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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 1126 to 1150 out of 1481:

  1. Fred Staples @1124, you jump too quickly from "it is not a multi-layer emissivity 1, zero convection atmosphere" (my summary) to it is "a top-of-atmosphere effect". In fact climate models (or at least Line By Line models, and Global Circulation Models) are multi-layer models. Importantly, they include terms for transmitted radiation, and energy transfer by convection and latent heat at each layer, and require energy balance at each layer. It is possible to develop an "effective altitude of radiation" plus lapse rate model of the atmosphere. It has the advantage of being very simple, and giving approximately correct results. It is, therefore, far better than the slab model you used in 1120 above, but it remains only approximately correct.
  2. 1124, Fred,
    These results are absurd, but they are derived from the original greenhouse “explanation”.
    Yes. Which means there is something drastically wrong with your model. A skeptical person would sit back and think "okay, that can't be right. What am I doing wrong? What am I misunderstanding? Which assumptions have I made that are incorrect?" Hmmmmm. A skeptical person would do that.
  3. 1124, Fred, If you wish, you can cheat. Visit this page and read through it, step by step. In chapter 12 he has the same problem that you do with effectively the same numbers, 302K for one layer, 334K for two. Unlike you, however, he takes the thinking further and resolves the issues by recognizing that there is more to the problem than this, rather than assuming at that point that all climate scientists and physicists have it wrong. If you read and understand it to the end, you will find that you do, in fact, get the right answers. At that point, you'll need to reevaluate your conclusion that the greenhouse effect violates the laws of physics and cannot exist. At that point I will then, again, be interesting in hearing your opinions on the subject.
  4. Yes, Spherica, a sceptical person would do that (ask what was wrong with the multilayer model). He would conclude that he was looking at the problem the wrong way round – bottom up instead of top down. The atmospheric greenhouse effect starts near the top of the atmosphere, where outgoing radiation to space must equal incoming radiation and the temperature of the effective emission level must be 255 degreesK. If the atmosphere is capable of absorbing and emitting energy, that level will be high up, at about 5 or 6 kilometers. The lapse rate, the cooling of the atmosphere with height, something you can observe on your car thermometer, is about 6K per kilometer and it has nothing (or almost nothing, Tom) to do with radiation. There, Spherica, you have a model which almost exactly fits what we see, and you will find it derived from first principles on page 113 of FWTaylor’s Elementary Climate Physics. However, a true AGW believer, Spherica, would resist the obvious and seek an alternative bottom-up multi-layer model One model which avoids second-law “back-radiation” problems is a shell model which calculates energy flow as the difference between the fourth power of the temperatures from the surface to the first shell, from the first shell to the second, from the second to the third and so on to space. First consider a single shell model. Simple Algebra, (difficult to type) shows that the fourth power of the surface temperature equals 2 x the fourth power of the shell temperature, or 303K. Now add another shell. Repeat the Algebra, and the surface temperature will rise to 335 degreesK, and so on. Exactly the same results as before – another model which does not work. I could appeal to Occam’s razor, but I won’t. The only plausible explanation of global warming is “higher is colder”, which fits all the observations, and which depends only on the lapse rate. Why any AGW proponents fail to accept this model is baffling. Add CO2 to the atmosphere and the outward radiation will be resisted. The effective emission level will rise. The emission temperature to space will consequently fall, as will the outgoing energy. The Sun will then warm the whole system to restore the balance. The observable lapse rate will shift to the right. A few years ago all the major pundits, RC for example, supported these ideas. There is only one snag. For this model to be true the troposphere temperatures must rise earlier and faster than the surface temperatures as CO2 concentrations increase. In a multi-layer model it would be the other way round. Over at the “After McClean” thread I have quoted some of the evidence.
  5. Fred, this comment of yours: Add CO2 to the atmosphere and the outward radiation will be resisted. The effective emission level will rise. The emission temperature to space will consequently fall, as will the outgoing energy. The Sun will then warm the whole system to restore the balance. The observable lapse rate will shift to the right. seems to amount to an admission that adding CO2 to the atmosphere causes global warming. Was this your intention?
  6. @Fred Staples #1129: Echoing what Composer99 said in #1130, What the heck are you trying to proove?
  7. 1129, Fred Staples,
    Yes, Spherica, a sceptical person would do that (ask what was wrong with the multilayer model).
