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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.

Last updated on 22 October 2010 by TonyWildish.

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Related Arguments

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 951 to 1000 out of 1393:

  1. L.J. Ryan - "To claim effective LW emissivity of 0.612 is measured, is specious. How do measure “effective emissivity”? "

    That's quite a statement you're making there, L.J., and quite unsupportable.

    (A) The effective emissivity is quite simply measured by looking at the surface temperature (well known, well measured, etc., not to mention being what we're interested in) and the integrated power emitted at the top of the atmosphere (about 240 W/m^2). The tool used for those measurements is an infra-red spectroscope, incidentally. That's about 61% of the power that a black body at 15C would radiate, and hence the effective emissivity is 0.61.

    (B) That number matches the physics, as per line-by-line spectral modelling of the atmosphere such as in the MODTRANS and more up to date computations. It's always nice when the model matches the data - it's excellent support for the model being correct.

    So - that's the data, and it's supported by the (correct) models.

    You also have stated that "Delta T must be a function (of) a non-radiative input", rather than the well understood greenhouse effect. Just what non-radiative input would that be??? Invisible volcanos? Little green men? Accumulated friction from the hand-wringing of climate skeptics? I quite simply cannot take your argument seriously when you invoke Mysterious Unknown Forces (MUF's) as a replacement for the last 150 years of science.

    Please, L.J.Ryan - read some of the references you have equation-mined. Learn a bit more about the science. You're approaching the issue with a lot of erroneous preconceptions, and those are leading you to incorrect conclusions.
  2. CBDunkerson 950

    I should have addressed my post to les 948 & 914...914 is linked within 948.
  3. 949 Ryan.
    You can paraphrase what you like. But I would rather advise learning the meaning of the orriginal phrasing, put together by better physicists than you or I.

    But you really should not invent things like that that is my "revised position". I revised nothing. And you really cannot put a paraphrase into quotation marks!

    Yes, clearly the 2nd law is universal. But it doesn't say that energy can not flow from cold to hot. it says that energy can not flow from cold to hot without work being done. Any one who doesn't realise that should get a cold beer from the fridge and think about it.
  4. les 953

    So when you said:


    884 KR
    " The "2nd law" objection to the greenhouse effect is based upon a mistaken notion.."

    I don't disagree with you. However I'd like to suggest there is another problem. In the post, the statement of the 2nd law has missed out the phrase: "whose sole result". This is a statement that the 2nd law only applies to a closed system.

    For practical purposes, the system which consists of: the sun, outer space, the solid earth and the earths atmosphere is not a closed system.



    What did you mean?
  5. 954 Ryan

    I meant

    " The "2nd law" objection to the greenhouse effect is based upon a mistaken notion.."

    I don't disagree with you. However I'd like to suggest there is another problem. In the post, the statement of the 2nd law has missed out the phrase: "whose sole result". This is a statement that the 2nd law only applies to a closed system.

    For practical purposes, the system which consists of: the sun, outer space, the solid earth and the earths atmosphere is not a closed system.

    HTH.

    I even already posted another phrasing of the same point from here

    "The planetary warming resulting from the greenhouse effect is consistent with the second law of thermodynamics because a planet is not a close system"


    what bit are you struggling with?
  6. les 955

    "This is a statement that the 2nd law only applies to a closed system."...Ok applies only to closed systems


    "For practical purposes, the system which consists of: the sun, outer space, the solid earth and the earths atmosphere is not a closed system. "...Ok the earth's system is not closed

    These together suggest you are saying the earth's open system does NOT have to follow the 2nd law. Otherwise, why would have "another problem" or for that matter the entirety of 914?
  7. Moderators - I'm noticing a similarity in approach, in some word choices, and the use of terms I previously used replying to one poster appearing in another; are damorbel and L.J Ryan the same person?

    We appear to be getting "trolled" again...

    Please delete this post if I am incorrect.
  8. 956 Ryan.

    As mentioned above, everything obeys the 2nd law and the 2nd law states "bla bla sole result bla bla ... " or words to that affect.

    But now I see you confusion. "another problem" refers to the observations of KR 849. I should have hyperlinked that as the numbering of the comments tends to change from time to time.

    I must say I can see absolutely no reason to infer from any of my remarks that I believe the 2nd law doesn't hold. The reason for my comment was, on the contrary, to suggest that because the important "sole result" or close system clause is missing from the blog post, many people seem to be very very confused. Be that as it may. Now we have cleared up to your confusion I am confident that you will agree that the green house affect does not violate the 2nd law and we can bring a stop to the physics abuse of this thread.
    Great!
  9. KR 951

    re (A) As I stated, it is not measured. Rather effective emissivity is calculated by solving solving for emissivity with given temperature and power...and the assumption GHG mechanics are correct. So when you calculate for unknown X and then turnaround and use X to calculate one of the given variables, you have simplified verified your formula ([ 240/(0.612 * 5.6704*10^-8 ]^0.25 - 273.15 = 15.2C). The problem is with your given variables. If you are measuring radiation via atmosphere, should not the temperature variable also be that of the atmosphere. Why use temp. from one source and use it to calculate emissivity of another?

    re(B) I assume the modals would match the data because both assume the wrong input variable..namely surface temperature and atmosphere radiation to measure atmos. effective emissivity. I refer the above reply, why not use atmosphere temperature?

    KR: I am not damorbel.
  10. addendum: In truth, I can see that when I pointed out that the 2nd law as stated in the blog doesn't hold, it may be read as "the 2nd law doesn't hold"... but, really, that is a bit silly given that I mentioned the "sole result" clause...
  11. les 958

    We agree it must follow. The physics used to validate GHG theory however, is at odds with this tenet.
  12. 961 Ryan.

    "The physics used to validate GHG theory however, is at odds with this tenet."

    Not at all.
    Although I've yet to see much discussion of physics in these posts. Never the less, if it's of help, I refer you, again, to the paper of Prof. Pierrehumbert for illustration.
  13. wot? Where's Ryan?

    I'm expecting something like:

    You say "Not at all", let me rephrase "yes exactly". Do I understand?

