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  1. On point (iv) there is an implication of this that confuses me. This is due to the fact that the atmosphere warms with height in the stratosphere [because of the ozone layer].

    In this explanation what is changing is the altitude at which emission occurs, and at higher levels it is colder, so this level needs to warm up to maintain the radiative balance; what would happen once the altitude of radiative emission reaches above the tropopause?

    Then temperatures increase with height, so the atmosphere presumably emits more energy, and it would force a cooling..?

    Perhaps this isn’t an issue because it would take an impossibly large amount of CO2 [and water vapour] for the emission altitude to reach the tropopause, but it’s an aspect of this sort of explanation that I haven’t been able to work out in my head.

    [Response: One key difference is that the troposphere feels warming from below, whereas the stratosphere receives a good portion of the energy from absorption of UV-light. If you contrast the temperature relationship in the troposphere with that of the ocean, you also see different characters, again because the ocean is heated at the top. When the level reaches the tropospause, then this simple picture gets more complicated - after all, I'm only trying to follow the advice “Everything should be made as simple as possible, but not simpler” and try to present a simple comprehensive picture of the situation. -rasmus]

    Comment by Timothy — 5 Jul 2010 @ 9:18 AM

  2. This post was far too complex. Too long, too much math, too advanced for 99% of the population.

    [Response: Not everything needs to be written for everyone to understand. Indeed, if we did that we'd rightly be accused of over-simplification and avoidance of complexity in order to bamboozle people ;) Thus, we need to provide information at all different levels. This is not difficult but organising search engines and blogs to reflect that hierarchy is tricky. All suggestions welcome. - gavin]

    Comment by RichardC — 5 Jul 2010 @ 10:03 AM

  3. This is an excellent and cogent summary of basic GHE principles. I would take exception, however, to the explanation offered for stratospheric cooling consequent to increasing atmospheric CO2. In fact, as the atmosphere warms, the “atmospheric window” tends toward closing (particularly because of water vapor effects), and excess escape through this window can’t account quantitatively for the reduction in stratospheric temperatures. A better quantitative explanation appears to involve the presence of upper stratospheric ozone, which absorbs solar UV and visible radiation, warming the stratosphere. That heat must be dissipated to space, and CO2 (which does not absorb in the UV or visible range), adds to the emissivity of the stratosphere at the warmed temperature, while adding much less to the absorptivity. The net effect is essentially that CO2 acts as an escape valve for ozone-trapped heat. In the absence of ozone, added atmospheric CO2 would be expected to warm the stratosphere slightly rather than cool it. (Note that this phenomenon is distinct from the cooling expected from ozone depletion, an entirely separate entity).

    [Response:Upper atmosphere cooling as a function of increased CO2 occurs at all levels including the mesosphere, implying directly that the mechanism can't rely on the presence if ozone or absorbtion of solar uv. -gavin]

    I believe that some of the quantitation regarding CO2-mediated cooling can be found in Raypierre’s forthcoming book, “Principles Of Planetary Climate”, due for release in January 2011.

    Comment by Fred Moolten — 5 Jul 2010 @ 10:22 AM

  4. What do you mean by “reduced optical depth” in the sentence “Hence, a reduced optical depth explains why atmospheres are not easily ‘saturated’” ?
    Why “reduced” ? (it increases with increasing CO2, isn’t it?)

    [Response: ]

    Comment by Philippe — 5 Jul 2010 @ 10:30 AM

  5. All great stuff if you are a professional or amateur scientist talking to peers or policy makers. Useless if you ar trying to reach Joe Public.

    The public are not interested in scientific explanations of the mechanisms, they are interested in the outcome (i.e. the results). More and more data, charts and explanations will simply turn them off.

    Try this…one sentance along the lines of ‘Emissions of CO2 and other gases from the buring of fuels allow more sunlight to be trapped by our atmosphere and causing the earth to warm up. Done.

    Follow up with relentless and overwhelming numbers of photos of the effects, from Greenland ice moulins to coastal storms to droughts, with comments from locals experiencing these changes.. ‘before’ and ‘after’ are good.

    The public will relate to this so much better……and this advice comes from a data junky and trained scientist.

    [Response: Thanks for this feedback! To me this is a simple physics exercise, but I do appreciate that it required a bit of training in physics. On the other hand, sometimes it may be useful to reach different segments of the society, and with this post I aimed for the more scientific/technological literate part. I'll, however, try to write simpler posts in the future more aimed for the average Joe and Mary. -rasmus]

    Comment by Peter K Miles — 5 Jul 2010 @ 10:44 AM

  6. Many thanks to Rasmus for this delightful essay. 

    The “Iris effect” as proposed by Lindzen is upside down. The more the tropical seas are warm, the more cloud seeds are propagated world wide (I propose the “anvil Seeding theory”), the more Cirrus clouds should be. Precluding cloud seeds, why would, there be less cirrus clouds ? Given warmer seas convective moisture is more shared with the atmosphere. I have read a direct relationship between the number of thunderstorms and El-Nino peaks, which basically confirms
    increase cloudiness during El-Ninos. Given that Cirrus clouds are formed in no small part by thunderstorms,
    I am at a loss to explain how there should be less Cirrus clouds.

    Also there is a link between ENSO cloud driven events and time of year they happen, an El-Nino during winter is best for heating the planet, as opposed to a summer El-Nino, as those in North America may remember summer 2009 great cloudiness (thus cooler wetter summer, as opposed to El-Nino continuing during winter, causing Canada’s warmest winter in history for 2009-2010.

    Comment by wayne davidson — 5 Jul 2010 @ 11:03 AM

  7. in the “Enhanced greenhouse effect” section you say…

    The term known as the ‘enhanced greenhouse effect’ describes a situation where the atmosphere’s becomes less transparent to infra-red light (reduced optical depth)

    shouldn’t that be increased optical depth? (i.e., less transparent = increased optical depth) or am I missing something that should be obvious?

    [Response: A reducedincreased optical depth means that the distance you can see things gets smaller - just like murky water which doesn't let you see the bottom at depth greater than the very shallow parts. -rasmus]

    Comment by Xavier Onnasis — 5 Jul 2010 @ 11:03 AM

  8. tl;dr

    That will be the response from your target audience, I fear. And that’s the problem with communicating climate science: the irreducible complexity.

    This article is a fascinating angle on the greenhouse effect, and I will give it more attention when I have time. But don’t fool yourself that it is accessible to the general public. Only people with a scientific bent or a strong existing interest in climate change will make it more than half the way through.

    [Response: I think you are right about this - but sometimes we also need to try to reach the people who have more training in physics. It also serves to show that certain issues - at least in my mind - are inherently complex and can only be simplified to a certain degree. Hence my reference to the quote from Einstein. -rasmus]

    Comment by Didactylos — 5 Jul 2010 @ 11:34 AM

  9. On that Einstein quote: It is from Albert Einstein: On the methods of mathematical physics, Philosophy of Science, vol 1 (1934) 163–169:

    “The basic concepts and laws which are not logically further reducible constitute the indispensable and not rationally deducible part of the theory. It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.”

    Sorry for the slightly off-topic comment.

    Comment by Harald Hanche-Olsen — 5 Jul 2010 @ 11:39 AM

  10. Thanks much, especially for the downloadable paper. You have made a Great explanation that I can direct some people to. I like your post, but it is too difficult for most people. It has numbers in it, and even worse, equations! Figure 1 has something unfamiliar to most people, wavelength. For that matter, graphs are too hard. ANY graph is too hard. Also, you require a reading comprehension level above second grade, and it is too long for the average attention span by about 4 or 5 times. Optical depth needs to be explained by means of a series of pictures in fog of various densities. Spell out all acronyms every time. Use no acronyms because they require memory.
    Use second or third grade students at bad public schools as your test subjects, a different group for each test, and re-write until the students can understand it on their own. Then you will be ready to go public.
    Publish as a second grade reading book for all ages and distribute free to elementary schools. Better yet, make it into an animated movie because you shouldn’t assume literacy, never mind numeracy. Keep the movie at the first grade level. Test on first grade students to see if they continue to pay attention until the end of the movie. Hire Bugs Bunny as your narrator.

    Comment by Edward Greisch — 5 Jul 2010 @ 11:51 AM

  11. I think your description of the cooling effect Rasmus is a bit poor!

    But having been confused about it, I found Grumbine has one that makes more sense to me. The rest of your post is OK though.

    I’ll now have to change my own description of the green house effect on my blog. One day I’ll have it perfected.

    Comment by The Ville — 5 Jul 2010 @ 11:54 AM

  12. I agree that the scientific community should help the general public understand the fundamentals of climate change. And you have presented a very good start.

    But, I fear that the article is too complex for the average citizen. I’m not a technical writer, but I would guess that this article is written at a college level. Most Americans read at a much lower level (jr high school level?). Average citizens of other countries are probably at a similar or even lower level.

    I find that most people get the concept of the greenhouse effect – that’s why greenhouses work, and why opening the window shades on a sunny winter day helps warm the house.

    The most common argument (or point of disbelief) that I hear against AGW is that humans cannot possibly affect something as vast as the global weather. Their view is that the atmosphere is so big and our output of greenhouse gasses is so small. This is the dilution-is-the-solution-to-pollution belief.

    A nice added topic would look at the effects of “baseline” (pre-industrial) greenhouse gas levels and 1.5X, 2X, 3X concentration effects. The calculation of burning fossil fuels is straightforward and shows how the atmospheric concentration levels increase.

    Comment by Bill S. — 5 Jul 2010 @ 11:55 AM

  13. “A completely transparent medium has an optical depth of zero.”
    (image credited to NASA)

    Comment by Hank Roberts — 5 Jul 2010 @ 12:11 PM

  14. To elaborate on my comment # 3 above, the mechanism for stratospheric cooling consequent to increased atmospheric CO2 appears to be one of the most misunderstood elements of the greenhouse effect. The primary mechanism is attributable to the role of CO2 in discharging heat in the upper stratosphere that results from ozone absorption of solar radiation in mainly the UV plus some in the visible range. – i.e. a “safety valve” for ozone-absorbed heat. Without ozone, added CO2 is predicted to warm rather than cool the stratosphere. Gavin has suggested that the mesosphere would also cool, and while I’m not familiar with the observational data, this result would not be inconsistent with the theorized mechanism, as well as the presence of ozone in the mesosphere.

    I hope Raypierre will forgive me for quoting from a recent draft of his upcoming book, “Principles Of Planetary Climate”, where more quantitation is provided. The passages relevant to solar absorption by ozone are the following:

    “The solution in Eq. 4.56 also explains why human-caused increases in CO2 over the past century have led to tropospheric warming but stratospheric cooling, as illustrated in Figure 1.17. Increasing the greenhouse gas concentration is equivalent to increasing tau(at infinity). If one plots temperature as a function of pressure for a sequence of increasing tau, the phenomenon is immediately apparent in cases where the upper level solar absorption is sufficiently strong. The behavior is explored in Problems ??. Without solar absorption, increasing tau warms the atmosphere at every level, though the amount of warming decreases with height as the temperature asymptotes to the skin temperature. With solar absorption, however, the increased infrared cooling of the upper atmosphere offsets more and more of the warming due to solar absorption, leading to a cooling there.”

    [Response: Perhaps Ray will chime in, but this model (which does not deal with the spectral nature of the emissions) is not a good explanation of the stratospheric or mesospheric cooling, even if it might show similar behaviour in a grey body atmosphere. - gavin]

    Comment by Fred Moolten — 5 Jul 2010 @ 12:22 PM

  15. Is the simple metaphor (“model”) of a thicker blanket reducing the temperature above the sleeping person correct? Or is it wide of the mark?
    Thanks, Don

    Comment by Don — 5 Jul 2010 @ 12:38 PM

  16. Too complicated for many purposes. How about:

    In the absence of carbon dioxide and other greenhouse gases, the temperature of a planet depends on how far away it is from the sun. As we know from laboratory experiments, mathematical calculations, and observations of Venus and other planets in the Solar System, greenhouse gases change things in two ways: they trap heat from the sun in the lower atmosphere, thus making the surface of the planet warmer; and they keep heat from rising, thus making the upper atmosphere colder. This pattern of warmer below, colder above is just what we’ve observed over the last century as the concentration of carbon dioxide in the atmosphere has increased. That’s why scientists don’t believe that an increase in the strength of sunlight is causing the warming of the Earth. It isn’t just that there is no evidence that the sun is shining any brighter. A hotter sun would warm the whole atmosphere, but we know that the upper atmosphere has been cooling. Incidentally, we also know that the extra CO2 results from human activity because lab tests can tell the difference between CO2 produce by burning fuel and CO2 that comes from other sources.

    Global warming is definitely happening; it’s not surprising; and we’re causing it.

    Comment by Jim Harrison — 5 Jul 2010 @ 12:54 PM

  17. When you say the optical depth is the depth at which (on average) a photon is absorbed, shouldn’t that be absorbed or scattered. Either way direct beam radiation is reduced, although only the former process results in heat transfer. At least in the visible range (SW to climatologists) scattering is important.

    Doesn’t Fred’s argument at (3) carry some truth? The excess warmth of the stratoshere is due to absorption of primarily UV. And the energy is lost via IR thermal radiation. So more CO2 means more thermal radiation from this optically thin region. Of course having lower IR radiation in these bands is also a negative feedback. But it should be possible to quantify the effects of these feedbacks. I would think thermal radiation in an optically thin stratosphere would scale lineraly with CO2 concentration.

    Comment by Thomas — 5 Jul 2010 @ 1:05 PM

  18. Re 1 Timothy – the idea of an effecive emitting altitude is a useful though rough approximation – the photons leaving for space originate over a range of altitudes at any given frequency (wavelength), and that range shifts over different wavelengths.

    The condition that portions of the upper atmosphere are significantly warmer than otherwise via direct solar heating should (so far as I know) enhance the GHG-induced cooling at those levels. In the absence of solar heating, there is an equilibrium ‘skin temperature’ that would be approached in the uppermost atmosphere (above the effective emitting altitude) which is only dependent on the outgoing longwave (LW) radiation to space in the case where optical properties in the LW part of the spectrum are invariant over wavelength (this skin temperature will be colder than the temperature at the effective emitting altitude). But when optical properties vary over wavelength, the equilibrium skin temperature will be different.

    There is also a difference between the cooling that initially occurs in the stratopshere and above when a change in GHG forcing occurs, and the ultimate equilibrium cooling (relative to prior to change in forcing), which may tend to be smaller. The upper atmosphere has a small heat capacity and reaches equilibrium temperature in considerably under a year; this feeds back on the forcing of the trosphere+surface, which are generally convectively coupled with the ocean (strongly with the upper ocean) and take a number of years to reach equilibrium. During that process, upward LW radiation reaching the upper atmosphere will increase (depending on albedo/ solar heating feedbacks), which will change the equilibrium temperature of the upper atmopshere again. In the case where there is a skin temperature that only depends on solar heating of the planet with no solar heating above the troposphere, an increase in GHG forcing would still result in upper atmospheric cooling, but this cooling would only be transient.

    If there is significant solar heating below the tropopause level then there must be a significant net LW flux up through the tropopause (assuming relatively small convective or kinetic energy transfer through that level), so increasing GHG optical thickness can never saturate the tropopause level forcing at all LW wavelengths (by bringing net LW flux at tropopause to zero) in an equilibrium climate. What could hypothetically happen if a very large change in GHG amount/type is made, is that the forcing could increase beyond a point where it becomes saturated at the tropopause level at all wavelengths – what can happen then is that the equilibrium climate sensitivity to the nearly zero forcing from additional GHGs may approach infinity, because in equilibrium the tropopause has to shift upward enough to reach a level where there can be some net LW flux up through it.

    Comment by Patrick 027 — 5 Jul 2010 @ 1:13 PM

  19. How long does a CO2 molecule at 5.5 kms height hold on to that absorbed IR photon before it is released (emitted or transferred though collision to another atmospheric molecule)? How far does an emitted photon travel before it is absorbed again by another molecule? What happens to a non-GHG molecule when it absorbs a photon by collision from a GHG molecule? Do the non-GHG molecules also re-emit those absorbed photons?

    I’ve read that the average molecule at sea level experiences 10 billion collisions per second and the length of time a CO2 molecule holds onto an absorbed IR photon is between 1 picosecond (trillionth of a second) to 10 microseconds (millionth of a second). Surely at the quantum level, there is more going on here.

    Comment by PaulW — 5 Jul 2010 @ 1:18 PM

  20. What I like for visualization purposes is to think of greenhouse agents (gases or other) as acting like macroscopic particles – for ease of reference, let’s say Ping-pong balls – suspended in the air. These balls are completely opaque and have a ‘color’ depending on temperature. (To illustrate scattering, through in some mirror-balls and prisms) At any one wavelength The amount of radiation (at that frequency) coming from a direction is equal to the ‘color’ you see. A higher density of these objects reduces the distances that you can see, so that the amount of radiation coming from a direction depends more on the ‘color’ nearby and less on the ‘color’ farther away.

    Alternatively, think of an incandescent fog…

    Comment by Patrick 027 — 5 Jul 2010 @ 1:20 PM

  21. I agree that it does not have to be understood by everyone – it´s well within the grasp of an engineer or medical doctor, I think.

    I believe that educated people that understand these basics make for good multiplicators of the available information.

    Comment by Alexandre — 5 Jul 2010 @ 1:27 PM

  22. Re 15 Don – that can be a part of it. In the most general sense, upper atmospheric cooling is a response to a forcing (reduction in net upward LW + SW radiation) that falls with height through the upper atmosphere.

    Comment by Patrick 027 — 5 Jul 2010 @ 1:38 PM

  23. Great post rasmus.

    I don’t agree with some of the comments above who feel that the rasmus’ explanation is too technical, and actually I think it is something that could be understood by a majority of the interested public. It’s a bit more complete than simple cartoons that have a yellow arrow coming into the surface and a red arrow bouncing off the surface and hitting the atmosphere, but it also leaves room for the curious reader with some background to read more into the details of radiant spectra and the influence of the lapse rate, feedbacks, etc that are developed in upper-level undergraduate and graduate texts. In fact it’s one of the easiest ways you can explain the greenhouse effect without over-simplifying it to the point of being wrong. Virtually the entire post is well-rooted in theory and does not require full blown General Circulation Models to appreciate, and my guess is that the general reader will take more kindly to such simple models which can be understood completely.

    Fred– hi, it is nice to see you here! You should post more often. I do hope raypierre drops in. Keep in mind the section in raypierre’s book to which you refer strictly applies to an atmosphere where the absorption is independent of wavelength. There cannot be stratospheric cooling in a grey atmosphere with more CO2 (neglecting upper level solar absorption), but in more realistic radiative models (with a window region around 10 um) this phenomena can emerge from increased opacity (And shielding of radiation into the stratosphere) in the 15 um spectral region and increase in the 10 um flux from the ground as the surface is made warmer. The stratospheric emission must be in a limited wavelength band to get cooling and still satisfy planetary energy balance.

    Comment by Chris Colose — 5 Jul 2010 @ 1:44 PM

  24. I beg to disagree with the basic thesis of this article: that the public are becoming more sceptical about climate change through a failure to understand the science. Most sceptics who are capable of understanding the science accept that GHGs increase temperatures.

    Those who understand the science also realise that the increase of temperature in the mid 20th and in the late 20th century were similar, that the current rate of sea level rise is similar to rates at other times in the 20th century. They realise that Arctic sea-ice is low but that the Antarctic ice is at maximum. Until the climate science community explicitly explains why such facts do not invalidate the claims of accelerating climate change their case will remain weak.

    It is also a fact that sceptical authors tend to produce more interesting books which tell, possibly fabricated, tales of deceit and skulduggery. There is a crying need for the climate change community to produce popular books that rebut those charges which have got traction with the public.

    Comment by Ron Manley — 5 Jul 2010 @ 1:46 PM

  25. Figure 5. Estimates of the global and annual mean temperature based on a number of different data sets, including both traditional analyses as well as re-analyses

    I remember that Phil Jones said that the Russians and the Japanese also have global temperature records that were a close match to the better known records. I searched for them a while back but had no luck. Can they be accessed online?

    Comment by barry — 5 Jul 2010 @ 1:55 PM

  26. I thought I understood the GHE but this article totally confuses me. I am an outsider in this field but I thought that I know at least the basics. So, here is my newbie question:
    Fig 1 shows earth receiving higher levels of infrared radiations from sun then the infrared radiation emitted by earth. If this is true then an increase in GHG would cool the Earth. What am I missing?

    [Response: The 'Near IR' that is part of the solar input to the system is not significantly absorbed by CO2 (though there is some absorption by water vapour). However, absorption of incoming IR does not significantly affect the greenhouse effect or even the surface temperature because of the dominance of convective activity in setting atmospheric temperature gradients. - gavin]

    Comment by mircea — 5 Jul 2010 @ 2:00 PM

  27. On the Stanford poll at the top of the post: I note that only 1% of Americans think that temperatures have risen but that human activity is not responsible.

    This is encouraging, because the 25% who do not “believe” that temperatures have risen are plainly in denial; the evidence for warming is so strong that just about all the prominent so-called sceptic scientists acknowledge it.

    Why is this significant? So much emphasis is placed on this 1% position by the deniers, but it simply isn’t an idea that we need to address. Hardly anyone is silly enough to think that temperatures are rising but we didn’t do it. So, what is the real issue for this 25% (up from 15%) of deniers? I suspect it is a political issue for most of them.

    Krosnick has a complicated theory about trust and scientists. While no doubt it is true for some people, I feel that politics and plain ignorance of global temperature and region variation plays a much larger role.

    Comment by Didactylos — 5 Jul 2010 @ 2:01 PM

  28. Gavin – I don’t mean to belabor the topic of STRATOSPHERIC COOLING (see #3 and #14), but it seems to be an important area of both interest and uncertainty for many people, and so I’d like to pose one more set of comments/questions to you before exhausting my own familiarity with the topic. I believe many readers may appreciate an informative discussion.

    Consider, as a thought experiment, an isolated layer of atmosphere, insulated from major conductive or convective influences or other non-radiative processes. Imagine that its only radiatively active moiety is CO2 – no ozone, no water to speak of, etc. – so that its temperature is determined by the balance between absorption of incoming infrared by CO2 and emission of infrared out of the layer by CO2. Do you agree that if CO2 is added to this hypothetical layer, with no change in infrared entering the layer, the layer will warm due to increased absorption, until a new steady state is reached wherein the higher temperature restores emission to a level once again equal to the incoming radiation?

    [Response: Yes. - gavin]

    Conversely, imagine a different scenario in which much of the heat in the layer comes from something else (e.g., ozone). Again, adding CO2 will increase absorption of incoming infrared (also absorption of ozone-emitted infrared within the layer, but the spectra are different and so that effect is small). Now, however, the extra CO2 does more than radiate away heat due to its own absorptive properties, but also can radiate away heat from the other source. Do you agree that when the heating effect of extra CO2 is due almost exclusively to what it itself absorbs from outside, but the cooling effect entails an ability to dissipate heat from the additional source, cooling can now outweigh warming?

    [Response: Depends on the relative size of the two effects. - gavin]

    To summarize this concept, do you agree that when a layer’s temperature is due to heat absorbed by CO2 alone, more CO2 will increase the temperature, whereas if the temperature includes heating from something else as well, more CO2 can help rid the layer of that extra heat?

    [Response: Yes, but this is not the same as deciding whether increasing CO2 will cause an increase or decrease of temperature. Especially not in the stratosphere or higher where the spectral issues are dominant. - gavin]

    Finally, in what ways do you believe the stratosphere is behaving differently from this hypothesized layer, and what data are available to confirm alternative explanations? To the best of my knowledge, increased atmospheric CO2 does not appreciably reduce the flux from below of CO2-absorbable infrared into the stratosphere when a new steady state is achieved at the higher CO2 concentration. Rather, the flux is restored through warming of the troposphere and surface. Thanks.

    Comment by Fred Moolten — 5 Jul 2010 @ 2:01 PM

  29. I don’t think these thread comments have much validity:

    “All great stuff if you are a professional or amateur scientist talking to peers or policy makers. Useless if you ar trying to reach Joe Public.”

    “This post was far too complex. Too long, too much math, too advanced for 99% of the population.”

    If that’s so, why was Steven Hawking’s “A Brief History of Time” so popular, selling over 9 million copies? People appreciate clear scientific explanations, generally speaking – which is why popular science books continue to be top sellers.

    The public could probably handle even more detail than included in this discussion. Quantum physics, for example, plays a key role in the fundamental processes involved in greenhouse physics, particularly during this step:

    Infra-red light is absorbed by molecules, which in turn get more energetic, and the excited molecules will eventually re-emit more infra-red light in any random direction or transfer excess energy to other molecules through collisions. In a optically thick (opaque) atmosphere, there will be a cascade of absorption and re-emission.

    This can be expanded in an interesting manner – From Quantum Physics: A Beginner’s Guide, by A.I.M. Rae (2005)

    “Sunlight passes through the atmosphere largely unhindered and warms the Earth’s surface; the warmed surface radiates heat and some of this radiation is absorbed in the upper atmosphere and re-emitted, about half of the re-emitted energy returning to the Earth’s surface. This is where quantum physics plays an important role…”

    If you’ve read Stephen Hawking’s “A Brief History of Time”, this next bit is along similar lines:

    “..when electrons are confined within an atom or a molecule, wave-particle duality ensures that the energy of the system must have one set of quantized values. Moreover, the excitation of such a system from its ground state can be caused by the absorption of a photon, but only if its energy matches the difference between the energies of the levels.”

    This explains the absorption characteristics of the atmosphere – high frequency short wavelength radiation is removed by the smaller molecules, like O2 and N2, ultraviolet is screen out by O3, a little longer, and long-wavelength infrared is absorbed by flexible vibrating molecules – CO2, CH4, N2O, H2O, etc.:

    “…such vibrations are not readily excited in molecules such as oxygen and nitrogen, but can be in others – particularly water and carbon dioxide. A photon that strikes one of these molecules can be absorbed, leaving the molecule in an excited state. It quickly returns to the ground state by emitting a photon, but this can be in any direction and is just as likely to return towards the Earth as it is to be lost to outer space.”

    Since long wave IR is at the heart of the greenhouse effect, Rae then considers the vibrations of molecules like CO2 and N2O in more detail:

    “…the energy required to excite an electron from the ground state of a typical atom corresponds to that of a photon associated with visible light. However, the energy of a photon associated with the heat radiated from Earth’s surface is about ten times less than this, so a different kind of process must be associated with the absorption of this low-energy radiation.”

    That process is not electronic excitation, as with visible light, but rather vibrational excitation, which is based on oscillation of the atoms in the molecule:

    “…the oscillator has a spectrum of energy levels, separated by Planck’s constant times the radiation frequency, so it follows that energy will be absorbed if this matches the oscillator frequency. Heat radiated from the Earth’s surface has a range of frequencies, which encompass the vibration frequencies of the gases in the atmosphere, including those of greenhouse gases such as carbon dioxide.”

    This should also be true for the main gases in the atmosphere, N2 and O2 – why aren’t they absorbing infrared as well? It has to do with the symmetry of charge distribution – consider O=C=O, CO2:

    “The net effect of this is that, although the total electronic charge on the molecule balances the total nuclear charge, each oxygen atom carries a small net negative charge, and a balancing positive charge is associated with the carbon atom. We now consider what happens when the molecule is subjected to an electric field directed along its length.”

    Recall that an electric and magnetic field is associated with light?

    “…this pulls the carbon in one direction and the oxygens in another, so an electromagnetic wave that vibrates at the correct frequency can excite the molecule into a vibrational motion in which the carbon atom moves in the opposite direction to the two oxygen atoms. This allows the absorption of energy which is then re-emitted in a random direction, so leading to a greenhouse effect.”

    It turns out, due to issues related to pressure of gases in the atmosphere, that adding fossil CO2 has the strongest effect around the level of the upper troposphere, some ten miles up in the atmosphere. In the pre-industrial era, more infrared energy would escape to space from this level, but as CO2 levels rose, an increasing amount was sent back to Earth, warming the surface and oceans.

    Quantum physics is only part of the story – classical fluid dynamics controls the response to the increased infrared energy. This split between classical physics and quantum physics is also seen in solar energy:

    “Solar energy comes in two main forms. It can be used to heat domestic hot water systems (for example) and again there is nothing particulary quantum about this process, but it can also be used to produce electricity in ‘photovoltaic cells’, whose performance does depend on quantum effects.”

    The advantage of taking this approach is that everyone, Joe Public included, is aware that quantum physics is a well-grounded theory with dozens of practical applications. The point should be obvious: if global warming is based on solid physical theories, then you have to discredit those theories if you want to preserve your ‘skeptical stance’ – and that isn’t possible.

    It’s similar to the tobacco debate – once people came up with clear evidence of tobacco smoke components, such as benzo(a)pyrene, forming complexes with DNA and damaging gene replication, there was really nothing to say. Such clear evidence already exists with respect to global warming, and has since the mid 1990s at least.

    Comment by Ike Solem — 5 Jul 2010 @ 2:06 PM

  30. A nice story, but way too simple. Radiation is the source of all terrestial influx of energy, but the atmosphere is not a glass sphere. Water vapour plays an important role, by taking energy at the surface of the oceans when water evaporates. It releases heat when water vapour condeses into rain, at varying levels in the atmosphere. This heat, energy if you like, will be lost to outer space, adding to the radiative loss, and exceeding it by factors. It is a dumd model, as are ALL models. That is why they are models.

    [Response: No latent heat is lost to outer space. - gavin]

    Comment by Iskandar — 5 Jul 2010 @ 2:11 PM

  31. I think the suggestion to make it clearly understandable by early elementary students is a bridge too far. It would not help the purpose.

    Comment by Rod B — 5 Jul 2010 @ 2:11 PM

  32. I’m sure that this is a good reference for scientific conversation, however, as a non scientist and the type of person that it is trying to reach it is far too complex and introduces confusion and will only deepen any gulf that it tries to bridge.

    I did trying reading the article and came across several areas that seem in conflict to what I had previously understood. In one instance the article states about cooling in the upper atmosphere:

    “…it’s hard to see any systematic long-term trend in the level of solar activity over the last 50 years, and it is difficult to see how solar activity may have an effect…”

    I just dug up what I remembered from a while ago about this same topic:

    “For the first time, researchers can show a timely link between the Sun and the climate of Earth’s thermosphere, the region above 100 km, an essential step in making accurate predictions of climate change in the high atmosphere.” (Taken from: Scientists from NASA’s Langley Research Center and Hampton University in Hampton, Va., and the National Center for Atmospheric Research in Boulder, Colo., presented these results at the fall meeting of the American Geophysical Union in San Francisco from Dec. 14 to 18.)

    I have also seen several articles about the sun’s activity decreasing of the past 50 years. Take a look at the NASA site for lot’s of info on this.

    These sorts of discussions are great and healthy for science to thrash out; however, they show that the science is still in very early stages of development and understanding. Add to this the constant media drip of scary scenario’s and politicians using it to raise taxes, and increase control, IMO, this is where the public starts to loose faith.

    Comment by Titus — 5 Jul 2010 @ 2:12 PM

  33. Great post, I am gonna need to read it thrice but thats how it should be for us lower beings of lesser ability. I like the way its a simple explanation but still make me head hurt. Great stuff and a challenge to understand, thanks for that as its the challenge that really matters.

    Comment by pete best — 5 Jul 2010 @ 2:17 PM

  34. Gavin in your response to 26, (if my reading is correct) you misunderstood his difficulty. By my reading mircea was concerned that since at any wavelength the plank function monotonically increases with temperature, the intensity of solar IR exceeds that of terrestrial, at all wavelengths. The resolution is that the plank function is intensity per unit of solid angle (usually expressed as the radiation flowing through a plane of given size), but that the solid angle of sunlight is roughly 6e-5 radians squared (pi times a quarter of a degree squared), whereas the solid angle for terrestrial upward going radiation is the entire half sphere.

    Comment by Thomas — 5 Jul 2010 @ 3:17 PM

  35. As a physicist, I winced when I read “This is because energy cannot just be created or destroyed (unless it involves nuclear reactions or takes place on quantum physics scales).” Energy cannot be created or destroyed, period. Forget nuclear reactions or quantum mechanics; they also can’t create or destroy energy. (As far as we know physics is time-translation invariant, and Noether’s theorem applies to quantum field theory just as much as to classical mechanics….)

    Comment by onymous — 5 Jul 2010 @ 3:19 PM

  36. The rest is a nice read, though. I’m curious: why is the moon cooler than the naive Stefan-Boltzmann prediction?

    Comment by onymous — 5 Jul 2010 @ 3:29 PM

  37. In fig 3, why is the measured temp of our moon significantly colder than the expected T?

    Comment by Patrik — 5 Jul 2010 @ 3:29 PM

  38. This summary is extremely useful. The people who want an explanation for lay people are focused on a different audience, which will require a different summary, but that shouldn’t take away from the value this technical summary brings to a more sophisticated audience.

    Comment by Jonathan Koomey — 5 Jul 2010 @ 3:41 PM

  39. Please explain why a higher humidity reduces optical depth for IR and not for other wavelengths.
    We all know that higher WLs have a hard time penetrating the oceans. At very modest depths, only blue remains and just a bit deeper, no visible light penetrates the water, leaving most of the oceans pitch black.
    What I mean is that a reduced optical depth due to H2O feedback logically would stop more sunlight from reaching the surface as well, or? The atmosphere and surface might very well heat up from enhanced GHE, but as soon as water vapor feedback kicks in it will actually act as both a positive and a negative feedback. However, the negative one (shielding the surface from sunlight) must “win” in the end, since it actually reduces the energy input across a wide(?) range of wavelengths?

    Comment by Patrik — 5 Jul 2010 @ 3:50 PM

  40. #30 gavin

    Why is latent heat once released not then potentially lost to outer space?

    Comment by simon abingdon — 5 Jul 2010 @ 3:56 PM

  41. Fred Moolten says:
    5 July 2010 at 10:22 AM
    This is an excellent and cogent summary of basic GHE principles. I would take exception, however, to the explanation offered for stratospheric cooling consequent to increasing atmospheric CO2. In fact, as the atmosphere warms, the “atmospheric window” tends toward closing (particularly because of water vapor effects), and excess escape through this window can’t account quantitatively for the reduction in stratospheric temperatures. A better quantitative explanation appears to involve the presence of upper stratospheric ozone, which absorbs solar UV and visible radiation, warming the stratosphere. That heat must be dissipated to space, and CO2 (which does not absorb in the UV or visible range), adds to the emissivity of the stratosphere at the warmed temperature, while adding much less to the absorptivity. The net effect is essentially that CO2 acts as an escape valve for ozone-trapped heat. In the absence of ozone, added atmospheric CO2 would be expected to warm the stratosphere slightly rather than cool it. (Note that this phenomenon is distinct from the cooling expected from ozone depletion, an entirely separate entity).

    I agree with your point Fred, the upper atmosphere is also heated from above, ozone where it exists is a factor but even moreso is O2 and O, which absorb the very energetic UV photons. Collisional transfer to CO2 allows this energy to be radiated to space. Rasmus’s description applies at night, during the day direct heating from the sun must be considered, photodissociation of O2 produces O(D) which is quenched by N2 (which can’t radiate itself) which then can collisionally activate CO2 which then radiates (this is a very efficient process, it’s the basis of the CO2 laser).

    Comment by Phil. Felton — 5 Jul 2010 @ 4:00 PM

  42. I believe Mars and Venus share an equal atmosferic composition almost 96% CO2, but the density is dramatically lower on mars, is this the reason of the difference in temperature on Venus and Mars? If so, How does atmospheric density affect the temperature?

    Comment by Sordnay — 5 Jul 2010 @ 4:09 PM

  43. Re: onymous (#36 on the moon):

    The formula So*(1-albedo)*0.25 = sigma T^4 is valid only for an isothermal blackbody “bare rock” in space. It can serve as an approximation which is only useful for bodies such as Earth or Venus which, from a planetary climate perspective, are relatively uniform in temperature. For the moon or Mercury which exhibit day-night temperature gradients on the order of several hundred Kelvin it is not really appropriate to define a mean “effective temperature” in the preceding way. It is more useful to average over a hemisphere, or maybe a latitude band, or even at a single point that responds instantly to the solar flux (removing the factor of 1/4 from the equation) depending upon the nature of the problem.