    How could you so completely miss the point? The problem is not what is wrong with the model in general, but rather what is oversimplified in your mathematical representation of the model. [The answer, since you failed to find it, is that convection and evapotranspiration are still components of the system, and are not insignificant. They account for further heat transport from the surface up into the atmosphere, effectively cooling the surface below what an untempered greenhouse effect might achieve.]
    There, Spherica, you have a model which almost exactly fits what we see...
    Um, yes, the lapse rate successfully explains the drop in temperature with altitude, but it utterly fails to explain why the surface of the earth is warmer than 255K while the earth continues to emit into space at a perceived temperature of 255K.
    However, a true AGW believer, Spherica, would...
    This is just a transparent effort to be obnoxious and condescending, as well as an effort to try to diminish the science by implying that it is a religion. It is not, and any rational human being that understands the science knows it. You did succeed in being obnoxious, however. Sadly, rather than being annoyed, I am merely amused.
    Exactly the same results as before – another model which does not work.
    Which proves what? That you can create a lot of models that don't work?
    Why any AGW proponents fail to accept this model is baffling.
    It's not baffling at all. It is because the model you present is wrong. But you go on...
    Add CO2 to the atmosphere and the outward radiation will be resisted. The effective emission level will rise. The emission temperature to space will consequently fall, as will the outgoing energy. The Sun will then warm the whole system to restore the balance. The observable lapse rate will shift to the right.
    Yes! You understand GHG theory. Now you have it! So what's your problem?
  8. Fred Staples @112:
    "[A] sceptical person would do that (ask what was wrong with the multilayer model). He would conclude that he was looking at the problem the wrong way round – bottom up instead of top down."
    This is simply wrong headed. It does not matter where you start your calculations with multi-layer models (top or bottom) so long as you iterate until equilibrium is reached, the final result will be the same. Further, with multi-layer models if you want to solve for the equilibrium surface temperature algebraicly, you must start with the outer most layer. Therefore characterizing multi-layer models as "bottom up" models is at best meaningless, and at worst, simply false.
    "The lapse rate, the cooling of the atmosphere with height, something you can observe on your car thermometer, is about 6K per kilometer and it has nothing (or almost nothing, Tom) to do with radiation."
    The lapse rate is not a constant 6 degrees C/km. Rather, it depends primarily on the local relative humidity. If humidity is 100%, the lapse rate will be 5 C/km, whereas for dry air it is 9.8 C/km. The lapse rate is also effected by lateral heat transport, which is why in polar winters it is near 0, or even negative. In simplified one dimensional models, the lapse rate is treated as having a single constant value, but that is a simplifying approximation only. It should no more treated as reality than the assumption of point masses in standard Newtonian calculations of gravitational force should be considered evidence that the sun's diameter is zero. More importantly, the role of radiation is not neglible. At all levels of the atmosphere, gross radiative transfers of energy exceed those by convection or latent heat, although net transfers are typically smaller. Indeed, there is a complicated interplay between radiation and convection. Without the radiatively induced lapse rate, the atmosphere would be near equal in temperature at all altitudes, and convection would be limited. Convection is best understood (for these purposes) as a negative feedback on the radiatively induced lapse rate.
    "First consider a single shell model. Simple Algebra..."
    You have simply returned to the multi-layer radiative only, emissivity 1 model which I described as "unphysical" above. Why do you inist on this false dilemma of either a purely radiative model or a purely convective (higher is cooler) model. The world does not fit into simple compartments like that. Both radiation and convection are important within the atmosphere. Indeed, I have already described a model which includes both (and which because it does not fit your false dilemma, you ignore).
    "There is only one snag. For this model to be true the troposphere temperatures must rise earlier and faster than the surface temperatures as CO2 concentrations increase. In a multi-layer model it would be the other way round."