    Well?
  14. L.J. Ryan - If you feel that integrated spectra are not measurements, well, then, I'll pass that on to the spectroscope manufacturers I work with. That should be good for a laugh.

    "Effective emissivity" is a useful summary of surface temperatures, atmospheric temperatures, band blocking, emission altitudes, and the lapse rate. You get the same results from either orbital measures of emitted spectra compared to surface emitted spectra, or from computationally modelling the entire atmospheric physics. That's the fractional efficiency of TOA energy radiation due to surface temperatures, relative to a black body.

    Incidentally, do you recognize that the black body temperature required to radiate a fixed power is the absolute minimum temperature required for a gray body to radiate the same power? With the gray body temperature going up as emissivity goes down? I've raised that point a few times with you, but you have not responded.


    Your objections to this are beginning to consist of nothing but flat denials with no backing; until and unless you post a physical argument that actually makes sense, preferably with references that support it, I don't believe I'll bother replying to any more of your posts. After almost 1000 posts, I believe there's more than enough information present for anyone who isn't sticking their fingers in their ears and singing "La la la la la..."

    Do some reading, L.J. Ryan, including the sources you yourself have linked to.
  15. les#948: "we pay respect to this great moment by giving up on this assault on the nodal discipline of physics by attempting to prove/disprove another of it's great achievements"

    That's a great point. Perhaps this will be the year when the deniers swear off the 'I am right and all of physics is wrong' arguments. Out of respect for past great physics achievements ... probably not. But maybe for their own self-respect?
  16. LJRyan @932:

    First, anybody who has read anything that I have written knows I am not given to knee jerk responses from my writing style alone, even if they do not understand the content. The fact that you are so completely wrong does not make a post which points that out a knee jerk response. Perhaps it is time you reconsidered your arrogance which believes, on this topic, that you alone have the truth, and the world's physicists from Arrhenius on have been barking up the wrong tree. A little humility is the first step to wisdom, so it is about time you learnt some.

    Second, my equations (1xx) are not equivalent to yours. That is because the Earth absorbs most of its energy in as visible light, but emits most of it as IR light.

    I would of course be delighted for you to prove me wrong. Don't just cite Kirchoff. Apply his proof to the actual situation on Earth and prove that his results have the consequences you claim. To do so remember that you must use all of the following sinks and sources:

    i) The Sun;

    ii) The Earth's surface;

    iii) The Earth's atmosphere; and

    iv) Space.

    For greater realism, you must also include clouds. For greater realism still you must split the atmosphere into about 30 odd layers, treating each as a separate sink/source, and treating clouds in each layer distinctly; but we won't expect that from you (though it is what we expect, and more, from climate scientists).

    I note that nobody understands a law of physics unless they can use the proof of the law to set up an appropriate model to model any situation in which it applies. So if you cannot make the argument called for above, it is because you do not know what you are talking about when you cite Kirchoff.

    Of course, if you do set up an argument as called for above, you will find that either your model contains obvious, and obviously relevant disanalogies with real life; or that it simply confirms the theories of the physicists. I am also not interested in any other argument from you because, quite frankly, I am tired of your bullshit and obfustication.

    For your help in setting up the model, the SW absorptivity of the surface is, on average 0.875, although if you exclude clouds for simplicity, you may want to treat it as 0.7.

    Third, you certainly did quote mine Professor Jin-Yi Yu's lecture slides. The thing about lecture slides is that they are never self explanatory. They are designed to be accompanied by a lecture which explains the slides, and without that lecture you are always missing crucial information, including, in this case, the definition of the symbols. lecture notes are much better, but not ideal because they are often too compressed. Text books are best of all, but rather hard to directly link to.

    However, despite the deficiency of lecture slides, even the slides you quote contain enough information to prove you wrong. Specifically on the slide titled "Greenhouse Effect"(about page 15), we have the following two formulas:

    a) Ta = Te = 255K

    b) Ts = (2^0.25)*Ta = 303 K

    Clearly the effective temperature (Te) does not equal the surface temperature (Ts) as you require for your version of equation 3 to be correct. Note that your comment about black body surfaces is irrelevant. The effective temperature is the temperature of a theoretical black body the would radiate the same power as is actually radiated from the the top of the atmosphere. It does not imply that the TOA has that temperature, or that all the OLR at the TOA is radiated from a surface at that point. It is no wonder you are so confused if you do not even understand basic terms of the science.

    Fourth, nothing else in your post is worth responding to IMO. This is because of your tantrum. I am not going to dignify your "shouted" comments and those bracketed by them with anymore response than to note that it is irrational to treat a tantrum thrower as both a tantrum thrower and a rational disputant at the same time.

    If you want to debate, be polite.
  17. Gosh . I dislike quoting the luminaries directly, but here are quotes from RC and Open Mind:

    RayPierre Humbert

    In a nutshell, then, here is how the greenhouse effect works: From the requirement of energy
    balance, the absorbed solar radiation determines the effective blackbody radiating temperature Trad. This is not the surface temperature; it is instead the temperature encountered at some pressure level in the atmosphere prad, which characterizes the infrared opacity of the atmosphere, specifically the typical altitude from which infrared photons escape to space. The pressure prad is determined by the greenhouse gas concentration of the atmosphere. The surface temperature is determined by starting at the fixed temperature Trad and extrapolating from prad to the surface pressure ps using the atmosphere’s lapse rate, which is approximately governed by the appropriate adiabat. Since temperature decreases with altitude over much of the depth of a typical atmosphere, the surface temperature so obtained is typically greater than Trad, as illustrated in Figure 3.6.

    Increasing the concentration of a greenhouse gas decreases prad, and therefore increases the surface temperature because temperature is extrapolated from Trad over a greater pressure range. It is very important to recognize that greenhouse warming relies on the decrease of atmospheric temperature with height, which is generally due to the adiabatic profile established by convection.

    The greenhouse effect works by allowing a planet to radiate at a temperature colder than the
    surface, but for this to be possible, there must be some cold air aloft for the greenhouse gas to work with.

