answer that, first, we need to know how global warming works. Then, we need to know what the second law of thermodynamics is, and how it applies to global warming. Global warming, in a nutshell, works like this:

The sun warms the Earth. The Earth and its atmosphere radiate heat away into space. They radiate most of the heat that is received from the sun, so the average temperature of the Earth stays more or less constant. Greenhouse gases trap some of the escaping heat closer to the Earth's surface, making it harder for it to shed that heat, so the Earth warms up in order to radiate the heat more effectively. So the greenhouse gases make the Earth warmer - like a blanket conserving body heat - and voila, you have global warming. See What is Global Warming and the Greenhouse Effect for a more detailed explanation.

The second law of thermodynamics has been stated in many ways. For us, Rudolf Clausius said it best:

"Heat generally cannot flow spontaneously from a material at lower temperature to a material at higher temperature."

So if you put something hot next to something cold, the hot thing won't get hotter, and the cold thing won't get colder. That's so obvious that it hardly needs a scientist to say it, we know this from our daily lives. If you put an ice-cube into your drink, the drink doesn't boil!

The skeptic tells us that, because the air, including the greenhouse gasses, is cooler than the surface of the Earth, it cannot warm the Earth. If it did, they say, that means heat would have to flow from cold to hot, in apparent violation of the second law of thermodynamics.

So have climate scientists made an elementary mistake? Of course not! The skeptic is ignoring the fact that the Earth is being warmed by the sun, which makes all the difference.

To see why, consider that blanket that keeps you warm. If your skin feels cold, wrapping yourself in a blanket can make you warmer. Why? Because your body is generating heat, and that heat is escaping from your body into the environment. When you wrap yourself in a blanket, the loss of heat is reduced, some is retained at the surface of your body, and you warm up. You get warmer because the heat that your body is generating cannot escape as fast as before.

If you put the blanket on a tailors dummy, which does not generate heat, it will have no effect. The dummy will not spontaneously get warmer. That's obvious too!

Is using a blanket an accurate model for global warming by greenhouse gases? Certainly there are differences in how the heat is created and lost, and our body can produce varying amounts of heat, unlike the near-constant heat we receive from the sun. But as far as the second law of thermodynamics goes, where we are only talking about the flow of heat, the comparison is good. The second law says nothing about how the heat is produced, only about how it flows between things.

To summarise: Heat from the sun warms the Earth, as heat from your body keeps you warm. The Earth loses heat to space, and your body loses heat to the environment. Greenhouse gases slow down the rate of heat-loss from the surface of the Earth, like a blanket that slows down the rate at which your body loses heat. The result is the same in both cases, the surface of the Earth, or of your body, gets warmer.

So global warming does not violate the second law of thermodynamics. And if someone tells you otherwise, just remember that you're a warm human being, and certainly nobody's dummy.

Basic rebuttal written by Tony Wildish


Update July 2015:

Here is the relevant lecture-video from Denial101x - Making Sense of Climate Science Denial

 


Update October 2017:

Here is a walk-through explanation of the Greenhouse Effect for bunnies, by none other than Eli, over at Rabbit Run.

Last updated on 7 October 2017 by skeptickev. View Archives

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Further reading

  • Most textbooks on climate or atmospheric physics describe the greenhouse effect, and you can easily find these in a university library. Some examples include:
  • The Greenhouse Effect, part of a module on "Cycles of the Earth and Atmosphere" provided for teachers by the University Corporation for Atmospheric Research (UCAR).
  • What is the greenhouse effect?, part of a FAQ provided by the European Environment Agency.

References

Comments

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Comments 326 to 350 out of 1016:

  1. damorbel, I offered three explanations in my comment. The first one (1, 2, 3, 4) was addressed to you, in response to your comment that "The idea that planetary temperature is affected by its albedo is quite mistaken" and all the subsequent comments in which you've spread confusion about the relationship among albedo, temperature, and radiation balance. The second explanation I provided addresses the subject of this thread -- the (erroneous) claim that the greenhouse effect violates the second law of thermodynamics (a claim that you make, e.g., here). The third part of my comment above goes into more detail about why the greenhouse effect doesn't violate the second law of thermodynamics. That part of the comment is not addressed directly to you because even after seven pages of mostly incoherent commentary it's hard for me to be sure what exactly your claim is. The most common (and indeed, the only) skeptical argument I've seen re: the second law is the one discussed in this thread -- the claim that radiation from a colder atmosphere cannot flow to / reach / be absorbed by a warmer surface. See, for example, this comment at Science of Doom, which includes the following: “Does this radiation from the colder surroundings “reach” the solid body in the middle of the diagram?” Answer: No, the colder body radiation cannot reach and be absorbed by the warmer solid body causing the warmer solid body to heat-up. and Trenberth clearly shows the colder Atmosphere Back Radiation of 324 w/m^2 being ABSORBED by the warmer Earth’s surface. Anytime a body absorbes heat energy it’s temperature has to increase, the warmer Earth’s surface was warmed by the colder atmosphere. A CLEAR Violation of the 2nd Law. and AGW theory and the Greenhouse Effect has been proven to violate the 2nd Law of Thermodynamics and the Law of Conservation of Energy. [...] If Back Radiation actually reached and heated the Earth as Trenberth shows, then Parabolic Mirror Solar Ovens would produce heating Day and Night! and so forth, ad nauseam. If you can see the flaws in that person's argument, then congratulations! We have some common ground to work from. However ... if you still think there's some problem with the second law of thermodynamics, you need to be much clearer and more coherent in explaining where you think that problem lies. Your comments in this thread have tended to wander diffusely from one incoherent remark to another (e.g., the entire digression about albedo). If you're unhappy that I or others are failing to correctly restate the subtle nuances of your views, you could help out by being a bit more straightforward about what those views are.
  2. “The net heat flux is from the surface to the atmosphere; it's just a smaller flux than it would have been if the atmosphere weren't there (or didn't contain greenhouse gases)”. “This is all completely uncontroversial among physicists, earth and planetary scientists, and others who deal with radiation balances in their work. There is no fertile ground for AGW-skepticism here” In your post, Ned, there remains a failure to differentiate between heat and energy which is at the heart of the confusion in most of the AGW blogs. Heat (the ability to do work or raise temperature) is, by definition, the net transfer of energy between two bodies. It is wrong to consider source to sink, and sink to source, energy flows in isolation. That way madness (and perpetual motion) lies. That is why the revised Trenberth diagram is vastly superior to its misleading predecessor. Whether or not energy can do anything at all depends on its surroundings. That is why there are cooling towers on power station sites. The backward radiation on which SOD harps at inordinate length is the negative term in the Stefan-Bolzmann equation. Given that, with a few simplifying assumptions, it is very easy to calculate the greenhouse effect. Assume a spherical, heated, source in a vacuum, in direct contact with the absolute (more or less) zero of space. If the temperature of the source is Tsource, it will radiate energy, W, at a rate proportional to the fourth power of Tsource. Now surround the source with a spherical sink, close enough for us to neglect surface area corrections and (this is a thought experiment) with zero resistance to thermal energy, so that we can ignore temperature gradients. Assume that the sink is capable of absorbing all the energy radiated by the source. The sink will warm until, at equilibrium, it radiates to space the original source energy. In other words, to Tsink will rise to equal Tsource. Meanwhile, the source must warm to Tsource1 so that it can radiate the original input energy to the sink. That energy output, W, will now be proportional to the difference between the fourth power of the new source temperature, Tsource1 and the sink temperature, Tsink which will have risen to Tsource. In other words, Tsource1 to the fourth – Tsink to the fourth = Tsink to the fourth, because the sink is radiating the original energy, W, to space. But Tsink = T Source, the original source temperature, so : The new source temperature (to the fourth) = 2 * the original source temperature (to the fourth). So, finally, Tsource 1/Tsource = fourth root of 2 = 1.19 Since the moon is at 255K, we arrive at a plausible explanation of the greenhouse effect (0.19*255= 48.5K). The atmosphere does not warm the earth directly in a second law violating way; instead it acts as a radiative insulating blanket. Do we believe this explanation, Ned? Woods tried to test it by building two greenhouses – one radiative (ie OLR absorbent) and one non-radiative. Their internal temperatures were the same. And if we do believe it, ignoring Woods, what will happen if we increase the absorption of the atmosphere? Its temperature cannot increase because it must continue to radiate W to space. The source to sink temperature difference must also remain the same. So nothing will happen. Would you agree, Ned, that there is ample scope here for rational scepticism about the impact of increased CO2 in the atmosphere?
