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All IPCC definitions taken from Climate Change 2007: The Physical Science Basis. Working Group I Contribution to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Annex I, Glossary, pp. 941-954. Cambridge University Press.

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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)

 

At a glance

Although this topic may have a highly technical feel to it, thermodynamics is a big part of all our everyday lives. So while you are reading, do remember that there are glossary entries available for all thinly underlined terms - just hover your mouse cursor over them for the entry to appear.

Thermodynamics is the branch of physics that describes how energy interacts within systems. That interaction determines, for example, how we stay cosy or freeze to death. You wear less clothing in very hot weather and layer-up or add extra blankets to your bed when it's cold because such things control how energy interacts with your own body and therefore your degree of comfort and, in extreme cases, safety.

The human body and its surroundings and energy transfer between them make up one such system with which we are all familiar. But let's go a lot bigger here and think about heat energy and its transfer between the Sun, Earth's land/ocean surfaces, the atmosphere and the cosmos.

Sunshine hits the top of our atmosphere and some of it makes it down to the surface, where it heats up the ground and the oceans alike. These in turn give off heat in the form of invisible but warming infra-red radiation. But you can see the effects of that radiation - think of the heat-shimmer you see over a tarmac road-surface on a hot sunny day.

A proportion of that radiation goes back up through the atmosphere and escapes to space. But another proportion of it is absorbed by greenhouse gas molecules, such as water vapour, carbon dioxide and methane.  Heating up themselves, those molecules then re-emit that heat energy in all directions including downwards. Due to the greenhouse effect, the total loss of that outgoing radiation is avoided and the cooling of Earth's surface is thereby inhibited. Without that extra blanket, Earth's average temperature would be more than thirty degrees Celsius cooler than is currently the case.

That's all in accordance with the laws of Thermodynamics. The First Law of Thermodynamics states that the total energy of an isolated system is constant - while energy can be transformed from one form to another it can be neither created nor destroyed. The Second Law does not state that the only flow of energy is from hot to cold - but instead that the net sum of the energy flows will be from hot to cold. That qualifier term, 'net', is the important one here. The Earth alone is not a "closed system", but is part of a constant, net energy flow from the Sun, to Earth and back out to space. Greenhouse gases simply inhibit part of that net flow, by returning some of the outgoing energy back towards Earth's surface.

The myth that the greenhouse effect is contrary to the second law of thermodynamics is mostly based on a very long 2009 paper by two German scientists (not climate scientists), Gerlich and Tscheuschner (G&T). In its title, the paper claimed to take down the theory that heat being trapped by our atmosphere keeps us warm. That's a huge claim to make – akin to stating there is no gravity.

The G&T paper has been the subject of many detailed rebuttals over the years since its publication. That's because one thing that makes the scientific community sit up and take notice is when something making big claims is published but which is so blatantly incorrect. To fully deal with every mistake contained in the paper, this rebuttal would have to be thousands of words long. A shorter riposte, posted in a discussion on the topic at the Quora website, was as follows: “...I might add that if G&T were correct they used dozens of rambling pages to prove that blankets can’t keep you warm at night."

If the Second Law of Thermodynamics is true - something we can safely assume – then, “blankets can’t keep you warm at night”, must be false. And - as you'll know from your own experiences - that is of course the case!

Please use this form to provide feedback about this new "At a glance" section. Read a more technical version below or dig deeper via the tabs above!


Further details

Among the junk-science themes promoted by climate science deniers is the claim that the explanation for global warming contradicts the second law of thermodynamics. Does it? Of course not (Halpern et al. 2010), but let's explore. Firstly, we need to know how thermal energy transfer works with particular regard to Earth's atmosphere. Then, we need to know what the second law of thermodynamics is, and how it applies to global warming.

Thermal energy is transferred through systems in five main ways: conduction, convection, advection, latent heat and, last but not least, radiation. We'll take them one by one.

Conduction is important in some solids – think of how a cold metal spoon placed in a pot of boiling water can become too hot to touch. In many fluids and gases, conduction is much less important. There are a few exceptions, such as mercury, a metal whose melting point is so low it exists as a liquid above -38 degrees Celsius, making it a handy temperature-marker in thermometers. But air's thermal conductivity is so low we can more or less count it out from this discussion.