    Tamino
    “If a parcel of air rises, because of the reduced pressure the parcel will expand. It generally takes much longer for a parcel of air to absorb/emit heat from/to its surroundings than to expand/contract, so during its expansion it will, for all practical purposes, exchange no heat with its surroundings; in other words, the expansion of the parcel of air will be adiabatic”

    For a text book derivation I quoted page 45 of Elementary Climate Physics by FWTaylor (mentioned in the far distant introduction). The lapse rate is a function of gravity and specific heat and is about 6K per kilometre of altitude.

    If we cannot accept this very basic Physics, we are entitled to ask who are the denialists in this debate. Anyone can see the compression/decompression effect for themselves by inflating a bicycle tyre or releasing the pressure in a gas cylinder.
    The question of the transparent atmosphere is frequently raised. An atmosphere which was totally transparent to radiant energy, unable to absorb or emit, would still have a lapse rate. Its low pressure at altitude would be colder than its high pressure at the surface. However, it would be a very strange gas indeed. Unlike everything else in nature with a temperature, it would not radiate. It would allow the surface to be in radiative equilibrium at 255 K, and would not affect this temperature by thermal insulation, convection, conduction, or evaporation. Not worth debating, I think.

    As I said in a previous response
    "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 possibility of AGW. The argument is that increasing CO2 in the cold, dry, upper atmosphere, impedes outgoing radiation, and moves the effective radiation point to higher (and therefore) colder temperatures.

    Outgoing radiation is reduced, incoming radiation remains the same, and the whole atmosphere and surface warms up to restore the balance. As your drawing demonstrates, the lapse rate moves to the right".

    The dominance of water vapour in the AGW stakes (often quoted by the sceptics)is not a factor because, at this altitude, the air is dry.

    This is a plausible explanation, unlike all the others. It implies that AGW is a top of the atmosphere effect, and that the temperature increase (right shift of the lapse rate) should be greater at altitude than at the surface. More subtly, it suggests that increasing the concentration of CO2 in the stratosphere will absorb and emit energy more efficiently, and thus cool the stratosphere.
    Response: [muoncounter] Please do not quote long passages from other blogs; we are fully capable of following links to them. And to avoid the possibility that you might be quoting selectively or out of context, you must provide those links anyway.
  18. What others (explanations of AGW) someone may ask. I collected the following explanations from one thread at RC:

    Ekholm in his 1901 paper:
    . . . radiation from the earth into space does not go directly from the ground, but on the average from a layer of the atmosphere having a considerable height above sea-level. . . The greater is the absorbing power of the air for heat rays emitted from the ground, the higher will that layer be. But the higher the layer, the lower is its temperature relatively to the ground; and as the radiation from the layer into space is the less the lower its temperature is, it follows that the ground will be hotter the higher the radiating layer is.

    Chris Colose
    This is one of the problems I have with the simple layer model as it is introduced in some textbooks, such as Dennis Hartmann’s or David Archer’s “Understanding the Forecast.” This is where you simply add up the influence from successive blackbody “layers” with a final result of something that usually ends up looking like T_s=T_eff*(N+1)^0.25, where N is the number of layers, and T_s and T_eff are the surface and effective temperatures, respectively. Archer discusses some of the incompleteness of this model in his class lectures (lack of convection, layers are not fully transparent in the shortwave nor fully opaque in the longwave) but I think the whole presentation misses the point completely

    Barton Paul Levenson
    Your CO2 absorbs an infrared photon, one of its electrons jumps a level, and it either radiates another photon of the same level, or more likely, crashes into a nearby nitrogen or oxygen molecule and transfers some of the new stuff as kinetic energy. Temperature is a measure of kinetic energy at the molecular level; the faster the molecules jiggle, the hotter the object. Thus the atmosphere warms up. Those collisions transfer energy *back* to the CO2, which radiates by the (wavelength-specific) Stefan-Boltzmann law. Some of the energy goes back down to the surface and heats it above what it would be from sunlight alone.

    Eli Rabett
    The short answer to the question of where the energy comes to warm the surface is from energy that left the surface but was turned around by backradiation. Without the greenhouse gases it would just keep going

    And RayPierre
    “The way the greenhouse effect really works is that adding CO2 reduces the infrared out the top of the atmosphere, which means the planet receives more solar energy than it is getting rid of as infrared out the top. The only way to bring the system back into balance is for the whole troposphere to warm up. It is the corresponding warming of the low level air that drags the surface temperature along with it”

    Settled Science?
    Response: [Dikran Marsupial] Some of those explanations are completely consistent with the "Top of the atmosphere" explanation, particularly that of Ekholm, Rabbet and RayPierre. Colose seems to be merely arguing a point on the details and Levinson is discussing part (anl only a part) of the same mechansim.
  19. Certainly it's settled science.
    No need to post from another blog to show that there are folks who misunderstand part or,indeed, all of it; just read the posts here!

    Mind you, if you want to understand the science your self you'll need to read one of those book things, possibly with the support of a physics (or physical science) degree. If you haven't done that, probably tre next best thing is to pist rubbish on a blog...
    ... Oh!
  20. Fred,

    You're making much of the perception that there are somehow two contradictory theories of GHE. As Tom and others have tried to explain to you, this is a false perception. The explanation relying only on backradiation is often referred to as the idealized or simple greenhouse model. It is a simplification, not a contradiction. The full explanation relies on both backradiation and the altitude of effective TOA radiation.

    I don't understand why you're having so much difficulty grasping this. Do you believe that atomic theory is in dispute because the Bohr model is still taught in elementary school?
  21. Fred Staples @967 & 968, you quote a number of well informed people expounding the theory of the GHE which I expounded @944, and which is the only theory of the GHE expounded by regular defenders of climate science on this site. You also quote three people who may be considered to be defending a grey slab model (which is physically false), if that quote was all you knew of there opinions. However, Ray Pierre fully and explicitly defends the lapse rate theory in your first quote, and Tamino quotes Eli Rabbett as defedning it in your second; so we know that your selected quote does not represent their whole opinion, which is in agreement with Ray Pierre's first exposition. So, on the evidence you present, there is a consistently accepted theory of the GHE which has been expounded since at least 1901 - as shown by earliest quote.