  3. Fred Staples wrote "if we increase the absorption of the atmosphere? Its temperature cannot increase because it must continue to radiate W to space. The source to sink temperature difference must also remain the same. So nothing will happen." Fred, you are using only the rules for equilibrium, but by increasing the absorption of the sink you've pushed it out of equilibrium. While the sink moves toward a new equilibrium, additional rules apply. Increased absorption by definition means that the sink retains some of the energy W that hits it. There is no rule insisting that the retained energy instantly be radiated. Instead, the rule about how much energy is radiated depends on the temperature of the sink. The temperature of the sink does not rise enough to cause all of the newly retained energy to be radiated.
  4. Fred Staples "Woods tried to test it by building two greenhouses – one radiative (ie OLR absorbent) and one non-radiative. Their internal temperatures were the same." Which proves very nicely that greenhouses work by limiting convection rather than by absorbing radiation. It tells us nothing about the atmospheric greenhouse effect other than that it's poorly named. "And if we do believe it, ignoring Woods, what will happen if we increase the absorption of the atmosphere? Its temperature cannot increase because it must continue to radiate W to space. The source to sink temperature difference must also remain the same. So nothing will happen." You're very nearly correct. The effective radiating temperature does indeed stay the same, but it moves upwards in the atmosphere. The result is that the surface temperature must rise This is the best simple explanation I've ever seen of it and may clarify for you (thanks to Science of Doom): Soden & Held, 2000
  5. Fred Staples - "Would you agree, Ned, that there is ample scope here for rational scepticism about the impact of increased CO2 in the atmosphere?" I would say that there is not. Greenhouse gases reduce the efficiency of emission (emissivity), as is clearly seen by satellite spectra of the Earth. Given the P = e * s * A * T^4 relationship of Power to emissivity, Stephen-Boltzmann constant, Area, and Temperature, if the emissivity goes down temperature must rise to radiate the same power.
  6. Fred> Assume that the sink is capable of absorbing all the energy radiated by the source. This is an incorrect assumption for your simple model, and it invalidates your conclusions. Instead of absorbing all the energy, picture your sink absorbing a fraction of the energy emitted by the source, with that fraction increasing as the absorptivity of the sink increases. You will find that your simple model does indeed predict warming with increasing absorptivity of your sink.
  7. VeryTallGuy, thanks! The figure in your comment here is the exact one I had in mind when composing this comment in the other thread. I couldn't remember where I'd seen that figure (from Soden & Held, 2000), spent a lot of time looking for it, and finally ran across the similar (but not quite as good) version at Chris Colose's website.
  8. The second law also desribes:increasing entropy and heat loss. Heat and temperature are 2 different things. Also it is the.zeroeth law that desribes two bodies next to each other,at two different temps,and the resulting heat flow from a warmer to cooler body as well, in terms of equilibration.
  9. Chemist1 @333 Also it is the.zeroeth law that desribes two bodies next to each other,at two different temps,and the resulting heat flow from a warmer to cooler body as well, in terms of equilibration. No, the zeroth law only establishes temperature as the property that is invariant when two systems are in thermal equilibrium, it says nothing about the direction of heat flow when they are not. This is covered by the 2nd law.
  10. important note: net heat flow Heat doesn't from warmer objects doesn't avoid cooler objects.
  11. I am sorry to have delayed a reply to the comments on my post. I quite literally lost the thread. The explanation you offer, Very Tall Guy, is the only plausible explanation of the AGW effect. It is the preferred explanation of the founding fathers over at RC, and you can find it in the Rabbet rebuttal of the G and T paper, (immediately following their absurd multi-layer, back-radiation explanation). It begins with the lapse rate, a function of gravity and specific heat, which has nothing to do with radiative effects. Without this lapse rate there would be no AGW. Increasing CO2 in the cold, dry, upper atmosphere, impedes outgoing radiation, and moves the effective radiation point to higher (and therefore) colder temperatures. Radiation is reduced, incoming radiation remains the same, and the whole atmosphere and surface warms up to compensate. As your drawing demonstrates, the lapse rate moves to the right. In the trade