    As a visualization,

    (T_night + T_day)/2 which becomes a flux upon dividing by sigma and taking the fourth root. Call this value “A.” Or, we can convert the temperatures into fluxes right away and then find the average flux. i.e., (Flux_day + Flux_night)/2…call this value “B.” In general, A=/= B due to the non-linear relationship between radiant flux and temperature. As you can see, it is more appropriate to divide the planet up into a bunch of patches which are relatively uniform in temperature (and surface emissivity). I’m not sure exactly how rasmus defined the “observed” surface temperature for the bodies in Fig.3, especially the ones that depart significantly from the uniform-temperature approximation, but a comparison results from the mathematics of the equation given in the post and has little physical meaning.

    Comment by Chris Colose — 5 Jul 2010 @ 4:16 PM

  44. Gavin,

    All heat is lost to outer space, not only latent heat.

    [Response: No it isn't. Only radiative fluxes are lost to outer space. You know, there is a vacuum and all.... - gavin]

    Comment by Iskandar — 5 Jul 2010 @ 4:17 PM

  45. Whether or not this post is too complex for us lay people it should certainly be required reading for any journalist reporting on climate issues. If they are not able to understand the maths and science presented here then hopefully they will think twice before offering their analysis.

    Comment by Heraclitus — 5 Jul 2010 @ 4:22 PM

  46. mircea (26), Thomas (34):

    Clearly the intensity of the solar spectrum is greater than that of the Earth spectrum in the infrared since the derivative of the Planck function with respect to temperature, dB/dT, is positive at all values of wavelength lambda. Though, it is useful to define a threshold at where both the Earth and sun emission are very small, which occurs at around 4 microns. See this image. This allows us to treat the fluxes independently. Note the solar spectrum is scaled by a factor of a millionth in order to see them together, since the total area under the curve is about (6000/300)^4 = 160,000 times larger for the hotter object.

    Comment by Chris Colose — 5 Jul 2010 @ 4:33 PM

  47. Dear Gavin,

    Temperature is defined as being the energy in the motion of individual molecules/atoms or ions. Collisions between molecules etc. will cool down the upper atmosphere by expanding the upper layer of the atmosphere. And there is no vacuum, there is only a lower concentration of matter. That is why the void of space has a temperature of 2 to 4 K.

    [Response: Let's imagine how much water vapour we can be losing to space for it to be an important number for climate purposes: For instance, let's imagine it is as important as the geothermal heat flux (itself too small to pay much attention to): 0.075 W/m2. What amount of water loss (as vapour) would that be? Divide by the latent heat and multiply by number of seconds in a year to get a mass flux per year ~ 1 kg/m2/yr. If that was coming from the ocean (70% of the area), that would imply 1.5 mm each and every year in sea level loss. I think we would have noticed. Given that the uncertainties in the sea level budget are on the order of 0.1 mm/year, that implies that the 'latent heat' loss to space has to be some many times less than what I first postulated. There is no climatically important latent heat loss to space. - gavin (Note: numbers corrected (made smaller) after initial posting - sorry for the confusion)]

    Comment by Iskandar — 5 Jul 2010 @ 4:37 PM

  48. I find that I best identify with the “great unwashed” inspite of education, training, technical expertese and interest. The alternative seems to be elitism. I enjoy a re-iteration of basics as others seem to capture nuances either in wording or perspective that helps me learn and refine, which, I guess is the whole point of the exercise. There are fundamental issues not addressed but this was never a discourse on the whole pie. Thank you.

    Comment by RiHo08 — 5 Jul 2010 @ 4:39 PM

  49. Unfortunately, better communication from scientists will have only limited effectiveness as long as the press continues to drop the ball. Take Washington Post for example. I’ve noticed it takes at least 2 reporters now to write every story concerning global warming. One to write the original article, and one to walk down the street and have lunch with CEI, for the contrarian paragraph. I’m not sure if anyone has alerted them to the fact that CEI representatives will recognize AGW when hell freezes over.

    The article on the exoneration of Michael Mann last week is one of many examples of their lazy and inaccurate style.

    Comment by The Wonderer — 5 Jul 2010 @ 4:45 PM

  50. oops I didn’t read the point iv before asking, sorry about that.
    Anyway, the question I had in mind is, corrected the surface temperature with the lapse rate how do temperatures fit with measurements? could you replot figure 3 taking into account the lapse rate correction?

    Comment by Sordnay — 5 Jul 2010 @ 4:50 PM

  51. Re 29- Ike Solem:

    If that’s so, why was Steven Hawking’s “A Brief History of Time” so popular, selling over 9 million copies? People appreciate clear scientific explanations, generally speaking – which is why popular science books continue to be top sellers.

    Hardly anyone read “A Brief History of Time”.
    I have a copy and gave up half way through. 22 years later it remains on the bookshelf, still only half read.

    People bought it because it was cool to have a copy. When it became a best seller, even more people bought it.

    Comment by The Ville — 5 Jul 2010 @ 4:51 PM

  52. One small typo just above the “feedback” section:

    You typed: “Planets with a thin atmosphere and insignificant greenhouse effect, on the other hand, have a surface temperature that is close the the estimates from the planetary energy balance model (Figure 3).”

    Presumably you wanted “close TO the estimates…” rather than “the the.”

    Comment by wili — 5 Jul 2010 @ 5:08 PM

  53. 29 asks: “Why was Steven Hawking’s “A Brief History of Time” so popular, selling over 9 million copies?”

    Answer: Because he is in a wheelchair and needs a voice synthesizer to speak (although when the book first came out he didn’t have that and could only be understood by a few people), and this captured the imagination of the world. How many people who bought the book actually read it past the first few pages?

    My two cents: I gave up on the current article not even half way in. I would not have minded more equations, but that was not the issue. It was just not a clear exposition to me, although no doubt it will be for some people.

    Comment by wab — 5 Jul 2010 @ 5:11 PM

  54. Heat due to random molecular motion is not lost to space. Heat due to radiation can be lost to space.

    Comment by David B. Benson — 5 Jul 2010 @ 5:17 PM

  55. Sorry, one more quible: in the second paragraph above the last graph, you start the third sentence “In other word” while the usual phrase is “In other words.”

    In general, I think it is a good article, mostly well written. Reading the (substantive) responses then going back over the article certainly helped.

    It reminded me of old “Scientific American” articles from the ’70′s that I would struggle to understand as a highschooler and college student. Often I didn’t get past the first page or so, but if I really worked at it and talked about it with my nerdy, more-scientifically-literate friends, I could usually figure out most of it and felt better for the mental exercise.

    Comment by wili — 5 Jul 2010 @ 5:24 PM

  56. “If that’s so, why was Steven Hawking’s “A Brief History of Time” so popular”

    The book contained a grand total of one equation. Look up the related anecdote….

    And maybe you should remember that 9 million copies equates to one copy for every 744 people on earth – or one for every 34 Americans. Compare that to the hundreds of millions of book sales for more popular fiction.

    I’m quite happy to conclude that the 9 million readers of “A Brief History of Time” are not a random sampling of Joe Public.

    This leads me to the subject of making information accessible to everyone. Obviously, this isn’t easy. I’m fairly sure Edward Greisch was indulging in irony when he spoke of using Bugs Bunny as a narrator, but he made some good points. Just because our audience are mostly adults doesn’t mean that the level they can best grasp isn’t sometimes the same level that is taught in primary school.

    Terry Pratchett and his scientific collaborators coined the term “a lie-to-children”. This is one of those scientific “facts” you learn in school that simply isn’t true. But it’s close enough to the truth for you to deal with it, and understand everything you need to. The lie is then discarded trivially as you learn more detail.

    This should apply to climate science just as easily. Does our model for how the greenhouse effect causes surface cooling need to include such nuances as stratospheric cooling? Heck no! How many people even know what the stratosphere is? Sure, people probably have a general idea, but the technical details? Not a chance!

    Rasmus used the word “simple” 10 times in his article. Gavin can try and backtrack if he wants, but Rasmus even wrote it in the title! Yes, the article fills a niche. But I’m not sure it was the niche you had in mind.

    Comment by Didactylos — 5 Jul 2010 @ 5:25 PM

  57. I think I have my head sorted regarding cooling in the upper atmosphere.
    Probably worth noting a previous RealClimate post:

    Which links to this very useful page that has a nice clear explanation of the cooling effect CO2 has in the upper atmosphere:

    My summary would be:
    Upper atmosphere receives less IR energy from below, yet the greenhouse gases in the upper atmosphere remain a potent emission source of IR, so there is a net loss to space in the upper atmosphere. eg. Input from below is less than that being emitted.

    Comment by The Ville — 5 Jul 2010 @ 5:27 PM

  58. What a confused post. I don’t fault the science at all – I’m not a scientist! What I do fault is that you never pin down who your intended audience is. Are you writing for science nerds? For the general public? You start off talking about “communicating science to the public” but then throw in charts! Equations! Numbers! Would Carl Sagan have done that? Does David Attenborough?

    As a piece of science communication for the masses, this is a great section for a science textbook.

    Comment by pointer — 5 Jul 2010 @ 5:37 PM

  59. You know what? My main gripe here is that rasmus said he was selling me an orange and then gave me a persimmon. Where’s my orange?!

    Comment by pointer — 5 Jul 2010 @ 5:43 PM

  60. Oh, this is priceless. From wili (#55):

    It reminded me of old “Scientific American” articles from the ’70’s that I would struggle to understand as a highschooler and college student. Often I didn’t get past the first page or so, but if I really worked at it and talked about it with my nerdy, more-scientifically-literate friends, I could usually figure out most of it and felt better for the mental exercise.

    That’s right. This blog post on explaining the GHE in “simple” terms — an exercise in “communicating science to the public” — is only a success if every member of the public has access to “nerdy, more-scientifically-literate friends”. Because that’s so likely.

    Comment by pointer — 5 Jul 2010 @ 5:47 PM

  61. If any of the “general public” that this post ostensibly targets actually reads it, it will only reinforce the idea that scientists are arrogant and so out of touch that they can be safely ignored. This could have been entirely avoided by not referring to this explanation as “as simple as possible” for the purpose of “communicating science to the public”. Treating people like they’re stupid doesn’t communicate science to them, it pisses them off.

    Comment by Rich Thompson — 5 Jul 2010 @ 5:56 PM

  62. “why is the measured temp of our moon significantly colder than the expected T?”

    because the Apollo astronauts secretly painted the back side of the moon with Dupont Lucite Acrylic White Lacquer, which increased its visible albedo, but maintained its thermal emissivity near 0.9

    Comment by Brian Dodge — 5 Jul 2010 @ 6:04 PM

  63. For a super simple explanation to a general audience, I quote what John Tyndall wrote back in 1862:
    “As a dam built across a river causes a local deepening of the stream, so our atmosphere, thrown as a barrier across the terrestrial [infrared] rays, produces a local heightening of the temperature at the Earth’s surface.”

    This is essentially a 100% correct analogy. I may go on to explain that you can look at a rising water level as equivalent to the rise in temperature necessary to “push” energy out to maintain energy out = energy in (less the amount embedded in the warming).

    For the upper-atmosphere cooling, I simply remark that infrared coming up from below is blocked more, as more greenhouse gases are added, so of course it’s cooler above the blocking. Maybe not 100% accurate but good enough for a one-sentence explanation.

    Comment by Spencer — 5 Jul 2010 @ 6:10 PM

  64. I am not a scientist.

    As a communcator & activist I feel it is my job to apply the Duck Test– if it looks like a duck, and walks like a duck and quacks like a duck, it is a damn duck! And if weird weather matches my understanding of what we expect to see as expressing the climate changes produced by global warming, I think it is my duty to say so, and I hope more climate scientists find ways to say so as well. (Yes, I know it really is “trickier” for y’all.)

    This is the kind of post I need to keep my level of understanding at a decent level, so I can play my role.

    Comment by John Atkeison — 5 Jul 2010 @ 6:21 PM

  65. The post starts off wondering if there may have been a recent decline in public concern over global warming and then considers if a simpler method of communicating the science would help. In other words they would be concerned if only they understood. Have you considered that if people begin to question the motives of those espousing the science then it doesn’t matter how good or robust the science is; how well it is communicated; or even how perilous the situation appears to ‘those in the know’, the average person will filter that communication out at the start and you won’t get a look in? Climategate has done an enormous amount of damage to the credibility of climate science, rightly or wrongly, and that is what I believe to be driving this recent (real) decline in concern.

    Comment by Michael — 5 Jul 2010 @ 6:31 PM

  66. Re 39 Patrik – water vapor absorbs both LW (terrestrial) and SW (solar – UV,vis,solar IR) radiation. But not to the same extent. Solar heating at all levels beneath the tropopause, whether at the surface or aloft, still must be approximately balanced by the net upward LW flux at the tropopause in an equilibrium climate. At the point where there is so much H2O vapor in the atmosphere that there is very little solar heating of the surface (very very far from happenning), there will also tend to be almost no net LW cooling at the surface, so a tropospheric-type lapse rate could still tend to extend down to the surface (as long as the net LW cooling is smaller than the SW heating, there will be some non-radiative flux from the surface for equilibrium conditions).

    Re 40 simon abingdon – there is very little mass loss to space (can be significant for evolution of conditions over geologic time or in more extreme conditions, but not for Earth like conditions over the timescales over which climatic equilibrium is determined), and latent and sensible heat are transported by conduction and convection and mass diffusion, which can’t significantly extend outside the atmosphere.

    Non-radiative heat fluxes drop to approximately zero (at least for the global time average) going above the tropopause (there is a little leakage of convection through the stratosphere and mesosphere via upward propagation of kinetic energy and the Brewer-Dobson (does that term include the mesospheric part?) circulation that it drives, but even that can’t really go directly to space. Maybe some of the kinetic energy in the ionosphere produces radio waves that take energy into space ? (radiation, but not of the sort emitted as a function of temperature) – I’m quite sure that’s small enough to ignore in this context.

    (PS I only know that those non-radiative fluxes are small – I would very much like to know numerically what they are (the upward kinetic energy flux and the heat flux of the thermally-indirect overturning).)

    Re 32 Titus – the amount of mass of the atmosphere above the mesosphere is an extremely small amount compared to the total atmosphere. The thermosphere experiences huge temperature swings over the diurnal cycle and due to solar variability that vastly dwarf anything seen at the surface or troposphere. For at least some purposes one can calculate the energy budget of the surface and tropopshere and stratosphere while ignoring anything the thermosphere does.

    Re 42 Sordnay – the most obvious radiative effect is that less atmospheric mass in total means that, for a given composition, there is less mass of any given substance within the atmosphere. There is also (via weight given to mass by gravity, which itself varies among planets) the effect on pressure-broadenning of the lines that make up absorption bands – this alters the optical properties for a given amount of material (temperature also has an effect). The lapse rate(s) that would be found in a troposphere also depend on composition and gravity and (depending on vertical coordinate and whether or not a layer has a dry-adiabatic lapse rate) pressure and temperature.

    Comment by Patrick 027 — 5 Jul 2010 @ 6:58 PM

  67. pointer (58-60), and others–

    Please. This consistent talk about “the post is too technical when rasmus wanted to talk to lay audiences” is rather tedious, and it takes away from the possibility of more interesting discussion. IMO it also underestimates the curiosity of those “regular joes” who took the time to find this post at all. For the one-stop readers who wanted an orange, they did not get a persimmon…they got an orange in addition to an apple (complements of rasmus, thanks again) so it should make their day.

    I say this because it is not an overly-demanding post to follow. There is nothing that assumes knowledge like calculus or physics that takes several years to build up, and there are plenty of linked references such as “CO2 problem in 6 easy steps” or “Saturated Gassy Argument” which allows one to explore different approaches to the same issue. There are a few elements (e.g., stratospheric cooling) which are not necessary to bring up right away, and the part about negative feedbacks is a bit of a confused complication, but they can safely be skipped over by a reader without a loss of much information if necessary. Further, it is easy to find slightly less laborious posts on the internet (e.g., wikipedia) which still provide adequate background for building an intuition. If the “regular joe” wants to learn the broad-brush picture he can do so easily if he spends just a few hours on the web.

    In addition to the myriad web sources, we are fortunate that this post appears on a site which allows comments, and happens to be full of commenters who are well familiar with what was written and can answer additional questions people may have. They can also elaborate on points Rasmus already made. Still further, those knowledgeable commenters are a supplement to a handful of experts who can even provide further nitty gritty details if it comes to that. I suppose RC has a nice professor ==> teaching assistant ==> student hierarchy and I find no reason that any of the posts RC does should be beyond the realm of accessibility. Even for those people pretty sketchy with the all that has been written, it will be a great mental exercise (as nicely stated in post #55 by wili) to track through the steps, ask questions in the comments, visit the linked websites, etc.

    Consider this though: Since the discussion surrounds science to public communication, it is necessary to have such intermediate level information of high quality that is accessible for people who are beyond wiki cartoon diagrams but not yet at differential equations. This IMO, is one large gap that requires filling. Those wanting more details will search it out at university and in textbooks, and those seeking less detail can already find it on the web (assuming they can sort out the good stuff from the wingnut stuff, but it’s hard to get rid of that issue in a world where anyone can write anything they want). Accessibility of info is not the issue; the largest audience out there is the “regular joes” who have no desire to learn climate change, in the same way that many here have no desire to learn about medicine. It’s not that they don’t believe in climate change, take wrong sides, or don’t understand it…they just don’t think about it. I don’t claim to know anything about social or psychological sciences to elaborate, but this might just be a consequence of the fact that climate change operates on timescales much larger than a political term or the time it takes to schedule your son’s soccer practice. Experts in a lot of fields want the regular public to understand elements of their field that people just don’t think about…I had an ecology professor a while ago who was angry that I didn’t really know about mercury contamination issues in a local water source. I’m sure that is a big issue for such scientists and has public repercussions, but admittedly I did not have the interest to read up on it, and it’s time we accept the fact that most people aren’t going to unless it personally influences them (whether it be climate change, mercury pollution, mudslides, landfills genocide in Africa, etc etc). C’est la vie. Perhaps the answer to the science==> public communication gap is that it can’t improve except that bloggers, authors, etc have to keep doing what they do. Many of them do it quite well. If the concern of climate scientists continues to go unheard, there will be severe social and ecological repercussions but maybe that undesirable outcome is precisely what will manifest itself. If not, awesome. If so, we tried, and hopefully industrial mistakes will be avoided by people hundreds or thousands of years from now in this grand history lesson.

    Comment by Chris Colose — 5 Jul 2010 @ 7:03 PM

  68. I like the summary, but you’re going to cause most non-scientific readers to go crosseyed with it. I agree with #2 – there’s other ways of explaining it that are easier for non-scientific people to understand, without misrepresenting the current state of the science.

    When I teach it, I just show a chart that shows watts coming in, watts reflected by the surface and atmosphere, watts trapped by GHG, and then talk about climate sensititivity, do a couple multiplications to show the math matches predictions (also accounting for the ocean buffering effect), and there you go.

    You can also just mention that greenhouse gasses respond differently to different wavelengths of light without asking people to understand black body radiation or use those scary, scary equations.

    Comment by Foobear — 5 Jul 2010 @ 7:13 PM

  69. Ref: Spencer #63 gives an analogy with which I can associate:

    “As a dam built across a river causes a local deepening of the stream, so our atmosphere, thrown as a barrier across the terrestrial [infrared] rays, produces a local heightening of the temperature at the Earth’s surface.”

    “Greenhouse” does not work at all for me and creates confusion. It is not how I know a greenhouse works.

    As a lay person I would recommend the adoption of this analogy as it appears as Spencer says; 100% correct.

    Comment by Titus — 5 Jul 2010 @ 7:30 PM

  70. For the record, I know someone who read “A Brief History of Time” when he was in elementary school and understood it. (Maybe it helps that young minds are stretchy?)


    It might help to show the spectra of upward and downward LW fluxes at different heights. It should be easy to understand why increased opacity (decreased distances travelled by photons from emission to absorption)generally causes the LW fluxes to change and ultimately approach local blackbody values (thus bringing the net LW fluxes to zero except where there is a sharp temperature discontinuity, such as (relative to optical thickness) the ‘top of the atmosphere’ (TOA) – space acting in this context as a near zero-K blackbody. The increase/decrease of net upward LW flux going from one level to a higher level equals the net cooling/heating of that layer by LW radiation – in equilibrium this must be balanaced by solar heating/cooling + convective/conductive heating/cooling, and those are related to flux variation in height in the same way. (change in forcing from bottom to top of a layer = forcing of that layer; equilibrium temperature response of a layer changes the LW and convective fluxes to restore balance).

    Showing how a change in CO2 amount causes different LW flux changes at different heights would show how stratospheric cooling occurs, and the spectra (overlayed for 0.5 x, 1 x, 2 x, 4 x, 8 x preindustrial CO2) would also show the origin of the logarithic proportionality for tropopause-level forcing once the center of the band is saturated. One could also show how the spectra of LW radiation is affected by the resulting temperature increase and also by the water vapor feedback.

    (the temperature response to a forcing tends to be spread out from the location of that forcing, because the temperature change at one location changes the LW fluxes reaching other areas. Hence, for GHG forcing in general, stratospheric cooling (assuming either that the cooling extends to the base of the stratosphere or that the stratosphere has a sufficient band of wavelengths with significant but not large optical thickness, etc…) reduces the tropopause level forcing downwar, while tropospheric-surface warming reduces the stratospheric cooling. The temperature response also spreads out from the forcing via convection, which is why the surface and various levels of troposphere tend to shift (to a first approximation, setting aside the structure of the circulation and the occurence of stable air masses and the moist lapse rate feedback and surface dryness, etc) about the same amount in response to a tropopause-level forcing.)

    Comment by Patrick 027 — 5 Jul 2010 @ 7:36 PM

  71. Re 63 Spencer – I like that!

    Comment by Patrick 027 — 5 Jul 2010 @ 7:37 PM

  72. It is true that the majority of the American public does not understand climate science—improving biophysical climate literacy is important. But we have made a major mistake by framing climate change as a scientific and environmental issue. That’s the primary reason why the public doesn’t “get it”. Climate change is merely a symptom of maladaptive human thinking and beliefs that have been translated into maladaptive norms and values, technologies and policies. It is this sphere—in social science climate literacy–that increased understanding and better solutions will be found. My program at the UO has been part of an extensive research program on communicating climate change to the general public. Just one sample of the findings—many people don’t know what a greenhouse is or if they do, they think of its as a good thing. Thus, our long term use of the greenhouse effect term or enhanced greenhouse effect does not resonate with the majority of Americans. Good climate communications is framed in a way that motivates people to alter their thinking and behavior. For the most part we have failed in this task (for other findings and to obtain a copy of our handbook on climate communications and behavioral change see our website: I think a major enhancement of the social science principles of climate literacy is in order.


    Comment by Bob Doppelt — 5 Jul 2010 @ 7:38 PM

  73. I don’t think many informed skeptics have a problem with textbook greenhouse gas physics. I think you lose most of them on the issue whether there are strong positive feedbacks that amplify the initial warming caused by CO2. If the net feedbacks in the climate system are close to zero, then the warming from CO2 will be at or below the low-end projections of the IPCC. Your discussion of feedbacks is weak and not convincing.

    Comment by PaulD — 5 Jul 2010 @ 7:42 PM

  74. Pointer and Richard Thompson, We’ll work on a post communicating the greenhouse effect through monosyllabic grunts just for you.

    Jeez, Dudes, if you didn’t understand something why not ask questions. Or did you really think that you could communicate everything you need to know about the greenhouse effect in 500 words?

    Comment by Ray Ladbury — 5 Jul 2010 @ 7:43 PM

  75. I agree that many posts at RC are beyond the average reader. I teach freshman/sophomore non-science majors and they have difficulty here.

    Having said that, RC posts and the subsequent comments are the best resource for people like me who have a science background (or for people are well read on the topic of climate change) but who are not experts in the many fields associated with climate change. (But who is?) What I learn here I can then bring to others with the confidence that I have the correct science.

    Kudos to RC and the regulars who comment here. Keep it coming. You are providing a very valuable service.

    I took a whack at stratospheric cooling if anybody is interested. I agree that it is difficult to simplify and I admit to oversimplification.

    Scott A. Mandia, Professor of Physical Sciences
    Selden, NY
    Global Warming: Man or Myth?
    My Global Warming Blog
    Twitter: AGW_Prof
    “Global Warming Fact of the Day” Facebook Group

    Comment by Scott A Mandia — 5 Jul 2010 @ 7:48 PM

  76. The figure 3 confuses me a little. First of all, there seems to be 9 planets, which for the time beeing are allowing Pluto into the gang of planets… ;-)
    Next, it make sense to then expect the upper right planet to be Merkur, earth and Venus is marked and named. Then it make sense that Merkur, Mars and Pluto is more or less with same temperature as expected, while the gas-giants are a bit hotter than expected.
    The strange thing is Venus, which is plotted as expected to be colder than earth?! Even though it is a bit closer. Here the earth is expected to be about 260K while Venus is expected to be 240K (I´ll guess the scale is in Kelvin?), while messured are something like 290K and 720K respectively?

    Comment by Kjell Arne Rekaa — 5 Jul 2010 @ 7:54 PM

  77. Titus,
    You need to be careful in trying to interpret scientific results–the solar-thermosphere connection in your article has very little to do with climate. Also, when you say “solar activity”–what activity? Magnetic? Luminous? Coronal Masss Ejections?

    Solar luminosity–which is the main solar influence–has been relatively constant for 50 years or more. And as to your contention that our understanding of Earth’s climate is still primitive–that is complete utter BS. Where on Earth are you getting this idea?

    Iskandar, What you are posting bears zero relation to the real science. Where are you getting your information? Note especially that the 2.7 K temperature of space is a relic of the Big Bang. It is the blackbody temperature of the radiation left over from that event.

    Comment by Ray Ladbury — 5 Jul 2010 @ 7:57 PM

  78. Very good but I think you could improve on the stratospheric cooling part. I have an undergrad degree in Meteorology and that part I had to read twice ;)


    Comment by Dan Satterfield — 5 Jul 2010 @ 8:10 PM

  79. Re Ray 69: I’m a scientist who has in the past taught, among other things, the science of climate change to large classes of non-science major undergraduates. It’s not that I didn’t understand the post, it’s that nobody without at least some technical background would. Which is fine, unless you introduce the piece with the message that anybody who can’t understand it is stupid. Like this post did. Which is why a lot of people don’t like or trust scientists.

    Comment by Rich Thompson — 5 Jul 2010 @ 8:14 PM

  80. Kjell Arne Rekaa #72,

    Venus is indeed closer to the sun, but it is not just the fraction of solar energy it receives that counts…you have to weight that by the amount it actually absorbs. Venus has a much higher albedo (reflectivity) than Earth because of its thick cloud cover (and would even have a high albedo without the clouds due to Rayleigh scattering from the dense CO2 atmosphere). When this is accounted for it actually turns out Venus absorbs less solar energy than Earth, and thus would be colder than Earth if you fixed the albedo and removed the greenhouse warming. It is common in these simple radiative balance calculations to hold the albedo at present day values and compare from there. The famous “255 K” value for no greenhouse effect on Earth is an example of this, although in reality if we got that cold you would expect a snowball-like Earth and a much higher albedo from the increased brightness of the surface…and thus the “no-greenhouse temperature” would be even colder than 255 K. You can’t model these feedbacks on the back of a napkin though so it’s not really an important point for simple descriptions.

    Comment by Chris Colose — 5 Jul 2010 @ 8:28 PM

  81. Hello RealClimate folks,

    I was delighted to read the second paragraph of this post: “… We can look at climate models, and they tell us what we can expect, but it is also useful to have an idea of why increased greenhouse gas concentrations result in higher surface temperatures…”.

    In other words, the fundamental reason scientists think atmospheric CO2 strongly affects the global temperature is not climate model output – it’s just *basic radiative physics*! Now, if you are an atmospheric scientist, this is taken for granted. But among the general educated public, it is my anecdotal impression that this has been largely missed, and that the public discourse gives the “climate models predict that…” wording rather than the “physics says…” wording.

    So, as a result, it seems to me (again informally) that almost all educated people, including technically-educated people who have had considerable college physics courses, needlessly lack confidence in the pronouncements of atmosphere and earth scientists about the reality of the global-warming threat. Now, here’s my point: to remedy this, I find that you rarely need to explain the whole nine yards laid out in this post! You merely have to say that it’s *physics*, and if they are technically-educated explain the general thrust of this physics (e.g. triatomic or larger molecules, which are scarce in the atmosphere, generally have vibrational modes that will be active in the IR, where Earth emits due to Wien’s law, and thus will act as a blanket or lid, and Earth would be 255K = -18C = 0F by Stefan-Boltzmann if this weren’t the case) and they go, “Oh, ok! Why didn’t anyone say that before?”

    If on the other hand they don’t know much physics, then it’s even easier… they know the power and track record of physics (e.g. electricity, nuclear power, gadgets, modern life, etc.) so they have confidence if it is said that “physics” is the reason for the CO2-climate connection.

    To illustrate this, could you imagine if during the effort to convince the U.S. government to embark on the Manhattan Project, the word “physics” was hardly ever used by the advocates of atom bomb development (who were simply known in this alternate reality as “nuclear *scientists*”), to such an extent that many well-placed non-physicists didn’t even realize that the claims of destructive power were based on it? I imagine they would have had a harder time convincing the government that this might actually work.

    So I guess I agree with the spirit of this post, but in some way I think you’re trying too hard. It’s just a simple matter of stating what we take for granted, but is not at all obvious to those outside our discipline–the *physical* (and chemical) nature of the science we do. “Earth science” or “climate science” does not have the same connotation, and sounds vague or untrustworthy or ungrounded to a lot of people.

    [I am a graduate student in the atmospheric sciences department of a large state university in the USA. Your contributors eric and raypierre know me.]



    Comment by Jack — 5 Jul 2010 @ 8:44 PM

  82. The Stanford research supports the other two sources AND provides a simple, reasonable (to a sociologist) explanation for the small decline based on analysis of hte data. I quote: ‘”Our surveys reveal a small decline in the proportion of people who believe global warming has been happening, from 84 percent in 2007 to 74 percent today,” Krosnick said. “Statistical analysis of our data revealed that this decline is attributable to perceptions of recent weather changes by the minority of Americans who have been skeptical about climate scientists.”‘, but still shows high levels of support.

    Comment by sue — 5 Jul 2010 @ 8:54 PM

  83. 74: Kjell. Please read the text and the caption. The predicted temperatures for the planets were calculated by neglecting the greenhouse effect. The Venusian temperature is not at all strange.

    Comment by John E. Pearson — 5 Jul 2010 @ 8:59 PM

  84. Keep it simple, use the approach that has already worked = CFC emissions. (a) state your objective clearly = GHG causes X, which is bad for humanity because of Y. In the case of CFCs, they cause X = UV increases at the earth’s surface, and Y = skin cancer & cataracts.

    This approach resulted in the Montreal Protocol, which is one of the most successful global efforts in history. We are at a disadvantage, since the short-term effects of climate change aren’t as nasty. Humanity has a hard time concentrating on the long-term.

    I often focus on oceanic acidification as a primary, here/now concern that most people can identify with. Very straight-forward, just pull out an Alka-Seltzer or equivalent & drop in a glass of water.

    Comment by CStack — 5 Jul 2010 @ 9:04 PM

  85. Kjell Arne Rekaa @72, although Venus is closer to the sun it has a much higher albedo than Earth, so it reflects more incoming solar energy back out to space before it can be absorbed.

    Comment by Jim Eager — 5 Jul 2010 @ 9:15 PM

  86. We have lots of opportunities to tell the story different ways, because there are lots of different people out there with differnt points of view and differnt notions of what is happening in the world. (One culd also say that there are many “audience segments” out there. )

    There is one set of facts that best expresses our current understanding of the physical processes, but there are a whole bunch of wildly differing sets of assumptions and mindsetsamong people that we need to communicate with.

    Please remember that most people do not have a college degree, but that this does not mean they are stupid.

    Comment by John Atkeison — 5 Jul 2010 @ 9:33 PM

  87. A minor point:

    “Molecules composed of three or more atoms tend to act as greenhouse gases because they can possess energy in terms of rotation and vibrations which can be associated with the energy of photons at the infra-red range.”

    could be improved as

    “because they can both absorb and emit infra-red light. When they absorb IR light they rotate or vibrate faster. When they emit it they lose the excess energy. Excited molecules can also lose energy by collisions, heating the atmosphere.”

    Comment by Eli Rabett — 5 Jul 2010 @ 9:51 PM

  88. Those looking for simple explanations of the greenhouse effect might try this java applet

    Or this equation free (two graphs) one or if you are not math averse, this one from Chris Colose

    Comment by Eli Rabett — 5 Jul 2010 @ 9:57 PM

  89. As you point out, many of the negative feedback effects that have been proposed would tend to decrease not only the effect of increased CO2, but also of whatever natural variability there may be. But this is also true of the positive feedback mechanisms that have been proposed, at least those that work through temperature as an intermediary. This would seem to pose a problem to any model that includes only positive feedback mechanism (and no “controversial” negative feedback mechanisms), for the climate has remained relatively stable despite the occurrence of natural variations such as volcanic veiling, solar variability, etc. Without negative feedback, a system will tend to have a dynamic much like that of a billiard ball balanced on a knife edge; any minor perturbation will send it hurtling off in one direction or the other. Thus, in view of the past stability of the climate system, the existence of negative feedback is not controversial, but rather an observed fact. This does not rule out the possibility that the negative feedback can be overwhelmed by other effects, but if we are to believe that, some explanation would be required. Your discussion leaves the impression that negative feedback is merely being dismissed as “controversial” and is not being addressed at all.

    Comment by Ron DeWitt — 5 Jul 2010 @ 10:36 PM

  90. It’s not in the presentation, gents, it’s in the false dichotomy. It’s in the lying. It’s in the spinning.

    So long as doubt is allowed to be presented as equal to truth, you haven’t a prayer. Until there is a large, undeniable response to denialism such that only that 30% will believe a shred of the lies and BS, you haven’t a prayer.

    Take legal action when the opportunity arises.

    Get the President on the TV and do a week-long series on the climate science and make the denialists look as bad as they are.

    I’m a teacher. Trust me, this isn’t an issue of presentation. They can see the melting Arctic, they have noticed the warmer winters, the earlier springs. This is about overcoming ideology. And fear.

    Doubt is easy to sow, hard to root out. If you don’t collectively hit back really, really hard, doubt wins.

    It’s that simple.

    But, hey, pretty pictures. An “A” for presentation. Once the seeds of doubt have been ripped out of the soil, they should be quite useful.


    Comment by ccpo — 5 Jul 2010 @ 10:46 PM

  91. From # 82

    “Statistical analysis of our data revealed that this decline is attributable to perceptions of recent weather changes by the minority of Americans who have been skeptical about climate scientists.”

    I rest my case.

    Comment by ccpo — 5 Jul 2010 @ 10:50 PM

  92. Figures 3 and 5 should give the temperature units (K and C respectively) along the vertical axis. It would be good to see units for the vertical axis of fig. 1 since there are numbers. The animation in Fig. 4 is quite good but I think there is a problem with the description. If the atmosphere is less transparent, that is increased optical depth rather than reduced. A perfectly transparent atmosphere has zero optical depth.

    This abstract which seems to simply state that BAU means everybody dies is intriguing: A post on it would be appreciated. Thanks and keep up the good work.

    Comment by Chris Dudley — 5 Jul 2010 @ 11:05 PM

  93. Thanks Eli :-)

    In addition, there is another blog by a physical chemist which has a multi-series post about radiation, absorption by gases, the GHE, etc which is very good but seems to have escaped the attention of the blogosphere. It is written at a fairly technical level but I encourage readers to have a look

    Comment by Chris Colose — 5 Jul 2010 @ 11:10 PM

  94. Guy says:

    Hey Gavin,

    This is my first reply to any Real Climate post. I became convinced that AGW was a major problem for the future of the planet back in the late 1980’s. I am one of the co-authors of the Records Study posted under the following credentials:

    “Relative increase of record high maximum temperatures compared to record low minimum temperatures in the U.S.”, was in Geophysical Research Letters.