    So yes, that part of the theory is settled science. And while even settled science is always up for grabs if a better theory comes along, given that this settled science rests on such fundamental theories as quantum mechanics and the laws of thermodynamics, and literally millions of observations including some on systems as diverse as Venus, Earth, and Mars, if any better theory every comes along, it will be a close observational approximation of the current theory.

    So what is your point? (Please find a thread relevant to this discussion to answer this question, for it is plainly not relevant here.)
  22. The real problem in fitting Greenhouse Theory to observation is comparing a planet with an atmosphere to a planet with no atmosphere; this is not possible. A hypothetical atmosphere that contained no GHGs is still held in place by gravity and it will still have a temperature like any other gas in contact with an illuminated surface that can absorb and emit radiation from a star.

    When considering a planet with an atmosphere without any radiating/absorbing GHGs (or with, for that matter) it is important to remember that the rocky surface is no longer the planetary surface but it is the atmosphere; leaving the problem of deciding where the atmospheric surface is exactly located.

    The concept of an atmosphere without GHGs is perfectly valid; such an atmosphere would still have a temperature gradient due to the effect of gravitational compression, any satisfactory theory needs also to account for the gradient.
    Response:

    The claim that lapse rate or gravitational compression is responsible for the GHE is not directly relevant to this thread, as has already been addressed in multiple links provided. Please take this particular point of discussion elsewhere.

    Edit: "responsible for the GHE" should read "responsible for the warming attributed to the GHE"

  23. damorbel @973:

    Are you saying that we cannot test GH theories because we cannot compare planets with and without atmospheres? In that case, the presence of the moon refutes the claim. Such comparisons are easily made. Or are you saying that we can only test GH theories by comparing planets with GHG concentrations in their atmospheres to planets with atmospheres but no GHG? Again, you are wrong; for we can certainly compare planets with different concentrations of GHG, and that is sufficient.

    Continuing on, certainly the concept of an atmosphere without GHG is perfectly valid. Let us assume, for example, a planet with only nitrogen in it's atmosphere so that, for practical purposes, it is transparent at all wavelengths. It will be heated slowly at the surface until energy flow from the surface matches that to the surface (on average). The atmosphere above the surface will have a temperature gradient defined by g/c(p) = 9.81/1.039 = 9.44 K/km. I know this because we already have a theory that accounts for the gradient. That theory is independent of GH theory in the same way that the laws of thermodynamics. IE, it is an independent theory from which (along with some other theories) GH theory is derived.

    Curiously, the derivation is a logical derivation. Therefore, the standard theory of the GHE cannot be false unless at least one of:

    The laws of thermodynamics;
    The ideal gas laws;
    Quantum mechanics;
    The relativistic version Maxwell's theory of electricity; or
    The theory of gravitation,

    is false. So would you please acknowledge (after having been told inumerable times) that there is a well grounded theory of the lapse rate, and hence a theory that incorporates gravitation into the physics of atmospheres; and tell us just which fundamental branch of physics you think needs to overthrown by your no doubt brilliant, but never revealed proof of an error in GH theory.
    Response: [muoncounter] In keeping with above moderator responses, please do not attempt re-starting the lapse rate conversation ad nauseum.
  24. If anyone is feeling that their science-senses have been badly assaulted and would like some reading for restoration, SoD has started a new series Simple Atmospheric Models which is part one. I have no doubt we can look forward to some elegant prose and explanations.
  25. In a series of posts, I have tried to demonstrate that “higher is colder” is the only theory of AGW that does not contradict basic thermodynamics. Sadly, it is the only theory that G and T do not address.

    It is a top-of-atmosphere theory (where CO2 effects are not swamped by water vapour) and it depends on the existence of the lapse rate. The climate models are based on this theory, (which does not mean that it is correct, Tom) and predict mid-troposphere temperatures trends about about 20% higher than surface trends (50% higher in the tropics, where increased evaporation should produce the famous missing hotspot).

    To test the theory, we can look at the satellite data (from 1979) and, separately, radio-sonde data compiled by the Hadley Centre.

    At first sight, any debate is settled by the satellite data, which shows trends in the opposite direction to the models (wikipedia - satellite temperature measurements):
    Mid Troposphere : 0.52 degrees per century
    Lower Troposphere : 1.4 degrees per century

    However, the commentators cast doubt on the upper atmosphere results because they are contaminated by readings weighted from the stratosphere, which is said to have cooled (see below).

    A more straightforward source is the radio-sonde data from the Hadley Centre, which provides data at all levels. The trends over the satellite era, in degrees C per century, are as follows:

    Lower Troposphere 1.45 kilometers : 1.54
    Mid Troposhere 5.56 kilometers : 1.58
    Upper Troposphere 9.13 kilometers : 1.27
    Lower Stratosphere 11.74 kilometers: -0.28 (not significantly different from zero)
    Upper Stratosphere 21 kilometers : -8.10

    Has the stratosphere cooled? In the upper reaches, unquestionably, but these tenuous regions will not effect satellite readings.

    The lower stratosphere has not cooled significantly, but the more or less constant temperatures might mask (to some extent) warming in the troposphere as viewed by the satellites. Those whose business it is are working on this.

    I tested the significance of all the data (the use of second decimal places presumably shows that scientists have a sense of humour), and there is 1 chance in 18 that the trend difference between the lower and upper troposphere arose by chance, (ie from random fluctuations in the data) which is just less than the conventional 5% level.

    What can we conclude from this data? Warming there has certainly been but the data lends no support to any theory of causation. If I were an AGW enthusiast I would be particularly worried about the lower trend in the upper troposphere. And the satellite data would be conclusive (against “higher is colder”) were it not for the constant (ie not cooling) lower stratosphere temperatures.

    The data also confirms another piece of conventional sceptical wisdom. Working back from the latest data, we can ask how far we must go to detect a statistically significant period of warming. The answer, for the mid and lower troposphere, is 15 years. For the upper troposphere, 19 years.
  26. As I posted my last contribution, I noticed that we are to be favoured by another post from SOD. I debated back radiation theories with someone I believed to be SOD in Eli Rabett’s blog, some time ago.