this is the “higher is colder” explanation. It is plausible, but is it true? There was no sign of unusual global warming until the mid-seventies, when satellites began to measure temperatures across all levels and latitudes of the atmosphere. The UAH charts at Global Warming at a Glance show the temperature movements in the lower and upper troposphere, every month. At the very least these temperatures movements should be the same. In fact, the upper atmosphere temperature has hardly changed, while the lower temperature increase is 1.4 degrees C per century. Several years ago RC claimed that this contrary effect was the result of cooling in the stratosphere, which distorted the readings. (If the facts don’t agree with the theories, so much the worse for the facts). Sadly, from 1995 to date (15 years), lower stratosphere temperatures have been constant. Before that, minor falls appear as step changes associated with violent volcanic eruptions. (HadAT radio-sonde results). So there we are, Ned et al. The only plausible AGW theory is doubtful, at best. The others, (back-radiation, heat trapping, blanket-style insulation etc) are either absurd or directly contradicted by experiments (Woods and Angstrom’s) or the second law. Incidentally, the point of the second law is that energy is not capable of doing anything (work or heat) without an increase in entropy. One final point. It is always entertaining to see my fellow physicists at RC patiently explaining that everything with a temperature above absolute zero will radiate energy. They then go on to exclude Nitrogen and Oxygen in the atmosphere, leaving it to the greenhouse gasses (in the thin upper atmosphere) to radiate most of earth’s surface energy to space.
  12. Fred Staples - "Higher is colder" is certainly part of the greenhouse effect. So is band broadening as greenhouse gases increase. Both effects (dropping the emissive power of GHG bands in the upper atmosphere and widening those bands) reduce overall thermal emissivity of the Earth to space. Reducing emissivity, as per the Stefan–Boltzmann law, reduces the power emitted to space at any particular temperature. This causes an imbalance, energy accumulates, temperatures rise, emitted power returns to match incoming power - and we're a bit warmer. Now - if you think the radiative greenhouse effect is contradicted by the second law of thermodynamics (as per the various canards of the G&T paper), I suggest you go discuss that on Science of Doom. SoD has written far more (and far better) than I on that subject.
  13. KR, I find statements like this "SoD has written far more (and far better) than I on that subject" are not verifiable without a link. Would you care to provide one so we can discover the point you are making? In 329 VeryTallGuy wrote "This is the best simple explanation I've ever seen of it and may clarify for you (thanks to Science of Doom): You are referring no doubt to the diagram in your post I do hope there are better explanations. Your diagram does not show how CO2 or any other GHG has a warming effect; all it shows is the standard averge lapse rate which is known to arise from the increase in pressure on descending through the atmosphere. What it also shows is that, when the Earth gets warmer it... does... indeed... get warmer! What your diagram shows applies equally to the heating effect of the Sun at different latitudes; there are quite different tempertures at different latitudes because of the lower angle of the Sun in the sky; it's called the cosine effect; it is one of the reasons for different climates in the first place! To have a diagram with the tropopause at the same height for different surface temperatures just illustrates how far from observational measurements it is possible to get; changes in the surface temperature are always reflected in the height of the tropopause. The height of the tropopause is governed by a number of factors of which the surface temperature is one. An equally important matter is the Stratosphere where the temperature increases with height, very nearly to the surface temperature, almost reversing all the temperature drop due to the lapse rate.
  14. damorbel - I would suggest looking at SoD's excellent Imaginary Second Law of Thermodynamics. Use the search function on his website - as I recall he has multiple pages on the subject. Gerlich et al 2009 is a horrible paper - there are plenty of discussions across the web discussing them in detail, which are quite easy to find. I personally regret the time I spent reading it, as I will never recover those wasted hours - the more advanced version of this page covers it pretty well, but SoD digs in to much greater depth. Arthur Smith is worth reading on it as well, as is the excellent peer-reviewed Halpern et al 2010 reply. The other major point of my post was in regards to blocked band widening and deepening due to increased GHG's and increasing altitude of effective emission, seen in the graphs here. Reduced emissivity to space means reduced power to space - an energy imbalance; the temperature will change until said imbalance is zeroed out again.