    The complete citation is

    Meehl, G. A., C. Tebaldi, G. Walton, D. Easterling, and L. McDaniel (2009), Relative increase of record high maximum temperatures compared to record low minimum temperatures in the U.S., Geophys. Res. Lett., 36, L23701, doi:10.1029/2009GL040736.

    The public, especially in the U.S. has lost interest in the global warming issue mainly due to the fact that there has been a lack of extreme heat and major U.S. hurricane landfalls in the last few years. Our last major heat wave occurred in August 2007. Also, there has not been a major hurricane hitting the U.S. since Katrina, Rita and Wilma in 2005. Odds are that our “luck” is about to run out. The records study that I was a part of demonstrates, statistically, that deadly heat waves during the summer are becoming increasingly more likely. The study indicates that the ratio of record highs to record lows is increasing for every month of the calendar year: thus, during the summer months in the future record heat will be a more likely phenomenon than weather patterns that produce relatively cool conditions. The Northeast is currently in the throes of a major heat wave. The weather pattern in the Atlantic this season is conducive for above average tropical activity. I’m a meteorologist, not a climatologist, although I have taken a great interest in that field of science in the last decade. I think that it’s important to relate day to day and monthly weather with long term climate trends. Only then will be public become more inclined to pay attention to the issue of AGW.

    Thanks for keeping up the Real Climate site. I’ve enjoyed reading posts from the site for roughly the last five years.

    Comment by Guy Walton — 5 Jul 2010 @ 11:15 PM

  95. Re 89 Ron DeWitt and everyone – I think Ron DeWitt’s comment illustrates perhaps a common misunderstanding. Based on the definitions many would use, they would describe the climate system, as understood by climate scientists in general including the author of this post, as have a net negative feedback to forcings in general (that are not too idiosyncratic).

    In the convention of climate change jargon, one very important negative feedback is not counted as a ‘feedback’ because it is taken more as a ‘given’. This is the ‘Planck response’ – the change in emission of radiation as a direct function of temperature. When climate scientists state that there is likely a net positive feedback, they mean ‘besides the Planck response’. The Planck response is included in the basic physics and in conceptual, simple, and complex models. If this were not the case, then absent other sufficient negative feedbacks, climate sensitivity would be infinite. Given only the Planck response, climate sensitivity for a doubling of CO2 would be around 1 K. If the other feedbacks combine to be a net positive feedback as expected, then the (Charney**) climate sensitivity for a doubling of CO2 would be around 3 K, give or take 1 K. This is larger than 1 K, but it is still finite, indicating a stable climate (including the Planck response as a feedback, the net feedback is negative, but smaller than if it were only the Planck response).

    Comment by Patrick 027 — 5 Jul 2010 @ 11:41 PM

  96. Regarding the graph of planets – unnecessary to the main point, but it might help to know how the ‘surface’ temperature of the gas giants is defined. For something roughly analogous to terrestrial planets, that might be the temperature at a depth between where solar heating dominates and where the geothermal flux dominates.

    Comment by Patrick 027 — 5 Jul 2010 @ 11:47 PM

  97. I think I understand, Patrick. Do I understand correctly that in the way engineers and such use the term, the feedback can always be expected to be negative, and people’s fears that a catastrophic response to CO2 will destroy life on the planet are misplaced?

    Comment by Ron DeWitt — 6 Jul 2010 @ 12:01 AM

  98. Ray Ladbury @77

    Sun activity here (there are shed loads more if you take a mo to look):

    You ask where I get the idea that climate science is primitive (your words): Well, it appears that the more powerful the computers the more we know we don’t know. I’m not trying to be discourteous but please take a wider look at what’s going on and you may understand a bit more about why folks have lost faith.

    [Response: I'd recommend a reading of 'A Vast Machine' (2010; MIT press) by Paul N. Edwards. -rasmus]

    Comment by Titus — 6 Jul 2010 @ 12:21 AM

  99. Ron DeWitt (#89),

    Your comment is very confused, although admittedly, the discussion of feedbacks in the main post left way too much room for confusion unless the reader already knew what to make of it beforehand. Perhaps RC could do a related post that deals specifically with this issue. I will do a general outline here for anyone interested who has happened to stumble this far into the comments. Apologies for length…

    There are many radiative feedbacks: some positive, some negative. To be clear, rasmus was generally talking about the net effect. When we say “positive” and “negative” feedbacks in the sense of radiation (so I’m not talking about carbon-cycle responses such as methane release from the oceans or such) we’re referring to temperature-sensitive variables which themselves affect the radiation budget of the planet. Examples for clarification to come briefly. A “baseline” no-feedback scenario can be shown, through taking the derivative of the Stefan-Boltzmann law, to have a sensitivity of about 0.25 degrees Kelvin per W/m2 forcing. A doubling of CO2 (or close to a 2% change in solar irradiance) corresponds to a forcing of about 4 W/m2 and so the no-feedback response should be on the order of a degree temperature change. Whether the net effect of feedbacks is to be positive or negative depends on the temperature rise relative to this baseline. If the temperature increases by only 0.1 degrees for a 1 W/m2 forcing or 4 degrees per 1 W/m2 forcing, then you know the system is dominated by negative and positive feedbacks, respectively. We don’t generally call the Planck response (i.e., the increase in radiation with an increase in temperature) to be a “feedback” in the popular sense, because as I’ve just said, the “feedbacks” modify the Planck response (which is necessary to come back to equilibrium anyway). Part of the misunderstanding may come from the jargon used by the community, but we’ll have to deal with it. So, net positive feedback does not imply any runaway scenario (at least not a priori), it just means the temperature response is larger than what you’d get with just the radiative forcing acting.

    A net positive or negative feedback does not in itself say much about how prone the system is to being temperature-stable or prone to “running away.” The system can have a net negative feedback and still change very much provided a radiative forcing from sunlight or CO2 is sufficiently large, although for typical changes in these variables that Earth encounters, one would indeed expect only relatively small climate changes to occur if negative feedbacks did in fact dominate. Although the sensitivity of climate does change itself as the boundary conditions change, the past (PETM, glacial-interglacial cycles, etc) does not support sensitivities as low as 1 degree per doubling of CO2, and it doesn’t support very high ones (like 10 degrees per doubling) either. It does show that positive feedbacks are dominant, and for timescales of anthropogenic global warming about 2 to 4.5 degrees Celsius per doubling, and a bit higher if you include century-timescale “slower feedbacks” such as ice sheets. The primary radiative feedbacks are as follows–


    Water Vapor is a very important greenhouse gas, and the amount of it in the atmosphere is also strongly coupled to the temperature. We expect, through the Clausius-Clapeyron equation, that the specific humidity will increase roughly 20% in response to 3 degrees of warming provided the temperature and humidity vary in such a way as to keep the global relative humidity roughly constant. This is the most important feedback in terms of magnitude and it makes the Earth much more sensitive to climate changes of all sorts by making the OLR vs. T curve a bit more linear than T^4. This alone essentially doubles the sensitivity from the Planck-only radiation response. The extreme end of this, at very large optical depth throughout a deep part of the atmosphere, is when the OLR slope flattens out to a horizontal line and the outgoing emission becomes completely decoupled from the surface temperature, which is when a runaway greenhouse can kick in. Earth is quite far from this limit.


    Suppose the planet in consideration has a surface of high albedo surrounded (or on top of) a surface of lower albedo, and the extent of such a surface is temperature-dependent. This is particularly the case for snow and ice on Earth which tend to be surrounded by relatively dark ocean or vegetation. Decreasing the ratio of the high albedo to low albedo surface increases the solar absorption. Such an issue provides a positive feedback and also underlies the amplification of temperature in the Arctic, which has recently clearly emerged in observations. The loss of sea ice cover (dominated by extent and only slightly influenced by thickness) allows for a change in the heat fluxes between ocean and atmosphere (heat absorbed by the ocean in summer is released back to the atmosphere, growing heat transfer in the colder months as decades pass). It’s not very strong in the summer when energy is used for evaporation or melting but is particularly pronounced in the Autumn and should emerge even stronger in the winter as time progresses.


    As Rasmus noted, the strength of the greenhouse effect is sensitive to the vertical temperature structure of the atmosphere. Moist adiabats themelves change with temperature (see figure: changing the moist stability of the atmosphere. In the tropics which are prone to deep convection, the water vapor response to warmer temperature also promotes a less steep lapse rate owing to latent heat effects. This is the popular upper troposphere amplification or “hotspot” as is often discussed in connection with observation vs. models in the tropics. With a reduced lapse rate comes a reduced greenhouse effect (the situation is opposite at the poles but tends to be a negative feedback globally). This partially offsets the water vapor feedback and because of the strong coupling it is typical the combined WV+LR feedback instead of the two individually (interesting the model spread for WV+LR is smaller than either of the two feedbacks considered on their own). See figure:


    This is a big uncertainty in the climate system response and I don’t personally have a great background in all of the various model/observation/theory developments of the last few years. In brief, it’s complicated because clouds have different impacts (generally lower clouds cool since the albedo influence dominates and high clouds warm since their greenhouse role dominates) and also depends upon latitude and other things. Clouds exert a profound influence on the shortwave and longwave parts of the energy budget and trying to find the difference between two large and competing effects is problematic.

    The longwave component of cloud feedbacks being positive tends to be a robust result of models, and model spread is primarily from the shortwave part of the response. A compelling argument for the positive longwave response is a leading alternate to Lindzen’s IRIS although it receives less attention, and is known as the FAT hypothesis (from Dennis Hartmann) and arises from the fundamental physics of convection only heating the atmosphere where radiative cooling is efficient, and thus the temperature at the top of convective cloudiness should be near constant as it becomes warmer. There is some evidence (e.g., Clement et al, Science) for regional positive feedbacks from albedo, but there is no widespread agreement in the community or amongst models as to the size and sign of this influence. A related issue is that clouds are not readily resolved in GCM’s but must be parameterized, leaving room for a wide variety of plausible feedbacks.

    Comment by Chris Colose — 6 Jul 2010 @ 12:23 AM

  100. [All suggestions welcome. - gavin]

    Who is your target audience?

    Comment by EL — 6 Jul 2010 @ 12:41 AM

  101. Re: #2 or #3

    This is actually a big project. Teachers know not to produce something that tries to be all things to all people. Decide on content. Lay it out in the clearest way you can at your level, then take that and translate it for age/target. Have four or five of the same presentation, all at different levels.

    Likely best to recruit people to do the various levels who have the “knack” for that level. I realize that is sort of what you are doing, but it’s a bit haphazard. Define the audience for *this* iteration, design from there.

    Just a thought. Probably already thought.


    Comment by ccpo — 6 Jul 2010 @ 12:54 AM

  102. And there is no vacuum, there is only a lower concentration of matter. That is why the void of space has a temperature of 2 to 4 K.

    Where I come from, we study the subject first before shooting off… the vacuum of space “has” a temperature of 2.7 degrees because it is filled with black-body radiation at that temperature. Any matter present may equilibrate with that.

    Comment by Martin Vermeer — 6 Jul 2010 @ 1:49 AM

  103. “The records study that I was a part of demonstrates, statistically, that deadly heat waves during the summer are becoming increasingly more likely.”

    I think that the main issue for the public is : WTH does this have to do with the extinction of human race that is supposed to happen above some threshold ? “deadly heat waves” (in France at least, in 2003) has only abridged the life of weak and old people by some months – it has been almost exactly compensated by a decrease of mortality the year after. To my knowledge, the overall impact on the French population after some years has been statistically zero. And of course there have been many heat waves in the past.

    So the main issue for me is that all “serious” studies show only “statistical trends” having some effects on some measurable quantities , (slight increase of average temperature , slight increase of sea level , slight decrease of northern , but not southern , sea ice, ..), but actually none of this would have been noticed by average people in their all day life, if these studies wouldn’t have been done. If we wouldn’t we have modern satellites , network of thermometers, and so on, and we had asked people how their life has changed for 30 years due to climate, the general answer would probably have been :” climate? eeeeh? what are you talking about ?”

    The divorce between scientists and population starts here : scientist congratulate themselves for having found a statistically significant difference in 30 years data, but they have almost no influence on the all day life of most people.

    Comment by Gilles — 6 Jul 2010 @ 2:20 AM

  104. Gavin, thanks for the effort. You have distilled a good deal of difficult to understand information into a coherent whole, and as someone already pondered, this moderately intelligent physician has no major difficulty grasping most of it, but it does take quite a bit of mental effort to do so, and to follow your arguments. But here I must observe a contrary difficulty – one of the most vociferous, extreme and dismissive to the point of rudeness global warming deniers that I have ever met is a medial colleague of mine here in Wellington, he’s obviously not as intelligent as I am ;-), but he is a qualified doctor, and a very good one too. So our attitudes to global warming, GHE or whatever you call it, are not predicated by intelligence of the capacity to understand, but our capacity to refuse to do so and to rationalise this refusal. It’s difficult to know what motivates this man, a mature man, much of my age, married with a family, to so manifestly deny the patently obvious, which he does exactly in the same way as all the other contrarians, using the same spurious arguments, the same fallacies and the same plainly wrong information as all the other contrarians use ad nauseam -the sort of arguments that he would see through in an instance if advanced by homeopathy practitioners or iridologists.

    I think you are dealing in GHE with something that is immune to logic or intelligence or reason. Try telling a German before the Second World War for instance that following Adolf Hitler would lead to ruin, how many would have believed you? Or take your own country before your dreadful Civil War, how could so many in the southern states be so destructively stupid? The only thing that would change any of these people’s minds is their personal experience of the need to do so which, of course, is rather too late.

    I think it is the same with global warming. I don’t think it matters how “simply” or intelligently you present the science or the reasoning, or even the ethics, until the majority of people are inconvenienced or damaged by what is happening, they will not change their life-styles for any non-immediate threat, especially when they can rationalise their actions on the basis of the arguments around global warming, or in the case of those that do have a capacity to understand, their choice not to do so.

    As someone very concerned indeed about global warming, all I can do is fervently hope that there isn’t quite enough oil, or gas, or coal, or methane available to mankind to burn in sufficient quantities to make this planet entirely uninhabitable; that the high emissions scenario of the IPCC is itself fundamentally flawed because there aren’t enough fossil fuels available to power it, or that getting them productive would be so prohibitively expensive, or not producing sufficient energy out for energy invested, to make it worth while. Or that the oil leak in the Gulf of Mexico gets a lot worse over the next ten years, and so pollutes a vast area of the American continent that this change of mind is forced by other realities. Another worthwhile hope would be that continuing our dependence on the diminishing fossil fuels resources will produce such a profound and long lasting economic depression, the problem won’t arise.

    I’m sorry to be such a party-pooper, but I have on my side of the argument about 10,000 years of so-called civilised human history to back me up.

    Comment by John Monro — 6 Jul 2010 @ 2:27 AM

  105. Thank you, good to see the same explanation that was in my studies in university (on Environmental Protection Studies 1st year), but of course this course didn’t go to the details of Stefan-Boltzmann, optical depth measurements or Plancks law, these were explained in more detail in the spectroscopy courses, I took for the chemistry studies.

    One might also try to explain GHE thus: One builds a house, with an unheated greenhouse all around it, this doesn’t cover the roof of the house (this is for eliminating the direct heat transfer by gas movements, so the greenhouse mainly gets radiative heat transfer only). What happens to the temperature difference between the greenhouse and the house if one changes simple glazing to double glazing in the house? This situation is somewhat analogous to Stratosphere-Troposphere relation to me, the glasses have some optical depth (as does any material by spectroscopic principles, though for helium this is somewhat high).

    Comment by jyyh — 6 Jul 2010 @ 3:02 AM

  106. Your formula should be more exact if you took emissivity in account. This correction is of the same order of magnitude than GHG effect (a few percent).

    Also, why not to simply say that : Unlike major gases of the atmosphere, GHG (mainly water vapor) are heated by IR radiations and cool by IR emission and/or by convection. (This is never said in simple terms, physicians talk always about rotation and vibration of molecules and photons emission which is not very clear for most people).
    Convection acts so that temperature of surrounding gases and temperature of GHG become equal, while IR emission tends to decrease temperature of the whole system. But convection is less and less efficient when pressure decreases, while cooling by radiation is more and more efficient. So the amount of energy lost to space by radiation is proportionally more and more important when pressure decreases (at higher altitude). That explains why temperature is lower and lower with altitude.
    That is the (always simple) view of a thermic engineer who prefers radiation to photon emission and temperature to vibration and rotation of molecules.

    Comment by Pierre Allemand — 6 Jul 2010 @ 3:07 AM

  107. Spencer@63 wrote:

    For a super simple explanation to a general audience, I quote what John Tyndall wrote back in 1862:
    “As a dam built across a river causes a local deepening of the stream, so our atmosphere, thrown as a barrier across the terrestrial [infrared] rays, produces a local heightening of the temperature at the Earth’s surface.”

    This is essentially a 100% correct analogy.

    You highlight the problem by stating it is an analogy.
    Analogies, although useful, don’t explain the science. They are also open to ridicule by those opposing the science.

    I think it is important not to be afraid of explaining science as best as we can in all it’s glorious detail. However I do think scientists need help with good quality media producers and creators. Sadly I think sometimes media people shy away from the detail and do not know how to tell a story about the science (even though that is supposed to be their speciality!).
    I think sometimes this is due to their own misunderstandings of the science.

    Every so often though, the right scientist(s) and the right artist(s) or the right interpreter(s) of science manage to get together and do a good job.

    Comment by The Ville — 6 Jul 2010 @ 3:34 AM

  108. A great overview of the background of the GHE workings; thank you!

    Comment by Bart Verheggen — 6 Jul 2010 @ 4:43 AM

  109. “Optical depth” is greater with more GHGs. The definition is:

    tau = k rho ds

    where k is the extinction coefficient, rho the density of the absorber or scatterer, ds the distance. Clearly greater rho of the GHG means GREATER optical depth.

    If you mean “reduced distance at which tau = 1,” you’ll need a new term.

    Comment by Barton Paul Levenson — 6 Jul 2010 @ 4:46 AM

  110. I think I have to side with the folks that say this post doesn’t really work–and I hate to say that about ANY RealClimate post. But it is too complicated for anyone who isn’t interested in learning about science in the first place. The target audience should be those who

    A) do NOT have any particular interest in learning more science, but

    B) want a clear explanation of how the greenhouse effect works. Just enough and no more.

    I’d go with something like this:

    * * *

    Radiation physics is very well understood. We know, from how far Earth is from the sun, and how much light it reflects, that it should be a lot colder than it is. The French physicist Jean-Baptiste Fourier first noticed this in 1824.

    The greenhouse effect keeps Earth warm enough to be habitable. Some gases in Earth’s atmosphere–mostly water vapor and carbon dioxide–let sunlight pass through mostly unhindered, but absorb infrared light from the ground. That heats up the atmosphere, and the warmer atmosphere warms the Earth, as well. And the more of these “greenhouse gases” or “GHGs” in the atmosphere, the warmer Earth’s surface gets.

    With a very few exceptions, every material object above absolute zero radiates! Really hot things, like the sun, radiate visible light. Things at room temperature, like the Earth’s surface, and you and me (!), radiate less powerful infrared light. And gases are material objects! When GHGs absorb infrared light from the Earth, they warm up–and that means they radiate more. And some of that radiation goes right back down to the Earth. So Earth has both sunshine and “atmosphere shine” warming it. The more GHGs, the more “atmosphere shine.”

    The energy isn’t coming out of nowhere. It all comes from the sun, but it stays in the system longer, and gets distributed differently, the more GHGs you have in the atmosphere. We’ve been adding GHGs by burning fossil fuels, and as a result, the Earth has gotten warmer. And that could be a big problem. Our agriculture and industry are exquisitely adapted to the relatively stable temperatures we’ve had for the past few thousand years. Raise the Earth’s average temperature just a degree or two, and you can move agricultural growing belts hundreds of miles! And it moves the rain. We could wind up completely crashing our agriculture. No food.

    Sea-level rise is a long-term danger of global warming. But drought is one we’re already having trouble with–ask the Australians! Without hurting our standard of living significantly, we can get all the power we need from other sources–solar, wind, geothermal, biomass. But if we just let things go on as they are, burning more and more oil and coal each year, we’re going to be in serious trouble.

    Comment by Barton Paul Levenson — 6 Jul 2010 @ 5:04 AM

  111. I’ve revised the explanation I posted to make it simpler still, without making it stupid. It’s now posted at my web site:

    Comment by Barton Paul Levenson — 6 Jul 2010 @ 6:25 AM

  112. Hi,

    I’ve been using the solar flux and planck’s law and ground heat conductivity and capacitance to build a (very simple) ‘climate’ simulation model that showed the energy exchanges over a day. I began with no atmosphere, and now I want to add one.

    I started off thinking that maybe I could treat the atmosphere like I was treating the surface of the earth, as a black body which had an emissivity and temperature and heat capacity. I looked around for some equations to tell me how much solar energy got absorbed by the atmosphere, and how much of the IR emitted by the surface of the earth got absorbed in the atmosphere. I’ve not managed to find these equations yet.

    But I have a new problem. From what I’m reading, CO2 absorbs photons of a particular energy, and no other. And then it re-emits photons of the same energy in some random direction. While a CO2 molecule is ‘holding’ a photon, it remains in an excited state (variously described as electron orbit shifts or inter-atomic bond flexings). It’s not at all clear to me that this excited state corresponds to an increase in temperature. It seems much more like photons are captured by CO2 and re-emitted (much like footballs are captured by soccer players and then kicked away to be captured by some other players).

    So which is it? Do photons from the surface of the earth heat up the CO2 molecules that absorb them (where heating up would mean making them move faster), and transmit this heat to other air molecules by collision. Or is it that photons are captured by CO2 molecules, and the captured energy stored internally in the molecule (like energy is stored in a spring), until released as a photon of the same energy?

    Comment by idlex — 6 Jul 2010 @ 6:48 AM

  113. 72 Bob Doppelt: You added a “)” to a URL so it won’t open. Thanks for doing research on communication for GW. It is sorely needed.

    Comment by Edward Greisch — 6 Jul 2010 @ 7:09 AM

  114. BPL, yes I was thinking of that, strike over the last sentence concerning Helium) in my prev post and change accordingly (that’s for not tackling optics in the university).

    Comment by jyyh — 6 Jul 2010 @ 7:13 AM

  115. Some nice formulations in the comments here–Jim Harrison back at #16, Chris Colose on feedbacks (#98, I think), Pierre Allemand (#105) and Barton just now at #109, as well as others. Thanks to all–very useful!–and of course to rasmus, too, whose essay succeeds IMO, though not at the simplest possible level. (The trouble, I think, is that “no simpler than necessary” necessarily invokes subjective value judgments, some of which are illuminated by the various alternate formulations such as those that I listed.)

    Comment by Kevin McKinney — 6 Jul 2010 @ 7:14 AM

  116. BPL,

    I don’t see why RC shouldn’t also cater to those who do have a particular interest in learning more science.

    It will indeed be more complicated to cater to different audiences with different posts, as some audiences will like one post and not another. The alternative, to only cater to the not-so-interested-in-learning-science, would be a missed opportunity.

    One might even say that those who are interested in the science are a very important target audience, as they could be very important in shaping other people’s opinions in their personal network. As Michael Tobis has noted ( ), currently a large fraction of this group (scientifically literature layfolk) are taken in by the likes of McIntyre. We should perhaps do more, not less, effort to educate them with the basics so that they’re not as easily swayed by the scientifically-sounding-but-in-the-end-not-so-scientifically-sound “skeptics”.

    I wrote down some thoughts about this group of skeptics (“citizen scientists”) on my blog here:

    Comment by Bart Verheggen — 6 Jul 2010 @ 7:21 AM

  117. That should be “scientifically *literate* layfolk” of course…

    Comment by Bart Verheggen — 6 Jul 2010 @ 7:23 AM

  118. Can I ask a really basic question about the vibration bending mode of CO2 and it’s energy levels?

    Am I right in saying that CO2 has 4 energy levels that correspond to IR radiation absorption?

    Does this mean it can absorb up to 4 IR frequency photons (hence causing vibration), after which it effectively becomes IR transparent?

    eg. under intense IR radiation CO2 will effective ‘fill up’ and become saturated, unable to absorb any more until it has emitted some IR photons?

    Answers from commentators or blogging scientists would be apprciated.

    Comment by The Ville — 6 Jul 2010 @ 7:28 AM

  119. Eli is too modest to mention his own helpful contribution. Here’s his simplest explanation FYI.

    Comment by Mike Donald — 6 Jul 2010 @ 7:31 AM

  120. For those complaining that the article is too mathematical etc.: remember, there is a large group of scientists out there who need to be reassured that the basic science is correct. Many of these people are in other fields, retired, etc., and may not have the time, resources or inclination to read a text book or do a detailed literature survey. Material like this is great for that group, as well as for science journalists who know enough to read a few equations.

    Others whose skill is more in communication to the nonscientist can take it from here, but I found this a useful summary (PhD computer science, working with biologists, involved in Green politics – not illiterate but by no means an expert). Thanks very much for the time and effort that went into this.

    One point I really like to emphasise when talking about the science is that we are not talking about a theory of AGW, but a theory of climate, which predicts AGW. This is important because it emphasises that AGW is something that is not a peculiar discovery that can be knocked down by attacking a few trivia.

    Comment by Philip Machanick — 6 Jul 2010 @ 7:36 AM

  121. Gilles #102: many scientists do influence everyday life of ordinary people, including biologists, who work to a much lower standard of evidence than you advocate.

    Comment by Philip Machanick — 6 Jul 2010 @ 7:38 AM

  122. I think you have missed the mark as far as understanding why John Q. Public does not worry about global warming. The reason he doesn’t need to worry is explained here:

    Comment by bestquest — 6 Jul 2010 @ 7:50 AM

  123. idlex, one thing you are missing is that most CO2 molecules relax not by emitting a photon by by colliding with, say a Nitrogen, molecule and imparting the extra energy to that molecule. You can look at this in terms of equipartition. The IR flux from the warmer surface excites much of the CO2–much more than would be excited at thermal equilibrium at the temperature of the atmospheric layer where the photon is absorbed. To move toward equilibrium, the CO2 then has to impart energy to the surrounding gas. Make sense?

    Comment by Ray Ladbury — 6 Jul 2010 @ 8:15 AM

  124. A nice, simplified explanation suitable for a high school graduate, or perhaps a grade or two less.

    Of course, the willfully ignorant stopped reading after the first sentence.

    Do you expect to improve things when you appeal to a minute minority between those who are smart enough to understand the science and who are already convinced, and those who will remain willfully ignorant to the grave?

    Your chosen method might make some progress over the next 30 to 60 years, as it has with smoking.

    I think progress is needed at a slightly faster rate.

    Don’t you?

    Where is the AGU or the APU review of the scientific merrit of the Trash coming from Inhofe’s office of disoonfirmation?

    Rapidity requires breaking some heads.

    Polite explanations are just more of the same failure that has been tried before.

    Comment by Veidicar Decarian — 6 Jul 2010 @ 8:18 AM

  125. Further to my #92:

    In the section ‘Enhanced greenhouse effect’ The first sentence is incorrect. ‘reduced optical depth’ should read ‘increased optical depth.’

    The sentence starting ‘The effect of heightened level of heat loss’ is awkward since it is not a matter of increased heat loss but rather a changed altitude where heat loss mainly occurs. ‘The effect of heat loss from a higher altitude’ might be better.

    The sentence starting ‘Hence reduced optical depth explains’ is both incorrect and somewhat incongruent with the next link. Something like ‘Hence increased optical depth, particularly from a well mixed gas like carbon dioxide which affects the altitude of heat loss, explains’ might get the idea across better.

    In the section: ‘So why is the upper atmosphere cooled then?’ I think either mention ozone destruction as a current cause or say the subject is complicated and link here:

    Hope that helps.

    Comment by Chris Dudley — 6 Jul 2010 @ 8:43 AM

  126. bestquest:

    Nice troll. Sorry, nobody is falling for it. Bye bye.

    Comment by Didactylos — 6 Jul 2010 @ 9:25 AM

  127. Great post! As someone who has a long unused undergraduate degree in chemistry, the level of math and physics in this post was near perfect for me. I can understand the complaints by some that the post was too complex, but I appreciate your efforts to provide information at different levels. Keep up the good work.

    Comment by MarkLPolska — 6 Jul 2010 @ 9:37 AM

  128. Martin Vermeer, radiation has what has been defined by convention of convenience as a “characteristic” temperature. It is not a real temperature in the common physics accepted meaning. Ray’s answer was more apt.

    Comment by Rod B — 6 Jul 2010 @ 9:53 AM

  129. @Ray Ladbury

    I understand what you mean, but you’re the first person I’ve encountered who’s said that. Got a link?

    Comment by idlex — 6 Jul 2010 @ 10:03 AM

  130. idlex asked:”Am I right in saying that CO2 has 4 energy levels that correspond to IR radiation absorption?

    Does this mean it can absorb up to 4 IR frequency photons (hence causing vibration), after which it effectively becomes IR transparent?”

    Ray’s answer was about why multiphoton absorption is not important, however, I will answer your particular question about your understanding. Multiple photon absorption is certainly possible for each vibration. In IR spectroscopy there are “hot bands” (where the first excitation is presumed via thermal) for quantum number v=1 to v=2. This frequency is almost the same as the fundamental absorption (v=0 to v=1), so the hot band peak may be difficult to see within the fundamental band.

    Electronic absorption has a tendency to “bleach out” like you describe.

    Comment by t_p_hamilton — 6 Jul 2010 @ 10:42 AM

  131. Thank you for the answers! I think I understand, but this article is sign that I need to go back relearn the basics.

    Comment by mircea — 6 Jul 2010 @ 11:00 AM

  132. Ray : “The IR flux from the warmer surface excites much of the CO2–much more than would be excited at thermal equilibrium at the temperature of the atmospheric layer where the photon is absorbed.”

    actually if the medium is optically thick , the IR flux has a characteristic radiation temperature from the location where it was emitted, that is around one mean free path away. It may be not “much more” if the optical depth is high enough (the order of magnitude is ∆T = l.grad T = grad T .h/tau ) ; it can be a small difference for high tau , but it insures the gradual transfer of heat from one layer to another one. That’s the essence of diffusion approximation.
    The fact that the energy of a photon is most often transferred by collisions to other molecules does not really matter, since it means that collisions can also excite molecules that will sometime emit a photon – both process cancel exactly in LTE. In thermal equilibrium, there is no net “heating” in the sense that the atmosphere would gain temperature, the temperature is steady on average everywhere. This is really a transport process, heat flows throughout the atmosphere but without temperature variation. Locally, absorption and emission do cancel exactly : only the DIRECTION of photons is slightly anisotropic : a little bit more photons come from the lower, hotter layers and a little bit less from the upper, colder ones. They are reemitted isotropically, so the budget is slightly positive outwards and negative inwards , but vanishes when integrated on all directions. The net result is a transport outwards.

    Comment by Gilles — 6 Jul 2010 @ 11:03 AM

  133. #110 BPL
    Excellent clear post and pitched just right for the general public such as me (although I would politely suggest fewer exclamation marks! They come over a touch patronising).

    I am with you all the way until you get to this bit:
    But drought is one we’re already having trouble with–ask the Australians!

    Actually, over the last 110 years average annual rainfall totals have (apparently) been on an upward trend. Variability over the last 40 years has been more pronounced (though that may have more to do with more accurate and extensive measurement).

    I can easily find this graph:
    and there are others on the net showing the same thing, although the Australian Met Office rather unhelpfully does not have one.

    The problem for Australia is less to do with climate change driven drought and more to do with water shortage. Easily confused but very different cause.

    They have a big problem of chronic over-use of scarce water resources, both for farming and rapidly expanding cities. This means that when of their perfectly normal occasional droughts hits they are much more vulnerable to its effects.

    We must be very careful not to repeat easily falsifiable climate change myths like this as that simply plays into the hands of the likes of WUWT and their ilk.

    Keep up the good work, your site are an invaluable source of good data.

    Comment by Matthew L — 6 Jul 2010 @ 11:32 AM

  134. Gilles says “…both process cancel exactly in LTE”

    Yup, but by definition as we add greenhouse gasses, we depart from equilibrium, so the processes do not cancel and there is a net flow of energy from radiative to kinetic.

    Comment by Ray Ladbury — 6 Jul 2010 @ 11:35 AM

  135. idlex, the gist of the argument is here.

    Basically, it comes down to the long lifetime of CO2 in its excited state–much longer than the collision time.

    Comment by Ray Ladbury — 6 Jul 2010 @ 11:41 AM

  136. Found one from the Aussie Govt clearly showing the upward rainfall trend.

    If that link does not work try this tinyurl:

    Comment by Matthew L — 6 Jul 2010 @ 11:41 AM

  137. Rod B #128, don’t try to confuse the issue. You know damn well what I meant. And so, I hope, do the other readers.

    Comment by Martin Vermeer — 6 Jul 2010 @ 11:58 AM

  138. A “scientific fact” thrown around is that at current levels CO2 is already at 97% of its absorption limit and therefore further CO2 makes little more difference. The analogy of putting on a second ski hat is offered.
    I do not understand (and maybe they don’t!)where this plays in the science and whether or not it has any substance as an argument. Apologies if this is too basic to merit comment.

    [Response: Not facile at all. Indeed, that you suspected that the '97%' (or sometime '98%') number is bogus is to your credit. The fact is that you can keep increasing CO2 forever and it will not saturate in this sense (see Venus for an example). CO2's effectiveness per ppm does decrease as you go to higher concentrations (which is why we discuss the sensitivity to 2xCO2 rather than per 100 ppm for instance), but this is very well understood and has been incorporated into the models from the beginning. - gavin]

    Comment by john aislabie — 6 Jul 2010 @ 12:16 PM

  139. Mr. Rasmus,

    I found this entry on the following blog. A study ( ) Published in the Proceedings of the National Academy of Sciences confirms what people who have been paying attention already know:
    97–98% of the climate researchers most actively publishing in the field support the tenets of ACC outlined by the Intergovernmental Panel on Climate Change, and (ii) the relative climate expertise and scientific prominence of the researchers unconvinced of ACC are substantially below that of the convinced researchers.

    Furthermore, researchers with fewer than 20 climate publications comprise ≈80% the UE group, as opposed to less than 10% of the CE group. This indicates that the bulk of UE researchers on the most prominent multisignatory statements about climate change have not published extensively in the peer-reviewed climate literature.

    If these claims are true…does that not suggest that restraint & caution are indeed needed in light of the Fact that reformating the economies of both the developed and developing world, are not without their own set of dire & destabilizing consequences?

    Comment by A. Ros. — 6 Jul 2010 @ 12:20 PM

  140. I can’t understand climate science. I never took Physics, and I am a senior citizen. Still, I try to keep up on new developments in science.
    I’ve voted Republican for many years, but that may change.

    I know that scientists are a lot smarter than I am and that they aren’t communists plotting against me. So-called “conservatives” who are saying this do not speak for me.

    The Guardian seems to be pretty sure that much of the blame for this propaganda is coming from the U.S. Maybe we have met the enemy and he is (the)US.

    Still, I never hear you all discuss the Russian oil/gas politics. Do you really think the Russian monopolies or the Russian government won’t mount the sort of political operations that the American corporations seem capable of? I read the American scientists complain about the “right wing,” in the Guardian, but they don’t seem to realize that the “right wing” is saying exactly the same thing as the Russian media. They even cite some of the same scientific “experts.”

    At first, the Russian media bragged about the Russian hackers. They stopped bragging when the FSB (domestic security) denied it was involved. But maybe the SVR (foreign intelligence service) mounted this from the US.

    It is no accident that Pravda and Russia Today really played up Climategate in both their Russian and English-language media. People from the CATO Institute appeared on Russia Today in English. Pravda is quoting FOX. Media in Russia is often owned by the oil/gas industry and the political line is controlled by Russia’s ruling Unity Party. Gazprom is half owned by the Russian government and pays the government’s bills. President Medvedev is the former Chairman of the Board of Gazprom. They have a lot of power. So maybe talk about Gazprom when you talk about Exxon.