    Quoting from memory, SOD based his argument on the conservation of Energy (“where does the energy go”?)
    He freely admitted that, for him, entropy “never seemed real” and its formula deltaS = DeltaQ/delta T did not make sense (which, since that version is wildly wrong, is not surprising).

    No-one should comment on AGW (or anything else, in my opinion) without a reasonable grasp of the second law of thermodynamics. For any spontaneous transaction, anywhere in the known universe, the change in entropy must be positive.

    Now if a quantity of energy deltaQ leaves the atmosphere at a temperature Ta, the change in entropy is -deltaQ/Ta.If it is absorbed by the surface, at a temperature Ts, the change in entropy is +deltaQ/Ts. Now, since Ta is less than Ts (the lapse rate again), the combined change in entropy is negative, which is forbidden.

    If it happens on the microscopic level (vibrating molecules in a steel bar, heated at one end, or photons from a cold plate to a hot plate), it must be accompanied by a greater transfer in the conventional direction, hot to cold. It cannot be considered or analysed in isolation, which would take us immediately to a search for perpetual motion, as G and T point out at excessive length.

    By transferring from a hot source to a cold sink, energy becomes heat which can produce work. No net change is possible in the opposite direction without a heat engine.

    So to answer the question posed in the introduction, have climate scientists made an elementary mistake in explaining AGW? Of course not. Have most of the bloggers, politicians and journalists? Undoubtedly.
  27. 976 Staples SoD seems quite comfortable with Entropy.
  28. Fred@975 It seems to me that the source of the disagreement here is that you view backradiation as a separate theory, rather than as a component part of the "top of the atmosphere" explanation. AFAICS this is incorrect, it is backradiation that causes the surface to warm until equilibrium is re-established following an increase in the height of the emitting layer at the top of the atmosphere.
  29. Les @977, an excellent read, and profitable for anyone following this debate. I particularly liked propater's comment:

    "If you take ScienceOfDoom example 3 and reverse it to consider radiation emmited by the atmosphere and absorbed by the earth’s surface, you can see that entropy is lost when the radiation from the atmosphere is absorbed by the hotter surface :

    Atmosphere: δS1 = -(390-301)/270 = -89 / 270 = -0.33 J/K
    Surface: δS2 = (390-301)/288 = 89 / 288 = 0.31 J/K

    This is right, net entropy equals -0.02J/K (as you say, “radiation quality” has increased since that energy will be re-emitted at a shorter wavelength)

    Entropy is reduced. This looks wrong. And it is! Because in that calculation you forgot one term: the radiation from TOA to space :

    If we suppose radiation from space to be j* = sigma * T^4 = 5.67*10^-8 * 3^4 = 4.59*10^-6 W/m²

    Let’s consider the entropy budget for one square meter for a second :

    Atmosphere: δS1 = -(390-0.00000459)/270 ~= -390/ 270 = -1.44 J/K
    Space: δS2 = (390-0.00000459)/3 ~= 390/ 3= 130 J/K

    Net entropy production from TOA-Space exchanges : 128.56 J/K

    Net entropy production from atmosphere exchange with the earth’s surface and space : 128.56 J/K – 0.02 J/K = 128.54 J/K.

    When you take all terms into account, no entropy is lost (even though some of it gets moved away.) In fact you see a massive amount of entropy created and, as Nick Stokes points out, it is the place where the entropy production is the largest (Sun-earth ~ 10 J/K.s.m², earth-atmosphere ~ 10^-2 J/Ksm² , atmosphere-outer space ~ 10² J/Ksm² )"


    What more could we ask for - an actual worked example proving that back radiation does not violate the 2nd law of thermodynamics. Given this example, and the ease of the mathematics, I think it should be a minimum denier wanting to mount the tired old 2nd law argument that they provide such a worked example of their model of the greenhouse effect. It should make the arguments much shorter and to the point, and provided an easy way to keep score of who is correct, and who is simply full of it.
  30. Fred Staples @976, I believe Les has adequately rebutted your comments about SOD.

    For any spontaneous transaction, anywhere in the known universe, the change in entropy must be positive.


    This is incorrect. The Earth is infested with a spontaneous transaction which results in the formation of very low entropy products. It is called life. Of course, if you look at all energy flows involved in life, then the net entropy of the whole system increases, even though that in the living system decreases temporarily. So, only when we account for all energy flows within a boundary can we apply the 2nd law to the system within the boundary, and then it applies only to the entropy of the whole system, not to any arbitrary subpart of the system.

    As the worked example quoted above shows, when all energy flows are accounted for, the interchange of energy between Earth and atmosphere including back radiation involves a net gain in entropy, and hence no second law violation. And the second law applies only to the whole system, not to any arbitrary subpart - say, the backradiation alone.

    "Now if a quantity of energy deltaQ leaves the atmosphere at a temperature Ta, ..."


    Plainly your accounting considers only one energy flow within the system, not all of them. Therefore it is an attempt to apply the second law to an arbitrary subpart of the system rather than to the system as a whole, which is as explained above, a misapplication of the second law.
  31. 979 Tom - "What more could we ask for..."

    I wait, with trepidation, to find out! To me, it all seems so straightforward.

    Still, just because this discussion has certainly not gone on long enough - nor has it been repeated nearly sufficiently enough times on nearly enough blogs - can I suggest a further place for doubt?

    It turns out that in many multiverse models it is not clear that conservation of energy holds for the whole universe nor, indeed, for every universe. As such, I'm guessing I admit, it should be possible to have infinitely many universes in which the 2nd law doesn't hold, or possibly doesn't hold only for those gases which don't transmit/radiate/absorb evenly at all wavelengths or something.

    see, always room for doubt.
  32. Tom Curtis 966 and KR

    Tom Curtis you said:
    “First, anybody who has read anything that I have written knows I am not given to knee jerk responses from my writing style alone, even if they do not understand the content.”

    Ok Tom, I have to admit, for the most part you are well considered;...though still wrong. So knee jerk was not appropriate, rather I should have said dismissive response.