Convection

Convection

Figure 1: Severe thunderstorm developing over the Welsh countryside one evening in August 2020. This excellent example of convection had strong enough updraughts to produce hail up to 2.5 cm in diameter. (Source: John Mason)

Hot air rises – that's why hot air balloons work, because warm air is less dense than its colder surroundings, making the artificially heated air in the balloon more buoyant and thereby creating a convective current. The same principle applies in nature: convection is the upward transfer of heat in a fluid or a gas. 

Convection is highly important in Earth's atmosphere and especially in its lower part, where most of our weather goes on. On a nice day, convection may be noticed as birds soar and spiral upwards on thermals, gaining height with the help of that rising warm air-current. On other days, mass-ascent of warm, moist air can result in any type of convective weather from showers to severe thunderstorms with their attendant hazards. In the most extreme examples like supercells, that convective ascent or updraught can reach speeds getting on for a hundred miles per hour. Such powerful convective currents can keep hailstones held high in the storm-cloud for long enough to grow to golfball size or larger.

Advection

Advection is the quasi-horizontal transport of a fluid or gas with its attendant properties. Here are a couple of examples. In the Northern Hemisphere, southerly winds bring mild to warm air from the tropics northwards. During the rapid transition from a cold spell to a warm southerly over Europe in early December 2022, the temperatures over parts of the UK leapt from around -10C to +14C in one weekend, due to warm air advection. Advection can also lead to certain specific phenomena such as sea-fogs – when warm air inland is transported over the surrounding cold seas, causing rapid condensation of water vapour near the air-sea interface.

Advection

Figure 2: Advection fog completely obscures Cardigan Bay, off the west coast of Wales, on an April afternoon in 2015, Air warmed over the land was advected seawards, where its moisture promptly condensed over the much colder sea surface.

Latent heat

Latent heat is the thermal energy released or absorbed during a substance's transition from solid to liquid, liquid to vapour or vice-versa. To fuse, or melt, a solid or to boil a liquid, it is necessary to add thermal energy to a system, whereas when a vapour condenses or a liquid freezes, energy is released. The amount of energy involved varies from one substance to another: to melt iron you need a furnace but with an ice cube you only need to leave it at room-temperature for a while. Such variations from one substance to another are expressed as specific latent heats of fusion or vapourisation, measured in amount of energy (KiloJoules) per kilogram. In the case of Earth's atmosphere, the only substance of major importance with regard to latent heat is water, because at the range of temperatures present, it's the only component that is both abundant and constantly transitioning between solid, liquid and vapour phases.

Radiation

Radiation is the transfer of energy as electromagnetic rays, emitted by any heated surface. Electromagnetic radiation runs from long-wave - radio waves, microwaves, infra-red (IR), through the visible-light spectrum, down to short-wave – ultra-violet (UV), x-rays and gamma-rays. Although you cannot see IR radiation, you can feel it warming you when you sit by a fire. Indeed, the visible part of the spectrum used to be called “luminous heat” and the invisible IR radiation “non-luminous heat”, back in the 1800s when such things were slowly being figured-out.

Sunshine is an example of radiation. Unlike conduction and convection, radiation has the distinction of being able to travel from its source straight through the vacuum of space. Thus, Solar radiation travels through that vacuum for some 150 million kilometres, to reach our planet at a near-constant rate. Some Solar radiation, especially short-wave UV light, is absorbed by our atmosphere. Some is reflected straight back to space by cloud-tops. The rest makes it all the way down to the ground, where it is reflected from lighter surfaces or absorbed by darker ones. That's why black tarmac road surfaces can heat up until they melt on a bright summer's day.

Radiation

Figure 3: Heat haze above a warmed road-surface, Lincoln Way in San Francisco, California. May 2007. Image: Wikimedia Commons.