    Why don’t you discuss the scientific fallacies in some Pravda articles or Russia Today programs?

    Historically, some anti-scientist campaigns have come from Russia, tho’ America has its share among religious fundamentalists and conspiracists.

    The Guardian says the hacking happened from the East Coast of N. America, but that doesn’t mean an American individual or entity did this. There are tens of thousands of computer experts in America who are not Americans. Eleven of them seem to have been Russian agents. So far, the FBI only told the court enough to arrest them for probable cause. That’s right in the complaint.

    Russian operatives (usually the military intelligence) steal secrets, but the KGB and its successors also run influence operations.

    The very shrill tone of this Climategate hysteria sounds exactly like the short-lived Stalinist KGB Doctors’ Plot (Jewish doctors were supposedly plotting to exterminate the Soviet leaders) or the KGB lie that crafty Pentagon scientists cooked up AIDS as an instrument of genocide.

    In both those cases, the KGB finally admitted there was no substance to the conspiracy theories and threw their collaborators under the bus. Even the Russians have to face reality and solve problems.

    Just my personal view.

    Comment by Snapple — 6 Jul 2010 @ 12:31 PM

  141. Scientists disastrously overestimate their ability to communicate their findings to non-scientists. Their idea of what a simple but adequate explanation of something would be is far beyond what most adults can understand. I recommend the following experiment: assemble a group of well-educated non-scientists and give them a half hour lecture on any real scientific topic you choose. Write down an estimate of how much of your message was communicated and then share this prediction with your audience. The results will obviously vary, but the typically outcome will be that the scientist will be afraid that he or she was guilty of patronizing the listeners by oversimplifying too much while the lay audience will express utter bewilderment. So much of what technical people take as obvious is news to the general public.

    In the (very good) explanation of the effect of greenhouse gases that begun this thread, we read that “Molecules composed of three or more atoms tend to act as greenhouse gases because they can possess energy in terms of rotation and vibrations which can be associated with the energy of photons at the infra-red range.” Unfortunately, the concept that particular molecules emit radiation at wavelengths dependent on specific modes of vibration and rotation is news to people who don’t know how electromagnetic waves are produced (ask ‘em!). Of course you can explain about modes of molecular vibration and rotation, indeed you can explain everything eventually, but it not only takes time and many sentences to unpack these concepts, it takes time to comprehend them, years, in fact.

    Comment by Jim Harrison — 6 Jul 2010 @ 12:44 PM

  142. I should add that Russian scientists publically dissociated the Soviet Academy of Sciences from the AIDS propaganda in 1987, long before the KGB’s 1992 admission that it had spread this lie.

    The Russian scientists stood up to the KGB, so this is really your fight.

    I support you and believe you because I can see enough of the other side’s TRICKS, but you can’t really expect ordinary people to see through all the sophistry.

    I think scientists are doing pretty well, but keep it up.

    If it’s the Russians, they will probably come clean long before Monckton or Morano do. After all, they have to run their country and they can’t look like total idiots to their own scientists.

    Comment by Snapple — 6 Jul 2010 @ 12:50 PM

  143. @139 Huh? How does you suggestion of proceeding cautiously follow from the findings you quote. The findings indicate that the more an expert understands the evidence, the more he/she finds it convincing that we are warming the climate and that this is an issue. Maybe you want to revisit that post or just chalk up an “own goal”.

    Comment by Ray Ladbury — 6 Jul 2010 @ 12:57 PM

  144. Gavin said, “Not everything needs to be written for everyone to understand.”

    But this is an attempt to reach those who don’t know or care what the Stephen-Bosnian whatever constant is. At best, math stopped with Algebra2, and that was a decade ago.

    One of the best lines in the post was, “Energy is also transferred through vertical motion (convection), evaporation, and condensation too (latent heat), but that doesn’t affect this picture, as they all act to restore the vertical structure toward the hydrostatically stable lapse rate in the long run.” Add a few sentences of explanation and you’ve got a grand answer to a core skeptic argument. Add answers for each of the Skeptics claims and you’ll end up with a stellar first primer. Provide a link to this post for those who care about Stefan-Boltzman and everyone’s happy.

    Comment by RichardC — 6 Jul 2010 @ 1:32 PM

  145. I have written a brief response to the comments here focusing on communication style and level of technicality of Rasmus’ effort.

    Rasmus and all are welcome to offer opinions…

    Comment by Chris Colose — 6 Jul 2010 @ 3:09 PM

  146. Hi!

    I suppose I agree with the comment above that your explanation here is too complex for many segments of the population, though if you were in fact going for a particular segment (the educated? Doctors? Amateur scientists?) maybe it’s okay.

    The problem I see (as a communications scholar and a social scientist) is two-fold. One, you start out pretty slippery in terms of who you are aiming at as your audience, and why you’re aiming at them in particular. Having a clear sense of Audience and Purpose are key elements of basic communication.

    But I think the much bigger problem is that there is no “basic communication” when it comes to climate science. I don’t think we can assume that if people/the public/laypersons (whatever audience you are defining) have the same information as us (the “educated,” the scientists) they will agree with us. There’s loads of social science out there indicating that things like values are more important predictors of viewpoint and policy attitudes than scientific knowledge.

    I’m not saying science education isn’t important, of course. But having a more informed public shouldn’t have to be the prerequisite for democratic debate or science policymaking. If scientists wait for the public to be as well-informed as this post supposes in order to move forward with the science policy scientists want, they’ll be waiting for a long time.

    I guess I would argue for improved forms of public dialogue and participation as much for improved science literacy (see for an example). But engagement is a lot more work intensive than just saying the public needs to understand better.

    I sound overly harsh, and don’t mean to. I think you do great work. I hope I’m being constructive and not overly critical.


    Comment by Jen Schneider — 6 Jul 2010 @ 3:15 PM

  147. Question: Is pressure broadening really secondary?

    In other words if you ran a model at zero pressure (as far as the spectra are concerned) would it really make little difference?
    Are we really being invited to suggest improvements? It would be an interesting example of collective teaching. I’m not surprised at the number of critical comments given the potential size of the team.

    I support the person who wanted this deleted:

    (unless it involves nuclear reactions or takes place on quantum physics scales).

    Why attract criticism?

    At first glance I thought of the following ignorable suggestions:

    It might perhaps be easier for beginners if it was preceded by a qualitative discussion/summary of the energy balance of the whole globe rather than jumping straight into the distinct issues of tropospheric warming and upper atmospheric cooling.

    E.g. “it all boils down to the fact that cool bodies emit less heat than hot ones and as we have seen (shall see) the radiation escaping from a greenhouse planet tends to come from higher in the atmosphere where it is cooler”; if less energy escapes the globe as whole will warm (on average)until…..

    The next bit might come as a shock to those used to seeing the over-simplified discussions. It might be worth softening this by some additional comments such as:

    (a) the vertical distribution of the enhanced effect is important to understand because observing it can be used as a finger-print.
    (b) The greenhouse effect involves two mechanisms, absorption (normally emphasised) and emission (occasionally omitted from the discussion although vital to the physics) .
    (c) A possible mechanism for cooling which can be understood easily is when, for some reason, the first of these is unimportant for the energy balance of a small volume of gas. For example if the temperature is being determined by a short wave heater from above rather than a long wave heater from below. In that case we might as well start by ignoring the latter altogether. The cooling follows.

    I know that you can’t cover everything, but most of the discussions you see in the blogs rapidly move on to feedbacks, so I suggest that this section might be extended and deepened a bit. Otherwise you may be confronted early on by Lindzen’s disciples. After all the positive feedbackfrom water vapour was in the theory from its inception and is now more secure than before.

    Comment by Geoff Wexler — 6 Jul 2010 @ 3:22 PM

  148. Re 97Ron DeWitt Do I understand correctly that in the way engineers and such use the term, the feedback can always be expected to be negative, and people’s fears that a catastrophic response to CO2 will destroy life on the planet are misplaced?

    1. The feedback can become zero – or to avoid confusion regarding what is and is not a feedback – the equilibrium climate sensitivity can become infinite (or negative) in some conditions. That is refered to (in climate terms) as a runaway feedback. This isn’t expected to occur for present Earth-like conditions or a range of conditions encompassing that.

    Also, when runaway occurs, it occurs over some range until it reaches a limit and then stops. For example, if the Earth got cold enough, the encroachment of snow and ice toward low latitudes (where they have more sunlight to reflect per unit area), depending on the meridional temperature gradient, could become a runaway feedback – any little forcing that causes some cooling will cause an expansion of snow and ice toward lower latitudes sufficient to cause so much cooling that the process never reaches a new equilibrium – until the snow and ice reach the equator from both sides, at which point there is no more area for snow and ice to expand into. (There are equilibrium climates between the points where the runaway starts and where it ends, but they are unstable equilibria, and the equilibrium coverage of snow/ice increases with forcing that would cause warming.) Once the ice reaches the equator, the equilibrium climate is significantly colder than what would initiate melting at the equator, but if CO2 from geologic emissions build up (they would, but very slowly – geochemical processes provide a negative feedback by changing atmospheric CO2 in response to climate changes, but this is generally very slow, and thus cannot prevent faster changes from faster external forcings) enough, it can initiate melting – what happens then is a runaway in the opposite direction (until the ice is completely gone – the extreme warmth and CO2 amount at that point, combined with left-over glacial debris available for chemical weathering, will draw CO2 out of the atmosphere, possibly allowing some ice to return). The combination of such freezing and thawing is an example of hysteresis, where the equilibrium climate for a given ‘external’ forcing is different depending on prior history.

    2. It is possible to have runaway effects over shorter ranges. On the very small scale, one could have a runaway between whether or not a weather pattern has a thunderstorm at a specific time and place or whether it is dry and sunny at that specific time and place – but that’s not the same as a change in climate (see internal variability, chaos, butterfly effect). It’s possible to imagine a scenario where, once we hit x degrees of warming, we hit a runaway process that jolts us some additional y degrees of warming, and then stops. I’m not saying that’s expected though.

    3. The approx. 3 K expected warming for a doubling of CO2 or equivalent forcing doesn’t include some longer-term processes and also doesn’t include feedback via CO2 or CH4 themselves. The sensitivity of the climate system to human activity (ie how much fossil C we emit, etc.) can be a bit different – especially in the more distant future trajectory. Charney sensitivity refers to the climate sensitivity when fast-reacting feedbacks (Planck response is a given – also, water vapor, clouds, … I think sea ice, seasonal snow) occur but with other things (land-based ice sheets, … vegetation(?)) held constant. Charney sensitivity can be expressed for such forcings as CO2 changes; longer term processes involve CO2 as a feedback (ice ages).

    4. Depends on what you mean by ‘destroy’. From either human activity or likely natural forcings out to some hundreds of millions of years, extinction of all life is quite unlikely (so far as I know) – needless to say anhilation of the Planet Vogon-or-Death-Star style is even less likely still. A mass extinction, however, is possible, though I’m not sure if it’s expected for BAU AGW. A smaller extinction event might be more likely(?). (Of course, other anthropogenic pressures besides climate change (and ocean acification) are/will be contributing to extinctions.) However, it needn’t take a significant extinction to make things unpleasant. If a wild species survives but in low numbers, that might be a loss of food or some other ecosystem service for us humans. Plus, there’s the direct effect of climate change (and associated sea level rise) on agriculture and infrastructure and living. So destruction of wealth (conventional and otherwise) and health is a very real concern.

    Comment by Patrick 027 — 6 Jul 2010 @ 4:12 PM

  149. It does seem that many readers are not aware of the molecular processes that play around in a “vacuum”. As Gavin showed, even when assuming a ridiculously low effect, it still boils down to a yearly 800 mm of ocean evaporation. What Gavin, the joker, did not mention was that most of the evaporated water came back to earth by precipitation. In the mean time, it carried enough energy into the upper troposphere where it could be emitted into space. As for molecular cooling, when a hot gas comes into contact with a very dilute, very cold gas, energy is exchanged with every collision, cooling the hot gas down to slightly above the temperature of the surrounding diluted gas, thus tranferring lots of energy to the upper layers of the atmosphere, as Gavin calculated. From these layers it will be emitted to the background temperature of space. Concluding: not only radiative process contribute to the transfer of energy from the surface to outer space.

    [Response: The numbers above aren't quite right - I've corrected them though. The answer is still that there is no climatically important contribution of latent heat flux to the flux to outer space. You are getting confused between fluxes that are important at the surface and fluxes that are important at the Top of the Atmopshere (TOA). There are multiple non-radiative energy fluxes at the surface (latent and sensible heat fluxes predominantly) which obviously affect the atmospheric temperature profiles, but when it comes to outer paces, that flux is purely radiative. - gavin]

    Comment by Iskandar — 6 Jul 2010 @ 4:40 PM

  150. Section ii states: “The planetary energy balance says that our planet loses heat at the same rate as it receives energy from the sun (otherwise it would heat or cool over time). This is because energy cannot just be created or destroyed (unless it involves nuclear reactions or takes place on quantum physics scales).” This appears to state that the energy content of the entire Earth system remains constant, so that energy gains for the troposphere/land surface/ocean are precisely offset by energy loss for the stratosphere. This obviously is true at equilibrium, but the quotation appears to state that it is true continuously, that is, there are no transient imbalances. Do I correctly understand the point?

    Comment by Robert Means — 6 Jul 2010 @ 5:06 PM

  151. One of the largest problems with keeping concern up for AGW within the public is the policy that goes with it, not the science itself.

    The solution domestically seems to consist of A) raising taxes (such as on gasoline and electricity) and B) inventing new taxes (carbon taxes).

    The solution globally seems to pretty much consist of handing over large sums of money to “developing” countries, with the USA tagged to pay most of it.

    It looks to the average Joe to just be another excuse for a money grab out of his pocket. I don’t know if y’all are keeping up with the economic news, but folks aren’t real excited about having to pay more for things or have the government just hand over huge amounts of cash to some of the most corrupt nations on the planet under the guise of “saving the planet.”

    Comment by Frank Giger — 6 Jul 2010 @ 5:08 PM

  152. Dear Gavin,

    I am not getting confused, you are. In a “vacuum” a “hot ” molecule can travel a long way, losing kinetic energy due to increasing gravitional energy. It will collide with an other molecule, exchanging energy, thus cooling down. Both can and will emit IR radiation when in in excited state, going down in temperature in the process. It is exactly this process which has made sure that Earth still has an atmosphere.

    Comment by Iskandar — 6 Jul 2010 @ 5:11 PM

  153. That is far too complicated for consumption by the general public. Right up front you define photons as electromagnetic radiation going above most folks’ heads. Conduction? Is that like convection? Etc.

    I’ve thought about this a lot, and I think the best initial strategy is to simply lay out how unprecedented the current situation is:
    1. Temperature as high as it’s been since the discovery of fire.
    2. CO2 as high as it’s been since the continents separated.
    3. This has all happened in the years since we began extracting and burning fossil fuels.
    4. Natural change cannot account for how fast the planet is changing.
    5. If we do nothing in the next few years, it will either be impossible or much, much more expensive to clean up the atmosphere in the future.
    6. Reversing global warming is possible, but it will require real sacrifice from you and everyone else.

    These are more likely than not to be correct statements, but probably aren’t accurate with a ton of confidence. That doesn’t matter. It’s important to be accurate, but any statement will be assailed regardless of its accuracy.

    Comment by Zach — 6 Jul 2010 @ 5:35 PM

  154. Gavin:

    Mohaaaa! You calculated the 800 mm sea level decline in stead of the 1.5 mm, not I. It seems my objections are within the error range of your calculations, so why do you dismiss them as being ridiculous?

    [Response: Perfect I am not, and I apologise for the error. There is still no latent heat loss to space (though the margin by which I demonstrated this is substantially less than I first suggested). And note that for this to be as important as the radiative forcing associated with anthropogenic CO2, you'd still need to multiply it by 20. If you think sea level has been falling at between 15 cm a century or 3 meters a century because we are losing water to space, then point to some actual evidence. - gavin]

    Comment by Iskandar — 6 Jul 2010 @ 5:55 PM

  155. Further to my #125,

    Gavin especially, do you remember when the sense of the Arctic Oscillation was wrong in this article and I provided the correction? The markup is still present in the discussion of fig. 6 and I believe the corrections propagated into subsequent versions. I am quite sure there is a similar sort of mistake in this article as described in my #125. You need to fix it or else the article remains misleading and confusing.

    I know you get a lot of posts but do please respond to this one.

    Comment by Chris Dudley — 6 Jul 2010 @ 6:41 PM

  156. Iskandar,

    Gavin has corrected you numerous times and judging by your responses it seems only to be an exercise in futility. Your comment #152 is even more confused. The vertical presence of our atmosphere is allowed by a rough balance between gravity and a vertical pressure gradient force, the so-called hydrostatic balance. Here’s one last attempt.

    The Earth is surrounded by the vacuum of space. For a compressible fluid like air, there is no well-defined top such as the ocean surface and so it is possible to find trace molecules even half way out to the moon. But this does not at all matter for the argument, and in fact once you get above the stratosphere or so the air is so thin as to have a negligible impact on planetary energy balance. There is a whole science to uppermost atmosphere physics, where a lot of stuff typically breaks down (like the ideal gas law and Local Thermodynamic Equilibrium which climatologists take for granted) but it’s almost a different field all together with little, if any, influence on surface temperature and energy budget discussions.

    All of the other energy transfer terms (sensible and latent heat fluxes, advection, conduction, etc) require some medium and are not operative as space-to-planet energy transfer terms. If the planet was held up by giant tortoises or in contact with some other object (or in the case of early Earth, when there are significant extraterrestrial impact events) then this would not be the case. Gas giants like Jupiter also have significant internal energy sources although this is negligible on rocky planets with a surface which reduce the interior heat flow to several orders of magnitude less than the solar flux. There is also very small mass flux to the Earth associated with particles from the solar wind, but again, it has no measurable impact on Earth’s surface temperature. It is quite safe to say that ~100% of the energy Earth receives is radiation from the sun. Similarly, radiation is the only way you can get rid of energy going out to space by similar rationale.

    This is not the case with surface-to-air heat exchange(which involves evapo-transpiration, sensible heat flows, and radiation) or even within the troposphere where impacts of latent heating on atmospheric circulations are realized on scales ranging from hundreds of meters to thousands of kilometers. The distinction between the top of atmosphere energy budget and the surface or troposphere energy budget is crucial, and are explicitly considered separate in many texts on global climate, such as in Dennis Hartmann’s “Global Physical Climatology” or in Ray Pierrehumbert’s upcoming text. In fact, it is the TOA energy balance which takes primacy in many climate change discussions (there are some exceptions, such as if you could introduce a moist surface in the Sahara desert, the evaporative cooling would likely be more important regionally than CO2 increase). The general argument however is being discussed by rasmus in the context of planetary energy balance: the impact of additional CO2 is to reduce the outgoing longwave radiation term and force the system to accumulate excess energy; the imbalance is currently on the order of 1.45*(10^22) Joules/year over the globe, and the temperature must rise allowing the outgoing radiation term to increase until it once again matches the absorbed incoming stellar flux.

    In equilibrium, both the top of atmosphere and bottom of atmosphere energy budget must be satisfied of course, but there’s no non-radiative heat flux to space. There is non-radiative heat flux in the atmosphere though and energy can be transported above the level where the greenhouse effect is dominant but eventually must be lost by thermal radiation. This is accounted for going back to simple radiative-convective models half a century ago.

    So no more “Earth loses latent heat to outer space” please? Otherwise I’d challenge you to find a data set that is measuring this latent heat loss to space if you’re so convinced it exists.

    Comment by Chris Colose — 6 Jul 2010 @ 6:54 PM

  157. Matthew–how much rain is falling on the periphery of Australia as opposed to the center? Has that changed?

    Comment by Barton Paul Levenson — 6 Jul 2010 @ 7:11 PM

  158. Snapple 140,

    You raise a salient point. I think the emphasis on the US right wing is due to the fact that most editors and posters on RC are Americans. Different countries have different interest groups.

    Comment by Barton Paul Levenson — 6 Jul 2010 @ 7:14 PM

  159. FG 151: The solution globally seems to pretty much consist of handing over large sums of money to “developing” countries, with the USA tagged to pay most of it.

    BPL: Where in the world did you get that idea?

    Comment by Barton Paul Levenson — 6 Jul 2010 @ 7:17 PM

  160. Re 150 Robert Means – That could be clarified. If there is any place where more energy goes in than comes out or vice-versa, then energy is accumulating or being depleted, or else there is a conversion to some other form of energy (which must then accumulate or be depleted or go to or come from somewhere else, etc.). For energy in the form of heat, such an imbalance tends to cause a change in temperature. Changes in temperature cause changes in emission of radiation, so that as the temperature changes in response to an energy flow imbalance, the imbalance tends to decay toward zero as equilibrium is approached. Within the troposphere and between that and the surface, convection (and at the surface, conduction and molecular mass diffusion) are also important – these also respond to changes in temperature so that an imbalance causes a temperature change that causes the imbalance to decay.

    Of course, the planet as a whole is losing geothermal (and tidal) energy, but that is a very very small flux that is insignificant to the climates (surface of crust, ocean, atmosphere) of the inner planets. The layers that make up the climate system can come to equilibrium with both the solar heating and the geothermal flux from below by adjusting temperature (and circulation, water vapor and clouds, etc.) until the LW radiation to space is equal to the sum of solar and geothermal (and tidal) heating and the LW and convective/conductive heat fluxes within the system are such that the energy (as well as momentum and mass) fluxes in and out of each part are balanced (for a time period over which a climatic state can be characterized; obviously there will be redistributions of energy, mass, and momentum over the course of a day, a year, or on the time periods of weather patterns and some internal variability).

    (PS the production and consumption of kinetic energy is relatively small compared to heat fluxes, although it is very important to the circulation of the atmosphere (and ocean); kinetic energy is converted from heat by motions that act like heat engines; it can be converted back to heat by the opposite kind of motion, and also by viscosity. …

    (It can also be converted from gravitational potential energy that originates from density variations that are not due to thermal expansion – this is not very important in the atmosphere (clouds, water vapor) but it is important in the ocean (fresher vs saltier). Ultimately, though, such potential energy in the ocean or atmosphere is produced by (differential) heat(ing).)

    … Thus, for the purposes of accounting for heat gains or losses, the propagation of kinetic energy ultimately accomplishes a transport of heat analogous to convection. As with sensible and latent heat, transport of kinetic energy to space is insignificant.)


    Re 153 Zach – some minor corrections:

    2. CO2 as high as it’s been since the continents separated.

    No. But it is considerably higher than it’s ever been before in at least the last several hundred thousand years. (?) Maybe a few million (?). Which is plenty.

    3. This has all happened in the years since we began extracting and burning fossil fuels.

    Production of cement and deforestation also have made contributions, and the later extends farther back in time (And then there’s CH4 from agriculture), though it is true that the changes were small before fossil fuels became a significant source.

    Comment by Patrick 027 — 6 Jul 2010 @ 7:55 PM

  161. Re 151 Frank Giger

    To those, I say:

    Do we not respect property rights, etc.?
    Should we not generally have responsibility for the consequences of our actions?
    Should our moral principles not extend to how we deal with other countries?
    Is change always unfair?

    Comment by Patrick 027 — 6 Jul 2010 @ 8:00 PM

  162. Titus #77: if you think more powerful computers revealing gaps in knowledge is a problem, you’ll probably want to close down the whole field of biology. The problem there is far more extreme than in climate science, where the basic physics is well known and widely tested. In biology, we don’t have a plausible theory of the overall system yet. Every time we can drill down to more detail and do better computer models, it’s back to the drawing board. I see no sign of that in climate science, rather the basic physics has been confirmed repeatedly.

    Back to the article:

    In other word, why would a negative feedback act for GHGs but not for solar forcing?

    As someone else noted, this should be “other words” – but otherwise this is a great point, one I’ve made several times before. This goes back to the other point I raised earlier: we are talking here about a general theory of planetary climate, not a theory of AGW.

    Comment by Philip Machanick — 6 Jul 2010 @ 8:03 PM

  163. Frank Giger,
    What would be your proposal to developing countries for foregoing the use of fossil fuels in their development?

    If they agree to limit CO2 emissions to avoid catastrophic warming, should they not expect some assistance in development of a replacement energy infrastructure at the very least?

    Comment by Ray Ladbury — 6 Jul 2010 @ 8:13 PM

  164. Re 103 Gilles
    I think that the main issue for the public is : WTH does this have to do with the extinction of human race that is supposed to happen above some threshold ?

    It is very obviously that humans will go extinct beyond some threshold(s), but that isn’t really what we’re dealing with here. We’re dealing with loss of comfort, wealth, well-being, health, and some life, plus the ethics of the unfair distribution (in space and time) (given the distribution of the responsibility of the cause), plus the natural human reactions (war, etc.) – though on that point, I of course recognize that people like the Janjaweed (sp?) must be held responsible for their actions even though a drought was involved.

    “deadly heat waves” (in France at least, in 2003) has only abridged the life of weak and old people by some months – it has been almost exactly compensated by a decrease of mortality the year after.

    Implying that the people only lost a year (or less) of their lives from that cause? I agree that premature death at 70 is not the same as premature death at 1 (when keeping in mind that death eventually gets everyone), but it’s still not desirable.

    Comment by Patrick 027 — 6 Jul 2010 @ 8:22 PM

  165. Re 147 Geoff Wexler
    Question: Is pressure broadening really secondary?
    (and temperature broadenning, compositional dependence of pressure broadenning, and temperature-dependence of line strengh)

    We must of course distinguish between the relative importance to a condition in total verse the relative importance to relatively small changes. (ie all these things are important, but would be minor contributors (so far as I know) to climate feedbacks, relative to the Planck response, water vapor, snow, ice, lapse rate, biological stuff, etc.)

    Comment by Patrick 027 — 6 Jul 2010 @ 8:30 PM

  166. Further to my #155,

    You all are posting my comments but without response. One more try, I think this is simple. From the article:

    ‘Hence, a reduced optical depth explains why atmospheres are not easily ‘saturated‘ and why planets such as Venus have surface temperatures that are substantially higher than the emission temperature. Planets with a thin atmosphere and insignificant greenhouse effect, on the other hand, have a surface temperature that is close the the estimates from the planetary energy balance model (Figure 3).’

    This paragraph simply does not make sense as written. If the word ‘reduced’ is changed to ‘increased’ then it starts to. Look at it schematically: a ‘reduced’ optical depth situations is proposed as opposite to (on the other hand) a thin atmosphere. A thin atmosphere is also optically thin, it is the ‘reduced optical depth’ situation, not the former.

    The paragraph contradicts itself.

    [Response: Thanks, You''re right. The optical path is indeed defined as: τ = ln(I0) - ln(I). I got my signs mixed an apologize for that. -rasmus]

    Comment by Chris Dudley — 6 Jul 2010 @ 8:57 PM

  167. Jim Harrison @ 141
    “Scientists disastrously overestimate their ability to communicate their findings to non-scientists.”

    Or perhaps paraphrasing another commenter, scientists don’t always adequately define their target audience. I’m not saying that applies to this article. On the other hand, if you’re trying to cast the broadest possible net, I would say it’s of utmost importance to communicate what excites you about the subject (and NOT just that you happen to be one of those rare breed who are obsessed with solving problems that no one else can).

    Climate scientists are probably at a disadvantage in this regard. Topics like space (think Sagan) and dinosaurs are automatically interesting. Even string theory, which apparently nobody understands, is captivating (‘Whoa, dude! Like reality is so weird!’). Climate science, not so much. Just a bunch of soupy chemistry that doesn’t explode when you light it and heaping gobs of multi-layered physics that can’t even make your car go faster. It’s an uphill slog for you guys in that regard, and you have my deepest sympathies for that and your tireless patience with the public.

    Sad to say though, this discussion does remind me a little bit of the comments I saw on an article somewhere else a while back. The article was about the problems of getting Harry Potter translated in to Scottish Gaelic and what effect that had on promoting the language. One commenter demanded that Harry Potter be damned and all that was needed to promote the spread of Gaelic was for the best writers to write more poetry. This was rightly pounced on. Think about it, would being able to read the obscure scribblings, in their original form, of a handful of professional academics make you want to go out and learn Gaelic to use as a living language?

    I mean really?

    Comment by Radge Havers — 6 Jul 2010 @ 9:10 PM

  168. Re #151 (Frank Giger)–

    I have to agree with Barton’s questioning stance about this post: I haven’t noticed anything resembling an actual climate change policy in the US yet.

    I’m eagerly awaiting same, and I’ve heard some proposals. But so far, I don’t think we’re all that much past the vaporware stage.

    As to the policy proposals, I don’t think they resemble Frank’s caricatures all that closely.

    Comment by Kevin McKinney — 6 Jul 2010 @ 9:22 PM

  169. “The divorce between scientists and population starts here : scientist congratulate themselves for having found a statistically significant difference in 30 years data, but they have almost no influence on the all day life of most people.” True – for now – but what the science shows is validation for a model that makes more dire predictions for the future and with increasing costs associated with delays to action. 3mm/year of sea level is fine, but over 10mm/yr? The risks to human lives in my opinion is in starvation from food production disruption, and in risk of war from migrations triggered by delta losses and drought. The rich in the west being the least vulnerable to both but whose emissions are the ultimate cause.

    Comment by Phil Scadden — 6 Jul 2010 @ 9:38 PM

  170. Radge Havers @ 167

    “Just a bunch of soupy chemistry that doesn’t explode when you light it …”

    Maybe methane-fuel-air explosions will get everyone’s attention!

    Comment by Garrett — 6 Jul 2010 @ 10:58 PM

  171. Re 166 Chris Dudley, quoting main post ‘Hence, a reduced optical depth explains why atmospheres are not easily ‘saturated‘ and why planets such as Venus have surface temperatures that are substantially higher than the emission temperature. Planets with a thin atmosphere and insignificant greenhouse effect, on the other hand, have a surface temperature that is close the the estimates from the planetary energy balance model (Figure 3).’

    The best way I can interpret that (using what I already know) is that, as climate reaches equilibrium after any forcing changes, the outgoing longwave radiation (OLR) has to balance the solar (SW) heating (setting aside typically tiny geothermal and tidal heat fluxes). IF the atmosphere is optically thick, then most of the OLR is not coming from the surface, and in fact is coming from the upper atmosphere – in a region whose optical thickness is smaller than the total atmosphere (hence, ‘reduced’).

    If the temperature declines with height through much of the OLR source, then adding more LW optical thickness will still reduce the OLR. If the temperature doesn’t decline with height in that layer (perhaps because of solar heating), it is still the case that increasing the LW optical thickness will, by concentrating the source of OLR into a yet thinner layer at the top of the atmosphere, remove some of the cooling of the lower part of the original OLR source (by adding additional downward LW flux from above, replacing the darkness of space), thus tending to cause warming there. In general, so long as there is some solar heating beneath some level, there must be a net LW + convective heat flux upward at that level to balance it in equilibrium; convection tends to require some nonzero temperature decline with height, and a net upward LW flux requires either that the temperature declines with height on the scale of photon paths (from emission to absorption), or else requires at least a partial ‘veiw’ of space, which can be blocked by increasing optical thickness above that level. But there will always be some layer of air at the top of the atmosphere that has a partial to nearly complete ‘veiw’ of space.

    (PS a skin temperature can be lower than the brightness temperature of the OLR because a very thin layer at the top of the atmosphere will absorb a tiny fraction of OLR, thus barely affecting OLR, but must in equilibrium emit that same amount of energy both upwards and downwards; if it were as warm as the brightness temperature of the OLR then it would emit twice what it absorbs and thus cool. But OLR and the necessary thinness of such a layer can vary over wavelength and there’s also solar heating.)

    If the optical thickness varies over wavelength, then it is possible to saturate OLR at some wavelengths – but the greenhouse effect generally can’t be saturated at all wavelengths, because there has to be some net upward LW flux (above the level where convection becomes insiginificant) that balances solar heating (beneath that level) to maintain equilibrium, and there will generally always be ‘room’ to reduce that net upward LW flux at the wavelengths where it occurs. (CO2 is saturated at the tropopause level in the central portion of it’s dominant (for Earth) band (centered near 15 microns), but the optical thickness per unit CO2 declines away from the center in such a way that the width of the band exceeding a given optical thickness tends to widen by some amount with each doubling; it is this shifting of the ‘edges’ of the band where adding more CO2 has an effect.)

    Comment by Patrick 027 — 6 Jul 2010 @ 11:19 PM

  172. Note that it is possible, hypothetically, to introduce so much optical thickness that the tropopause level or any level besides the very top of the atmosphere becomes saturated (zero net LW flux); however, the resulting climate response will tend to ‘unsaturate’ the effect at some level(s) – for example, by shifting the position of the tropopause so that convection balances solar heating where the net LW flux is zero and convection carries the heat to where a net LW flux can balance the convective heat delivery.

    PS a question came up earlier about absorption lines of CO2:

    Generally, absorption lines in the absence of any line-broadenning, would absorb over an infinitesimal portion of the spectrum, and saturate (ie reduce the photon travel distances to a scale where there is very little temperature variation) relatively more quickly. Line broadenning takes the optical thickness and spreads it out a bit. For a very thin layer or very small amount of substance, the fraction of radiation absorbed wouldn’t change (so far as I understand), but the saturation at the line centers is delayed while significant absorption can occur over some finite interval of the spectrum, so that absorption can increase to some significant amount as the layer is thickennned or more material is added.

    The absorption bands of gases are generally not the result of the broadenning of a single line; they are actually groupings of lines; the variation in optical thickness over the band would be related to variations in line strength (and line spacing, I’d assume). The line broadenning takes some optical thickness from the line centers and puts it into gaps between closely-spaced lines, so that there can be significant absorption over a contiuous band of wavelengths.

    PS when molecular collisions are frequent relative to photon emissions and absorptions (as is generally the case in most of the mass of the atmosphere), the radiant heat absorbed by any population of molecules is transfered to the heat of the whole population within some volume, and molecules that emit photons can then gain energy from other molecules. Then the temperature of the whole population of molecules in some volume is approximately the same temperature as the molecules that are responsible for emitting and absorbing photons. This is approximately LTE.

    If collisions are more rare, then molecules might absorb photons, become exited, and then emit photons. This can still produces a greenhouse effect (analogous to a scattering greenhouse), but the mathematics is different. (You could even have a greenhouse effect based on LW-phosphorescence (maybe with nanoparticles suspended in the air) – but that’s a bit exotic.)

    Comment by Patrick 027 — 6 Jul 2010 @ 11:35 PM

  173. Re my second to last comment, about a skin layer: “but must in equilibrium emit that same amount of energy both upwards and downwards” – I mean in total – it would emit half that energy upward and half downwards.

    Comment by Patrick 027 — 6 Jul 2010 @ 11:41 PM

  174. Just to note that BPL in #109 agrees with my assessment (#92 and forward) that there is a problem with using the word ‘reduced’ in the article. Sorry I did not see that sooner Barton.

    Comment by Chris Dudley — 7 Jul 2010 @ 12:03 AM

  175. Fine article. However, before for a litmus test, try asking someone to explain the basic mechanics of the relationship of the Sun and the Earth with respect to annular seasonal change. If they can’t pass that test, then it is very unlikely an understanding of an enhanced greenhouse effect is in the range of possibilities. However, these same folks feel confident holding an opinion about anthropogenic climate change (or the lack thereof).

    As others point out, a basic scientific literacy is pre-requisite and necessary to understand to most basic of climate concepts. Regrettably, a scientific literacy is not necessary to hold public office, or to guide the reins of a global corporation: cleverness, cunning, greed, and a lust for power are more potent indicators.

    Comment by Jim Redden — 7 Jul 2010 @ 12:13 AM

  176. “Molecules composed of three or more atoms tend to act as greenhouse gases because they can possess energy in terms of rotation and vibrations which can be associated with the energy of photons at the infra-red range. ”

    I liked how Scott Denning explained this in a way that even economist understand.