    First, there is no "uniquely correct" model of the greenhouse effect. There is a correct physics, the radiative-convective physics discovered by Manabe. That can be modeled by either multi-layer models which track both radiation and convection at each level, or by a simplifying TOA radiation plus lapse rate model. The second is a simplified version and so is not entirely accurate (although it is the best of the simple models). Because both approaches describe the same physics, there is no fundamental difference in their predictions. Second, the tropospheric hotspot is not a direct consequence of the greenhouse effect. Rather, it is a consequence of increased humidity at altitude which is predicted for all warming scenarios. Because the vertical transfer of heat in the atmosphere is rapid, taking days (for radiative transfers) and hours (for convective), the hotspot is most definitely not a consequence of which portion of the atmosphere heats first. And please note, as the lapse rate is a function of humidity, the hotspot is predicted equally by the multi-layer and the TOA plus lapse rate models once the lapse rate is allowed to adjust for humidity changes. To sum up, your entire post consists of nothing but a series of misunderstandings of climate science. You refuse to acknowledge the existence of the type of multi-layer models that are used in GCM's on a regular basis, insisting on a false dilemma between two crude models only used for teaching purposes. Because you insist on that false dilemma, you do not recognize the existence of the models actually most used in climate science, which are mulit-layer, but have the same general properties (though more accurately) of the model you insist we use.
  9. There is a whole class of 1-D climate models called "radiative-convective models" that combine realistic radiative calculations (in the vertical) with convective energy transfer constraints on the resulting temperature profile. Tom Curtis mentions the name of Manabe in #1133. Here is a link to one of the classic papers: Manabe and Wetherald (1967) Thermal Equilibrium of the Atmosphere With a Given Distribution of Relative Humidity
  10. "Without the radiatively induced lapse rate, the atmosphere would be near equal in temperature at all altitudes, and convection would be limited. Convection is best understood (for these purposes) as a negative feedback on the radiatively induced lapse rate". We live on a planet the surface of which is 75% water. The correct (in my opinion) interpretation of the earth's energy budget is set out by Grant W Petty (no denialist he) on page 13 of his book on Atmospheric Radiation. What he does (absolutely correctly) is to redraft Trenberth to avoid the nonsense associated with back-welling radiation from the cold atmosphere, by analysing the net energy transfer, which is heat. He works in percentages. About 30% of the solar radiation is reflected to space, either by the atmosphere, clouds, or the surface. About 20% is absorbed by the atmosphere and clouds, leaving about half to be absorbed by (and to heat) the earth. Of that 51%, 23% is carried upwards by the latent heat of evaporation. A further 7% is carried aloft by conduction and convection, which leaves 21% to be transferred (net)by radiation. Of that 21%, 6% is transmitted directly to space, leaving just 15% to be absorbed by the atmosphere. That is a thermodynamically acceptable description The idea that the lapse rate (which Petty does not mention anywhere) could be caused by the net radiation alone is absurd, Tom. Incidentally, I did not mention the tropical hot-spot, but since you bring it up, have a look at the satellite and radio-sonde data and see if you can find it. I do not want to continue to repeat myself. The lapse rate is derived, from the gas laws for an ideal gas, on page 44 of Taylors Elementary Climate Physics. It is a function of gravity (compression) and specific heat. You can demonstraete the effect by using a pressurised antiseptic container, or a CO2 capsule to create soda water. The lapse rate has nothing to do with radiation. Without the lapse rate there would be no possibility of an AGW effect.
  11. "nonsense associated with back-welling radiation" It so happens that this nonsense should be dealt with, as the downwelling IR radiation does exists and has been modeled and measured. Extensive discussion of downwelling IR at the South Pole in this paper, with comparison of measured values and LBLRTM values under clear skies and various levels of cloud cover: http://www.webpages.uidaho.edu/~vonw/pubs/TownEtAl_2005.pdf In fact, in order to better deal with the nonsense, long term research has been conducted with the goal of refining the agreement between radiative models and observations, different lattitude this time: http://www.whoi.edu/mvco/description/InfRad.html Downwelling IR can be followed over the past few days at Martha Vineyard's Coastal Observatory: http://www.whoi.edu/mvco/description/InfRad.html Any kind of atmospheric model that denies or dismisses the downwelling IR radiation is inaccurate.
  12. 1135, Fred Staples, You are mis-interpreting (or mis-representing?) what you have read in Petty's book. He does not "avoid the nonsense associated with back-welling radiation." He simplifies the diagram to represent as much as he needs at that point in the book (which is, after all, only page 6 out of 459 pages). Also note that all he does, for his purposes, is to simplify it for the reader who is only just learning the concepts, by translating the diagram from W/m2 to percentages and eliminating the atmospheric layer where possible for simplicity. There is nothing there but basic simplification to help educate a reader. [My strong advice to you would be to keep reading, instead of stopping on page 6.] The remainder of your comment is a gross misrepresentation of what his diagram conveys, and the mechanics of the atmosphere. You also thoroughly abuse the term "thermodynamically acceptable" as there is nothing at all in this discussion so far that has anything at all to do with thermodynamics. You are throwing the term around as if it must be accompanied by the ringing of chimes, heavy incense and Gregorian chants, and yet you misuse the term, or rather apply it with your own grand connotation or denotation, but entirely out of context.