  15. Re 339 KR this is what your link to SoD's explanation of the 2nd Law actually says:- "In the case of the real “greenhouse” effect and the real 2nd law of thermodynamics, net energy is flowing from the earth to the atmosphere. But this doesn’t mean no energy can flow from the colder atmosphere to the warmer ground." "It simply means more energy flows from the warmer surface to the colder atmosphere than in the reverse direction." I repeat the relevant GHE blind spot; "But this doesn’t mean no energy can flow from the colder atmosphere to the warmer ground". How is it possible to say this and claim 'net flow' in the other direction? Net flow causes temperature change. It is a temperature increase in the cold upper atmosphere that takes place due to net (warm) radiation from the surface, not the surface being warmed by a (net) heat loss from the surface to the upper atmosphere as 'explained' by GHE 'theory'. Without the 'net flow' from the surface the GHGs will lose heat through radiation and cool down catastrophically, GHGs radiate IR as well as absorb it, that is what Tyndall discovered.
  16. damorbel - "Net" == summed, total, the amount actually moving after all elements are considered, etc. I suggest you read Roy Spencers excellent discussion, Yes, Virginia, Cooler Objects Can Make Warmer Objects Even Warmer Still. If you've already read it and disagree, read it again. Repeat until understood.
  17. damorbel - Rereading this thread, I have decided that it's not worth my while to rehash issues that have been discussed ad infinitum with you. You've been pointed at the appropriate information; I would suggest reading the thread over and working on understanding it. You've been given the data, you've been given multiple explanations - but your last post indicates you are repeating the same errors you've displayed from the very beginning. >300 comments later, and you're still holding to those physically incorrect views. Rehashing this topic with you yet again is a repetitive rhetorical exercise, unless you show some propensity towards learning. I'm not going to waste my time. Sorry about the rather harsh attitude; I'm just getting tired of people who simply refuse to learn.
  18. KR you write:- ""Net" == summed, total, the amount actually moving after all elements are considered, etc." Follow your own logic, KR. The Earth's surface is a 'net' loser of energy; the upper atmosphere a net gainer. My conclusion is that 1/the surface is a net loser because it is warmer than the upper atmosphere so it (tends) to cool down, being a net loser of energy to the upper atmosphere. And 2/ the upper atmosphere is a 'net' gainer, therefore it tends to warm up with the (net +ve) heat gain from the surface since the upper atmosphere is cooler than the surface. No need for SoD's explanation or a visit to the good Dr. Spencer to understand this, is there?
  19. damorbel I've thought about the difficulty of getting this particular point through to you, and have a small Excel exercise for you. First row (1): "Sun" "Earth" "Atmosphere" "Space" Second row (2): "240" "=A2+0.5*C2" "0" "=B2-0.5*C2" Third row (3): "=A2" "=A2+0.5*C2" "=0.2*B2" "=B2-0.5*C2" Copy the third row and paste it in the 4th-20th rows. The "0" in the second line is to avoid a circular reference, but the actual guts take place in the third row. This represents solar input energy (240), surface radiated energy, energy intercepted/spherically radiated by the atmosphere, and energy radiating out to space. Constants (such as the 0.2 of IR intercepted by the atmosphere) are illustrative, but not tied directly to real values. The 0.5 radiated up and down from the atmosphere goes directly to space or the surface, so this is essentially a single-layer radiative atmospheric model without convection. What you will see is that the atmosphere, due to redirecting half of the energy back to the surface, warms it so that it radiates ~267 rather than 240. Meanwhile, the output to space is still 240, regardless. A cool object (atmosphere) has warmed a warmer object (the surface). Try constants other than 0.2 for IR absorption, and see how it goes; a 0.3 absorption brings the surface radiation to 282. Energy comes in from the sun, goes out to space - and reflecting insulation keeps the surface warmer than it would be otherwise, while maintaining the conservation of energy. Think about it.
  20. I don't suppose RW1 or Co2isNotEvil can help in explaining things to damorbel? Would be nice to see the skeptics helping each other out rather than leaving all the hard work to KR :)
  21. damorbel Here's another Excel exercise. "Row 1: "Emissivity" "0.6" Right click the 0.6 and "Name a range" to "Emissivity" Row 3: "Sun" "Earth" "Emitted" "Difference" Row 4: "240" "=A4" "=B4*Emissivity" "=A4-C4" Row 5: "=A4" "=B4+D4" "=B4*Emissivity" "=A5-C5" Copy Row 5 and paste it into the next 20-30 rows. As the Earth emissivity goes down relative to a theoretic black-body, due to the widening/deepening GHG bands in the spectra of the total planetary emission, surface radiation must go up due to the difference (energy conservation) between incoming and outgoing radiation. I find an emissivity of 0.606 and input of 240 gives a surface radiation of 396, emission to space of (again) 240 on convergence. Interestingly enough, this is just about what the planetary emissivity has been calculated to be...
  22. Re 344 KR You very kindly provided an excel sheet for doing calculations showing energy tranferred by radiation without any indication of the relative temperatures between the heat source and the heat sink. Now it is a fundamental of physics that, without knowing these temperatures, you cannot make any energy transfer calculations or predict any temperature changes. You claim that I do not understand your arguments, do you understand my need to know what the various temperatures are involved in you 'warming' model? PS Your EXCEL explanation will not load in my MS EXCEL, Would you be so kind as to provide a clearer version; perhaps just the cell identities and the cell entries? Thanking you in advance.