    Comment by Harmen — 7 Jul 2010 @ 1:25 AM

  177. Excellent to have this review of the science of atmospheric warming for us who have not been fully blessed with a scientific education. One thing that I have never had explained and that I would very much like to understand is this: I believe carbon dioxide and methane are greenhouse gasses effectively because they retain heat more or longer than the Oxygen and Nitrogen that make up the bulk of the atmosphere. But why are these carbon gases more retentive of heat? I assume it is something to do with the electronic structure of the molecules and the quantum energy levels in the molecules? Can someone please givean explanation sufficiently simple for a non scientist to grasp.

    Comment by McGahill — 7 Jul 2010 @ 2:02 AM

  178. [removed - please calm down]

    Comment by Edward Greisch — 7 Jul 2010 @ 3:28 AM

  179. If I was targeting the general population for my audience, I would not bother to mention a formula of any kind because the general population has very little to no understanding of algebra; instead, I might put a technical note in some places with formulas for those who are comfortable enough with algebra to use it, but my entire article would not depend on any formula of any kind, and I would make an effort to keep them separated. The general population is probably around a 7-8th grade level. So any story targeting these people must be geared for that level. (Most people seem to have trouble grasping fractions.) Also, technical words should be avoided completely. And I wouldn’t use any kind of graphing.

    I would try to show people the greenhouse effect instead of telling them.

    Comment by EL — 7 Jul 2010 @ 4:24 AM

  180. Chris Dudley 166,

    the optical depth is reduced at higher altitudes, which means it never saturates. The upper reaches of an atmosphere will always be at lower pressure–less mass in the same gravitational field. With five guys lying on top of each other (perhaps on Fire Island?) the one at the top is the one experiencing the least pressure.

    Comment by Barton Paul Levenson — 7 Jul 2010 @ 4:27 AM

  181. I’m normally a lurker but I feel compelled to post because several people have said that this is inappropriate for the non-scientist. Wrong, oh so wrong. I am not a scientist (I’m a teacher of IT) and I found it comprehensible, well explained and very useful. Like the man said – you can’t please all the people all of the time, so don’t try.

    Comment by Chris S — 7 Jul 2010 @ 4:42 AM

  182. #157 BPL
    It is difficult to tell the long term trends as the Australian Govt. don’t appear to have done maps or graphs showing variance, only absolute figures. They do have some long term maps at the Australian Bureau of Meteorology showing 10, 20 and 30 year rainfall averages. Examples:
    30 years 1911-1940

    30 years 1976-2005

    Practically no rain falls in the Australian interior. From a quick visual comparison there appears to be very little change in the coastal areas. However it would seem that rainfall is penetrating further into the interior from the north coast towards Alice Springs and from the South West corner inland away from Perth. However, these areas are so sparsely populated, I wonder how accurate rainfall measurements were in 1911-1940?

    They last did a full climate assessment in 2006, and another one is due in 2011.

    Comment by Matthew L — 7 Jul 2010 @ 4:50 AM

  183. This is an excellent summary of the principles of the GHE and it is well aimed and highly needed for professional scientists who are in one way or another engaged in climate change research. “Climate change” has an enormous scope, and there are probably more non-physicists/chemists engaged in the science than not, and this article is excellent for that community. (Our community should do the same for you guys!)

    So thanks very much.

    A question: as I understand it, the radiation aborption characteristics of GHG molecules is dependent on the fraction of time they spend in particular dipole configurations. Is this fraction dependent on temperature or on the partial pressure of other gas species in the atmosphere?

    Comment by Mike Ellis — 7 Jul 2010 @ 6:13 AM

  184. In your notation to Figure 4 you say “At the top of the atmosphere, the infra-red light escapes freely out to space, and this is where the planet’s main heat loss takes place.” But surely the planet’s main heat loss takes place on the side of the globe facing away from the sun. You seem to have assumed permanent sunlight.

    Comment by Confused — 7 Jul 2010 @ 6:37 AM

  185. I applaud your interest in communicating with the broad spectrum of humanity, but I believe you are neglecting a significant aspect of human psychology. Ernest Becker wrote a book, several decades ago, called The Denial of Death. In it he investigates the ideas put forth by Otto Rank, a contemporary of Freud, who believed that fear of death (or, more properly, anxiety about mortality) is the primary motivator for the vast majority of humans. Rank supposed that, in order to assuage this anxiety, persons attach themselves to a hero, or to a heroic notion (such as “western culture,” or “science,” or a religion), convincing themselves that so long as their hero persists, they, too, will “live on,” becomming “immortal,” like their heroes. To give up the hero is to give up “immortality.”

    Climate change, and its anthropogenic source, directly challenges the “heroism” of western culture. To it up will be to give up the dream of immortality for billions of people. All the careful explanation in the world will not help.

    Comment by Gordon — 7 Jul 2010 @ 6:46 AM

  186. EL:

    A good graph can explain a lot. This is the reason (probably the only genuine reason) why the hockey stick graph has been attacked so brutally. The adage “a picture is worth a thousand words” remains true to this day.

    Not all graphs are created equal, of course. Try to cram in too much information, distort it, or choose to express concepts that can’t be easily grasped, and your graph is useless to most people. Do it well, and your graph will project an idea that can live beyond simply reading the accompanying prose.

    Graphs can also be deployed in a “lie-to-children” sense, expressing a simpler version of a more complicated truth. The Al Gore ice core graph is a good example – the basic fact, that CO2 and temperature are linked, is expressed perfectly. The more complicated details of feedbacks are glossed over.

    Comment by Didactylos — 7 Jul 2010 @ 7:59 AM

  187. Philip @120 describes the receptive audience best: scientists in other fields who can understand the numbers, graphs & equations in this piece, who need reassurance that the science is sound, and having read and understood the piece, will be able to pass along their explanations to other people.

    Make no mistake, this article is far too complex for John Q. Public*: not because John Q. couldn’t possibly understand it (he could, with some assistance from the helpful and infinitely patient people posting here), but because very few people work that hard to understand something unpleasant, unless it’s a direct and immediate threat, and even then… End of story.

    *I say this as a representative John Q: high test scores, master’s degree in literature, an engineer father, and an aptitude for reading technical material outside my field. This piece tested my capability, but I persevered & I think I get it. The concept of “optical depth” was useful, and for some reason, this is the first time I’ve encountered it in the 100′s of explanations of AGW I’ve read.

    Comment by Steve R — 7 Jul 2010 @ 8:06 AM

  188. Confused–you are indeed living up to your moniker. Outgoing IR increases with temperature. Since the daytime side is on average warmer than the night-time side, then all other things (e.g. cloud cover, etc.) more IR will escape on the day side. Also, day or night side, the planet is warmer than the inky blackness of space, so both sides radiate IR.

    Comment by Ray Ladbury — 7 Jul 2010 @ 8:58 AM

  189. Edward Greisch@178,
    Fossil fuels are cheap and demand no advanced technology for exploitation. Alternative energy technologies are more expensive and have greater technology requirements. With respect, why should a developing country with a growing population and on the verge of economic takeoff not tell you to pound sand when you tell them not to take the cheapest and most rapid route to economic prosperity?

    And with regard to bombing countries using coal, I’m afraid I will not follow you down that slippery slope to genocide. You’re on your own there, pal.

    Comment by Ray Ladbury — 7 Jul 2010 @ 9:08 AM

  190. The lead story at right now is
    “‘Climategate’ review clears scientists of dishonesty”
    Unfortunately, their other stories at are about the politics, not the science.

    Comment by Brian Dodge — 7 Jul 2010 @ 9:08 AM

  191. Ed’s #178 is an amazingly hate-filled comment. Hopefully these off-topic fantasies about US taxpayers financing “their” population growth can be put to rest with a reality check: has figures for US economic aid by major recipient countries (table 1263). I added up everything except Iraq and Afghanistan for the latest year available (2007): 13.2 billion dollars, over 10% of which went to Russia. By comparison, the USA’s trade deficit was 711.6 billions dollars in 2007.
    Going to, here are latest numbers for the holdings of US treasury securities: UK +167.4, Japan +109.6, China & HK +107.6 and so on (from April 2009 to April 2010, billions of dollars).

    [Response: The comment has been removed. No further OT commentary please. - gavin]

    Comment by Anonymous Coward — 7 Jul 2010 @ 9:18 AM

  192. Barton (#180),

    I tried to read it that way but it does not work. Consider also where the term ‘reduced optical depth’ is introduced:

    ‘The term known as the ‘enhanced greenhouse effect’ describes a situation where the atmosphere’s becomes less transparent to infra-red light (reduced optical depth)’

    As you also pointed out: less transparent=increased optical depth.

    Comment by Chris Dudley — 7 Jul 2010 @ 9:20 AM

  193. I like the article. I also wonder if the reception to the quite excellent piece would be warmer if the presentation media were changed from more static text/graphics to more animation, at least for online presentations. In that, I’m thinking of the way that The Mechanical Universe programs illustrated physics principles, and especially the math manipulations. (I might be biased, because I loved that series, viewable here: If it is a useful goal to give the interested viewer a comfortable understanding that the physical model is logical, sensible, and correct/reliable, rather than to convey a firm everyday grasp of the precise details to most, then it seems to me that animating the mathematics could help toward that end. The atmospheric math certainly is more complex than Newton’s First Law, but maybe any progress toward simplifying the communication would be worthwhile. We probably are happy when non-specia-lists comprehend the material, but it probably is more important to know how and why the non-comprehenders react to the material. I also wonder how audiences with demographics different from RC’s audience would react to the presentation, and to various presentation formats. Maybe younger audiences would comprehend better with a more animated format. I don’t know what sites would have younger audiences–maybe Kate from ClimateSight could chime in on that question.

    RE: Gordon # 184, I see merit to your thesis. Especially as, the more synthetic our daily existence becomes, the more difficult it is for the average person to comprehend the vulnerability of our habitat and the notion that humans aren’t the only species in that habitat. Maybe I disagree a little with a possible implication that western culture can maintain only if AGW does also. It seems to me that the grail is whatever type of energy is required to run that doomed amusement park ride. In that vein, the hero worship doesn’t care whether it is sustainable energy rather than the rapidly depleting fossil sources, as long as the music continues. A person might think that more readily/easily available energy simply will turbocharge population growth and consumption, but that’s a different train wreck discussion.

    Comment by ghost — 7 Jul 2010 @ 10:08 AM

  194. McGahill says: 7 July 2010 at 2:02:
    “… I believe carbon dioxide and methane are greenhouse gasses effectively because they retain heat more or longer ….”

    That’s wrong. Don’t get confused by the guy who often posts confusing energy and temperature. The explanation won’t make any sense as long as you read it while assuming that mistaken idea is correct.

    Start from scratch with the explanation.

    Authors, it might help to address commonly held misunderstandings and areas of confusion — assumptions people may be holding as they read your piece that undermine comprehension.

    Comment by Hank Roberts — 7 Jul 2010 @ 10:42 AM

  195. [edit - sorry, the original offensive comment was removed, and so are any replies].

    Comment by Nick Gotts — 7 Jul 2010 @ 10:44 AM

  196. Fred Moolten’s comments made me go back and re-check my understanding of the stratosphere and GHG cooling. Please correct me where needed.

    The stratosphere is found between the tropopause to about 51 km or so. The tropopause heights varies between 8 km and 18 km due to latitude and season. Cooler latitudes and seasons result in a lower tropopause height.

    The greatest ozone density is around 20-25 km because the ozone destruction processes are slower there. Maximum incoming solar heating occurs there but the greatest temperatures are near 50km where the low density air requires very little energy to raise its temperature (think KE=1/2 mv^2 and fewer collisions with fewer air molecules yield greater v). Therefore, there is a temperature inversion throughout the stratosphere above the ozone maximum. This inversion severely inhibits convection (mixing) so radiative and conductive processes dominate. The inversion also means that air from the troposphere has difficulty entering the stratosphere so heat is not easily transported between the two by convection or conduction. (Note: Srongly thunderstorms can transport gases such as water vapor up across the tropopause and there are breaks in the jet stream westerlies allowing interchange of stratospheric and tropospheric air. Also, gravity waves can help mix the air in the stratosphere.) One can assume that radiative transfer must dominate between these two spheres.

    So what cools the stratosphere?

    1) Increased GHGs and the tropospheric enhanced GHE
    2) Ozone loss
    3) Decreased solar radiation

    The simplest explanation is that the troposphere is warming primarily through enhanced GHE and not because incoming solar radiation is increasing (in fact it is decreasing recently). There should be less heat available to the spheres above which means they will all cool. Energy cannot be created, right? If there is more energy in one sphere there must be less for the others assuming an energy balance with the sun.

    As mentioned here, as the troposphere becomes more optically thick, the height at which IR is released to space is higher and cooler which means there is less upwelling IR to the regions above the troposphere. So is this causing the stratospheric cooling? It appears that the answer is “yes, to some degree” but there are other factors that make it difficult to nail down this thing.

    Before 1995, it appears that the most significant cause of the lower stratospheric cooling was ozone depletion which means less absorption of solar radiation. Because ozone rapidly decreases with height (very little ozone above 35 km), ozone loss is estimated to have caused only half of the cooling at the higher levels of the stratosphere. Increased CO2 in the stratosphere at higher levels increases upwelling radiation to space which appears to have been greater than absorption from below resulting in cooling at higher levels.

    Since 1995, ozone is increasing in the lower stratosphere and ozone absorbs incoming sunlight to cause warming. Since 1995, there has been no cooling of the lower stratosphere but no real warming which one would expect due to the rebound of ozone. This may suggest that the decreased upwelling IR from the troposphere is offsetting the warming caused by increasing ozone.

    It also appears that increased CO2 is cooling the mesosphere and thermosphere and there is very little ozone in that region. A complicating issue for all spheres is that the sun has been “very weak” recently which has resulted in some cooling of these spheres, especially the thermosphere.

    Some good references:,0/2__Ozone/-_Cooling_nd.html

    Scott A. Mandia, Professor of Physical Sciences
    Selden, NY
    Global Warming: Man or Myth?
    My Global Warming Blog
    Twitter: AGW_Prof
    “Global Warming Fact of the Day” Facebook Group

    Comment by Scott A Mandia — 7 Jul 2010 @ 10:54 AM

  197. McGahill @177, I’m just a lay reader here, but I’ll take a shot at your question. I’m sure I’ll be corrected shortly if I get it wrong.

    CO2, H2O (water vapour), CH4 (methane), N2O (nitrous oxide), O3 (ozone), etc. are greenhouse gases because their molecular structure allows them to absorb packets of infrared light energy (photons) of specific wavelengths and become vibrationally excited. (Yes, it is a quantum effect.)

    But they can’t retain this extra energy for very long. Almost immediately (nanoseconds) they relax from their excited state by either 1) emitting that energy as a new photon, some of which will continue up towards space, some of which will go back downward to be reabsorbed, thus keeping the energy in the atmosphere longer, or 2) by colliding with another gas molecule, most likely an O2 (oxygen) or N2 (nitrogen) molecule since they make up over 98% of the atmosphere, thereby converting the extra vibrational energy into kinetic energy by transferring it to the other gas molecule, which will then collide with other molecules, and so on, making the air warmer.

    In other words, greenhouse gases don’t retain heat themselves, but rather redirect outgoing energy radiated by the surface and lower in the atmosphere, thereby delaying it’s ultimate escape to space. You might say energy is retained, but it is the vastly more numerous O2 and N2 molecules that are warmed and retain the heat, even though they can not directly absorb outgoing infrared energy themselves.

    Another way to think about it to is to compare outbound IR photons to the child’s game of snakes and ladders. Progress around the game board is hindered when your game piece (outgoing photon) lands on a slide (greenhouse gas molecule) that sends you backwards (photon emitted back downward), but eventually your game piece will make it to the finish line (space), it’ll just take longer.

    Comment by Jim Eager — 7 Jul 2010 @ 11:18 AM

  198. Mike Ellis asks:”A question: as I understand it, the radiation aborption characteristics of GHG molecules is dependent on the fraction of time they spend in particular dipole configurations. Is this fraction dependent on temperature or on the partial pressure of other gas species in the atmosphere?”

    As a first approximation, no. The molecules, even in the vibrational ground state are vibrating back and forth about the equilibrium value (in CO2 the primary importance is bending away from linear, back and forth). Vibration excited states primarily increase the amplitude, but not so much the rate of change in dipole moment as a function of angle, which is what IR intensity depends upon.

    Comment by t_p_hamilton — 7 Jul 2010 @ 11:19 AM

  199. [edit - please, no more. This is a thread about the GHE!]

    Comment by Edward Greisch — 7 Jul 2010 @ 11:21 AM

  200. Yes, the GHE basics constantly need to be retaught to each new generation, and to those who at long last are tuning in.

    It’s probably still too complicated, except for those with some time on their hands.

    I was fortunate as a teen in the early 60s either to learn about the natural GHE in school science class or in my outside readings in science. When AGW came to public consciousness in the late 80s, I was well prepped to understand it.

    A more simply scheme is the idea of a real greenhouse, or a car in summer with windows up. Even tho this may not be totally scientifically correct, it is a good way to get the point across. A simple picture — like — is a very good start.

    When people understand the GHE from this greenhouse or car analogy and from such simple images, then it becomes very easy to understand that adding more GHGs to the atmosphere will increase the global warming. For a sincere person, this is all they need to know to understand it — plus learning something about how the warming will affect the earth and life thereupon — for them to be motivated to mitigate AGW. For the heartless, fearful denialists, no amount of science and no amount of making it easy to understand will ever help them to accept AGW and start mitigating.

    Comment by Lynn Vincentnathan — 7 Jul 2010 @ 11:26 AM

  201. I recommend editing this article to take into account some of the comments that have been made here. I agree with ononymous that the sentence regarding conservation of energy and nuclear reactions is really really jarring. Also I agree with Chris Dudley that the discussion of optical depth is incoherent. For starters optical depth is not a distance. Second, optical depth increases with increasing CO2. If you are trying to convey some subtlety regarding optical depth and the enhanced greenhouse effect, it is opaque. This is not a journal article; it can be edited after publishing. I know that writing these things is a lot of work and I do appreciate the effort.

    Comment by John E. Pearson — 7 Jul 2010 @ 11:27 AM

  202. McGahill 177,

    No, greenhouse gases don’t particularly retain heat. They absorb infrared photons, which heats them up, and they then emit heat.

    Comment by Barton Paul Levenson — 7 Jul 2010 @ 11:29 AM

  203. McGahill (#177),
    In addition to what’s been said already, the difference between O2 and CO2 (as an example) is that O2 is perfectly balanced while CO2 is not and that makes it excitable. Specifically, you might say that an electric field can bend the molecule by pulling at the carbon because it does not have the same charge as the oxygen.
    If you want a full explanation, David Archer recorded accessible video lectures “for English majors”. Lecture 6 explains this stuff but I recommend you check lectures 2 and 3 first which explain the basics in detail (skip if you’re familiar with the material already of course).

    Comment by Anonymous Coward — 7 Jul 2010 @ 11:47 AM

  204. Didactylos
    “A good graph can explain a lot. This is the reason (probably the only genuine reason) why the hockey stick graph has been attacked so brutally.”

    If and Only if people are able to interpret the graph. Most people do not know the difference between the y axis and the x axis. And the attacks on the hockey stick graph have been successful for this very reason. The average person does not have much mathematical training.

    The general population, by that I mean soccer moms and football dads, needs different explanations than people with technical backgrounds.

    Comment by EL — 7 Jul 2010 @ 12:17 PM

  205. [edit - OT topic, original comment removed]

    Comment by Joseph Sobry — 7 Jul 2010 @ 12:26 PM

  206. To Scott Mandia (#196), who states: As mentioned here, as the troposphere becomes more optically thick, the height at which IR is released to space is higher and cooler which means there is less upwelling IR to the regions above the troposphere. So is this causing the stratospheric cooling? It appears that the answer is “yes, to some degree” but there are other factors that make it difficult to nail down this thing..

    Scott – In a steady state (where the models predict stratospheric cooling just as they do under current forcing conditions), for the troposphere to radiate IR to space in an amount that balances the heat absorbed from solar radiation in the troposphere and at the surface, it must radiate at a temperature averaging about 255 K (that’s the temperature needed to reradiate the absorbed heat via the Stefan-Boltzman equation). That radiation doesn ‘t occur at any single altitude, but the “radiating layer” (i.e., the level with a 255 K temperature is a hypothetical altitude equivalent to the average of the multiple layers that actually radiate, some warmer, some cooler. The 255 K altitude rises with greenhouse effects, but the calculated temperature doesn’t change (unless the sun heats up or cools down or the albedo changes). In essence, greenhouse effects change the level of tropospheric radiation, but not the temperature or the amount of radiation.

    To summarize the above, the amount of radiation leaving the troposphere to enter the stratosphere is fixed by the amount of heat the troposphere and Earth’s surface absorb, and is for practical purposes unaffected by CO2. Increased CO2 merely raises the average temperature below the radiating layers needed for that radiation to be emitted by those layers. In a circumstance of radiative imbalance, that scenario changes slightly, but the current imbalance is far too small to account for more than miniscule stratospheric temperature changes. Hence, one can’t explain stratospheric cooling mediate by CO2 on the basis of reduced IR radiation entering the stratosphere.

    What appears to be a critical role of ozone in permitting added CO2 to cool the stratosphere by serving as an escape mechanism for ozone-mediated warming is discussed in 3, 14, 28, and 41. The last of these mentions other heat-absorbing moieties beyond ozone, but in the stratosphere itself, ozone is probably the most important one. Item #14 is the one I would most emphasize, simply because of the credentials of the geophysicist I quote on the subject, Raymond Pierrehumbert, whose forthcoming book will address this topic quantitatively in some detail.

    Comment by Fred Moolten — 7 Jul 2010 @ 12:42 PM

  207. Optical Depth is such a tricky factor, but the atmosphere becomes more or less opaque at various wavelengths, so when one adds CO2 it doesn’t mean it becomes more and more opaque at all IR wavelengths. Absorption varies with height and pressure as well.

    Is complicated a bit, but not too confusing.

    I am particularly interested in why the models have failed to predict Arctic sea ice volume going down so fast. I believe in extra IR downwelling responsible for more thawing and also CO2 becoming more prominent in dryer colder climates, but I have seen scant evidence in that area, and what I read mainly denies this, but it does make sense, the stratosphere cools due to lack of IR causing warming, ozone gets depleted further by a colder stratosphere. This is a great success as described by models. Yet sea ice extra depletion evades explanation.

    I am also a novice at this one: sea ice CO2 permeability , wow, this may be something worth understanding more.

    But all and all, the sun disks of the Arctic regularly expand in size almost every year like clockwork. 2010 has shown
    very large expansions, surpassing all previous years, the only thing doing this is lesser air density, pressure usually varies quite a lot along a well defined median, so only thing left is temperature. Warmer and warmer we go, as the world already knows, but little do we do something about it.

    Comment by wayne davidson — 7 Jul 2010 @ 1:23 PM

  208. The greenhouse effect can be explained by the urban heat island effect.
    Imagine a house in a rural area, surrounded by cool vegetation, that will be comfortable on a sunny spring day.
    Now imagine this same house, on the same day, but downtown in an urban area. In addition to the heat from the sun, it is also getting heated by Infrared radiation from the brick office building across the street, and the hot cars in the parking lot next door, and so on. The brick office building is made hotter by the Infrared radiation from the parking lot, and the parking lot is made hotter by the Infrared radiation from the office building; both are made a teeny bit hotter by the Infrared radiation from our little house. Some of the directions where our house used to lose heat by radiation now have warm objects in the way; our house is still radiating heat, but these objects are absorbing it, and radiating some of it back. As the neighborhood became built up, so did the total heat coming to our house. Convection, conduction, and latent heat transport move the heat around, but almost all the heat come in as visible radiation, sunlight, and it all (eventually) leaves the earth as Infrared radiation.

    Adding more CO2 (which absorbs & reradiates Infrared radiation) to the atmosphere has a similar effect to building an urban environment – it blocks paths where heat used to escape by Infrared radiation, and because it’s warmed by this IR, it reradiates additional energy (infrared) which adds to the energy coming from the sun in the visible, making things warmer. Because the additional CO2 from everybody’s power plants, and trucks, cars, cargo ships, furnaces etc quickly mixes into the atmosphere, the warming effect isn’t confined to where the CO2 emission occurs. The heating caused by urbanization in New York or New Delhi is greatest locally; the heating caused by CO2 is global, affecting Arctic sea ice, Himalayan glaciers, Antarctic ice shelves, rainfall extremes, and a lot of other things.

    Comment by Brian Dodge — 7 Jul 2010 @ 1:56 PM


    Motl has a rant about this article. He seems not to have heard of Einstein and E=mc²

    “Mr Benestad apparently believes that both nuclear reactions and quantum mechanics violate the energy conservation law! Well, they don’t, Mr Benestad. As Emmy Noether has shown, the energy is conserved whenever the laws of physics are invariant under translations in time.”

    Comment by turbobloke — 7 Jul 2010 @ 2:47 PM

  210. 177. Comment by McGahill ”
    Excellent to have this review of the science of atmospheric warming for us who have not been fully blessed with a scientific education. One thing that I have never had explained and that I would very much like to understand is this: I believe carbon dioxide and methane are greenhouse gasses effectively because they retain heat more or longer than the Oxygen and Nitrogen that make up the bulk of the atmosphere. But why are these carbon gases more retentive of heat? I assume it is something to do with the electronic structure of the molecules and the quantum energy levels in the molecules? Can someone please givean explanation sufficiently simple for a non scientist to grasp.”


    To put it simply, O2 and N2 are symmetric diatomic molecule that, while they have stretching like a spring, and can spin around, these motions to not possess a dipole moment between quantum states, and, hence, they cannot interact with an electro-magnetic field. Radiative process require EM field interations with dipole moment transitions.

    Tiatomics quantum states of CO2, N2O, O3, H2O, etc, do have dipole moments which can interact with EM waves, so they can absorb and emit photons at frequencies (determined by quantum mechanics) corresponding to energy level differences between the various states they can assume. An EM transition is permitted if there is a net dipole moment change between the states. It’s complicated, I know, but it’s How God Made It. CO2 is a particularly strong infrared active molecule which is also notoriously chemically stable.

    Comment by Garrett — 7 Jul 2010 @ 2:50 PM

  211. Re 185 Gordon says Climate change, and its anthropogenic source, directly challenges the “heroism” of western culture. To it up will be to give up the dream of immortality for billions of people. All the careful explanation in the world will not help.

    Or the hero could be a dynamic character, who drastically reduces his/her reliance on fossil fuels, etc, and triumphs over AGW.

    Re 201 John E. Pearson If you are trying to convey some subtlety regarding optical depth and the enhanced greenhouse effect, it is opaque.

    Nice pun!

    Re 177 McGahill – GHGs or other GH agents (clouds) affect the flow of radiant heat in somewhat the same way that replacing a layer of aluminum with a layer of cork affects the conduction of heat through the layer.

    Comment by Patrick 027 — 7 Jul 2010 @ 2:57 PM

  212. Re myself Re 177 McGahill – GHGs or other GH agents (clouds) affect the flow of radiant heat in somewhat the same way that replacing a layer of aluminum with a layer of cork affects the conduction of heat through the layer.

    (Actually, they can do the opposite in some cases – ie they can increase the heat transfer over shorter distances, until the optical thickness becomes sizable over such distances; then farther increases will act like insulation. Basically, the average distance the photons can travel from emission to absorption is on the order of unit optical thickness (depending on the relative roles of absorption verses scattering; LW scattering is relatively minor for Earthly conditions); they can travel as easily in one direction as they can in the opposite direction, so an imbalance in photon flow – a net flux of photons – will be directed from warmer to colder regions, depending most on the variation in temperature over the spatial scale of unit optical thickness. Changing the optical thickness relative to the temperature distribution will change the net photon flux. Energy accumulates or is depleted depending on convergences or divergences of fluxes; the climate tends to adjust to bring the fluxes into balance.)

    Comment by Patrick 027 — 7 Jul 2010 @ 3:14 PM

  213. Patrick #66>> But here is a quote from Wikipedia concerning water vapor:
    “Water vapor is a greenhouse gas in the Earth’s atmosphere, responsible for 70% of the known absorption of incoming sunlight…”
    So – increased amounts of water vapor in the atmosphere simply must reduce the amount of energy that reaches the surface – and in turn the amount of IR back radiation from the surface (since there is a smaller total amount of energy to reflect).

    This would also be hard to detect by sattelite, since there would still be an imbalance in/out, but the surplus energy will never reach the surface. Measurements will indeed show an increased imbalance between incoming and outgoing energy, but the energy will actually be absorbed further up in the atmosphere by the increased amounts of water vapor and it will never show up as IR back radiation and thus never be absorbed by CO2 or CH4…

    Sure – the atmospheric temp. will be higher than it was before if water vapor increases, but CO2, CH4 and any other surplus anthropogenic gases won’t play any special role due to their IR absorbing capabilities.

    This would be a true negative feedback, which can never be measured by sattelites that simply measures the in/out energy budget.

    Please excuse the choppy language, I’m neihter a scientist nor a native speaker of the English language.

    Comment by Patrik — 7 Jul 2010 @ 4:05 PM

  214. Patrik, You have a pretty severe misunderstanding of radiative balance. First, the vast majority of the sun’s energy is in the visible. Second, even if greenhouse gasses absorb incoming IR, that energy is STILL absorbed and so warms the planet. Third, the only way that energy would not warm the planet would be if it were re-radiated to space, in which case it would be visible to satellites and have the spectrum characteristic of the temperature of the atmospheric layer that radiated it.

    Now this brings up another question: If you are not a scientist, then why do you think you understand science better than the scientists?

    Hint: You don’t.

    Comment by Ray Ladbury — 7 Jul 2010 @ 4:39 PM

  215. Re 213 Patrik

    Water vapor is responsible for a majority of the absorption of solar energy *within the atmosphere*, which itself is less than half of the absorption of solar energy by the Earth (over half of solar heating is at/within the surface material).

    Besides that:

    Consider the approximation that convection is completely zero above the tropopause and that convection will not with a lapse rate smaller than a convective lapse rate and that convection easily keeps the lapse rate from getting any larger than the convective lapse rate. … (to be continued)

    Comment by Patrick 027 — 7 Jul 2010 @ 4:50 PM

  216. There is just never going to be 100% certainty about any future prediction, especially when the thing being predicted is complex and when the time involved begins to stretch out. It’s just not possible. But that is what the public demands. Thing is, with as many economic implications as GHG emissions mediation has that demand is not unreasonable.

    When you factor in widespread rightwing suspicion of things scientific, which suspicion their talking heads regularly feed into, together with some good historical reasons for a general skepticism (other “scientific truths” have fallen by the wayside over time) the task of convincing people of the need to protect our planet from AGW gets downright difficult. Factor in an active corporate disinfomation campaign and you’re fighting a real uphill battle.

    This is probably a case where convincing the public 100% simply cannot be achieved so it’s likely be a waste of time to try. Many people have become so jaded that only an in their face emergency will do it. By then of course it’s too late.

    That’s why I prefer the most concrete evidence I can see, photographic evidence.

    Still even with this I am not 100% certain of what the future holds myself. I happen to see AGW as just one of many important environmental threats, so I get edgy at predictions. There’s alway a random factor in any situation, and we are learning new things all the time. I think greedy corporatists love it when “the intelligentsia” make predictions because they so often fail. Then these corporatists can then tie that failure to other environmental issues in an effort to get the public to simply dismiss it them all, thus giving them more time to rape and pillage our planet.

    Comment by Ron R. — 7 Jul 2010 @ 8:33 PM

  217. (cont. from my 215)…

    In that case, outside the convecting layer, equilibrium is achieved by have a temperature distribution such that net LW cooling balances net SW (solar) heating. Above the tropopause, at any level, the net downward SW flux (equal to the amount of solar heating below) equals the net upward LW flux. Below the tropopause, it is the sum of upward non-radiative fluxes and net upward LW flux that balances the net downward SW flux. In order to sustain thermally-direct convection (setting aside thermally-indirect motions that might extend into the ocean or upper atmosphere, driven by kinetic energy produced within the troposphere), there must be some net radiative (SW+LW) heating lower in the troposphere and some net radiative cooling higher in the troposphere (higher and lower being relative; it can be the case that all the heating is at the base of the troposphere (surface) and the cooling is distributed over the rest of the troposphere).

    The net heating or cooling of a layer is equal to the difference in net fluxes at the base and at the top of the layer.

    The reason for the existence of the (radiatively-forced) troposphere, when one is sustained (as on Earth or Venus or…) is that, in order to eliminate any net radiative heating or cooling, for the given optical properties, the lapse rate becomes larger than what convection would sustain within some layer – thus being (conditionally or absolutely) unstable to convection. Convection would then occur, cooling the lower portion of that layer and heating the upper portion. Note that in doing this, it tends to increase the lapse rate at the boundaries (for example, at the top, there is convective heating below and lack of convective heating above), so that when radiative-convective equilibrium is reached, the convecting layer may extend beyond the original layer that was larger than the tropospheric lapse rate. (Also, it’s possible for kinetic energy to drive thermally indirect motion that can actually pull heat downward, with this process extending outside the region where convection is radiatively-forced, but we can set that aside for now.)

    Within this troposphere, temperature at one level is related to temperature at another as determined by the tropospheric lapse rate; however, the temperature of the layer as a whole (using the temperature at some reference level) (when the troposphere is heated via convection/conduction/diffusion from an underlying surface, this ‘whole’ includes that surface) must be such that, for the given optical properties, the radiative fluxes…

    (setting aside geothermal and tidal heating, which are relatively tiny for planets like Earth, Venus, Mars, Mercury, and the Earth’s moon, etc. – planets like Jupiter are a different matter (and Io?))

    into and out of the whole layer must balance. Thus, when the convection extends (via conduction/diffusion) to the surface, the temperature at any reference level of the surface+troposphere, given the tropospheric lapse rate, and optical properties, must be such that the net upward LW flux at the tropopause is equal to the net downward SW flux at the tropopause – note that this includes solar heating both at the surface and within the atmosphere. Unless the solar heating is redistributed so much that the troposphere lifts off the surface, the temperatures beneath the tropopause are (in this approximation) unaffected by lifting some solar heating off the surface and redistributing it through the troposphere.

    Hence the importance of tropopause level forcing.

    If the solar heating within the surface+troposphere could be redistributed upward so that the solar heating of the surface were less than the net LW cooling of the surface, then the troposphere could lift off the surface with a reduced lapse rate below (the temperature would fall at the surface to bring the temperature into radiative equilibrium, though that would still depend on the temperature of the air above at various levels, depending on optical properties. But I wouldn’t expect an increase in water vapor to do that, because as water vapor is increased, it becomes nearly completely opaque to almost all LW radiation when it still lets a lot of solar radiation through (this large opacity is limited to lower levels of the troposphere and thus leaves room for CO2 and clouds, etc, to change the net LW flux at the tropopause and above; this is because the water vapor mixing ratio generally drops ‘precipitously’ (pun intended) with height within the troposphere. There is also less line broadenning and (I think) decreased line strength with increasing height, but that affects all gases (though maybe not equally?)). Thus, at the point where the net downward SW flux is very small, the net upward LW flux may still be much smaller, necessitating some non-radiative heat flux; only if (at/near the surface) that non-radiative heat flux were so small that it could be carried by conduction/diffusion with a lapse rate smaller than the tropospheric lapse rate (and that would have to be very very small) would the troposphere disconnect from the surface.

    (As it is, LW cooling of the ocean is concentrated within a thin surface layer, while some wavelengths of SW heating penetrate tens of meters or more (depending on turbidity), and that can drive convection within the upper layer of the ocean. Also, evaporative cooling (both via effect on temperature and salinity) at the surface can drive mixing or overturning. Freshenning of the surface water by precipitation or other sources can inhibit overturning, while winds (and tides and planckton) can supply kinetic energy to force mixing against a tendency to become stably stratified. Of course, when water is sufficiently near the freezing point and sufficiently fresh, thermal expansion is negative, and spontaneous convection would be driven by cooling from below or heating from above; a sufficiently deep portion of a freshwater lake may tend to be near 4 deg C while the upper portion gets warmer in summer and freezes in winter.)