    I do not want to continue to repeat myself.
    Nor should you. You need to instead either make a substantive argument behind your already invalid comments or else to learn more about the topic at hand, and to stop assuming that you in fact know more than all atmospheric physicists and climate scientists. Along those lines you will find a wealth of information about radiative physics in Petty's book, specifically the text after the introduction from which you got your diagram: Chapter 2. Properties of Radiation Chapter 3. The Electromagnetic Spectrum Chapter 4. Reflection and Refraction Chapter 5. Radiative Properties of Natural Surfaces Chapter 6. Thermal Emission Chapter 7. Atmospheric Transmission Chapter 8. Atmospheric Emission Chapter 9. Absorption by Atmospheric Gases Chapter 10. Broadband Fluxes and Heating Rates Chapter 11. RTE with Scattering Chapter 12. Scattering and Absorption by Particles Chapter 13. Radiative Transfer with Multiple Scattering Chapter 14. Representing the Phase Function Hmm. I seem to have missed the chapter on what's "thermodynamically acceptable." I'll have to go back and look for it.
  13. 1135, Fred, Looking back at Petty's book, you would be very well served to simply even read his introduction (as you clearly have not) rather than skipping ahead to the pretty pictures and then misinterpreting them.
  14. For the casual reader attempting to follow Fred's misunderstandings, here is Trenberth's energy budget diagram: And here is the simplified version, presented by Petty and based 100% on Trenberth's diagram (simply converting W/m2 to percentages, and removing most of the atmospheric layer interaction which complicates the image -- to simplify it for the reader in the very introduction of his book):
  15. Why is this point so hard to understand Sphaerica?. Next time you pass a power station,ask yourself why all that energy from the cooling towers is being wasted as evaporation to the atmosphere? Why is it not fed back to heat the boilers? The answer is that it is sink energy, and the boiler is its source. Sinks cannot heat sources. The energy in the sink is of a (much) lower quality than the energy from the source. Entropy increases during the energy transfer. The earth is the source of heat for the atmosphere. The back-radiation energy from the atmosphere (Trenberth diagram – sink to source) cannot be considered separately from the primary radiation (source to sink). The useful energy, to heat the atmosphere, is the difference between the two. They net off, as in the Petty diagram. If you still cannot see this, ask yourself what would happen if the atmosphere and the surface were at the same temperature? They would radiate against each other, but the energy transferred could not do anything. The net transfer, and the heating effect, would be zero. Remember, also, that at its effective emission altitude, the temperature of the atmosphere cannot change. It must be 255 degrees K to radiate the “bare earth” energy to space, and balance the incoming radiation. The composition of the atmosphere might change the altitude of the effective emission level, as in the “higher is colder” theory. That is why we must look at the mid and upper troposphere temperatures to detect an AGW effect. Have a look at the Met Office charts at the Hadley Centre new radio-sonde product, and the UAH satellit records. Can you see any supporting evidence to link warming to CO2?
  16. 1140, Fred Staples, It's not hard to understand at all. You are simply misapplying what you know, and you can't see that.
    The back-radiation energy from the atmosphere (Trenberth diagram – sink to source) cannot be considered separately from the primary radiation (source to sink).
    Yes it can. They do not "net off." Read the book instead of looking at the pretty pictures.
    ...ask yourself what would happen if the atmosphere and the surface were at the same temperature?
    The atmosphere would cool by radiating half of its energy up into space, and half down back to the surface, which would warm further. You now have an imbalance. The surface would radiate even more up to the atmosphere, which would thus not be able to cool as much/quickly as if it had been left alone, but would then cool further by radiating half of the energy up and out into space, and half back to the surface. In this way both the surface and the atmosphere would cool. This would continue until radiative equilibrium was restored and things returned to their current temperatures, with a surface that is warmer than the atmosphere. No magic required. Now ask yourself: how does the atmosphere know not to radiate energy downward, because the surface is warmer? What if the surface is cooler? How does the atmosphere "know" the difference? What form of magic do you use that science cannot?