  23. damorbel - When I worked up the two spreadsheets, I transcribed the content as individual cells with values surrounded by quotes. I've had little (read that, 'no') success in copy/pasting entire spreadsheets as text - hence the approximate formatting. Sorry about the difficulties; if it doesn't work blame my typing! For the first spreadsheet the initial setup is a set of 4 columns, 3 rows, with the items in quotes in each cell in order (don't type in the quotes!). Then copy the last line (4 columns) and paste it into the next 20-30 to converge. Here radiation to space is what's left over when the atmosphere returns some to the surface, and it converges when outgoing=incoming. For the second spreadsheet, the emissivity driven model, there's a single line with a "named range" of "Emissivity" (getting a bit tricker), initial value 0.6. Two rows down there's a section 4 columns across, 3 rows high, with items in quotes in individual cells (don't put in the quotes!). Copy those last 4 cells and paste into the next 20-30 lines for convergence. Try different planetary emissivities to see how the surface energy changes. Here "Emitted" is what's sent to space, and it again converges when outgoing=incoming. These are radiation only models, lacking (in the first example) any convection/evaporation, in order to make the point. In the first, I'm just looking at radiative energies - 240 W/m^2 from the sun, and in convergence 240 W/m^2 to space as IR. Since it's such a simple model temps are not going to be accurate, but it clearly shows that in the presence of an absorbing/spherically emitting atmosphere the surface will be radiating more than the input energy in order to put the total input energy out to space. The primary take-home from the first model is that surface radiated energy goes up in the presence of a GHG containing atmosphere, and that only happens if the temperature goes up. In the second model we can look at temperatures related to those energies; it's a simpler yet more accurate model looking at only the radiative elements. 240 W/m^2 is indeed the incoming solar power. 0.6 is close to the Earth emissivity (zero dimensional model). 396 W/m^2 is the energy radiated from the Earth's surface (surface temp of 14°C which should radiate ~390 given an emissivity of .91-.95, but surface variations and the T^4 relationship raise that to 396). This really simple model quite accurately captures surface emissions and hence surface temperature. I was actually quite surprised at how closely this agrees with the data. In either case - re-emission back to Earth, which shows as reduced emissivity of the planet to space, results in driving the surface to emit more energy to get the incoming 240W/m^2 back out to space, and hence conserving energy.
  24. damorbel - For temperatures in the second model, add a second "named range" of "Surface_E", value of ~0.97 (a better surface estimate, once I looked it up), and another column starting at E5 containing: =SQRT(SQRT(B5/(Surface_E*5.6704*10^-8)))-273.15-4 Copy this cell and paste down the column. This reverses the Stefan-Boltzmann equation to get degrees Centigrade, with a "4" fudge factor (sets the ~18C final result back to ~14C, accounting at least in part for the surface variations and T^4 increase in radiated power). Not perfect, but a reasonable back of the envelope correction. Given this model and that a doubling of CO2 should result in an imbalance of 3.7 W/m^2, the effective decrease in emissivity of 0.606 * 236.3/240 =.597, which fed into the model results in a temperature rise of ~1.1C, just about what everyone expects from a CO2 doubling with no feedbacks.
  25. Re 348 & 349 Thank you for your contributions, they enable me to appreciate how you calculate your results. But all that you write makes it increasingly clear that the idea that the upper atmosphere (UA) can raise the surface temperature simply doesn't work. Let us imagine for a moment that the surface and the upper atmosphere are at the same temperature. In this situation both surface and the UA are emitting photons with the same energy, that is a consequence of your formula SQRT(SQRT(B5/(Surface_E*5.6704*10^-8)))-273.15-4. The temperatures are the same because the energies of the photons from both sources are the same; there would be thermal equilibrium i.e. no energy transfer and no temperature change. In reality the UA is colder than the surface and your formula shows that the energy of its photons is lower than those of the surface, so the consequence is that energy is transferred to the UA (accordind to the 2nd Law of thermodynamics) where it is further radiated into deep space. Perhaps you find this difficult to accept but if the UA contained no GHGs at all it would not have a different temperature (apart from the stratosphere - which is warmed by O2 absorbing ultraviolet from the Sun) because heat is transferred in the atmosphere mainly by fluid flow e.g. convection. Below the stratosphere the temperature profile is largely determined by two factors, the temperature of the surface and the compression of the air due to gravity.

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