Energy balance

What has all of the above got to do with global warming? Well, through its radiation-flux, the Sun heats the atmosphere, the surfaces of land and oceans. The surfaces heated by solar radiation in turn emit infrared radiation, some of which can escape directly into space, but some of which is absorbed by the greenhouse gases in the atmosphere, mostly carbon dioxide, water vapour, and methane. Greenhouse gases not only slow down the loss of energy from the surface, but also re-radiate that energy, some of which is directed back down towards the surface, increasing the surface temperature and increasing how much energy is radiated from the surface. Overall, this process leads to a state where the surface is warmer than it would be in the absence of an atmosphere with greenhouse gases. On average, the amount of energy radiated back into space matches the amount of energy being received from the Sun, but there's a slight imbalance that we'll come to.

If this system was severely out of balance either way, the planet would have either frozen or overheated millions of years ago. Instead the planet's climate is (or at least was) stable, broadly speaking. Its temperatures generally stay within bounds that allow life to thrive. It's all about energy balance. Figure 4 shows the numbers.

Energy Budget AR6 WGI Figure 7_2

Figure 4: Schematic representation of the global mean energy budget of the Earth (upper panel), and its equivalent without considerations of cloud effects (lower panel). Numbers indicate best estimates for the magnitudes of the globally averaged energy balance components in W m–2 together with their uncertainty ranges in parentheses (5–95% confidence range), representing climate conditions at the beginning of the 21st century. Figure adapted for IPCC AR6 WG1 Chapter 7, from Wild et al. (2015).

While the flow in and out of our atmosphere from or to space is essentially the same, the atmosphere is inhibiting the cooling of the Earth, storing that energy mostly near its surface. If it were simply a case of sunshine straight in, infra-red straight back out, which would occur if the atmosphere was transparent to infra-red (it isn't) – or indeed if there was no atmosphere, Earth would have a similar temperature-range to the essentially airless Moon. On the Lunar equator, daytime heating can raise the temperature to a searing 120OC, but unimpeded radiative cooling means that at night, it gets down to around -130OC. No atmosphere as such, no greenhouse effect.

Clearly, the concentrations of greenhouse gases determine their energy storage capacity and therefore the greenhouse effect's strength. This is particularly the case for those gases that are non-condensing at atmospheric temperatures. Of those non-condensing gases, carbon dioxide is the most important. Because it only exists as vapour, the main way it is removed is as a weak solution of carbonic acid in rainwater – indeed the old name for carbon dioxide was 'carbonic acid gas'. That means once it's up there, it has a long 'atmospheric residency', meaning it takes a long time to be removed. 

Earth’s temperature can be stable over long periods of time, but to make that possible, incoming energy and outgoing energy have to be exactly the same, in a state of balance known as ‘radiative equilibrium’. That equilibrium can be disturbed by changing the forcing caused by any components of the system. Thus, for example, as the concentration of carbon dioxide has fluctuated over geological time, mostly on gradual time-scales but in some cases abruptly, so has the planet's energy storage capacity. Such fluctuations have in turn determined Earth's climate state, Hothouse or Icehouse – the latter defined as having Polar ice-caps present, of whatever size. Currently, Earth’s energy budget imbalance averages out at just under +1 watt per square metre - that’s global warming. 

That's all in accordance with the laws of Thermodynamics. The First Law of Thermodynamics states that the total energy of an isolated system is constant - while energy can be transformed from one component to another it can be neither created nor destroyed. Self-evidently, the "isolated" part of the law must require that the sun and the cosmos be included. They are both components of the system: without the Sun as the prime energy generator, Earth would be frozen and lifeless; with the Sun but without Earth's emitted energy dispersing out into space, the planet would cook, Just thinking about Earth's surface and atmosphere in isolation is to ignore two of this system's most important components.

The Second Law of Thermodynamics does not state that the only flow of energy is from hot to cold - but instead that the net sum of the energy flows will be from hot to cold. To reiterate, the qualifier term, 'net', is the important one here. In the case of the Earth-Sun system, it is again necessary to consider all of the components and their interactions: the sunshine, the warmed surface giving off IR radiation into the cooler atmosphere, the greenhouse gases re-emitting that radiation in all directions and finally the radiation emitted from the top of our atmosphere, to disperse out into the cold depths of space. That energy is not destroyed – it just disperses in all directions into the cold vastness out there. Some of it even heads towards the Sun too - since infra-red radiation has no way of determining that it is heading towards a much hotter body than the Earth,

Earth’s energy budget makes sure that all portions of the system are accounted for and this is routinely done in climate models. No violations exist. Greenhouse gases return some of the energy back towards Earth's surface but the net flow is still out into space. John Tyndall, in a lecture to the Royal Institution in 1859, recognised this. He said:

Tyndall 1859

As long as carbon emissions continue to rise, so will that planetary energy imbalance. Therefore, the only way to take the situation back towards stability is to reduce those emissions.