    Keeping the total solar heating constant, an increase in solar heating above the tropopause would have a negative radiative forcing at the tropopause level by shading it. With stratospheric adjustment, the forcing could be smaller because the stratosphere would warm to increase the LW fluxes out to balance the increase in SW heating, and some of that change could be for the downward LW flux at the tropopause (a decrease in downward LW flux at the tropopause can occur for stratospheric cooling caused by GHGs – I say ‘can’ because it depends on the optical thickness of the stratosphere at the wavelengths where it can emit LW radiation, and if the optical thicknesses are high, it depends on where the warming or cooling occurs within the stratosphere. On Earth, the stratosphere is not very optically thick over most of the spectrum where it is significant (this being mainly from water vapor absorption bands in the stratosphere), so it radiates about the same flux upward to space as it does down at the tropopause even though the temperature is generally warmer in the upper stratosphere.)

    However, an increase in absorption of solar radiation in the stratosphere or troposphere can reduce the albedo (by absorbing photons that would have been or have been reflected) and increase the total solar heating.

    Comment by Patrick 027 — 7 Jul 2010 @ 8:43 PM

  218. What about reducing the feedback section and adding climate sensitivity, which is the sum of all feedbacks? This would define and counter a skeptic argument. I still think answers to skeptic arguments is a good use of space.

    Comment by RichardC — 7 Jul 2010 @ 9:01 PM

  219. Probably the best that can be said is:

    This is the evidence we have to date.

    This is what we believe that evidence means, and this is why we think that. However we acknowledge that there can never be 100% certainty in future predictions. Thus there is a chance that we are wrong; we estimate that our level of certainty is this while our level of uncertainty is this.

    Taking all of this into account this is what we believe will likely occur we fail to act on GHG.

    We believe that based on those risks the right thing to do would be to do something concrete about the issue.

    This is what we propose to be done about the issue, and this is what we estimate the cost would be to do it.


    An idea, new reports are coming in all the time and the public wonders how they relate to the overall picture. Perhaps wwe should have a system where every new legitimate study (by legitimate I am leaving out conflict of interest studies by industry hacks. Those studies should first be reproduced by others before inclusion) can be factored into a certainty/uncertainty index for quick checking by the public, e.g. a particular report now increases the certainty factor from 95.23% to 95.25% or perhaps lowers it from, 95.25% to 95.23% …

    Comment by Ron R. — 7 Jul 2010 @ 9:35 PM

  220. 209: Lubos is right about that (maybe only about that). Energy is conserved in nuclear processes. All that E=mc^2 tells you is that a massive object at rest has an energy equal to its mass (in appropriate units). I think the post really should be corrected on this point; it’s a shame to give ammunition to right-wing zealots by getting a basic physics point wrong in a discussion like this (it’s a physics point that has essentially nothing to do with the argument, of course, but it’s still silly to get it wrong).

    Comment by onymous — 7 Jul 2010 @ 9:43 PM

  221. I raised a genuine objection at 184 and it has been ignored. At 188 Ray Ladbury talks about IR radiation, but my objection is that HEAT loss occurs at night, and the “simple recipe for GHE” explanation seems to assume permanent pervasive high noon for each point of the globe. Perhaps it is the extreme simplification that rasmus has done – and for which I am grateful. Nonetheless I would also be grateful if we could ask whether latitude, longitude, the earth’s daily rotation and its yearly circumnavigation of the sun could also be remembered. If the Earth loses its heat at night, and if the night lasts half a day at the equator, and half a year at the poles, then why is the night not long enough to lose the extra heat that comes when C02 goes up by a tiny fraction? If C02 goes up by a few parts per million then why does not the speed of heat loss at night slow down by a similar proportion?

    Comment by Confused — 7 Jul 2010 @ 10:47 PM

  222. Re 220 onymous – Energy is conserved if mass is considered a form of energy; outside of nuclear reactions and relativity, mass is often not considered energy, so I think it might be a matter of perspective (?)

    Comment by Patrick 027 — 7 Jul 2010 @ 10:47 PM

  223. Please not that there is nothing magic about molecules having three atoms to have vibrational and rotational absorption. Homonuclear diatomics have no change in dipole moment with vibration, so there is no interaction with dipole radiation without changing electronic state, which is too much energy for IR. The same is not true of hetero-nuclear diatomic molecules.


    Comment by Rich — 7 Jul 2010 @ 11:06 PM

  224. Can we call optical thickness per unit distance (or per unit mass path or whatever other coordinate is convenient) ‘optical density’? If we could, ‘optical density’ = cross section per unit volume (cross sections can be absorption, scattering, extinction, or emission; emission = absorption at least for emission in one direction and absorption from that direction, at LTE, at a particular frequency, and when it matters, at a particular polarization; extinction cross section = scattering cross section + absorption cross section).

    About stratospheric cooling:

    Increasing LW optical thickness (emphasizing absorption/emission, as opposed to scattering) does this:

    Case 1 – constant optical thickness over all LW frequencies:
    1a. – isothermal stratosphere, positive tropospheric lapse rate: lapse rate :

    The upward LW flux at the tropopause (first, by blocking radiation from the surface and replacing it with less radiation from a cooler troposphere, then, by blocking radiation from the warmer lower troposphere and replacing it with less radiation from a cooler upper troposphere, etc.) – this saturates when all the radiation at the tropopause is emitted from very near the tropopause.

    The downward LW flux increases (by replacing the darkness of space with radiation emitted from the stratosphere) – this saturates when the stratosphere hides almost all of the darkness of space.

    Both of these effects reduce the net upward LW flux at the tropopause.

    When both of those effects are saturated, the net LW flux at the tropopause is zero (that tends not to be sustained in equilibrium climate because there has to be some net LW flux out to balance the net SW flux in – the climate response may involve a shift in the tropopause to ‘unsaturate’ the LW flux (such as by shifting upward to make the stratosphere thinner)).

    The upward LW flux at the top of the atmosphere declines; this saturates when all fhe flux is coming from the isothermal stratosphere.

    If the decrease in net upward LW flux at the tropopause is greater than the decrease in upward LW flux at the top of the atmosphere (which it will be, because the LW fluxes emitted from the stratosphere up and down both increase, and the decrease in the upward LW flux at the tropopause will be greater than the decrease in the upward LW flux into space that originated at/below the tropopause because of stratospheric absorption), the difference is a LW cooling of the stratosphere; holding the troposphere and tropopause steady, the stratosphere will cool until the downward LW flux at the tropopause and the upward LW flux to space have together decreased to bring the stratosphere back to equilibrium; this reduces the change to the net upward LW flux at the tropopause. When the troposphere and surface warm up to bring the net upward tropopause LW flux back into balance (equaling the net downward SW flux at that level), this increases the LW flux up into the stratosphere, and because some of that is absorbed in the stratosphere, the stratosphere warms a little bit and so there is a feedback in the downward LW flux at the tropopause causing some more warming below. The stratosphere could return to it’s original temperature – this will at least be true in the portion that acts like a skin layer if there is no albedo feedback and if there is no direct solar heating of the stratosphere (in which case, in order to be isothermal, the whole stratosphere must be a skin layer). Note that any solar forcing or decrease in albedo will tend to increase the stratospheric temperature even if there is no direct solar heating of the stratosphere, because the stratospheric temperature is a function of the upward LW flux from below. If there is direct solar heating of the stratosphere, then the full equilibrium involves a stratospheric cooling; as the LW optical thickness increases, the layer that is thin enough to be a skin layer shrinks, and by shrinking (while holding the distribution of solar heating constant), reduces the solar heating of that layer, so that the skin layer’s temperature declines towards the value it would have in the absence of direct solar heating.

    1b. The stratosphere’s temperature increases with height (due to direct solar heating), either from the base or above a lower isothermal portion.

    In that case, if the cooler lower isothermal portion is thick enough relative to the whole stratosphere, the downward LW flux will increase until it saturates; otherwise, it might increase, and then decrease as the lower cooler stratosphere blocks radiation from the warmer upper part; it would saturate when all the downward radiation at the tropopause originates from an isothermal portion or else from very near the tropopause.

    The upward LW flux to space will decrease until a sufficient portion originates in the upper stratopshere; it will then start to increase.

    If the lower cooler portion of the stratosphere is sufficiently thin and the upper warmer portion is isothermal over some thickness at the top, then when the optical thickness is large enough, farther increases could reduce the LW fluxes out of the stratopshere (by reducing the downward flux at the tropopause while the flux to space is saturated). If this effect overcomes the cooling from the portion of the reduced upward LW flux from below that would have been absorbed, then the stratosphere as a whole could warm. However, that warming would not be evenly distributed; There will be some cooling in the uppermost stratosphere at least because the LW emission to space gets concentrated toward the top of the atmosphere. As LW opacity increases, the top of the atmosphere could eventually approach the skin temperature as it would be with no direct solar heating.


    (Note that if there is a very very small amount of direct solar heating in a very very thin layer at the top of the atmosphere, it would be possible to reach the skin temperature (for no direct solar heating) in a portion of the uppermost atmosphere below the solar-heated top layer, if the LW opacity is not too large.)


    Case 2. optical properties vary with wavelength; optical thickness is increased at some wavelengths and not others.

    The LW fluxes change at each wavelength where optical thickness is added, in the same way (qualitatively) that they do for all wavelengths in case 1.

    However, the LW fluxes respond to temperature at all LW wavelengths. But it is true that (absent other feedbacks) the temperature changes so that, at the tropopause and above, the net LW flux leaving a layer in total changes to balance the optically-forced changes in the net LW flux leaving that layer.

    Stratospheric cooling would reduce the downward LW flux at the tropopause at wavelengths where the stratopshere has some optical thickness (but this is not necessarily the case if the optical thickness is large). It would also reduce the LW flux to space at wavelengths with some optical thickness within the stratosphere. But at wavelengths where the stratosphere is optically thick, the change in the LW flux depends more on the stratospheric cooling in the closest portion of the stratosphere; the base of the stratosphere could actually be warming, in which case, the downward LW flux from the stratosphere would actually increase at those wavelengths where the optical thickness of the stratosphere is large enough.

    When the troposphere+surface warm, the upward LW flux increases at all wavelengths (except, see next paragraph). Some of that would be absorbed by the stratosphere, causing warming of the stratosphere (not necessarily evenly distributed; it would tend to be concentrated in the base of the stratosphere at wavelengths with larger optical thickness, assuming some of the increased upward LW flux occurs at those wavelengths (see below)).

    However, the top of the troposphere and the base of the stratosphere have the same temperature (the tropopause temperature), so the changes in dowward LW flux and upward LW flux at the tropopause must be equal and thus have no effect on the net LW flux at those wavelengths where the optical thickness is so large that both fluxes originate from isothermal regions or very near the tropopause. Also, the tropopause will tend to shift a bit, and if the tropopause temperature manages to stay constant while the troposphere and surface warm (by rising in proportion to the warming divided by the lapse rate), then the resulting change in downward and upward LW fluxes will both individually be zero at wavelengths where there is sufficiently large optical thickness.

    Thus, after all levels have together reached a new equilibrium, even assuming no SW (albedo) feedbacks, there could be the same upward LW flux at the tropopause in total, or there could be slightly more if the tropopause shifted across a layer that absorbs solar radiation (thus ‘sequestering’ solar heating into the troposphere from what was the stratosphere), but the amount of that flux that is absorbed by the stratosphere could decrease because it might be shifted into wavelengths where the stratosphere doesn’t absorb as much of it. That would tend to cause stratospheric cooling (somewhere within the stratopshere).

    Comment by Patrick 027 — 8 Jul 2010 @ 12:10 AM

  225. …”That would tend to cause stratospheric cooling (somewhere within the stratopshere).” – even if the stratosphere had no direct heating from the sun.

    PS about feedback from shifting the tropopause:

    The only effect on the stratosphere would come from the changes in the upward LW flux at each level within the stratosphere caused by warming of the layer that was above the tropopause that is now below, because while the total solar heating and the total LW optical thickness of the stratophere may be reduced, the shift in the tropopause doesn’t directly affect either for the portion of the stratosphere above the new tropopause.

    But the upward shift in the tropopause could reduce the downward LW flux at the tropopause by decreasing the LW optical thickness of the portion of the atmosphere remaining above. However, by bringing the warmth underneath the tropopause closer to the rest of the remaining stratosphere, the remaining stratosphere could warm up a bit and radiate a greater LW flux downward; if the LW optical thickness were only either large or insignificant at any wavelength, then (would they tend to balance resulting in no net change in downward LW flux from that effect?)

    Comment by Patrick 027 — 8 Jul 2010 @ 12:24 AM

  226. Confused, Earth’s surface radiates day and night. As such it loses energy day and night. The only difference time of day or time of year or longitude or latitude make is the amount of INCOMING radiation. The processes are the same, and the simple picture Rasmus defined applies. In point of fact, the thing to remember is that Earth absorbs energy over 2pi steradians and radiates over 4pi steradians. Does that make it any clearer?

    Comment by Ray Ladbury — 8 Jul 2010 @ 4:10 AM

  227. Patrick 027 says:

    Re 220 onymous – Energy is conserved if mass is considered a form of energy; outside of nuclear reactions and relativity, mass is often not considered energy, so I think it might be a matter of perspective

    This distraction provides support for deleting the reference to it in the lead article. It was supposed to be about the greenhouse gas mechanism! Before you can say Jack Robinson, we’ll get on to the other populist nonsense attributing nuclear weapons to poor old Einstein in 1905.

    You could go further and argue that heat can never be created, outside of certain dissipative mechanisms ….that too is all a matter of perspective. I shall not reply again to this OT stuff.
    This is on topic. I don’t agree with your dismissal of my question about pressure broadening, which includes temperature. It is obviously vital otherwise the spectral absorption would consist of a series of delta functions. The question is whether we can get simplify it so as to avoid getting bogged down. One way would be to ask a climate model.

    Comment by Geoff Wexler — 8 Jul 2010 @ 6:13 AM

  228. A simple question:
    Suppose GHG stabilize at some level, say double the pre-industrial one.
    Will the forcing, and temperature rise, continue or will they stabilize too, at some (higher) level ?
    Is the danger of a runaway positive feedback just a vague fear, or is it based on robust calculations ?

    Comment by Jacob — 8 Jul 2010 @ 6:16 AM

  229. I think there should be a note at least that usually the term ‘enhanced greenhouse effect’ means that portion of the greenhouse effect which is owing to human activity. In the article, it might be owing to some natural fluctuation.

    Comment by Chris Dudley — 8 Jul 2010 @ 6:20 AM

  230. Re: my previous comment

    Not delta functions but sharp spikes. (I may make more mistakes then George Monbiot but I aim to correct them a bit quicker.. see Guardian)

    Comment by Geoff Wexler — 8 Jul 2010 @ 6:27 AM

  231. 222 Patrick 027 wrote: “Energy is conserved if mass is considered a form of energy; outside of nuclear reactions and relativity, mass is often not considered energy, so I think it might be a matter of perspective ”

    No. You can directly estimate the energy released in a fission event without reference to E=mc^2. The theory of nuclear fission is nonrelativistic. The mass lost in E=mc^2 is tiny compared to the total mass, not as tiny as the mass lost in a chemical reaction, but tiny none-the-less. The argument that was used in the 30s to estimate the energy released in a fission event follows. It is identical to the argument one would use to estimate the energy released in a chemical reaction. No change in mass is assumed.

    For a nucleus with Z protons and radius R the binding energy, E = Z^2 e^2/R where e is the charge on a single proton. They first estimated that E is about 10^8 times what it would be for a low Z chemical reaction because for, say, uranium, Z~=100 (Z=92 but we’re among friends). R is about 10^4 times smaller than atomic distance scales. Thus the binding energy in a nucleus is 10^8 times a typical chemical bond. It turns out that there is an empirical relationship for R based on the number of nucleons in a nucleus: R = ro A^1/3 where A is the number of neutrons + number of protons in the nucleus. If we split the nucleus into two identical pieces so that A-> A/2, Z->Z/2, R-> R / 2^1/3 ~= R/1.25 .
    The binding energy of the two remaining pieces is: 2 x (Z/2)^2 1.25 E = .6 E
    The first “2″ comes from there being 2 pieces. Thus the energy released from the fission event is about E-.6E = .4 E and remember that E is about 10^8 times the energy released in a typical chemical reaction.

    There are numerous points in this article that need work and deleting the remark about conservation of energy is a really easy one. The stuff on optical thickness needs improvement too.

    Comment by John E. Pearson — 8 Jul 2010 @ 8:06 AM

  232. Perhaps a bit nitpicky, but you imply that most or all of the energy in solar radiation is visible. This is not correct – only approximately 43% is visible [] . The important point is that most of the non-visible is “near” infrared which is much less absorbed by GHG molecules than “far” infrared.

    Comment by Nightvid Cole — 8 Jul 2010 @ 8:58 AM

  233. Ray, I think your making Confused’s explanation too complex — or I’m missing his question. Climate assessments are all based on long term averages, both time and location. Incoming solar is normalized and assumed mathematically to enter evenly throughout the 4pi steradians of the whole globe, 24 hours per day, 365 days per year. The fact that it physically actually varies by (vertical) hemisphere, by time of day, by one day’s weather, etc. matters not a twit in the analysis. The fact that upwelling IR radiation actually is relatively constant over time and place is just conveniently makes it easier to plug into the analysis. One other point I think Confused was asking about: the radiation leaving and cooling the surface is not the same as that leaving and cooling the entire biosphere, nor does it include the downwelling IR radiation returning to the surface.

    Comment by Rod B — 8 Jul 2010 @ 9:09 AM

  234. Jacob #228 : I think that your question sadly illustrates how it is difficult to explain properly simple things. The answer should be obvious to anyone who is interested in the GW issue, and still more after having read a supposed “simple presentation” for general audience. The forcing IS directly linked to the increase of GHG so it will of course stabilize if GHG concentration stabilize. Concerning the temperature , it is very important to realize that GHG are not a heater , but a blanket. They do not produce heat, they hinder the heat transfer throughout the atmosphere. So the temperature increases only transiently, because of two phenomena
    * the Earth takes some time to reach its equilibrium temperature (there is a relaxation time)
    * the GHG concentration is slowly increasing so the Earth cannot yet stabilize (there is also a growth time)

    BUT in the case of a stabilization of GHG concentrations it should be obvious to anyone that the temperature would also stabilize after some relaxation times.

    It is also important to understand that the main reason for the uncertainty in climate sensitivity (in my opinion) is that the observed slope is a COMBINATION of both time scales, but it is very difficult to determine the influence of each one. The same slope could be observed with a large sensitivity AND a long equilibration timescale, or a small sensitivity and a small time – but the final result would be different, since in the first case the temperature would keep growing during a longer time and reach a higher asymptotic level. The problem of sea level rise is pretty much the same. This is rather uncomfortable since it allows many people to claim that “wait , the sensitivity could be much larger and the timescale be also much larger, so the final result would be much more catastrophic” , leading to all kind of dire predictions. This is not false — it COULD be higher – but the question is : how to compute properly this risk , to base a cost-benefit estimate ? this is really tricky. The principle of precaution would give absurd results if we should act as if the worse predictions were certain – nobody should go out of his home in the case of a meteorite could hit him for instance. Much of the complexity of the GW issue arises from this uncertainty, IMHO.

    Comment by Gilles — 8 Jul 2010 @ 10:50 AM

  235. Here is a denialist critique re AGW (the “log function” argument) I saw on a blog. Any good answers?

    [blockquote]“The radiative forcing is a log function of CO2 concentration.”…This is an example of how the warmers outsmart themselves. A linear CO2-temp correlation is actually inconsistent with greenhouse warming, not evidence for it. Given this inconsistency there are 3 generic possibilities. First, the correlation is a coincidence. Second, there is an unknown inverse log positive feedback mechanism that magically makes up for the log decline in CO2 forcing with concentration level. Third, the causality runs the other way and the CO2 increase is due to the temperature rise, as some have argued and the ice core data seems to show.[/blockquote]

    I know it is a log function relationship, and I pointed out that for short time frames it looks more or less linear, but I am not sure about how long that timeframe is (when the relationship between CO2 & warming can be viewed as linear. Is it a century, or what?

    Also, if anyone has a good response, I’ll post it on that Catholic blog.

    Comment by Lynn Vincentnathan — 8 Jul 2010 @ 11:34 AM

  236. How about this as a [reason]( to act on climate change instead.

    Comment by Jeremy C — 8 Jul 2010 @ 11:36 AM

  237. Re 177 McGahill – another way of putting that is that GHGs help the surface, or surface plus some portion of the atmosphere (when optical thicknesses are large enough) retain heat in the same way that a thermos bottle slows the cooling of a warm liquid inside. As opposed to the way that the heat capacity of the liquid itself would slow it’s temperature change.

    Comment by Patrick 027 — 8 Jul 2010 @ 12:30 PM

  238. Re 234 Lynn Vincentnathan – a few helpful points

    1. Any continuous smooth relationship can be approximated as linear over a sufficiently small interval. It’s conceivable that the small changes in CO2 that the blog was referencing were too small to show the logarithmic nature of the relationship.

    2. Of course, climate sensitivity needn’t be constant over temperature, though it is also true that greenhouse forcing itself depends on temperature – but see point 1.

    3. I don’t think it was ever asserted that the temperature would increase linearly in proportion to CO2.

    Comment by Patrick 027 — 8 Jul 2010 @ 12:35 PM

  239. 234: Lynn said about logs and time “I pointed out that for short time frames it looks more or less linear, but I am not sure about how long that timeframe is (when the relationship between CO2 & warming can be viewed as linear. Is it a century, or what?”

    I see a bit of confusion in this question. The relationship for climate sensitivity is based on the concentration of CO2 and as far as I know time doesn’t enter into it. If earth’s co2 concentration (which I’ll just write as co2 to avoid having to say “concentration” all the time) is doubled then the mean temperature change is described by a function which is approximately logarithmic. Thus one can write:

    dT = c log(co2/co2_0) where co2_0 is the reference concentration. If the temperature change, dT, is 3K per doubling then c= 3K/log(2) ~ = 4.3 K

    As far as I know, this is basically a result from a lot of climate simulations. I don’t think there is any simple first principles derivation of the logarithmic dependence. You will occasionally hear people claim that Beer’s law is somehow responsible for the logarithmic dependence but this is nonsense. It doesn’t hold on venus for example.

    If you were to double the concentration overnight and then wait for the new mean temperature to settle down it would take some time. First the atmosphere and top couple meters of ocean would equilibrate which takes about a year. Next the top few hundred meters of ocean would equilibrate taking about 30 years and then the remaining part of the ocean would take about 1,000 years to equilibrate. At the end of the 1,000 years radiative balance will once again be restored and the mean temperature would have increased by about 3K. But it takes time. My picture is admittedly crude; there are all sorts of upwellings and downwellings of heat into and out of the oceans so the atmospheric temerature goes up and down, but my timescales are about right. Note that the logarithmic dependence doesn’t specify the time course of the increase in temperature. It just says that if double CO2 and wait long enough the temperature will go up by about 3K. Since the atmosphere heats before the deep ocean we see the temperature increase fairly fast (compared to the deep ocean bottom). If we lived in Atlantis we probably wouldn’t have noticed it yet unless we had very accurate ways to measure the temperature in the deep ocean.

    About smoothness etc: for |x| << 1 it turns out that log(1+x) ~ = x. Thus for small changes in co2 = co2_0 + dco2 where dco2 << co2_0 we can use the property of the log mentioned in the preceding sentence to write:

    dT ~= c dco2/co2_0

    which does show a linear temperature change for small dco2/co2_0 . I hope this helps a bit.

    Comment by John E. Pearson — 8 Jul 2010 @ 1:30 PM

  240. Re 227 Geoff Wexler
    This is on topic. I don’t agree with your dismissal of my question about pressure broadening, which includes temperature. It is obviously vital otherwise the spectral absorption would consist of a series of delta functions. The question is whether we can get simplify it so as to avoid getting bogged down. One way would be to ask a climate model.

    I didn’t intend my 165 to be a dismissal. I agree it is important (see my 177 I think the justification for main post refering to broadenning (and would have presumably refered to line strenth’s temperature dependence) as being secondary was that, while important in total and also to variation over altitude (via T,p) in optical properties per unit material , they can also be feedbacks, but as climate feedbacks, they are relatively minor compared to the Planck response and some other important feedbacks like water vapor and albedo.

    Maybe one way to simplify it would be to say that the optical thickness added by some amount of material depends on temperature, pressure, and composition, but that, for climate changes that are not too large, the optical thickness per unit material can be approximated as constant at a given pressure level in the atmosphere.

    Or more briefly, optical thickness varies in proportion to the amount of a substance that supplies it, but also depends on the conditions in which that substance is found, but that we can set that dependence on conditions aside for introductory purposes.

    Comment by Patrick 027 — 8 Jul 2010 @ 1:30 PM

  241. The analysis is false.
    It says the only source of incoming energy is solar insolation.
    Are you denying that the force of gravity adds energy by the sun & Moon causing tidal effects and hence friction energy?
    Are you denying that Gravitational potential energy, when the Earth moves closer to the sun or to another planet will result in potential energy being reduced and becoming more kinetic energy as measured by temperature? ie it warms

    Then are you saying that simply adding more GHGs will cause more warming, even when all 1366 W.m^2 is already in use to create the existing 32c of GHE, but adding more GHGs will result in more than the 1366 being used to create more GHE? IF this is true then why doesn’t more warming result when the amount of GHGs water vapor increases from 33% to 100% when it rains?

    Arrheius’s 1896 thought experiment said that when you add a GHG to a supply of photons you get warming. So what happens when you add a GHG, but all the photons are already in use creating the existing 32C of GHE? Do you not get an excess of GHGs and NO ADDITIONAL WARMING, because there is no energy available?

    Sorry but you are mis applying the real greenhouse effect.

    Comment by John Dodds — 8 Jul 2010 @ 1:59 PM

  242. RE #238, Thanks, John, but it is still a bit confusing. You say that if we double CO2 and wait long enough the temperature will go up by about 3K. I’ve heard that is the most likely outcome. But I guess if it’s a log relationships, then it matters where you start when you double the CO2. Like if there are 800 ppm in the atmosphere and we double that to 1600, would it again increase by 3K? I’m assuming that they are talking about doubling CO2 from preindustrial 270ppm to 540 ppm or something like that, and it would be a different factor (not 3K) if we start way higher in ppm or way lower.

    This may be new denialist argument — that the “warmers” are asserting a linear relationship, when in fact it is a log relationship — and everyone knows the log function goes pretty flat, so increasing CO2 is no real problem, as the “warmers” assume….

    Comment by Lynn Vincentnathan — 8 Jul 2010 @ 2:03 PM

  243. I suspect you should revise your discussion and graph of predicted vs observed surface temperature. We haven’t sent probes to measure the surface temperature of all planets and four moons. We do have measured temperatures for some places on our Moon (where the temperature varies about 200 degK between day and night) and Mars (where there are also large temperature swings), one datapoint for Venus (confirming that the surface is extremely hot) and possibly one for Titan.

    Most of your “surface temperature” data is calculated from the spectrum of the radiation emitted by the planet (including a variable factor, emissivity). For the gas giants, we can’t directly observe radiation from the surface of the planet, so your “surface” temperatures presumably comes from some point high in the atmosphere. On your graph, planets and moons lie on the line when their “surface” temperature has been determined at a location where incoming and outgoing radiation are in equilibrium (adjusting the emissivity) and off the line when other locations are used. If the temperature of the atmosphere where incoming and outgoing radiation are in equilibrium had been used to determine the “surface” temperature of Venus, Venus would be colder than the Earth (because it has a much higher albedo)!

    Comment by Frank — 8 Jul 2010 @ 2:55 PM

  244. Dear Gavin, Chris,

    When you would have taken the time to read what I have written, you would probably have reacted a bit more moderate. To start with, Gavin made the assumptions about the impact of possible latent heat loss to space, not I. Chris, you did no even bother to read what I posted. What I did post was my opinion, that there are numerous processes which are not commonly recognized in a “vacuum” that contribute to non radiative energy transfer. I guess most of the respondents have not realized that cubic space increases with the third power of the distance from the centre of the earth? This means that any molecule with an above average speed will travel a long way into space before colliding. But it will collide. And in the process it will cool down, transferring energy to outer space.

    [Response: This is completely irrelevant for climate. - gavin]

    Comment by Iskandar — 8 Jul 2010 @ 4:00 PM

  245. Re 240 John Dodds The analysis is false.

    It’s an approximate description.

    It says the only source of incoming energy is solar insolation.
    Which is a very good approximation for at least the inner planets (and their moons).

    Are you denying that the force of gravity adds energy by the sun & Moon causing tidal effects and hence friction energy?

    You’re forgetting the energy from combustion of fossil fuels and the much larger geothermal heat flux from the interior. But all these together are on the order of 0.1 W/m2 for Earth, and will be small for the other inner planets as well. They add heat to the climate system; whereever that heat is delivered to the climate system (at the surface, or mostly within the ocean for the tides), the effect is the same as if it were from the absorption of solar energy. So it would be like solar heatinger were on the order of roughly 0.04 % larger, with less than a tenth of that difference managing to penetrate deeper into the oceans than the rest. The effect would be negligible, and it wouldn’t change how the greenhouse effect works. (There is another affect of the tides – the forced motion (the viscous damping of that being the way that the tidal energy is realized as heat) – this has some importance to oceanic circulation but it does not have a big impact on global average surface temperature; of course processes in the interior of the Earth shape the geography and chemistry of the surface and atmosphere over time, but that’s really on a different level).

    In other places in the solar system or elsewhere, where tidal and/or geothermal or some other heat source (like impactors or a stellar wind, etc.) is large enough relative to stellar heating to make a difference to the surface and atmospheric conditions of a planet or moon or asteroid, then these things could be taken into account with the known physics.

    Are you denying that Gravitational potential energy, when the Earth moves closer to the sun or to another planet will result in potential energy being reduced and becoming more kinetic energy as measured by temperature? ie it warms

    That’s not how it works. An object in the gravitational field of other objects has some gravitational potential energy and may have some kinetic energy. In a constant circular orbit about one other object, the two quantities stay constant; in an elliptical orbit or an orbit perturbed by other objects, there is some conversion between gravitational potential energy and the kinetic energy of the motion of the object through space. The only way such kinetic energy of these objects is converted to heat within or at the surface of such an object is via impacts with other objects (or via electric currents driven by each other’s magnetic fields, but in familiar interplanetary conditions, that’s not going to be significant either). On that note, there would be some (relativistic) doppler effect of the Earth’s motion on the energy of the photons it recieves from the sun (blueshift in morning, redshift at night, with the orbit and rotation being both prograde), but that’s probably insignificant (as are the gravitational lensing and redshift as photons reach, leave, or go by the Earth).

    Then are you saying that simply adding more GHGs will cause more warming, even when all 1366 W.m^2 is already in use to create the existing 32c of GHE, but adding more GHGs will result in more than the 1366 being used to create more GHE? IF this is true then why doesn’t more warming result when the amount of GHGs water vapor increases from 33% to 100% when it rains?

    Sorry but almost every part of that is wrong.

    The ~ 1366 W/m2 solar flux at Earth must be divided by 4 and then multiplied by approximately 0.7 to get the global time average solar heating (because the Earth’s albedo for the solar radiation is 0.3 and, being nearly spherical, has a surface area 4 times it’s cross-sectional area).

    Aside from (non-Planck response) feedbacks, that solar heating is not changed by the greenhouse effect or changes in the greenhouse effect. In climatic equilibrium, the same LW flux must go out as what comes in as solar radiation (plus the very small fluxes mentioned earlier). That flux depends on temperature and on the greenhouse effect. Changing the greenhouse effect changes where the LW fluxes come from within the system, and thus changes the temperatures required to have an equilibrium.

    The concentration of some greenhouse gases and other agents (clouds), and the amount and vertical distribution of solar heating, and the temperature and it’s vertical distribution, all vary over the globe and over a year and over shorter-term internal variability. But none of that changes the basic physics and how it works. It just means that a complete description is more complicated. But in terms of global time averages, the requirement of balances in vertical fluxes still applies for climatic equilibrium.

    Arrheius’s 1896 thought experiment said that when you add a GHG to a supply of photons you get warming. So what happens when you add a GHG, but all the photons are already in use creating the existing 32C of GHE? Do you not get an excess of GHGs and NO ADDITIONAL WARMING, because there is no energy available?

    That sounds like Beer’s law. First of all, not all of the available photons are used for the present-day GHE, in the sense that some of the radiation from the surface does escape directly to space. Secondly, the phrasing ‘all the photons are already in use’ could mean a number of things – see above, this paragraph, below, whatever…

    Thirdly, Beer’s law only applies when there is no emission of photons along the path considered. GHGs emit photons as well as absorb them, but they emit according to there temperature. In the most general description: because the atmosphere is generally heated by the surface, it must be colder than the surface, so that it absorbs more LW photons from the surface than it emits to the surface that are absorbed by the surface, and so that convection can carry heat from the surface to the atmosphere where there is a troposphere. The atmosphere reduces the outgoing LW flux to space by blocking radiation from below and replacing it with it’s own emitted flux, which, being colder than the surface, will be less than what it absorbed from the surface. There is a general decrease in temperature over height within the troposphere, so even if all radiation from the surface is blocked, the outgoing LW flux can still be decreased by having the colder upper troposphere block more radiation from the lower troposphere. What happens if there is no troposphere or what happens above the troposphere is different, but in that case, it doesn’t affect the surface temperature in the same way.

    Comment by Patrick 027 — 8 Jul 2010 @ 4:31 PM

  246. The paragraph immediately above the paragraph with the bold phrase should have been in italics indicating quotation.

    PS had similar error in above response to 239 in response to 227 Geoff Wexler

    Comment by Patrick 027 — 8 Jul 2010 @ 4:35 PM

  247. Re 231 John E. Pearson – but isn’t the energy that comes from such reactions is equal to a loss of mass (at least, once the energy leaves (?)). But good point about chemical reactions (as in, it’s not just nuclear reactions).

    Comment by Patrick 027 — 8 Jul 2010 @ 4:38 PM

  248. Re 238 John E. Pearson (and/re Lynn Vincentnathan)

    You will occasionally hear people claim that Beer’s law is somehow responsible for the logarithmic dependence but this is nonsense.

    So true. At any particular frequency (wavelength), Beer’s law does allow and call for eventual saturation in some conditions, which would not be logarithmic but rather asymptotic, and would occur when, at the point considered, photons reaching that point are being emitted from places all at the same temperature as at the point considered. A logarithmic function doesn’t have an asymptote; it keeps increasing, just more slowly. The logarithmic proportionality of forcing to CO2 amount is due to the shape of the CO2′s absorption band (glossing over finer scale texture and some bumpiness, going away from the center of the band, optical thickness per unit mass path of CO2 decays exponentially, within certain limits) and that it’s central portion is saturated (at the tropopause level, the net LW flux is zero at the center of the band; at the top of the atmopshere, the upward LW flux has reached a minimum within the CO2 band and farther increases in CO2 increase the upward LW flux at the center of the band (at least before the temperature responds). Aside from the central rebound in outgoing LW radiation at TOA, the changes in LW fluxes caused by changes in CO2 occur at the edges of where the CO2 absorption occurs, and are proportional to an expansion of that interval of wavelengths, which is approximately the same for each doubling (until the amount of CO2 is so much that other parts of it’s absorption spectrum come into play).

    Comment by Patrick 027 — 8 Jul 2010 @ 4:50 PM

  249. John Dodds (81): Brilliant! Your gravity theory of climate change is somewhat similar to that of the unorthodox genius Steven Goddard. You should not even waste your time here – contact the Best Science Blog immediately!

    Comment by Rocco — 8 Jul 2010 @ 4:56 PM

  250. Re 234 Lynn Vincentnathan
    the warmers that Catholic blog

    Maybe try recommending the movie “Evan Almighty” (it’s a good movie!)

    Comment by Patrick 027 — 8 Jul 2010 @ 5:00 PM

  251. Patrick027,
    Uh, I think you are wasting your time on Mr. Dodds. He is either a brilliant satirist or a loon. His name links to a paper purporting to show that gravity is responsible for climate change.