    Regarding your arguments to my post 924. You set up hallow challenges to my equations. For example, your parsing of emissivity between SW and LW is irrelevant. Why irrelevant you ask...simple, I do not conflate the two. For example, lets compare the equations I used to the simplified models equations via slide 14 of Jin-Yi Yu's lecture.

    From Jin-Yi Yu's lecture:

    For Earth's surface
    S/4 * (1-A) +σ TA4=σ TS4

    For Atmosphere
    σ TS4=2 σ TA4 (blackbody)

    Compare these equations to my Blackbody table. Notice the similarities.
    Blackbody
    The highlighted row confirms Jin-Yi Yu conclusion. The other rows simply evaluate this rightful equation prior to and following equilibrium. Why examine beyond equilibrium...simply as a point of comparison.

    Before I school you further, indulge me with a couple self-serving quotes:
    Tom you said:
    a) You have not established the appropriate groundwork, and are instead working on a host of demonstrably false assumptions.

    b) Your tables which carry your argument have unclear symbols, and are derived by an unexplained method. In other words, they are simply bare assertions.


    KR you said:
    Please, L.J.Ryan - read some of the references you have equation-mined. Learn a bit more about the science. You're approaching the issue with a lot of erroneous preconceptions, and those are leading you to incorrect conclusions.

    Do some reading, L.J. Ryan, including the sources you yourself have linked to.

    Do you favor your crow warm or cold?

    Back on point, the white and gray tables explore the same base equation save a change in emissivity. An atmosphere perfectly reflective to LW radiation will, according to GHG physics, get hotter faster as compared to ε= 1. The key question is, at what surface flux will SW emissions of 235 W/m2 be therein...when added to albedo reflection achieves equilibrium. According to blackbody emission curves ~1200K nets ~235 W/m2 at 700 nm.
    White
    Intuitively, these value make sense...(if you subscribe to GHG physics). With an atmosphere which reflects all LW radiation back to the surface, surface energy accumulation with respect to time is geometric.

    Lastly, a gray atmosphere with ε= .618 will, (according to GHG physics) increase equilibrium temperature. As KR said: As stated before, given a known amount of outgoing radiation, the black body temperature is an absolute minimum on the temperature of an equivalently radiating graybody, due to the relationship of emissivity and temperature. So, what is actually borne out by the math. Assuming a gray body reflectivity = .388 the following table results:Gray

    Look KR is right! A gray body emissivity does confer a higher temperature....341K. Now, all we have to do is get those thermometers to fall in line with GHG physics.
    Response: [mc] Please limit width to 500 when posting images: <IMG SRC="" width=500>
  33. L.J. Ryan

    A gray body with a LW emissivity of 0.618 (as you postulated above), radiating 240 W/m^2, will have a temperature calculated by the Stefan-Bolzmann equation of:

    P = SB const. * emissivity * T^4; hence T = [ P / (SB const. * emissivity) ] ^0.25

    [ 240 / (5.6704*10^-8 * 0.618) ] ^0.25 = 287.675°K, or 14.53°C


    That's 287.675°K required to radiate that power, not 341°K, as you claim.

    I haven't bothered to track your math and logical errors down in this case - I don't consider it worth my time. You are quite simply in error, as both Tom and I have noted in the past.
  34. LJ,

    You have again neglected to explain the derivation of your tables, none of the equations you cited list Teq as a parameter. At equilibrium, by definition, there is no longer any net accumulation of energy or temperature change, so your results are nonsensical as given.
  35. KR 984

    You are calculating the temperature of the atmosphere not the earths surface.

    Do you agree with my table showing blackbody atmosphere?

    Do you agree with the equation via Jin-Yi Yu's lecture...the exact equation, you suggested I consider?

    You also contradict your own words;"As stated before, given a known amount of outgoing radiation, the black body temperature is an absolute minimum on the temperature of an equivalently radiating graybody, due to the relationship of emissivity and temperature."
  36. e 984

    Teq is defined as the time it will take the earth to accumulate 235 W/m^2 and therefore radiate 235 W/m^2. The white atmosphere will reach Teg first...thus defining the interval.
  37. L.J. Ryan - The effective emissivity is from the surface to space, as has been repeatedly stated. The actual radiation point (depending on the wavelength) may be from upper tropospheric CO2, lower tropospheric H2O, or directly from the surface; determining that on a per-wavelength basis is the realm of atmospheric modelling. The effective emissivity, however, is the sum effect on power as radiated from the surface, through a GHG atmosphere, to space, relative to a black body at surface temperature. Please cease to misinterpret clearly defined terms. Particularly if you are using those misinterpretations to claim I'm contradicting myself - which I am not.

    Can you describe on what basis you disagree with the Stefan-Boltzmann equation? There could be a Nobel prize involved if you can.

    Your computations, again, reflect your incorrect assumptions and calculations. You've shown no interest in correcting said mistakes - I don't consider it a good use of my time to beat that dead horse.
  38. LJ,

    Your response described what you are trying to show qualitatively but does not tell me how you derived your results mathematically. For example for emissivity of 1 and time of 3Teq, you get a flux of 470 Wm-1. Can you please show us the mathematical equation you used to output the number 470? It should somehow have time as an input and energy flux or temperature as an output. None of the equations you cited so far do this.

    Also you didn't comment on my note that, by definition, temperature does not increase past equilibrium time. The fact that it does so in your results shows you are making a serious error.
  39. KR 964

    you said:
    If you feel that integrated spectra are not measurements, well, then, I'll pass that on to the spectroscope manufacturers I work with. Don't forget, when chortling with your work chums, "Effective emissivity" is a useful summary of surface temperatures, atmospheric temperatures, band blocking, emission altitudes, and the lapse rate. Ah...what knee slapping fun. As I said, ee is calculated...calculated explicitly to obfuscate GHG physics.