Update June 2023:

For additional links to relevant blog posts, please look at the "Further Reading" box, below.

Last updated on 29 June 2023 by John Mason. View Archives

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Comments 1026 to 1050 out of 1457:

  1. Tom Curtis (RE: 1025), "For RW1 convenience (and for the umpteenth time) there is no guarantee that energy absorbed by the atmosphere will make its way to the surface, and as most of it is absorbed in the stratosphere, most of it doesn't. In fact, most of it is radiated to space." Not according to the text of the paper (look on the 6th page where they give absorbed solar radiation ASR and NET down data). What you don't realize is the amount absorbed by the atmosphere that is radiated back out to space is included in the albedo of 102 W/m^2. This is why when you look at the amount of outgoing LW from satellites it tends to be about 250 W/m^2 instead of 240 W/m^2. 341 W/m^2 - 250 W/m^2 = 91 W/m^2 not the 102 W/m^2 albedo referenced. The difference of about 10 W/m^2 is the LW emitted back up out to space as part of the albedo. All the energy at and below the surface came from the Sun (excluding an infinitesimal amount from geothermal). In the steady-state, conservation of energy dictates that 100% of the post albedo - in this case 239 W/m^2, gets to the surface one way or another.
  2. Tom Curtis (RE: 1025), "Most importantly, the average 333 Watts/m^2 is not only that which has been calculated using Line by Line and Atmosphere-Ocean Global Circulation Models, it is the back radiation that has actually been observed. Any theory that does not predict it, in other words, is falsified by observation. Of course only greenhouse theories predict that back radiation, or at least they are the only ones that do so without violating the laws of thermodynamics. So and denier of green house theories is left to explain how there can be an average 333 Watts/m^2 back radiation given a 240 Watts/m^2 input energy from the sun, and without the absorption and reradiation of energy by green house gasses." I do not dispute there is downward emitted LW from the atmosphere significantly above the 157 W/m^2 required for the net flux of 396 W/m^2 at the surface (396-239 = 157), though obtaining an accurate global average is impossible without measuring equipment looking up all over the globe. That aside, what you don't seem to understand is that the downward emitted LW from the atmosphere has 3 potential sources. Some if it last originated from surface emitted radiation, some of it last originated from the Sun (yet to reach the surface) and some of it last originated from the kinetic energy (latent heat and thermals) moved from the surface into the atmosphere. The bottom line is that the surface cannot be receiving a net energy flux above 396 W/m^2 in the steady-state. All the energy entering and leaving at the TOA is radiative. Any net energy loss from the surface to the atmosphere from thermals (convection), for example, just offsets the amount of energy that would otherwise be need to be radiated from the surface.
  3. RW1> "Not according to the text of the paper (look on the 6th page where they give absorbed solar radiation ASR and NET down data)." If you are referring to Table 1a, those are TOA measurements, they not distinguish between energy absorbed in the atmosphere and energy absorbed at the surface. It in now way implies that energy absorbed in the atmosphere must make its way to the surface. If you are looking for measurements at the surface specifically, then you should be looking at Table 1b. "Solar down" to the surface is shown to be about 160, exactly as depicted in the diagram. In the steady-state, conservation of energy dictates that 100% of the post albedo - in this case 239 W/m^2, gets to the surface one way or another. No, it dictates that it gets either to the atmosphere or the surface.
  4. Tom Curtis (RE: 1025), Actually, the ASR and NET Down data is on the 8th page of the paper (not the 6th).
  5. RW1 "Actually, the ASR and NET Down data is on the 8th page of the paper (not the 6th). " Both pages show these values, they are for different time periods. Same thing I pointed out earlier goes for tables 2a and 2b, 2a shows TOA measurements, it does not distinguish between surface and atmosphere so it is irrelevant to your claim.