    Can you see any supporting evidence to link warming to CO2?
    Pages and pages of it. That you can't is a sign of your ignorance, your inability to understand what you misunderstand, and your unwillingness to look further (look up "cognitive dissonance"). Can you find a single, reputable scientist who agrees with anything you are saying? Or are you alone (with the exception of certain other outlandish characters that visit this particular thread) in your "understanding" of thermodynamics. Let's see, what's more likely... you are right, and the rest of the world's paid, educated scientists are wrong? Or you are missing something, and maybe should put more effort into unlearning what you misunderstand so that you can begin to contribute to a meaningful discussion on the numerous important and worthy aspects of climate science, rather than this nonsense.
  17. 1140 - Fred "Next time you pass a power station,ask yourself why all that energy from the cooling towers is being wasted as evaporation to the atmosphere? Why is it not fed back to heat the boilers? The answer is that it is" ... The Carnot Cycle - which describes the limits on amount of work that can be extracted between two 'heat' reservoirs at different temperatures. There's no concept of 'low quality' energy! I hope next time anyone passes a power station and wonders about steam evaporating from the cooling towers they actually think of the excellent physics of another of Fourier's generation - and not the dire butchery of physics that continues in the posts of Fred, damorbel etc.
  18. Fred: there are several fundamental principles that you seem unclear on. First of all, radiation transfer through a semi-transparent medium such as the atmosphere is not as simple as a "hot to cold" analogy with thermal transfer. Sphaerica has pointed out that radiation emitted will be in both the upward and downward direction - indeed it is omnidirectional: from a point, radiation will be emitted equally in all directions. When considering a plane (e.g., the atmosphere at a particular altitude), it is convenient to think of the upward and downward fluxes independently, and indeed this is also the typical sort of measurements that are made: one instrument with a 180 degree field of view facing up, and one facing down, to get the downwelling and upwelling fluxes respectively. The amount of IR radiation emitted at a particular altitude is a function of temperature at that point, but the measured flux is not just what is emitted there - it also includes any IR radiation that was emitted at other altitudes and is just "passing through". In general, radiation arriving at a point can be either transmitted, absorbed, or scattered. We can express this as t + a + s = 1. The amounts are typically expressed using Beer's Law, using an optical property called the optical depth. Overall, the principle is that flux at a point is only partly the result of emissions at that point. Conversely, heating or cooling at that point is not the result of the fluxes at that point, but the combination of emission and absorption. To add to this, in the atmosphere there is also energy transfer by convection, either through thermal transfer (usually called "sensible heat") or through vapour transfer (evaporation and condensation energies, called "latent heat"). Thus, to proper look at heating, cooling, and energy transfers, you have to look at it all together (although this does not imply that each individual component can't be discussed in isolation). The class of climate models that put all this together looking only in the vertical (i.e., ignoring horizontal variation) is the 1-D radiative-convective model.One of the very early papers in this area is Manabe and Strickler 1964. One aspect of this paper can be seen in figure 1, where they compare the vertical structure of at atmosphere that only allows radiation transfer with one that also does convective transfer. Here is that figure: The left side shows the radiative-transfer only atmosphere. The series of lines show the model approaching equilibrium from warm and cold states. Note that the lower atmosphere (troposphere) has extremely high lapse rates. This is not a stable condition in an atmosphere where convection can occur - the lapse rates exceed the point where free convection will happen. The right side of the figure shows the model results when convection is allowed - the modeled lapse rate is limited to the observed value. It is fundamental to understand that the observed tropospheric lapse rate is not the result of radiation transfer alone - it is controlled by the rates of convective heat transfer. Also note in figure 1 that the radiation-only and radiative-convective version show much the same structure in the stratosphere - the upper atmosphere is more or less at radiative equilibrium, and the resulting profile is stable.