    Also, if effective ε= .618 and 1- ε= reflectivity, then .382 of incident power is effectively reflected. Or maybe, working beyond the gray slab model, the atmosphere is partially transparent...like a crystal. A crystal that DOUBLES the light flux which transverses it's body. Now tell me KR, if an enterprising fellow was to manufacture crystal with REAL (not effective) ε= .618, will it also double light input? Or is energy doubling process contained to GHG physics alone?
  40. e 988

    I will post the equations this evening...I'm pressed for time at the moment. But quickly, it's rather a simple ratio of energy accumulation based on ε= 0 energy calculations.

    you said:
    "temperature does not increase past equilibrium time."

    Yes I agree. My rather simple spread sheet did not include comparative functions.
  41. LJ,

    BTW please do not post every single equation for every single value in that spreadsheet. Just show us the general equations you are using to derive it.

    >you said:
    "temperature does not increase past equilibrium time."

    Yes I agree.


    Your table clearly shows temperature increasing past equilibrium time. Since temperature / flux does not increase past equilibrium time, the fact that you are including Teq in your calculations suggests that you are doing something very very wrong.
  42. LJ >it's rather a simple ratio of energy accumulation based on ε= 0 energy calculations.

    I'm sorry but your ε= 0 energy calculations also do not make any sense. If you meant emissivity as in total emissivity across all wavelengths, then ε= 0 would mean that no energy is absorbed or emitted. Your temperature and flux would be 0 across the board into infinite time.

    If you meant spectral emissivity as in the emissivity in the LW is 0, while other wavelengths have ε>0, then that just means the surface will get hot enough until the power is emitted in wavelengths other than LW. It would certainly not accumulate infinitely as you have depicted. Again, without even posting your derivations it is obvious something is very very wrong with your math.
  43. LJRyan @982, thank you for the greater clarity about the source of your calculations. From your comments, I understand you to be basing your calculations on the following model:



    Science of Doom discusses just such a model in a recent post, and has this to say:

    So in this first model, which is very common in introductory books on atmospheric physics, three things are assumed - and none of them are true:

    * the atmosphere is isothermal – a slab of atmosphere all at the same temperature
    * the atmosphere is completely transparent to solar radiation
    * the atmosphere is completely opaque to terrestrial radiation


    The reason such simple but factually false models are used in introductory courses is the same reason frictionless surfaces are used in simple models of dynamics - it allows the introduction of important concepts without unnecessary complications. Because they do allow the introduction of important concepts, I am happy to work with such models so long as it is clearly understood that they do not represent any actual state in the universe. Attempts to calculate the surface temperature of the Earth are bound to be in error (and yours more in error than if the model was used correctly), and therefore are pointless except exposition of the relevant concepts. That is, they are not actual predictions of the real surface temperature. For a calculation of the Earth's average surface temperature using the simplest model of the GHE that is at the same time reasonably accurate to the actual physics, I refer you to equation six in my post 944 above.

    Having said that, if we wish to use the single slab model above for exposition, we need to carefully adhere to the assumptions of the model. Otherwise we just produce another example of "Garbage In - Garbage Out", and there are more than enough examples of that on the internet. Of course, the second assumption of the model is that it absorbs all outgoing radiation. Therefore any attempt to include a reflecting atmosphere with this model constitued GIGO, and in particular, this is true of your second and third tables.

    Your first table is better, but does not include a column for (1-A)*S/4, an important term without which the equilibrium state cannot be determined. Equilibrium is reached when (and only when) (1-A)*S/4 = σTa^4, ie, AtmU in your first table. The failure to include a term for insolation probably explains why your terms do not stabilize over a certain time period (unless I am misinterpreting your first column).
  44. Where I said second assumption, I should have said third. Sorry for any confusion.
  45. With regard to the slab model illustrated @993, and with (1-A)*S/4 = 240 w/m^2, then:

    The entropy of the incoming solar radiation per meter squared per second = 240 J/6000 K = 0.04 J/K.

    The entropy of the surface radiation = 480 J/303 K = 1.58 J/K

    The entropy of the back radiation (AtmD) = 240 J/255K = 0.94 J/K

    The entropy of the radiation to space (AtmU) = 240 J/255 K = 0.94 J/K.

    The challenge for the deniers is to find any partition of the system such that conservation of energy is maintained for that partition, and such that the Entropy decreases for that partition. That is, the partition must show an energy flow from E1 to E2 such that E1 = E2, but such that the Entropy of E1 is greater than that of E2.

    As an example, we have:

    1) Insolation + Back radiation => surface radiation

    which in terms of energy (per meter squared per second) is

    1') 240 J + 240 J = 480 J (so we have conservation of energy); but in terms of entropy we have:

    1") 0.04 J/K + 0.94 J/K < 1.58 J/K

    so there is no violation of the 2nd law in this partition.

    There is in fact no partition satisfying these conditions in which the energy in has a higher entropy than the energy out. Therefore, the 2nd law of thermodynamics is not violated by this model.
  46. e 992

    Understand e, it is my contention energy, radiative or otherwise, can NOT increase itself due to reflection, re-radiation or insulation. So when the input flux to the surface equals surface output flux the earth is at equilibrium...255K. The 33o delta is do to non-radiative energy input. My calculations set out to disprove back radiation by using the very tenets of GHG physics. That is, by using proponents equations to confound GHG physics conclusions, I will prove my supposition.

    Start with a solar input 240 W/m2 SW. Due to my confusion of KR take on albedo and earths surface emissivity/absorptivity I applied .98 absorption a second time...netting 235 W/m2 SW absorbed by the surface. Nevertheless, the number workout nearly the same. For consistency within this explanation, 235 W/m2 SW input will be used.

    All of the following presumes GHG physics:
    With the understanding a white atmosphere will reflect all terrestrial LW, the white atmosphere will “force” the surface to accumulate energy faster then any other emissivities. When the input flux 235 W/m2 SW to the surface equals surface output flux 235 W/m2 LW the earth SURFACE is at equilibrium (not the entire system). It is this instant which is designated Teq. Since the subsequent instance receives more energy then the prior instance, the accumulation happens faster, followed by an ever faster instance...ect. That said;
    I= solar input 235 W/m2 SW
    E= earths radiated flux
    A=atmosphere flux LW
    AU = atmosphere up
    AD = atmosphere down
    A=AD+AU

    With ε= 0
    Teq when E=I=A
    1.5Teq E'= I+A and E'=A'
    1.75Teq E''= I +A' and E''=A''
    1.875Teq E'''=I + A'' and E'''=A'''

    Assuming energy accumulation is linear, the time to reach 1.5Teqis half as long as time to reach Teq...1.75Teqis half as long as time to reach 1.5TeqfromTeq...etc. These calculation were continued some 20 times, as a geometric series 2Teq will never be reached. At the same time, surface flux will accumulate infinitum. Now, of course the visible spectrum will be emitted prior to runaway thereby achieving TOA equilibrium.