  6. e (RE: 1028), Look at the Global data in table 2a. for the row entitled "this paper". ASR is 239.4 W/m^2, OLR is 238.5 W/m^2, NET Down is 0.9 W/m^2. Are you seriously claiming that this means that of the 239.4 W/m^2 absorbed, only 0.9 W/m^2 gets to the surface and the remainder is radiated out to space without ever reaching the surface?
  7. e (RE: 1028), Furthermore, if you look at the surface components in table 2b, you see 161.2 W/m^2 of "Net Solar" and 78.2 W/m^2 of "Solar absorbed". Is it just a coincidence that 161.2 + 78.2 equals 239.4 W/m^ and this is exactly the same as the ASR at the TOA?
  8. RW1@1031 You are not understanding, please read carefully: TOA measurements do not distinguish between the surface of the earth and the atmosphere. They treat the entire surface/atmosphere system as a black box emitting and absorbing energy. The 239.4 W/m^2 could be absorbed by the surface or it could be absorbed by the atmosphere. The table you are looking at does not tell you how much is absorbed by each. For that you need to take a look at table 1b or 2b which treat the surface separately from the atmosphere. It shows that only about 160 W/m^2 of solar energy is absorbed by the surface. The 0.9 W/m^2 is just the difference between the energy entering the surface/atmosphere system and the amount of energy leaving. Again, it says nothing about where within the earth the energy goes.
  9. e (RE: 1028), What do you think a NET Down of 0.9 W/m^2 means? It's showing a positive energy imbalance at the surface of 0.9 W/m^2 - meaning more energy is entering the surface from the Sun than is leaving at the TOA as OLR (239.4 - 238.5 = 0.9 W/m^2). It's quite apparent to me that few people here actually understand the data in that paper and the constraints Conservation of Energy puts on the boundary between the surface and the TOA. Part of the problem is the diagram itself, which is only loosely connected to the text and details presented in the paper.
  10. e, You do know that the atmosphere cannot create any energy of its own, right? If, of the 396 W/m^2 emitted at the surface, 70 goes straight to space, then 326 W/m^2 is the amount absorbed by the atmosphere (396 - 70 = 326). Are you saying that this energy never leaves because there is 333 W/m^2 of 'back radiation' from the atmosphere? Where does the difference of 7 W/m^2 go? Where is the 169 W/m^2 emitted to space from the atmosphere coming from then?
  11. e, How can the surface be receiving 161 W/m^2 from the Sun and 333 W/m^2 of 'back radiation' from the atmosphere when it's only emitting 396 W/m^2? The surface cannot be receiving more than a net flux of 396 W/m^2 unless it is warming, but we are referring to the system in the steady-state (or at least an imbalance less than 1 W/m^2).
  12. RW1, I've explained this to you before. You are ignoring the 80 W/m2 from evapotranspiration and 17 W/m2 from thermals, or 97 W/m2 more. 396 W/m2 + 97 W/m2 = 493 out. 161 W/m2 + 333 W/m2 = (surprise) 494 in. They balance. Minus, of course, the net 0.9 which is being absorbed by the planet and thus increasing its temperature. You can't just ignore the thermals and evapotranspiration/latent heat because they are not in the form of radiation. They still represent energy transfer.
  13. e, Table 2b in the paper does not define 'back radiation' as the downward emitted LW from the atmosphere that last originated from surface emitted. It just defines it as "LW downward radiation to the surface". The problem is as I said in post #1027, not all of this is 'back radiation' as defined as that which last originated from surface emitted radiation. Some of it is LW 'forward radiation' from the Sun that has yet to reach the surface. What Trenberth does in the diagram is lump the 78 W/m^2 absorbed by the atmosphere from the Sun and the 97 W/m^2 of latent heat and thermals all in the same return path of 333 W/m^2 designated as 'back radiation'. This is highly misleading and why everyone is so confused. 157 W/m^2 from surface emitted (396 - 239 = 157) + 78 W/m^2 from the Sun designated as "absorbed by the atmosphere" + 97 from latent heat and thermals = 332 W/m^2 all lumped in the return path as 'back radiation'. Trenberth has an extra watt in there for at total of 333 W/m^2 to account for the NET Down of 0.9 W/m^2.