    Comment by Ray Ladbury — 8 Jul 2010 @ 5:18 PM

  252. John Pearson, Lynn…

    It is worth keeping in mind that radiative transfer encompasses a variety of different “regimes” for which different impacts are important. For instance, scattering by particles is negligible in the limit of small particle sizes and large wavelengths, but not so in various other scenarios. With regard to “logarithmic” arguments for GHG absorption, many of the popular talking points concerning how the greenhouse effect works is quite Earth-centric and may not apply in the same way to different atmospheric regimes.

    For instance, the notion that diatomic molecules like H2 or N2 do not behave like greenhouse gases is not at all the case in general, despite being true enough for Earth. That scattering of infrared radiation is very small on Earth may not be the case on early Mars where you could get condensation by CO2 and CO2 clouds. Similarly, the logarithmic nature of the radiative forcing does have a theoretical basis, but strictly speaking, is only a good approximation that is valid for a relatively narrow range of CO2 concentrations (although the range is broad enough to encompass what you’d expect to see for our present day climate change). In the limit of very low CO2 concentration as well as in very high amounts (~0.2 bars of CO2 for instance when many weaker absorption features that are unimportant now start to become vital) the log curve is no longer valid. CO2 also becomes a more effective greenhouse gas at higher atmospheric pressures (even if super-imposed upon several more bars of a non-greenhouse gas like N2 would generate a much stronger GHE by increasing absorption away from line centers). Line-by-line type radiative transfer calculations used to find a forcing for a certain fractional change in CO2 (e.g., the Myhre et al 1998 paper) cannot be applied to conditions like Venus or ancient Earth. Various parametrizations for line and continuum absorption by CO2 yield similar results in present-like atmospheres, but differ substantially in CO2-rich atmospheres in the past, and at the present day it is not possible to obtain quantitatively confident answers with the usage using current models to examine such climates (e.g., Halevy et al., 2009, JGR).

    Comment by Chris Colose — 8 Jul 2010 @ 5:45 PM

  253. Please forgive if I’m repeating something someone else said.

    I’m getting the impression that the general public is 10-20 years behind the basic understanding of the researchers. I say that because I like to think I’m pretty sharp, and it has taken me some years to get to the point where I think I have a pretty good understanding. Another reason I say that is because I’m answering a lot of yes-but challenges, with, true-but-that-is-already-factored-in answers.

    Q:”It’s the sun.”
    A:”The sun isn’t changing and, if you look, it’s the outbound flow of energy that originally came from the sun that we’re talking about. Yeah, we know the sun warms the earth.”

    Q:”More clouds.”
    A:”Well maybe, but also more water vapor. Else, what are the more clouds made from?”

    The above is a good explanation. However, I would not assume the public does a good job of keeping things in perspective, or even that they understand what K means. It would be good to explain that the energy coming in from the sun and re-emitted by the earth is orders of magnitude larger than any other energy exchange the earth is involved in. It should not be so hard to accept that doubling the concentration of a gas that interacts with earth’s radiative output (which is orders of magnitude larger than any other energy loss), over time and with feedbacks included, can change change the surface temperature by about 1%. Not a lot of the general public understand just how little change, on an absolute scale, is being predicted. (Or how that little change can affect them in large ways for that matter, but first work on getting them to accept that it will get warmer. (And more acidic, but that is another battle.)) That might not be terribly precise, but it’s in the right ballpark and it keeps things simple.

    Comment by Chris G — 8 Jul 2010 @ 6:58 PM

  254. Minor grammar error at the end:

    “claims of negative feedback is controversial”

    should be

    “claims … are controversial”

    Comment by Chris G — 8 Jul 2010 @ 7:19 PM

  255. Re my 246 Re 238 John E. Pearson (and/re Lynn Vincentnathan)

    You will occasionally hear people claim that Beer’s law is somehow responsible for the logarithmic dependence but this is nonsense.

    So true. At any particular frequency (wavelength), Beer’s law does allow and call for eventual saturation in some conditions, which would not be logarithmic but rather asymptotic, and would occur when, at the point considered, photons reaching that point are being emitted from places all at the same temperature as at the point considered.

    Swap ‘Beer’s law’ for ‘Schwarzchild’s equation’.

    Beers law: transmission of a beam of radiation decays exponentially over optical thickness (A flux distributed over solid angle decays as a sum of exponentials; if there is scattering it can get complicated).

    Including emission along a path (Schwarzchild’s equation), a flux will approach saturation as the optical thickness becomes large over scales where the temperature variation is small; at smaller optical thicknesses, the temperature distribution may vary and larger temperature variations make the nonlinearity of the Planck function important, but over short distances, the temperature variation can be approximated as linear and the associated Planck function values can be approximated as linearly proportional to distance for small temperature changes, so the flux will approach an asymptotic value as a hyperbolic function (the difference between the flux and the saturation value of the flux will be proportional to 1/optical thickness per unit distance (assuming isotropic optical properties (or even somewhat anisotropic properties), it will have that proportionality for all directions and thus for the whole flux across an area).

    The net flux goes to zero when both fluxes in opposite directions saturate, except where the net flux is across a temperature discontinuity; the top of the atmosphere can have such a discontinuity in effect.

    Comment by Patrick 027 — 8 Jul 2010 @ 7:21 PM

  256. Re 253 Chris G – sounds right to me.

    Comment by Patrick 027 — 8 Jul 2010 @ 9:19 PM

  257. Re 244 Iskandar – as stated several times in several different ways, the gist is this: Yes, space is not a complete vacuum and mass can flow in or out of the atmosphere, carrying energy. But the process is just not big enough to matter, except to long-term chemical evolution (very slow H escape) and things like aurora; the energy is too small to make a significant difference to climate. (PS I’m not sure about proportionalities on this point but at least some portion of what enters the atmosphere is matter that left the same atmosphere and vice versa – aside from gravity, charged particles can be trapped by the magnetosphere, which has a tendency to deflect charged particles coming from space; the particles within the magnetosphere can gain energy from electromagnetic interactions, but see previous statement.)

    Comment by Patrick 027 — 8 Jul 2010 @ 9:31 PM

  258. 172
    Patrick 027 says:
    6 July 2010 at 11:35 PM

    “Note that it is possible, hypothetically, to introduce so much optical thickness that the tropopause level or any level besides the very top of the atmosphere becomes saturated (zero net LW flux); ”

    Is it? Optical thickness depends on density; does it not? The density of an atmosphere is roughly a negative exponential; it declines very rapidly with altitude at first, but as the altitude increases, the rate of decline decreases. The rate of decline decreases so much that it is a bit of a judgment call where the atmosphere ends and space begins.

    Even if you had a pure CO2 atmosphere that had liquid CO2 at the bottom, there would still be a large region below what you would consider space that was not saturated optically. You would definitely have some greenhouse effect. If you doubled the mass of the atmosphere, the region below what you called space and above what you called optical saturation would get wider, and you’d have more greenhouse effect.

    OK, we aren’t doubling the atmosphere. However, we are converting carbon in a liquid or solid state to CO2 in a gas state and dumping that into the air. (Effectively trading O2 for CO2.) The number of moles (mass) of CO2 in the atmosphere is increasing and the CO2 molecules will interact with the IR photons regardless of what else is going on in the atmosphere.

    Comment by Chris G — 8 Jul 2010 @ 10:31 PM

  259. Uh, bad example, if you had enough mass above to liquify CO2 at the bottom, probably the added CO2 would just be more liquid on the bottom. So, let’s run it the other way. Start with just enough to get liquid at the bottom and half it. The region between space and saturation will be less, and you’ll have less GHE.

    Comment by Chris G — 8 Jul 2010 @ 10:43 PM

  260. I’m not doing a good job here. What I’m trying to get around to is that a lot of people treat the top of the atmosphere as a constant. It isn’t; in particular, it is not in terms of partial pressure (and hence density) of CO2.

    Comment by Chris G — 8 Jul 2010 @ 10:58 PM

  261. Rasmus in #166,

    I thought it must be something like that. Thanks again especially for fig. 4. That is a nice way to present the idea.

    [Response: My mistake, and since I'm away on holiday, it took a while to correct - my Internet connections are not as frequent as when I'm working. Anyway, thanks a lot! -rasmus]

    Comment by Chris Dudley — 8 Jul 2010 @ 11:07 PM

  262. Re 228 Jacob -

    Let T’ be the temperature departure from a reference equilibrium and For’ be an imposed forcing departure from a reference equilibrium, and let F’ be the feedback** (** including the Planck response) in terms of an increase in net outgoing radiation (from a reference equilibrium), where F’ = G*T’, so that G is positive if the feedback (including the Planck response) is negative (which is what we expect). Let C be the heat capacity (per unit area).

    The heating rate = the radiative imbalance = For’-F’
    C*dT’/dt = For’-F’ = For’-G*T’
    dT’/dt = (For’-G*T’)/C

    At equilibrium, T’ is constant and equal to Teq’, so G*Teq’ = For’, thus Teq’ = For’/G, so that equilibrium climate sensitivity = 1/G (perhaps G could be called the climate ‘insensitivity’).

    dT’/dt = -G*(T’-Teq’)/C

    C is not constant for the dT’/dt equation to apply because heat penetrates through different parts of the climate system (different depths of the ocean in particular) over different time scales (also, if T’ is supposed to be at some reference location or the global average at some vertical level, T’ at other locations will vary; C will have to be an effective C value, the heat per unit change in the T’ at the location(s) where T’ occurs)

    But if we held C constant, then
    for a fixed Teq’:

    dT’/dt = d(T’-Teq’)/dt = -G*(T’-Teq’)/C

    T’-Teq’ = (T’0-Teq’0)*exp(-G/C), where T’0 and Teq’0 are values at time 0.

    Thus the time scale for equilibration is proportional to the climate sensitivity * heat capacity.

    If Teq’ = Teqamp*cos(w*t)
    T’ = Tamp*cos(w*t-phaselag) = a*cos(w*t) + b*sin(w*t)

    Tamp = (a^2+b^2)^(1/2)
    tan(phaselag) = b/a

    dT’/dt = -w*a*sin(w*t) + w*b*cos(w*t)
    = -G*(T’-Teq’)/C
    = -G*[a*cos(w*t) + b*sin(w*t) - Teqamp*cos(w*t)]/C


    w*a = b*G/C and w*b = (Teqamp-a)*G/C
    b = (Teqamp-a)*G/C
    b/a = w*C/G
    (Teqamp/a – 1)*G/C = w*C/G
    Teqamp/a = w*(C/G)^2 + 1

    a = Teqamp/[w*(C/G)^2 + 1]
    b = a*w*C/G

    tan(phaselag) = w*C/G

    = (a^2+b^2)^1/2
    = Teqamp/[w*(C/G)^2 + 1] * [1 + (w*C/G)^2]^(1/2)

    Tamp/Teqamp = [1 + (w*C/G)^2]^(1/2) / [1 + w*(C/G)^2]

    I thought I could simplify that farther but I forgot what I did the last time…hopefully the algebra is correct.

    Comment by Patrick 027 — 8 Jul 2010 @ 11:43 PM

  263. Correction: solution for constant Teq’ and C:
    T’-Teq’ = (T’0-Teq’0)*exp(-G/C * t)

    Comment by Patrick 027 — 8 Jul 2010 @ 11:46 PM

  264. #253
    The public is more like 30-60 years behind I’d say. With hindsight and as far as the big picture is concerned, the consensual stuff published the 80s was already pretty good.

    Comment by Anonymous Coward — 9 Jul 2010 @ 7:49 AM

  265. #264,
    I think your estimate is better than my first one.

    The point is that the researchers have already been through something like

    A) What effect will more CO2 have?
    Ah, warming.
    B) How much warming are we seeing now?
    Whatever the increase is, about 0.7 K.
    C) How much warming can we expect from BAU?
    Likely in the range of 2 – 4.5 K per doubling.
    D) What effects will, say 3.5 K, have?
    Uh, Houston, we have a problem.
    E) How would we prevent this?
    Stop producing CO2 (and other GHGs).

    So, a lot of times, the focus of the argument is around points D and E, because for them, A-C are old news, while a lot of the public is still stuck at A. If you are stuck at A, arguments concerning B-E don’t mean anything to you.

    Incidentally, I get the impression that many people consider the answer to E to be a policy decision and take offense at scientists suggesting policy. It’s not policy; it’s a physical answer to a physical problem. Policy is how to go about reducing the use of fossil fuels which are producing the extra CO2. Personally, I like the idea of taxing fuels at their source. It was my favorite idea even before I read Jim Hansen’s book, but I’m not expecting that to happen.

    Comment by Chris G — 9 Jul 2010 @ 8:51 AM

  266. Rasmus,
    I think you’d achieve a greater comprehension from your audience if you used the inverse-square law instead of Gauss’ theorem. Even architects are familiar with the law in terms of inverse-square (for lighting). Gauss might be more precise, but I think it is a foreign concept to more people than inverse-square.

    Also, if you have a section for ‘(iv) The relationship between temperature and altitude’, IMHO, you should also have a section for the relationship between density and altitude, because you are previously talking about optical absorption, which, the rate of which I believe is more related to the density of the gas than to its temperature.

    Comment by Chris G — 9 Jul 2010 @ 9:52 AM

  267. Re Chris G – I often picture the situation in mass coordinates – how much mass is above a given level. The top of the atmosphere (TOA) would be at 0 to a first approximation…

    (and TOA would actually fill the space surrounding the Earth – though given the spherical geometry, W/m2 would have to be expressed as m2 at a reference radius or else W/m2 will drop as the inverse square; most of the mass of the atmosphere is within such a narrow range of radii that we can approximate the global area as constant with height (and ignore the apparent upward curvature of straight lines) (PS increasing index of refraction going downward would tend to counteract both effects by bending rays downward and increasing blackbody intensities and magnification of lower levels as they appear from above – and to a first approximation we can ignore that as well. etc… Relativistic effects, etc.) – so we can approximate TOA as extending downward to the same narrow range of radii and then just consider the fluxes at the base of TOA (refering to TOA specifically as the base of that region of zero mass) to get around the spherical geometry)

    About increasing optical thickness per unit mass path (via changes in composition or imposed conditions) –

    About hypothetically doing that until all levels are saturated except at TOA:

    Of course, there are realistic limits for realistic materials for how much optical thickness could be packed into a given mass path; I am refering the a limit wherein this approaches infinity – recognizing the nonzero mass at TOA, optical thickness would be held at finite or zero values at/above TOA.

    Approaching that limit, the net flux goes to zero except at TOA (and above). There always has to be a net flux at TOA (for nonzero temperature and assuming optical thickness is not entirely from scattering/reflection), so the process concentrates the emission to space into an ever thinner region next to TOA. Upward concentration of that source of flux to space would, in isolation, have a cooling effect within the upper portion of that region and a warming effect just below that.

    Comment by Patrick 027 — 9 Jul 2010 @ 11:55 AM

  268. Re my 245 The only way such kinetic energy of these objects is converted to heat within or at the surface of such an object – I forgot to include the raising of tides (in a process that is not completely elastic/inviscid/adiabatic) – the relative smallness of that for most familiar objects of course having already been covered…

    Comment by Patrick 027 — 9 Jul 2010 @ 11:59 AM

  269. It is all very well to argue the science, but what you have here is a question of leadership. Most of the people who even bother to look at your “simple” explanation of the Greenhouse Effect (instead of getting it third or fourth hand, from some pundit) will not have the background to vett your science. So, you are asking them listen to you based on the simple fact that you are “scientists,” and to take action on the basis of what you believe will happen (because, despite your best efforts, you are not yet gods, and cannot actually know the future). And you aren’t just asking them to change the brand of shampoo they’re using. You’re asking them to make serious changes in the way they do practically everything. Would it be surprising if they were to ask you what you are doing to reduce your carbon footprint?

    You are asking people to be lead by what you have to say. But, you don’t get to be a leader just because you say “follow me.” You don’t get to be a leader just because you are right. You get to be a leader by leading, by going first. If you want people to believe what you say, show them that you have the courage of your convictions by taking action, the kind of action you are asking them to take.

    Comment by Gordon — 9 Jul 2010 @ 12:43 PM

  270. Gordon says, “because, despite your best efforts, you are not yet gods, and cannot actually know the future”

    OK. I’m sorry, but this statement betrays an ignorance so profound that I can only conclude the poster has missed not just the 21st century, but the 20th and 19th centuries as well. It requires nothing godlike to predict the future when it comes to physical systems. It requires understanding the science sufficiently and playing the fricking odds. This is not divination. This is science that has largely been known for over a century!

    And I’m sorry you are going to have to change your life, but your life is going to change one way or another. Oil is running out and we don’t yet have anything to replace it. That is a reality quite independent of climate change. All climate change does is make it more imperative to develop a sustainable energy economy sooner rather than later. It means we don’t have the added luxury of burning up all the coal as well as all the oil.

    So, Gordon, get in your time machine, set it 200 years ahead and join us in the 21st century.

    Comment by Ray Ladbury — 9 Jul 2010 @ 1:25 PM

  271. Patrick,
    I’m not sure I’m following what your definition of the TOA is. It sounds like you are saying that TOA is where most of the mass is and that it is at a fixed height.

    For instance, you wrote, “Of course, there are realistic limits for realistic materials for how much optical thickness could be packed into a given mass path;”.

    Yes, but the upper part of the atmosphere will remain thin by virtue of the fact that if you add more gas, the TOA goes to a higher altitude.

    What I’m saying is that TOA, as far as radiative energy is concerned, for CO2 or other IR absorbing gas, is effectively the altitude where the chance that a photon will be absorbed, and emitted back in a direction that will lead it to being absorbed again by a molecule in the atmosphere, becomes negligible.

    The two heights are related, but they are not the same. Most importantly, the altitude of the TOA from a radiative energy standpoint is concerned, is not constant.

    Comment by Chris G — 9 Jul 2010 @ 1:34 PM

  272. It goes back to #1.

    The tropopause is where the energy being absorbed from the sun is approximately equal to the energy being absorbed from the earth. It is not fixed or constant either and varies with latitude and season.

    Comment by Chris G — 9 Jul 2010 @ 1:38 PM

  273. #269,
    We’ve entered into the commons problem. For instance, it would be better for the planet if I took my family off the grid. But it would put my children at a distinct disadvantage because my employment requires that I be on the grid, and my children’s college prospects depend a lot on me being employed.

    It’ll take legislation to give people the feeling that the sacrifices are being made fairly and across the board, but no one wants to go first – least of all the fossil fuel industry.

    Comment by Chris G — 9 Jul 2010 @ 1:44 PM

  274. Gordon,

    The RC Team has taken action by spending countless hours writing and moderating this world-class blog so that people like you and me can become better educated. The hope is that you and I can then carry this message to the masses. The Team is very busy with their own research and unfortunately, defending themselves against ridiculous accusations, and yet they persist. The Team are our “heroes” and we cannot ask them to be superhuman.

    Having said that, I agree 100% that scientists need to model Dr. James Hansen and others like him and begin to marry science and politics. Science alone had not been able to convince policymakers in the US, Canada, Auistralia, and others to take immediate, drastic action to curb and then reduce emissions.

    The latest Climate Interactive Scoreboard shows us that 4C is likely even in the unlikely event that countries actually do what they propose. 4C is catastrophic and yet there is still political hemming and hawing.

    Scientists need to start forcing themselves into the media limelight. People still respect scientists and if, as a large coordinated group, they keep showing what is likely to happen in a 3 – 5C warmer world, people would take notice and demand action.

    Stepping down now….

    Scott A. Mandia, Professor of Physical Sciences
    Selden, NY
    Global Warming: Man or Myth?
    My Global Warming Blog
    Twitter: AGW_Prof
    “Global Warming Fact of the Day” Facebook Group

    Comment by Scott A Mandia — 9 Jul 2010 @ 1:51 PM

  275. Chris G, and the optical depth discussion…

    The “TOA” is, strictly speaking, at pressure = 0, and of course above the tropopause. Radiative forcing at the tropopause and TOA are only similar in that regions above the tropopause are typically optically thin enough to not matter much for the net radiative budget (minus the strong UV depletion in the stratosphere). It’s not really the top of the whole atmosphere that shifts to higher altitudes, but the region of bulk emission to space which we can locate at one unit optical depth below the optical depth of the whole atmosphere (looking down from space). The definition of optical depth TAU is the integral from z1 to z2 of k*rho*dz where k is an absorption co-efficient with dimensions of area per unit mass, and rho is the density of the absorber. Thus one can make the optical depth smaller by moving two fixed altitude levels ever more close together until z1=z2.

    Looking down from space, a sensor will see emission coming from all levels of the atmosphere depending upon the opacity in that wavelength region. Regions around 10-12 um in the atmosphere window can originate from the surface and low atmosphere and make its way to space, while in the 15 um band even the stratosphere is opaque. The bulk of emission comes from the TAU=1 level which itself is the “radiating level” that balances the absorbed incoming solar radiation. Consequently, the transmission to space is the product of the transmissivity of all present absorbers and falls off with increasing atmospheric optical depth like t= exp(-TAU). Regions below TAU=1 tend to have radiation absorbed before its exit to space where the opacity is high, and regions above are thin enough to let radiation escape to space. The physical altitude of TAU=1 is what shifts to higher altitudes when you increase CO2, but the temperature here (say, T_rad) must stay such as to balance So*(1-albedo)/4 allowing one to define the surface temperature T(s) at the atmospheric pressure p_s to be T(s) = (T_rad)*(p_rad/p_s)^(-.286) (assuming the adiabat of a dry atmosphere). Thus, the ratio p_rad/p_s is close to unity in the optically thin limit and very small with a strong greenhouse effect.

    Comment by Chris Colose — 9 Jul 2010 @ 2:42 PM

  276. Well, Ray, you said it yourself, “playing the odds.” That means, your best estimate of what is likely to happen…not will happen. God (if he/she/it exists) gets to know what will happen. Us mere mortals have to “play the odds.” And, the thing about odds is, each of us, individually, gets to decide just how favorable (or unfavorable) the odds are before we bet. You want folks to reduce their carbon footprint because you say the odds are 99% that if they don’t we’re screwed. But, Bob figures he won’t really have to do anything until the odds are 99.9%. So…

    And, Scott… So, if I understand you, what you want everybody else to do is to spend countless hours moderating world class blogs so people can be better educated. You don’t want them to drive their cars less, or turn down the air conditioning in the summer and keep their houses cooler in the winter. You don’t want them to get their food locally, so it isn’t costing thousands of pounds of CO2 per ton-mile to have it shipped across the country. In fact, you don’t want them to do anything that would actually, in this moment, reduce the rate at which CO2 is being pumped into the atmosphere, you just want them to do some good blogging. That and forcing themselves into the media limelight. Well, shoot, that is what I call leadership.

    Comment by Gordon — 9 Jul 2010 @ 2:55 PM

  277. I have to apologize. It is not my intention to get into a pissing match. My point was, and is, about the effectiveness of the efforts of the people behind this blog, and about the nature of leadership. I still hold that it is not about being right (Ray), nor about media attention (Scott). I believe that to be effective with the larger society, it is not enough to be right nor to be seen on television. You have to show that you, personally, individually and collectively, are willing to do, now, the things you are telling everyone else they will have to do tomorrow. Sure, people will call you nuts, until their back yard is eaten away by the rising sea, or their favorite foods become too expensive, or someone they know dies in a heat wave.

    Comment by Gordon — 9 Jul 2010 @ 3:43 PM

  278. Gordon, we should all be energy conservative and we should all practice and preach it. However, doing so is a dent in the problem if we do not as nations greatly reduce our emissions. My point is that the best way to get people and nations on board is to be the squeaky wheel politically.

    Comment by Scott A Mandia — 9 Jul 2010 @ 4:05 PM

  279. Re 269 Gordon You’re asking them to make serious changes in the way they do practically everything. Would it be surprising if they were to ask you what you are doing to reduce your carbon footprint?

    Generally speaking, ‘we’ aren’t asking ‘you’ to do anything that we won’t also have to do (a policy like a tax on fossil C emissions wouldn’t somehow miss the scientists and environmentalists).

    You don’t get to be a leader just because you are right. You get to be a leader by leading, by going first.

    There is something to that, I guess. It’s not really fair, though – it’s not that I’m complaining, but I hope you realize that it’s not fair; you are asking ‘us’ to be the heroes, to make greater sacrifices. But politically, that may be how it has to be. So… what have Bill Nye and Ed Begley Jr, and some number of other famous people and a number I’ve wouldn’t have heard of … what have they been up to lately? Aside from which, there are things that a small number of pioneering individuals can’t (with some exceptions) do very well, such as speed up the development of affordable alternatives via their own buying decisions. There are some things that are easier for individuals to do when the whole of society shifts, such as buying an energy efficient home, which should become easier when more of those are being built, which will be more likely if more people want to buy them. To a great extent, we can’t go first, at least in an efficient way, with everything that we want to do because it requires the economy to move. Even assuming otherwise ideal market behavior, the economy now has a glitch – there is this big externality, and it requires public policy to correct it.

    If you want people to believe what you say, show them that you have the courage of your convictions by taking action, the kind of action you are asking them to take.

    Okay, but then ‘we’ run the risk of getting labelled as activists who are already invested in the idea and thus can’t be trusted. Better that than be labelled as hypocrites, though, because at least ‘we’d’ be doing something. But again, it isn’t truly hypocritical to demand public policy changes while not doing anything as an individual, because in that case you’re not asking anything of others that you aren’t asking of yourself (unless you’re planning to break the law and be lucky enough to get away with it).

    PS A week or two (?) ago I saw Hannity (ick) talking to someone with environmentalist credentials/reputation, and the issue of flying on a private jet came up. Hannity ridiculed the idea of emissions offsets as something like cheating on your spouse and making up for it with some expensive gift. This betrays an ignorance of the concept. What matters to climate is net emissions. A carbon offset would be like having the opportunity to cheat and then deciding not to do it. It isn’t like an indulgence at all. Of course there is the possibility that an offset might be measured incorrectly or perhaps fraudulent, but that doesn’t undermine the concept.

    Comment by Patrick 027 — 9 Jul 2010 @ 5:07 PM

  280. Gordon, Let us review the options open to us. First, what is NOT on the menu: Business as usual. The days of the petroleum-based economy are scarce. Reliance on petroleum will take us down a path of increasing energy insecurity where we seek oil in ever more difficult and risky locations (e.g. sucking it through a mile-long straw in the ocean) until we can no longer meet demand not just for oil but also for food. Not a good option.

    Now what we can do is
    1)develop a sustainable energy economy
    2)a)burn all the coal and other fossil fuels, buying us, if we make optimistic assumptions, perhaps a century of ever more elaborate schemes to meet energy needs with less and less suitable sources
    b)THEN in a severely degraded environment

    And this is not even taking into account the effect on climate. Option 2 raises CO2 above 1000 ppmv and results in catastrophic climate change.

    This is NOT divination. This is science, and the choice science gives us is simple. Either follow what the science tells us, which we’re 95% confident is the right path, or go against the science 180 degrees and bet the future of humanity on a 20:1 longshot. Feel lucky?

    Comment by Ray Ladbury — 9 Jul 2010 @ 7:17 PM

  281. @29 re Hawking – I agree with the earlier comments saying that the post, good as it it, is way too technical for Joe Public.
    The success of Hawking’s book does not disprove that view. For one thing, Hawking listened when his publisher told him that ‘each equation you include will halve the sales of the book’ (OWTTE) and included only the one (unavoidable) equation in his whole book. It probably helped that Hawking, by his own account (in ‘Black Holes and Baby Universes’) thinks in pictures, not in equations.
    And sales of 9 million copies, worldwide, over a couple of decades, still represent quite a small minority readership – on the order of 0.5% of the Western world – even assuming that every buyer finished the book. Just to give a personal slant on all that: most of my friends are tertiary-educated non-scientists, as I am, and I think only one of us who started the book actually finished it.
    I’m sorry, rasmus, but an explanation which will be meaningful to the people who still don’t understand the science needs to aim a lot lower. Visualising yourself telling it to truckies in a roadhouse over a pie and chips may be a useful mental exercise ;->

    Comment by MalcolmT — 9 Jul 2010 @ 10:23 PM

  282. Re 271 Chris G
    my response in addition to 275 Chris Colose’s response:

    It sounds like you are saying that TOA is where most of the mass is and that it is at a fixed height.
    No. TOA is not at a fixed height in geometric height (z) or geopotential height (Z), or geopotential (Φ); it is approximately at a fixed pressure (p) at p = 0; it is also approximately at a fixed sigma level at σ = 0. If optical thickness τ is measured downward as a coordinate, TOA would be approximately at τ = 0.

    That wasn’t all really necessary but I wanted to highlight the fact that there are several different coordinate systems, and the physics of the atmosphere (radiative, mechanical, etc.) are sometimes more conveniently expressed and evaluated in one or another coordinate system.

    dΦ = g*dz
    Z = Φ/g0, where g0 = 9.80665 m/s2 (Holton, “An Introduction to Dynamic Meteorology”, 1992, p.20)
    dp = -ρ*g*dz
    σ = p/psurf, where psurf is the pressure at the underlying surface at a particular time (the thickness of the whole atmosphere in σ is always 1 everywhere at all times)

    mass path, as measured downward from TOA (approx.), would be equal to p/g if g were constant (good approximation for most of the mass of the atmosphere)
    d(mass path) = -ρ*dz = dp/g
    on the other hand, one could use a mass coordinate that refers to how much mass lies above a certain level over the whole globe; that would be proportional to mass path except for the increase in global area with increasing radius (a minor issue for most of the mass of the atmosphere).

    θ = potential temperature, which is conserved for dry adiabatic processes and is a useful vertical coordinate for examining various fluid mechanical processes (like Rossby waves) when the atmospheric lapse rate is stable (for dry convection) (which is generally true on a large scale away from the boundary layer).

    measuring τ downward along a vertical path from TOA (approx.), τ would be proportional to mass path for a single frequency and constant mixing ratios (of radiatively important matter), except for the varying effects of p and T on line broadenning and line strength.


    The tropopause is where the energy being absorbed from the sun is approximately equal to the energy being absorbed from the earth. It is not fixed or constant either and varies with latitude and season.

    In the approximation of zero non-radiative vertical heat fluxes above the tropopause, net upward LW flux = net downward SW flux (equal to all solar heating below) at each vertical level (in the global time average for an equilibrium climate state) at and above the tropopause (for global averaging, the ‘vertical levels’ can just be closed surfaces around the globe that everywhere lie above or at the tropopause; the flux would then be through those surfaces, which wouldn’t be precisely horizontal but generally approximately horizontal).

    Comment by Patrick 027 — 9 Jul 2010 @ 10:41 PM

  283. Ray, as it happens, I agree with you about our options. And, in fact, I don’t feel lucky at all. The way it looks to me, the most likly scenario is catastrophy…the lessons of history teach that many, many people have to suffer horrendously before serious change is implemented…and that change as often by fiat as by careful consideration. So, I’d like to see the goals of this blog succeed.

    It is just this…I believe that what we are dealing with, at its root, is a deeply pshchological issue, a matter of the most basic elements of human motivations. Freud said we are all, at the root, motivated by sex. Otto Rank (at one time a protege of Freud), broke with his master and posited that we are, rather, motivated by the undeniable conflict between our sense of ourselves as “immortal souls,” and our realization that we exist by virtue of our all-too-mortal bodies, that we are desperate to believe that we will, somehow, live beyond our bodies, and that, in order to do so, we pursue “immortality projects,” that we invest in our activities the promise of eternal life. To tell people that this project we have been pursuing, this dream of “ever increasing quality of life/endlessly increasing consumption” is, instead, going to lead to our destruction is to tell them that the whole idea they have based their lives on is false.

    So, Patric, yes, it is not fair. And, yes, I am saying you…somebody…many somebodies…are going to have to be heroes. That is what it takes to be a leader (as opposed to what it takes to get elected): a willingness to go first, to do what you know needs to be done, regardless of how stupid you look, regardless of how you will be labeled, regardless of how unfair it is. Is the preservation of our species worth it?

    Comment by Gordon — 10 Jul 2010 @ 4:17 AM

  284. Rasmus in #261,

    Yes, I recall edits getting made more quickly but that was a case when an RC contributer was not an author. Better to have the contributers control their own content in this case.

    When explaining how this works, I usually try to get people to remember that they have experienced the lapse rate when they have climbed a hill and get them to understand that the lapse rate is suspended from a particular altitude. Then I point out that raising that altitude is like lifting the temperature profile over Death Valley and setting it at the valley edge. This seems to have helped some people.

    Comment by Chris Dudley — 10 Jul 2010 @ 7:29 AM

  285. “But, you don’t get to be a leader just because you say “follow me.” You don’t get to be a leader just because you are right. You get to be a leader by leading, by going first. If you want people to believe what you say, show them that you have the courage of your convictions by taking action, the kind of action you are asking them to take..”

    If you’re talking about being right, it seems to me that scientists have a pretty good track record. That matters. Otherwise, I doubt that most people give a flying duck whether scientists go off the grid or not: It’s just not interesting theater– anymore than trying to understand the issues at a basic level (even though it only requires exercising enough attention to realize that scientists will go the extra mile to explain the complicated problems while deniers only exercise rhetorical tricks).

    It is a problem in part, it seems to me, of reversing a spiral of lowered expectations. Turn on your TV and try to guess who is being targeted. Either the audience is swamped by the lowest common denominator, or programming is actively designed to dumb people down. Not good either way. While I agree that scientists have to expand their bag of tricks in order to reach people and grab their interest, nobody is well served by treating people like a compacted mass of dumbass sheep.

    Comment by Radge Havers — 10 Jul 2010 @ 12:24 PM

  286. Gordon, I have a lot more faith in the predictive power of physics than I do in that of psychology. As such, I think it is in our interest to push as hard as we can toward a solution in the hopes that enough our our fellow homo sapiens wake up in time.

    In actuality, the problem of denialism is mainly localized in a few nations–e.g. the US, USSR, Czech republic–where the blinkers of ideology get in the way of the citizens seeing the truth. That does not mean we are in the clear by any means, but it does belie the contention that human nature is the only problem. There are also a lot of people out there who get paid to make us believe comforting lies.

    Comment by Ray Ladbury — 10 Jul 2010 @ 1:32 PM

  287. Former USSR?

    Not sure I buy Gordon’s “concern” anyway. Sounds to me like a repackaged denialist talking point. I do not buy the assumption that scientists don’t practice what they preach or the implication that they are somehow hypocrites or that it even matters. I don’t even buy the notion that this is an efficacious talking point (except maybe among the very immature) or that the best way to offset it is for scientists to dance around to the tune of a bunch of wingnut noise in order to prove worthiness.

    Comment by Radge Havers — 10 Jul 2010 @ 5:16 PM

  288. “Many feedbacks, such as changes in atmospheric moisture, cloudiness, and atmospheric circulation should be similar for most forcings.”

    Why should they be?
    Increased cloud cover will raise albedo and cause cooling at the surface through diminished insolation. Sure it also increases back radiation, but this doesn’t penetrate the ocean, 7/10′s of Earth’s surface.

    This is the main reason for the re-convergance of the surface and tropospheric datasets since 1997.

    Polite discussion please at

    Comment by Rog Tallbloke — 11 Jul 2010 @ 5:24 AM

  289. Gordon, I have enough science background to trust the mainstream to be good enough vs. the denial side, which is close enough to every other denial campaign that I’ve followed that I am pretty sure there’s no substance to their case. You don’t have to be a climate scientist (physicist, or any of the other specialities) to figure this out. A competent journalist could figure this out. The pattern of the denial campaign is an absolutely classic Gish Gallop. You can even find the same suspects as in other campaigns like tobacco.

    The big failure is not one of science, it’s one of journalism.

    What can we do in practical terms? Write in to news media whenever they get the story wrong. Point out to them how naive they are being and hope you hit a nerve. Get it right on your own blog. Go into politics on a green ticket. That’s just a short list. But blaming the good people at RealClimate is a tad unfair. There’s just so much they can do.