  19. One last attempt, Spherica. You seem keen on Petty, so tackle the problem he sets on page 144, for radiative transfer between (up and down) n layers of the atmosphere. Here is a simple solution. To eliminate all constants, and any confusion over units, I will calculate the ratio of the surface temperatures with and without an atmosphere. Without an atmosphere the surface receives W from the sun and emits W to space. Now consider an atmosphere of just one layer, perfectly absorbing and emitting, half up and half back to the surface. If the solar radiation is W, the surface will receive and emit 2W, (W from the sun and W from the atmosphere). The atmosphere will receive 2W from the surface, return W, and emit W to space. Temperatures are proportional to the fourth root of radiation, so the ratio of the temperatures with and without the atmosphere is the fourth root of 2W/W or the fourth root of 2, which is 1.19. The presence of the atmosphere produces a temperature increase over the “bare rock” case of 19%, which is about 48 degrees C. Not a bad result, considering that the absorption is not really 100%. Now divide the atmosphere into 2 layers, radiating against each other. The top layer receives 2W, and emits W to space and W to the first layer. The first layer sends 2W up and down, and so must receive 4W, 3W from the surface and W from the top layer. The surface receives W from the sun, and 2W from the first layer, emitting 3W. Our temperature ratio is now the fourth root of 3, (3W/W), or 1.315.and the increase is 31.5% or 80 degrees C. Now try 3 layers of atmosphere. The top emits W to space and W down, as before. The second layer sends 2W up and 2W down, and receives 3W from the first layer and W from the top layer. The first layer receives 2W from the second layer, and 4W from the surface. The surface receives 3W from the first layer, W from the sun, and emits 4W. The temperature ratio is now the fourth root of 4, or 1.415, and the temperature increase a formidable 106 degrees C. For n layers, Petty’s answer is the fourth root of (n+1). Something, as G and T say, must be wrong here. Perhaps we should revisit the second law , and notice that every spontaneous energy transfer from a lower to a higher temperature (higher to a lower layer) reduces the entropy of the system, which is forbidden by the second law. I do understand the Carnot cycle, Les. I introduces "quality" much early in these posts to try to explain entropy. Entropy (more or less) is unavailable energy. The first law says that the quantity of energy will be conserved in any spontaneous transaction. Entropy, on the other hand, must increase, so quality is not conserved. It deteriorates. To try to explain the netting effect, Spherica, here is a simple example, extrapolated from Schaum’s Thermodynamics for Engineers, page 51. A 20cm sphere is suspended in a cold volume maintained at 20 degrees C What is the heat input required to maintain the sphere’s temperature at 200degrees C, if the emissivity is 0.8. The value of the constants is 5.7 e to the minus 9. Using the difference between the fourth powers of the temperatures in degrees K, the answer is 262 Joules per second. What is the heat input if the surround temperature is 350, 400, and 473 degrees K (200degrees C)? The answers are respectively 200, 139, and zero Joules per second. The energy radiated by the surround is the negative term in Stefan Bolzmann. In the 473 degree K case it is 262 Joules per second, which is what a pyrgeometer would measure. However, the net transfer (which is heat) is zero. Finally, Bob Loblaw, I really believe that atmospheric temperature are a complex function of many variables, including evaporation (latent heat from the sea), convection, and sensible transfer as well as radiation. However, the final transfer to space is wholly radiative, and must be from an effective "bare rock" temperature of 255 degrees K. Only the elevation of the effective transmission altitude can change with the composition of the atmosphere - hence the "higher is colder" theory, which G and T, sadly, did not address. To look for that effect we must look at the temperature records from satellites and radio-sondes. Not "pages and pages" Spherica, but two or three time series. Everything else, in my opinion, is anecdotal hand waving.
  20. Fred @ 1144: Something, as G and T say, must be wrong here. What is wrong is that the atmosphere is not opaque, so your multi-layer model has very little to do with reality. As it has very little to do with reality, the conclusions you draw from it also have very little to do with reality. Take a look at the figure I posted in #1143. Pick either side - it doesn't matter which. Left side is a pure radiative model; the right side includes convection. The figure shows two time-dependent progressions for each side. Each time series starts with an initial assumed temperature - one hot, one cold. In each case, over roughly one year of simulated time, the two simulations converge on the same equilibrium, showing that the model's final result does not depend on the initial assumed temperature. Now, think about the case where the initial temperature was hot. In these cases, the simulated energy balance leads to atmospheric cooling - until equilibrium is reached. In particular, note that the coldest section (at equilibrium) is in the middle section of the atmosphere - not the top; not the bottom. And here is the question that I would like you to attempt to answer: based on your understanding of the physics of energy transfer in the atmosphere, please explain how the middle section of the atmosphere is colder than the layers both above and below in the early part of the simulation, but continues to cool. How is is losing more energy than it gains? It may be easier to focus on the left side - the pure radiative transfer model - but the same answer applies to both panels. Alternatively, if you like looking at the two simulations that start "cold", and warm to equilibrium, ask yourself: why does the middle section stop warming before it reaches the temperature of the air below it or above it? Keep in mind that although the graphs are for a model simulation, not reality, the model is a good representation of what reality would do, and the final equilibrium result from the model is an excellent representation of the real global mean temperature profile. The reason why the model behaves this way is because that is also the way the real atmosphere works. I personally know the answer to the question that I am asking, but I'd like to see what you think it is before I explain it. Feel free to ask additional questions.