  14. RW1, You are tying yourself in knots making this more difficult than it needs to be. Before we move on, please answer the question posed by this simple analogy: Suppose I have two bank accounts. Now suppose you pay me $240, and I in turn spend $239 dollars, leaving $1 in bank account #2. From this information alone, can you tell me what the deposit amounts will be for each bank account? (Assumptions: I cannot create or destroy money, and nobody is paying me except you.).
  15. RW1, as e has pointed out, the correct values are listed in the paper on tables 2a and 2b under "this paper" for the TOA and surface respectively, with the solar radiation absorbed in the atmosphere listed with the surface values for convenience. Your apparent inability to read the paper or distinguish between TOA and surface values is not a problem with the paper. If you read my 1025 (sections (3b) and (4) I clearly do include atmospheric absorbed solar radiation, thermals and evapo/transpiration as sources of energy which is later reradiated to the surface as back radiation. Further, I included them as specific terms in the slab atmosphere model I mention in my section (4). Your insistence on attributing to me a view that would involve non-conservation of energy despite the evidence to the contrary is again your problem, not mine. Frankly your claim that, "the surface cannot be receiving a net energy flux above 396 W/m^2 in the steady-state" makes no sense. In the steady state (no change in the energy stored in the climate system), the net surface energy flux must be zero (ie, energy in - energy out = zero). Trenberth et al are claiming the climate system is not in a steady state. If your claim is about total energy flux, the downward energy flux at the surface by best estimate (excluding reflected solar, which self cancels) is 494 Watts/m^2 which almost exactly matches the net upward flux (excluding reflected solar) of 493 Watts/m^2. Your 1031 is an even more bizzare misunderstanding. Frankly your style of analysis seems to consist of taking a figure at random from what somebody writes and simply asserting a random falsehood about it, then attributing that falsehood to your opponent. I do not have the time to continuously rebut such inane ramblings. Nor should I need to as it is an obvious trolling strategy. I will not feed the troll, but request that the moderators also no longer permit you to troll this site.
  16. Sphaerica (RE: 1037), "I've explained this to you before. You are ignoring the 80 W/m2 from evapotranspiration and 17 W/m2 from thermals, or 97 W/m2 more. 396 W/m2 + 97 W/m2 = 493 out. 161 W/m2 + 333 W/m2 = (surprise) 494 in." I have not ignored the 97 W/m^2 from latent heat and thermals. It's a net zero flux at the surface. The diagram has 97 W/m^2 leaving the surface and 97 W/m^2 coming back as part of the 333 W/m^2 designated as 'back radiation' as explain in my post # 1038. Subtract 97 from 493 and you get a net flux of 396 W/m^2 - the amount emitted at the surface.
  17. RW1, Your post @1041 illustrates continued misunderstanding about how these numbers should add up. It is really much much simpler than you are making it. Since physical explanations are failing to make this clear to you, I think it might help if you thought of the diagram as illustrating the gross flow of money between three accounts: sun, atmosphere, and surface. You can start by answering my question @1039.
  18. Tom Curtis (RE: 1040), "RW1, as e has pointed out, the correct values are listed in the paper on tables 2a and 2b under "this paper" for the TOA and surface respectively, with the solar radiation absorbed in the atmosphere listed with the surface values for convenience. Your apparent inability to read the paper or distinguish between TOA and surface values is not a problem with the paper." From table 2b "Surface components of the annual mean energy budget for the globe", show me how numbers from the row of "this paper" yield a 'NET Down' of 0.9 W/m^2?
  19. Tom Curtis (RE: 1040) Also, is it just a coincidence the 'NET Down" in the surface components table 2b and the TOA components table 2a is exactly the same (0.9 W/m^2?).