    When ε= 1 the equation are:
    2Teq E= I+AD and E=A
    3Teq E'= I +AD' and E'=A'

    The time it takes E=A=I, is twice as long as when ε= 0.

    When ε= .612 reflectivity equals .388 . This introduces another value:
    AR = .388 A = atmosphere reflected
    AD=AU
    AD= .5 (.612A)= .306 A

    E= I+AR+AD and E=A
    E'= I+AR'+AD'and E'=A'

    The Teq is found by dividing A for white atmosphere of a particular surface radiation by AR+AD of the same E (gray), then multiplying by the Teq for that white E interval. For example; for the 470 W/m2 interval: A (white) =470, AR+AD=182+144....470/( 182+144)*1.5Teq=2.16Teq.

    The Teq provides only a non critical time component of surface equilibrium. In hindsight, I should not have included this information, it only confused my conclusions.
  47. Tom Curtis 993 995

    I read the SoD article and in fact was going to submit comments until the conclusions you list. That is, the model is wrong...but kinda works. I'll wait to see where SoD takes this simplified model stuff, before commenting.

    You said:
    "Your first table is better, but does not include a column for , an important term without which the equilibrium state cannot be determined. Equilibrium is reached when (and only when) (1-A)*S/4 = σTa^4, ie, AtmU in your first table"

    The constant input (1-A)*S/4 is assumed...but I get your point. Teq is, as I explained to e in the previous post, a time interval to mark surface equilibrium. That is, when SW flux to the surface equals LW flux out of the surface.


    Regarding your 995, I think you have double counted atmosphere radiation. Specifically:

    The entropy of the back radiation (AtmD) = 240 J/255K = 0.94 J/K

    The entropy of the radiation to space (AtmU) = 240 J/255 K = 0.94 J/K.

    Total atmospheric radiation 480J...confers 303K which is obviously wrong and/or it unbalances your conservation of energy equations.
  48. LJRyan @997, the atmosphere has an upper side and a lower side. Because thermal radiation is the same in all directions, if the atmosphere were 303 K, then it would radiate 480 w/m^2 up, and the same down. That would violate conservation of energy.

    However, with an atmosphere at 255 K, it will radiate 240 w/m^2 to space and 240 w/m^2 towards the surface. It follows that there is no violation of conservationof energy, and I did not double count.
  49. LJ,

    Thank you for taking the time to detail and formalize your thinking. There are several things wrong with your logic (none of which follow from standard GHG physics):

    One big issue is you are incorrectly defining the time to equilibrium. You wrote here:

    When the input flux 235 W/m2 SW to the surface equals surface output flux 235 W/m2 LW the earth SURFACE is at equilibrium (not the entire system)

    This is incorrect. Equilibrium only exists when there are no longer any temperature changes. The fact that the surface is emitting the same flux as the overall system input is not particularly relevant in this example, since equilibrium is not reached at that point. Nothing in the system will be in equilibrium until the net output of the system matches the net input of the system. That should be intuitively easy to understand, if input and output are different, then energy will either be accumulating or depleting. Nothing is changing if input and output are the same. Using your terms, you are looking for the point in time when AU = I.

    The other problem is that you are mixing up the effective emissivity model with a simple grey slab model as depicted in Prof Yu's lecture. These two models are describing the system in very different ways, and cannot be mixed and matched in the simple fashion you are attempting.

    The grey slab model assumes that each component in the system is a blackbody (among other assumptions) and describes the flow of energy between individual components in the system. The effective emissivity model completely abstracts away the internal exchanges of energy that are illustrated in the grey slab model. When someone says that the effective emissivity of the earth is .612, the value .612 already captures all the internal behaviors of the system. It applies to the system as a whole, it would not make any sense to insert this back into the grey slab model as the emissivity of the atmosphere.

    I would suggest starting by clarifying exactly which model you are using to draw your conclusions. If you're using effective emissivity, then it is simply a matter of plugging the emissivity into the Stefan-Boltzmann law and computing the temperature that results. If you are using the grey slab model, then you would calculate the result as given by the equations in professor Yu's lecture slides.
  50. I agree, Les,977,a vast improvement but a much later, and much up-dated, post than the one I quoted. Though much has gone, much remains from the original – “where does the back-radiation energy go”.

    It is obvious that there is no second law entropy (quality) problem if we consider only the transfers sun to earth, earth to space, and define the whole solar system as our closed system. Sadly, this ignores completely the transfers we are interested in - earth to atmosphere and back again.

    The most fundamental point is that you cannot consider the out and back long wave energy transfers in isolation. It is the net transfer (heat transfer) that counts. Petty, page 6, is correct and the version of Trenberth quoted here is grossly misleading. It is not just a matter of using the difference, as someone posted.

    We can follow G and T, and use heat engines to make the point.

    It is always possible in principle to convert an energy flow from a warmer source to a colder sink into work (first law). In the process the energy degrades (second law).

    It is never possible to do the same with an energy flow from a colder sink to a warmer source. If it were possible we would have perpetual motion. It is the net flow that counts (out minus back). The back radiation is the negative term in the Stefan Bolzmann equation.

    As to the “higher is colder” mechanism, 978,it has nothing to do with back-radiation. Atmospheric emission must balance incoming solar energy, and will be at an appropriate “goldilocks” temperature and elevation to make this happen. If increasing CO2 concentration elevates the emission point (for the sake of the argument) outgoing radiation will be reduced. Incoming radiation will remain the same, so the whole system warms up. The lapse rate moves to the right, and the surface warms.

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