  21. 1144, Fred Staples, You persistently insist on ignoring the problems in your model. This was pointed out to you in comment 1128, where you were directed to this explanation of how optical thickness, convection, evapotranspiration moderate the radiative effects of greenhouse gases, and result in a modeled outcome that very closely mirrors observations. Your own model is incomplete and therefore, while an important first step towards understanding how the real world operates, it is ultimately invalid. As far as this commentary of yours:
    anecdotal hand waving
    Words of wisdom.
  22. Fred Staples @1146, here is an example of the simple multilayer slab model you keep referring to. Note once again that it is not the model of the greenhouse effect used by climate scientists in making their predictions. It is only an instructional model used to teach basic concepts. SW-down LW-up LW-down Net up Temp TOA (1) 240 240 240 240 255 2 240 480 480 240 303 3 240 720 720 240 335 Surf(4) xxx 960 xxx 240 360 The model shows incoming Short wave (SW) radiation of 240 W/m^2, and has three layers of atmosphere plus the surface. Emissivity of 1 is assumed for all layers and the surface. Temperature is given in degrees Kelvin. The first and most important thing to note is that the net upwelling radiation at each level equals the SW radiation going down at that level. Therefore energy is conserved. The second important thing to notice is that at each level the net energy flow is from a hotter to a colder zone. The initial flow is from the sun, while subsequent flows are from the hotter surface to cooler layers of the atmosphere. That means that entropy increases with each energy flow. Consequently there is no violation of the second law of thermodynamics in this model. Further, and very importantly, we know that there is no violation of the second law of thermodynamics in this theory from every day experience. Anybody who cooks knows that by putting a cold lid on a hot pot, the contents of the pot will gain more heat. Most people will now know that if you put a low emissivity film on the outside of your glass windows on a snowy winter, the house will become warmer even though the glass is colder than the room. Examples are common place. It is only be carefully not thinking about the physics of everyday phenomenon that you can make the confused claims you are making.
  23. 1144 - Fred... "I do understand the Carnot cycle," If that was obvious from your text I wouldn't have posted the right answer... I think you missed the point. "I introduces "quality" much early in these posts to try to explain entropy." Do excuse me for missing that part of your personalized thermodynamics, but even so, I cannot make sense of your quality/deterioration terms. Maybe if you used the same physics as the rest of us learned and use professionally, it might help? Just a thought.
  24. I wonder if anybody in this blog actually tried to read Gerlich and Tscheuschner? I haven't seen any comment on this statement:
    Authors trace back their origins to the works of Fourier [37,38] (1824), Tyndall [39–43] (1861) and Arrhenius [44–46] (1896). A careful analysis of the original papers shows that Fourier’s and Tyndall’s works did not really include the concept of the atmospheric greenhouse effect, whereas Arrhenius’s work fundamentally differs from the versions of today. With exception of Ref. [46], the traditional works precede the seminal papers of modern physics, such as Planck’s work on the radiation of a black body [33, 34]. Although the arguments of Arrhenius were falsified by his contemporaries.... Falsification Of The Atmospheric CO2 Greenhouse Effects Within The Frame Of Physics,version 4.0, Gerlich and Tscheuschner, 2009, p13
    or perhaps this:
    There seems to exist no source where an atmospheric greenhouse effect is introduced from fundamental university physics alone.Falsification Of The Atmospheric CO2 Greenhouse Effects Within The Frame Of Physics,version 4.0, Gerlich and Tscheuschner, 2009, p15
    Of course the authors go on to attempt to do this or not do it as the case may be.
  25. TOP, G&T is the subject of this post, as far back as comment #2, which establishes the basis: They are wrong. You could also note that its the first paper listed under 'References,' with the comment by Halpern et al a close second. Try reading the posts.

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