  20. RW1>show me how numbers from the row of "this paper" yield a 'NET Down' of 0.9 W/m^2? Seriously, think of energy absorbed at the surface as "gross income", and energy emitted or transferred via latent heat as "gross expenditures", and the answer to this will be obvious. The first column applies to the atmosphere not to the surface and is simply shown for reference, so we won't add that in. We will also ignore "Solar reflected" as that is neither absorbed nor emitted. Our "gross income" comes from "Net solar", and "Back radiation". Our "gross expenditures" come from "LH evaporation", "SH", and "Radiation up". From here the math is easy: "net income" = "gross income" - "gross expenditures" = ("Net solar" + "Back radiation) - ("LH evaporation" + "SH" + "Radiation up") = (161.2 + 333) - (80.0 + 17 + 396) = 1.2. The .3 difference comes from measurement uncertainty. Also note that the "Net LW" field is just "Back radiation" - "Radiation up" which we already accounted for in the equation.
  21. RW1> is it just a coincidence the 'NET Down" in the surface components table 2b and the TOA components table 2a is exactly the same (0.9 W/m^2?). No it is not, but consider my question @1039 to see why this does not support the claim you are making.
  22. e (RE: 1039) "You are tying yourself in knots making this more difficult than it needs to be. Before we move on, please answer the question posed by this simple analogy: Suppose I have two bank accounts. Now suppose you pay me $240, and I in turn spend $239 dollars, leaving $1 in bank account #2. From this information alone, can you tell me what the deposit amounts will be for each bank account? (Assumptions: I cannot create or destroy money, and nobody is paying me except you.)." I know the diagram is depicting an energy imbalance of about 1 W/m^2. This is not related to the issues of COE in the diagram that I am addressing.
  23. RW1 @1043, for casual readers who may be confused by RW1's trolling: The columns of the table (and values in brackets) are: "Solar Absorbed" which is solar energy absorbed in the atmosphere, and hence not part of the surface balance (78.2); "Net Solar" which is the solar energy absorbed by the surface (161.2); "Solar Reflected" which is the solar energy reflected at the surface (23.1); "LH evaporation" which is the latent heat carried into the atmoshere by by evaporation or transpiration (80); "SH" or sensible heat, which is given as Thermals in the diagram (17); "Radiation Up" which is the Long Wave radiation from the surface, or Surface Radiation (396); "Back Radiation" which is, unsurprisingly, the Back Radiation (333); "Net LW Radiation" which is the Radiation Up - Back Radiation (63); "Net down" which is the total increase in energy at the surface per second per square meter (0.9) The casual reader should now be able to match these values to the surface components of the diagram in post 1019. They will therefore recognise that I have already met RW1's challenge in section (3b) of post 1025. But seeing as how RW1 presents himself as struggling with simple arithmetic and reading comprehension, the balance on the table is: Net Solar = 161.2 =~= 17 + 80 + 63 = SH + LH evaporation + Net LW. The difference is 1.2 rather than 0.9, but Trenberth et al use 0.9 because: a) The difference between 1.2 and 0.9 is well within experimental error; b) The TOA balance has smaller experimental errors (+/-3% for individual components), and hence is considered more accurate than the surface balance (+/-5% for individual components except for Surface Radiation and Back Radiation which are +/-10%); and because c) If the surface was absorbing 0.3 Watts/m^2 more than was the planet (TOA) over a five year period, the excess energy would need to come from the atmosphere, plummeting atmospheric temperatures by about 24 degrees C over that period, whereas atmospheric temperatures increased over that period.
  24. Also, here again is the Trenberth paper we keep referring to.
  25. Tom Curtis (RE: 1048), ""Solar Absorbed" which is solar energy absorbed in the atmosphere, and hence not part of the surface balance (78.2)" Not directly, no. It gets there indirectly, as I explained in #1038. Why even include it in the table? If the 78.2 W/m^2 does not get to the surface as you claim, how is it that the 'NET Down" in the surface components table 2b and the TOA components table 2a is exactly the same (0.9 W/m^2?)? Are you saying that 'Net Down' means something different in each table? Is it a coincidence that 161.2 + 78.2 = 239.4 W/m^2 and this is exactly the same as the ASR in table 2a? All I'm saying is that 239.4 W/m^2 from the Sun has to get to the surface one way or another if energy is to be conserved. Maybe you agree with this and we are just talking past each other, but it doesn't sound like it to me.

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