    Comment by Philip Machanick — 11 Jul 2010 @ 5:47 AM

  290. Ray,

    I agree but I still find that even those that trust the scientists about the human cause of climate change cannot get their heads around the potentially catastrophic consequences that await their grandchildren.

    I think it is critical that we keep showing the public about the likely dangers ahead and we cannot pull any punches for fear of being wrong or too strong.

    I am currently researching the impacts of climate change on various ecosystems and it is quite disturbing.

    Scott A. Mandia, Professor of Physical Sciences
    Selden, NY
    Global Warming: Man or Myth?
    My Global Warming Blog
    Twitter: AGW_Prof
    “Global Warming Fact of the Day” Facebook Group

    Comment by Scott A Mandia — 11 Jul 2010 @ 6:13 AM

  291. Ray, I don’t claim that human nature is the only problem, rather that it is a LARGE problem that is not being addressed. And, Radge, I don’t deny the realities of global warming, I don’t assume that scientists (as a body) don’t practice what they preach, nor do I intend to imply that they are hypocrites. What I am saying is that real, useful, competent action on reducing greenhouse gas emmissions will require an intellectual and emotional movement of great proportions, and my observation is that such movements do not arrise without leaders and heroes.

    Comment by Gordon — 11 Jul 2010 @ 6:19 AM

  292. Rog Tallbloke,
    What it comes down to is that a Watt is a Watt is a Watt. It may make some difference WHERE said Watt is supplied, but since the climate system is pretty efficient at spreading energy, this is likely a second order effect. Don’t forget the skin effect for the oceans. It is a pretty efficient warming mechanism.

    Comment by Ray Ladbury — 11 Jul 2010 @ 7:34 AM

  293. Gordon, the realities are changing. I heard recently that a Prius was now considered more of a chick magnet on campuses than a Porsche. Younger people seem to be more reality based than the old farts running things now. I only hope that we leave them enough options to save civilization.

    Really, what is going on is not complicated. If an organism is incapable of perceiving reality as it is, that organism will not survive. If a species is composed overwhelmingly of such individuals, the species will decline and eventually become extinct. As I’ve said before, we may be working out the answer to the Fermi Paradox empirically.

    Comment by Ray Ladbury — 11 Jul 2010 @ 7:50 AM

  294. Ray Ladbury,
    Thanks for the response. I ran some calculations from the satellite altimetry to calculate the additional Watts/m^2 the ocean must have been recieving over the 92-03 period to account for the steric component of sea level rise. This came out at around 4W/m^2. If some of this was greenhouse forcing then a bit more must have been additional insolation due to diminished cloud cover. The tricky bit is working out the proportions. The ISCCP data, although imperfect, gives at least some numbers to play with. I have asked a few oceanologists about skin effect and downward mixing of energy from short and long wave radiation, but there seem to be as many opinions as there are oceanologists.

    One thing I am pretty sure about is that the tendency for el nino to occur near solar minimum and la nina to occur near solar maximum, and the capability of the ocean to store solar radiation on decadal timescales has led to an underestimation of the solar forcing. Watts are watts but where they come from is as an important consideration as where they go.

    Comment by Rog Tallbloke — 11 Jul 2010 @ 11:24 AM

  295. Ray, I hope you are right. I’m an old fart myself, and don’t expect to live to see what could be the living-out of a worst case (or even bad case) scenario.

    I have spent some time trying to find the simple truths hidden within the IPCC reports. (Perhaps there aren’t any simple truths there.) If I understand them, a reduction of 50-85% of CO2 emissions will be required to stabilize at year 2000 levels, which may be expected to produce a global average temperature rise of around 2C. And will this mean that methane will not be released from deep ocean methane hydrates? Will it mean that CO2 sequestered in permafrost will not be released? And what other unknowns are lurking?

    The IPCC says that such reduction will require a reduction in global GDP. Are the citizens of the developing nations going to happily consent to the citizens of the US continuing to use ten times as much energy as, say, the Chinese? Or is the world going to demand that the citizens of the US step up and take responsibility for their past by reducing the US GDP by ten times more than everyone else? And are we going to be willing to do it?

    You say “If an organizm is incapable of perceiving reality as it is…” And I have to quibble with you a bit here. Most organisms (all but one, I believe) do perceive reality “as it is.” Their inhereted response systems may be incapable of adjusting to new environmental realities, but they aren’t having any trouble with perception. It is only the human animal, with all his psychology, that is capable of perceiving reality falsely, that is capable of so thoroughly filtering the evidence of his senses.

    How many Priuses will the US need in order to reduce our CO2 emissions by 85%?

    Comment by Gordon — 11 Jul 2010 @ 11:50 AM

  296. Re 288,294 Rog Tallbloke

    Relative to the entire depth, oceans are essentially both cooled and warmed from above, but within the upper layer of the ocean, it is often the case that the oceans are warmed from below and cooled from above. This is because solar radiation penetrates deeper into the ocean than LW radiation. (Evaporative cooling also takes place at the surface, and produces denser water via increased salinity, which can sink down. Addition of fresh water at the surface has the opposite effect. Winds (and tides and planckton) stir and mix the ocean and can force convection of heat downward.

    Reducing the net LW cooling at the surface reduces the upward flow of heat to the surface, thus heating the ocean over the depth of the upper layer.

    4 W/m2 seems way too high; the ocean heat content hasn’t been increasing that much (or am I getting my timescales mixed up?).

    The change in solar insolation can be measured. A change in clouds (which must generally be in response to something) will change solar heating but that isn’t considered solar forcing.

    Comment by Patrick 027 — 11 Jul 2010 @ 1:26 PM

  297. Hey Dr. Benestad,

    This article is a great start. As you suggested the Models tell us what may happen; but, not necessarily how it may happen. I would that we had more of the former then the later in the literature over the last 12 years; however, a start now is better then no start at all.

    I said all of this to only request the team to consider addressing more “cause and effect” articles in relation to climate change. If as you note the GHE without anthropogenic inputs would be approximately 32 Deg C.; Given the amount of CO2 by natural process would be approximately 280ppm would suggest roughly 9 ppm of GHG would increase temperatures approximately 1 Deg. C.

    The end result would suggest an increase of 105ppm of CO2 should cause an increase in temperature of roughly 12 Deg. C. Going further to add in other contributors such as more water vapor as a secondary effect of the increase in CO2 the temperature as a result of GHG should be even Higher. Given there could be hysteresis in the atmospheric and oceanic systems it would appear that the march towards inclement temperatures should be ever onward and dramatically higher each year.

    The problem is we do not appear to be measuring an change in any of the documented contributors to Climate Change; that seems to demonstrate the a rate of change similar to the rise in CO2. The expectation is that there should be a proportional change in the contributing factors.

    Also at issue is the relative balance between anthropogenic emissions and the ability of the Earth’s natural systems to absorb most of the annual emitted fossil fueled CO2 up through the 1950′s.

    Were that the case then the true difference of temperature change between the natural level of say 240 ppm and the 330ppm of the 1950′s would likely have to of been sourced somewhere other then fossil fuel emissions.

    Hence, a little clarification on the total processes would be very welcome. Then to go a bit further it would be even more useful if we could examine how the GHG warming was eliciting the warming of the surface temperature. It is clear that it is unlikely due to direct radiation. By the same token we do not seem to have sufficient insights into how the warming is manifest. I was hoping that the team would consider expanding on your initial article here to offer the laymen among us more insight into the current knowledge base.

    My Thanx!
    Dave Cooke

    Comment by L. David Cooke — 11 Jul 2010 @ 3:31 PM

  298. Re Gordon @295: “How many Priuses will the US need in order to reduce our CO2 emissions by 85%?”

    Enough to tide us over until plug-ins and full electrics arrive in the market in force.

    Think of the Prius not as a solution, but as a highly visible paver of the way. A necessary real-world test bed of electric drive systems, and a rolling billboard that we have to try something else.

    Comment by Jim Eager — 11 Jul 2010 @ 4:41 PM

  299. Hi Patrick,
    thanks for the insight on salinity and cooling from above. The ocean is a complicated body of water for sure. I too was surprised at my 4W/m^2 figure, but if the good folk at Colorado have done the job correctly (and I see no reason to think they haven’t) then that’s how the sums work out if the IPCC estimate of the percentage due to thermal expansion is correct. There may be some kind of issue with the splice between XBT and ARGO data to consider as well. I did some checking, and it seems to be more in line with the figures which were in Levitus et al 2000 (after correction for his maths error). The more recent figures in Levitus et al 2007 and after seem to have been revised downwards, and I’m not sure why. Perhaps he could tell us, though he didn’t answer my emails.

    Whether or not clouds changing the level of insolation at the surface is regarded as a solar forcing or not probably depends on your assumptions about what is changing cloud albedo levels.

    I think there are two ways round to see changes in cloud albedo levels. Either as a response to internal change (feedback to greenhouse radiative forcing) or as a response to external change (solar activity/GCR level feedback). In the second case it is a forcing as far as the internal climate system is concerned as I see it.

    Either way it would seem that quite small changes in cloud cover percentage have quite large effects on the amount of energy entering the ocean.

    Comment by Rog Tallbloke — 11 Jul 2010 @ 5:01 PM

  300. Hi Rasmus,
    If I was to turn this article into an animated cartoon would you be happy to provide input.
    If so. I will work out a storyboard with pen and paper, annotate it, then scan and send it to you, where you can comment.
    I will then make corrections until we are both happy, before I put it into Adobe Flash and turn it into a movie.

    Comment by Phil Burrows — 12 Jul 2010 @ 8:15 AM

  301. L. David Cooke (#297),
    You are mistaken. The 32C figure includes all gases and CO2′s greenhouse effect can not be deduced quite so straighforwardly from its concentration in the atmosphere. With the current amount of CO2 in our atmosphere, the effect is logarithmic: a doubling of the amount of CO2 in the atmosphere would raise temperatures by about 1.2C. To that figure, one should indeed add the feedbacks (or “secondary effects” as you put it).
    You should research the accepted scientific findings a bit more before indulging in such speculation, me thinks. At the top of RealClimate’s home page, you’ll find a link labelled “start here”.

    Comment by Anonymous Coward — 12 Jul 2010 @ 11:19 AM

  302. Gordon:

    That is what it takes to be a leader (as opposed to what it takes to get elected): a willingness to go first, to do what you know needs to be done, regardless of how stupid you look, regardless of how you will be labeled, regardless of how unfair it is. Is the preservation of our species worth it?

    I think Gordon is right about human nature, but wrong in thinking that scientists can lead by modelling the sacrifices required from everyone. Chris G @273 has it right: AGW is a tragedy of the commons. It’s been discussed previously on RC.

    Comment by Mal Adapted — 12 Jul 2010 @ 11:33 AM

  303. Hey Anonymous Coward,

    I am quite aware of the effects of CO2 in the atmosphere. What apparently you are missing is the point I am trying to make.

    An average person is going to apply a simple rule set based on the words of an expert. When such a one suggests that the warming in the atmosphere of 32 Deg. C is directly related only to CO2 then the response is going to be as I outlined. CO2 would have to rise in a linear manner because the expert implied it was so, without adding the caveat, as you indicate.

    Generally, if I recall correctly, the rule is roughly that a doubling of CO2 density in the atmosphere should result in roughly a 4 Deg. C rise in surface temperature. So if we apply this rule then the change between 385 and 280ppm of CO2 should only provide a change of about 1 Deg. C. (Your 1.2 Deg. C works just fine for this example.)

    However, if as the expert explained earlier that the CO2 in the atmosphere was responsible for a 32 Deg. rise from the insolation baseline then we need to discuss the initial value and the points of doubling. By inference I believe you are suggesting that the CO2 levels had to double 8 times between 0ppm and 280 ppm.

    Hence, what I see as being proposed in your inference is that the initial CO2 concentration had to be approximately 1.09ppm, doubling to 2.18, then 4.4, 8.9, 18, 35, 70 140 and finally 280ppm with each rise forcing a rise in temperature of 4 Deg. C each time. Sorry, but this line of thinking is absolutely ludicrous.

    It is likely that the change in temperature due to the change in concentration was more like when CO2 reached 280ppm from 140ppm the global average temperature would have rose roughly 2 Deg. C. Going back further, 70ppm would be 1 Deg. and so on down the slope. However, we also have to keep in mind that early Earth’s atmosphere appears to have been dominated by Carbon Oxides, so it is unlikely the Earth had CO2 levels below roughly 240ppm in the last billion years. If the levels had been much lower it would have reduced the level of the flora on the planet to subsistence levels not unlike during “Snowball Earth”.

    (As we know plants in the presence of light generally generate O2 from CO2 and in the Dark we see sugars being consumed causing flora to emit CO2. Hence, it is unlikely that after flora became common place the balance between CO2 and O2 was ever much out of sync. until the presence of fauna. (Such as Blue-Green Algae which could both emit and consume both CO2 and O2 having characteristics of both flora and fauna.))

    The heating ratio between IR re-emission and CO2 density seems to be a factor of doubling (double the concentration/double the intensity for the same distance from the surface), unlike the radiant outflow from a black body (double the distance from the surface, 1/4 the intensity). Hence, the rise in temperature may not be logarithmic. The rise in emitted energy seems a much simpler ratio, emitted energy in the case we are discussing does not change at a constant rate, it changes in relation to the intensity of the emitter, this change over time is a linear function due to the systemic processes which we are still working to describe, sorry.

    Would you like to explore this further? I for one would like to see a follow up of the current work by Dr. Benestad that more clearly defines the means of “cause and effect” and how this is resulting in high surface temperatures. However, I would prefer to start the discussion not with the anthropogenic influence baseline; but, the natural baseline. From here we could build the description of the basic physics in regards to the Earth and Sun’s relationship and the variances in insolation, emissions, reflections and re-emissions. If instead you would like to discuss this further here, I am interested.

    Dave Cooke

    Comment by L. David Cooke — 12 Jul 2010 @ 2:29 PM

  304. If you do the calculations as the formula is written, you get a T of over 300K
    The formula should be (So/4)*(1-A)=sigma*T^4
    That will give a T of 255K

    Comment by Bruce — 12 Jul 2010 @ 2:30 PM

  305. I think the explanation is too complex and certainly too long. Considering the public are acustomed to movies starring aliens who can see in the infrared I would propose that it would make a bigger impact on people’s understanding if they could “see” the sky with and without CO2, both from the ground and from orbit.

    Comment by LazyTeenager — 12 Jul 2010 @ 6:00 PM

  306. Well, Mal, I agree that it is a crisis of the commons. I went to look at the post you referenced, and, lo and behold, the solution to the fishing crisis is instigated by…what?…by leaders making sacrifices (the top 5 fisher-folk deciding to reduce their catch by 80%). Hmmm…

    Comment by Gordon — 12 Jul 2010 @ 6:28 PM

  307. Ray, please say whether you’re worrying about your great-great-grandchildren.

    Comment by simon abingdon — 12 Jul 2010 @ 7:01 PM

  308. Simon Abingdon,
    No children implies no further progeny. I leave no hostages to fortune.

    Comment by Ray Ladbury — 12 Jul 2010 @ 8:40 PM

  309. #307–

    I’d have thought you’d been hanging around RC long enough to know this: Ray has previously stated that he has no children, and does not expect to have any.

    Your point, Simon? (Or, if you prefer, ‘simon.’)

    Inquiry ad hominem, rather than refutation ad hominem?

    Comment by Kevin McKinney — 12 Jul 2010 @ 9:49 PM

  310. Patrick and Chris Colose,

    Referring to Chris’:
    “…only similar in that regions above the tropopause are typically optically thin enough to not matter much for the net radiative budget…”

    I’m sure you know your stuff, but only about 75% of the mass of the atmosphere is below the tropopause. If CO2 is relatively well mixed, I’d be surprised to learn that the last 25% of the CO2 has negligible effect.

    The first point I’m trying to make is that, in my opinion, if what we are talking about is the wavelength(s) absorbed by CO2, then where the partial pressure (or optical density) of C02 drops to near-0 is a lot more interesting than where the sum of all gas partial pressures, where the majority of other gases do not absorb at the wavelength of CO2, drops to near-0, which is the more traditional meaning for TOA.

    Comment by Chris G — 12 Jul 2010 @ 11:48 PM

  311. Uh Gordon, I assume you mean that the leaders of the fishers where the ones catching the most fish. I don’t think you originally meant that the scientists were leading in the sense that they were the ones producing the most CO2.

    Sure, if the top 5 producers of CO2, by absolute, over time, or per capita (different top 5 depending on how you measure it, US, Australia, UK, China, whomever), were to reduce their production by 85%, we’d be well on our way to a solution.

    Comment by Chris G — 12 Jul 2010 @ 11:58 PM

  312. Re 303 L. David Cooke

    The shape of the CO2 absorption spectrum: roughly, there is a peak in the absorption near 15 microns, with an overall tendency of exponential decay of the optical thickness outward from 15 microns (within limits). This means that, for any optical thickness smaller than the peak value, doubling the CO2 (which doubles the optical thickness from CO2 at every wavelength) shifts the wavelength at which that optical thickness occurs outward from the center by some amount. Thus, the absorption band widens a certain amount for each doubling (out to a point where parts of the spectrum that don’t fit this shape become important). But at the center of the band, the optical thickness increases.

    For sufficiently small intervals, any smooth continous function can be approximated as linear; for sufficiently small changes in optical thickness, two identical successive increments will have nearly the same effect. Thus starting at zero CO2, adding some small amount of CO2 has some effect, and doubling the amount of CO2 approximately doubles that effect. This would apply to sufficiently small amounts of any gas.

    But when optical thickness gets to a significant value (such that the overall spatial temperature variation occurs on a spatial scale comparable to a unit of optical thickness), each successive increment tends to have a smaller effect – when optical thickness is very large relative to the spatial scale of temperature variation, the flux at some location approaches the blackbody value for the temperature at that location, because the distances photons can travel from where they are emitted becomes so small that everything ‘within view’ becomes nearly isothermal. This is called saturation.

    In the approach to this limit, when optical thickness is sufficiently large, a linear approximation can be made (remember what was said earlier about small intervals), wherein each doubling results in half the change of the last doubling (that’s based on an approximately linear change in temperature relative to optical distances, and an approximately linear change in the Planck function over temperature – applicable for the small distances and small temperature variations implied).

    Within a continuum of material (ie not at TOA, but within the atmosphere), temperature generally varies continuously (at least if you are willing to use high enough resolution, so this should tend to apply to the surface as well), so a pair of oppositely directed fluxes will both eventually saturate, and at that point they will be the same, so that there is no net flux (assuming the optical thickness is also distributed continuously; net fluxes can persist where there is a transparent gap, for example (such as at TOA)).

    At sufficiently large amounts of CO2, the center of the band becomes saturated, so the band-widenning effect acts alone, thus a doubling of CO2 widens the absorption band by about the same amount as the last or next doubling.

    At present, the effect of CO2 is or is close to saturated at the tropopause (small or zero net flux at the tropopause), and because parts of the lower stratosphere are nearly isothermal while the upper stratosphere has a negative lapse rate, the effect CO2 at TOA is saturated in a sense (OLR reaches a minimum, beyond which, farther increases in optical thickness result in increasing OLR).

    PS (TOA forcing – Tropopause forcing = **forcing of the stratosphere (and mesosphere, etc, but almost all of that is the stratosphere by mass); increasing CO2 has a larger forcing at the tropopause than at TOA (this is dependent on the lapse rate of the stratosphere), hence stratospheric cooling; stratospheric adjustment returns the stratosphere to equilibrium by increasing the net flux out of the stratosphere by the same amount as the initial stratospheric forcing; thus, a portion of stratospheric cooling can be transfered to the forcing at the tropopause level (resulting in the tropopause-level forcing with stratospheric adjustment/equilibration). Warming must occur below the tropopause to increase the net LW flux out of the tropopause to balance the tropopause-level forcing; there is some feedback at that point as the stratosphere is ‘forced’ by the fraction of that increase which it absorbs, and a fraction of that is transfered back to the tropopause level – for an optically thick stratosphere that could be significant, but I think it may be minor for the Earth as it is (while CO2 optical thickness of the stratosphere alone is large near the center of the band, most of the wavelengths in which the stratosphere is not transparent have a more moderate optical thickness on the order of 1 (mainly from stratospheric water vapor; stratospheric ozone makes a contribution over a narrow wavelength band, reaching somewhat larger optical thickness than stratospheric water vapor) (in the limit of an optically thin stratosphere at most wavelengths where the stratosphere is not transparent, changes in the net flux out of the stratosphere caused by stratospheric warming or cooling will tend to be evenly split between upward at TOA and downward at the tropopause; with greater optically thickness over a larger fraction of optically-significant wavelengths, the distribution of warming or cooling within the stratosphere will affect how such a change is distributed, and it would even be possible for stratospheric adjustment to have opposite effects on the downward flux at the tropopause and the upward flux at TOA).

    **-it is correct to say that, right?

    Plants don’t necessarily stabilize the amount of atmospheric CO2; they could actually destabilize it in some ways (forest fires, etc.). What would affect atmospheric CO2 directly is the changes in the total amount of stored C in vegetation and soil, which is changed by imbalances between C-fixation and respiration/decomposition/oxidation.

    The geologic burial of organic C would contribute to an increase in free O2, but the impression I’ve gotten is that the dominant source of free O2 (at least before the Phanerozoic?) has been the escape of H to space (which is limited by the abundance of H above the tropopause (it must diffuse upward to feed the escape), which is limited by sources of H (which would also diffuse to feed dissociation reactions). Not so much by direct photolysis of water vapor (not generally a lot of that in the stratosphere), but from CH4, which could build up in a nearly oxygen-free atmosphere, and being largerly of biotic origin, with the H coming from photosynthesis (releasing O); O2 buildup itself was delayed because of geologic O2 sinks (in particular, the conversion of ferrous Fe (naturally present in the crust and mantle and which can dissolve in the oceans) to ferric Fe (precipitates out of the water, the source of banded-iron formations, which humans have used to get Fe).

    PS because of the lack of O2 and the presence of methanogens, CH4 could have had a more important role in the total greenhouse effect of the (late?) Archean Eon.

    Both geologic organic C and gelogic inorganic C are sources of CO2 to the atmopshere, ocean, and vegetation and soil. They are typically relatively small fluxes of CO2, as are the sequestration of C from those reservoirs to gelogic reservoirs either as organic C or inorganic C (carbonate minerals) – an exception being the result of recent human activity.

    Over geologic time, geological processes can change the amount of CO2 in the atmosphere+ocean+vegetation+soil (let’s say, AOVS) significantly via changes in the geologic emission rate. Chemical weathering (favored by warm wet conditions, and a supply of mechanically-weathered debris bearing some kinds of silicate minerals) can act, depending on the distribution of continents, and their topography (and minerology (?)) relative to weather patterns, as a negative feedback to climate changes, tending to stabilize the atmospheric CO2 level by allowing the climate to shift until the rate of removal balances the rate of supply (it has been suggested that the mechanism is relatively ineffective when the continents are concentrated at low latitudes – see articles about “Snowball Earth”). Because the flux involved is usually quite small (exception could occur in the hot, CO2 rich, glacially-eroded aftermath of a Snowball), this is ineffective in preventing larger changes over the short term. It is also possible for cold climates to increase chemical weathering in some ways, by lowering sea level to expose more land to erosion (though I’d guess this can also increase oxydation of C in sediments) and by supplying more sediments via glacial erosion for chemical weathering (of course, those sediments must make it to warmer conditions to make the process effective – downhill and downstream, or perhaps via pulsed ice ages (?)).

    (Chemical weathering supplies ions that are able to combine with CO2 to form carbonate minerals. Higher temperatures below the surface tend to favor the release of CO2.)

    More rapid fluxes occur within AOVS that tend to redistribute C towards some equilibrium for a given climate and given amount of C in total, etc (this doesn’t necessarily mean that the fraction of the total in each one tends to be constant). However, exchange with the deep ocean is still relatively slow, and the amount that the upper ocean can hold for a given atmospheric CO2 amount depends on various ions present, which are generally supplied at a slow rate (this involves chemical weathering and also the dissolution of carbonate minerals). Redistribution of C has acted as a positive feedback to orbitally-forced glacial-interglacial variations (ice ages) – but this depends on some particulars and isn’t necessarily a general feature applicable to every geologic age (?).


    The sun has gotten gradually brighter over geologic time. Thus more CO2, or more CH4, or ____, would have been required earlier in Earth’s history to maintain the same temperature.


    A signficant hysteresis is involved in Snowball episodes. Depending on meridional heat transport, when freezing temperatures reach deep enough towards low-latitudes, the ice-albedo feedback can become so effective that climate sensitivity becomes infinite and even negative (implying unstable equilibrium for any ‘ice-line’ (latitude marking the edge of ice) between the equator and some other latitude). For a combination of CO2, CH4, and solar brightness that would allow such an unstable equilibrium, there will be at least two stable equilibria – one is a Snowball (very cold), the other being significantly warmer. During a Snowball, chemical weathering is essentially shut-down, so CO2 from geologic sources can build up. When their is enough CO2 to start thawing near the equator, a runaway positive feedback would tend to ensue, not stopping until the climate is much warmer.

    Comment by Patrick 027 — 13 Jul 2010 @ 12:19 AM

  313. Chris G (# 310),

    Sorry– after going back to my previous comment which you quoted I see that I did not get that point across clearly or correctly. Indeed, the TOA and tropopause forcing can be quite similar, but also very different depending upon the nature of the forcing (see Hansen et al., 1997 for specifics). For instance, if the solar irradiance were to increase in a spectrally-uniform manner (over all wavelengths) then some fraction would be absorbed in the stratosphere, a region not well coupled by atmospheric motions to the lower atmosphere, and so a certain amount of energy will be radiated back to sapce without affecting the surface temperature. However, the traditional RF often used now (defined in IPCC 2001, 2007 although deviations from this exist, especially for aerosol evaluations) already incorporates stratospheric adjustment which occurs on timescales of several months and so TOA/tropopause forcings become comparable.

    Comment by Chris Colose — 13 Jul 2010 @ 12:35 AM

  314. No, Chris, I didn’t intend to imply that scientists (as a group?) produce the most CO2. However, if I understood Mal Adapted correctly, he implied that scientists wouldn’t (shouldn’t? couldn’t?) be leaders in the fight against global warming. (Is that anything like the “war against drugs?” And how successful the “government” has been in that one?)

    But, I expect that leaders are where you find them, not where they are “supposed” to be.

    Comment by Gordon — 13 Jul 2010 @ 6:34 AM

  315. Dear rasmus,

    You stated:
    “Thus, given the height and value of the emission temperature, we can get a simple estimate for the surface temperature: 255K + 5.5km * 6K/km = 288K (=15oC; close to the global mean estimated from observations given by NCDC of ~14oC).”
    Can you relate that to works like “Effect of CO2 line width on 15 μm atmospheric emission”, B. Kivel et al. (1976), which use the emission from CO2 to explore the Troposphere temperature? While the emission is a function of frequency and height, the general average for CO2 is usually assumed to come from a region with -53 deg. C which relates to almost double the height you use in your statement.


    Comment by Laws of Nature — 13 Jul 2010 @ 7:42 AM

  316. “There is less absorption by CO2 of upwelling infra-red light above the troposphere, but increased emission as a function of increased concentrations. Thus there is a cooling.”

    It would help me (and perhaps others)to understand CO2-related stratospheric cooling if you would clarify where the energy comes from for the increased emission by the greater concentration of CO2 in the stratosphere.

    Any clarification would be appreciated.

    [Response: It doesn't matter. In the stratosphere, it from solar and LW absorption by ozone, and a small amount from water vapour, but what ever the temperature is, there is radiation from the CO2. - gavin]

    Comment by Bill — 13 Jul 2010 @ 9:07 AM

  317. #311:
    It’s kind of important to know which countries are the largest emitters I think. And the UK is not close to being on either top 5 list. So there you are…
    Top 5 emitters (2007): China, USA, India, Russia, Japan
    Top 5 per capita emitters (2006, ignoring small countries emitting less than 0.5% of the world total which would other crowd the list): USA, Australia, Canada, Saudi Arabia, Khazakstan

    Comment by Anonymous Coward — 13 Jul 2010 @ 9:23 AM

  318. Regarding
    mircea (26), Thomas (34), and (46) Chris Colose:

    I think Thomas had it right, and Gavin and Chris Colose were misinterpreting mircea’s question.

    Ture, the sun’s radiation output at the sun’s surface, with a temperature of 5780K, is higher at any frequency than the earth’s output at the earth’s surface, at a temperature of 287 or 288 K, but we don’t receive the sun’s radiation at the sun’s surface. The radiation is attenuated by that
    factor in figure 2, which is what Gavin and Chris Colose should have referred to.

    The sun has a radius of 695,600 km, the earth is 1 astronomical unit away at 149,600,000 km, so we only receive

    (149,600,000/695,600)^-2 = 1/46,253 of the sun’s output at any frqueency.
    The net result is, earth receives a lot less infrared radiation from the sun than it radiates away.

    Comment by Alan D McIntire — 13 Jul 2010 @ 9:46 AM

  319. Dave Cooke (#303),
    +4C per doubling is a somewhat higher than usual (but still reasonable) number that includes feedbacks such as an increasing amount of atmospheric H2O but also non-greenhouse effects such as a diminshed reflective ice cover on the surface of the planet. +1.2C per doubling does not take such feedbacks into account. These numbers only apply in conditions similar to the ones we experience now.
    If we assume +4C per doubling, the effect of going from 280 to 385 ppm would be +1.8C.
    The atmospheric CO2 concentration seems to have fallen a good bit below your estimate several times in the past million (never mind billion) years during glaciations and these episodes were quite cold indeed.
    You’re confusing the rate at which radiation intensity drops from the surface of a sphere as opposed to a point source.
    And so on… please take some time to inform yourself before engaging in such reckless speculation. I think you’ll find that these things are better understood than you suspect.

    Comment by Anonymous Coward — 13 Jul 2010 @ 9:55 AM

  320. Gordon @306:

    I went to look at the post you referenced, and, lo and behold, the solution to the fishing crisis is instigated by…what?…by leaders making sacrifices (the top 5 fisher-folk deciding to reduce their catch by 80%). Hmmm…

    Um, you may want to read that post again. It refers to the actual collapse of the Newfoundland cod fishery. The crisis wasn’t solved, and the cod population of the Grand Bank has yet to recover. It’s a classic example of the TotC.

    Comment by Mal Adapted — 13 Jul 2010 @ 11:01 AM

  321. 234 Gilles, and Patrick,
    Thaks for your answers. I’m still learning them.
    I wondered why Hansen says we must stop below or at 350 ppm of co2.
    Suppose we get a co2 doubling by 2100 to 540 ppm, and a +3,4k temp, then stabilization. What’s so catastrophic about that ?

    [Response: What was the sea level rise the last time the planet was even close to that warm? - gavin]

    Comment by Jacob — 13 Jul 2010 @ 12:04 PM

  322. RE: 319

    Hey Anonymous Coward,

    Okay, I agree that for hard and fast values you are correct, that the value of change for the suggested 240ppm non-anthropogenic baseline for the last 614ky the values has varied by as much as 22ppm.


    To try to extend this back through geologic proxies is still a science in it’s infancy and I will abide by known accepted measurements. However, even this 614Ky period contained substantial glaciation, orbital, astronomical and volcanic events. The combination of flora and fauna bio-mass CH4 production and geologic sources have provided a fairly stable CO2 source. This was balanced by the land and marine flora conversion of CO2. (Though some have claimed in this thread that the balance of O2 generation may be related to the reduction of hydrogen by gravitational loss; most of the isotopic record still suggests that the balance of O2 appears to have a biologic influence and was not the result of planet wide respiration of H2.)

    As to “charges of speculation”, I have yet to see a reasonable explanation as to the 32 Deg C. offset above the accepted TOA insolation value as being founded in the CO2 balance. (Roughly the difference between the 255 Deg. K levels from the est. 1366 watts/m^2 at the TOA, plus the retention of roughly 284 Watts/m^2 insolation by all GHG and “Warming” contributors, resulting in a roughly averaged 283/284 Deg. K base temperature of the atmospheric column.) I would prefer that rather trying to change the subject we concentrate on the issue I have requested we focus on.

    The most recent paper I read from this past Spring does suggests that the CO2 levels have varied more; however, there is not sufficient geologic evidence that I have seen (Even with the examination of the foraminifera O2 isotope record. see side panels for graphs to compare to the ones from the URLs above and below.), except for Pre-Cambrian “Snowball Earth” and the Carboniferous period; of significant swings (>35%) in the CO2 and O2 balance, to my knowledge. The basis of the recent work appears to be primarily model based.
    However, as I have entertained this issue in the past here in RC, I am willing to keep an open mind.

    (BTW Note: The 4 Deg. C doubling was the estimate change for between the 280 and 560 ppm values. I made a mistake earlier suggesting the 1 Deg. C was between 280 and 460 when it should have been 280 and 560ppm, sorry. Thanks for the correction, (105/280ppm)=@.37 37%*4 should be near 1.5 Deg.)

    Dave Cooke

    Comment by L, David Cooke — 13 Jul 2010 @ 2:39 PM

  323. #321 [Response: What was the sea level rise the last time the planet was even close to that warm? - gavin]

    gavin, I am interested in what an x feet (for various x) increase in sea level means as a reduction in actual global land area but perhaps more relevantly in the resultant increase/decrease in habitable land area (increased I imagine in Canada, Siberia, Antarctica etc).

    I don’t think mass migrations have ever been a problem for the human race. When flying along the eastern seaboard of the USA I was always amazed that the cities I saw had been there for barely 200 years.

    Comment by simon abingdon — 13 Jul 2010 @ 3:38 PM

  324. Hey Patrick,

    Okay, for starters to clarify, you seem to be suggesting
    that the absorption window of the atmosphere to re-
    emitted (300nm-1.2um initialy) solar energy has a center
    frequency of roughly 15um. The first issue I am have with your explanation is you are not defining the bandpass bandwidth. Also, I seem to be having an issue in trying to understand what is the ratio of the bandpass window frequency in relation to the center frequency intensity.

    In short, at the attenuation levels of 15um say +/- 1um;
    how many db down would you suggest the throughput would
    be at +/- 1um? Also, we should would need to determine
    the db of Earth emitted 15um +/- 1um to try to determine
    the radiant output being emitted outside beyond the central frequency.

    As to the idea that the bandwidth changes in relation to
    the intensity I find difficult. The attenuation should
    remain constant, if only the initial value is greater
    hence, more energy “leaks past” the “filter”, then we are fine.

    Next as to what determines a “significant value”
    regarding the idea of optical translucence. The initial
    description of the acceptance window acting as a optical
    wave guide is fine. As the intensity increases yes the
    sidebands will begin to pass through to a point at which
    the attenuation exceeds the intensity of the signal. At
    this point it would appear you are suggesting that
    radiation of the energy no longer operates as the
    transport or waveguide. This would suggest that
    convection or conduction would have to take place to
    transport energy beyond the “Irising” of the absorption
    frequency of the atmosphere. So far I do not have any
    problem with that idea.

    Now as to the idea of then saturation of the CO2 window
    we have a problem. Saturation cannot expand the window
    beyond the attenuation limits of the bandpass or
    absorption limitation as defined by the photonic emission spectrum of the working material. It would depend on the various energy bands of the working materials making up the “filter”.

    I have seen absolutely nothing that suggests that the
    15um band at the tropopause has reached saturation. Were
    this true, if you removed convection, there would be
    virtually no release of the insolation from the
    atmosphere. We currently believe no less then 1080
    Watts/m^2 has to be released from the Earth’s atmospheric system. By the same token if saturation were true then we could continue to emit CO2 to our hearts delight as the maximum potential retention of insolation by GHG has been reached.

    There is a corundum in regards to your discussion of the
    Stratospheric forcing at this time, as I see it. When we consider that the average Ozone change between 1950 and 2000 in was approximately 280 Dobson units we have another contributor to the reduction in the Stratospheric temperatures that are missing from your strawman. I tend to disagree, in that I do not think the effect of the Ozone Optical translucence (300nm to 1.2um) of the Stratosphere is insignificant. As the higher frequency (300nm-1.2um) energy level in relation to that being returned at the lower frequency of 15um should be proportionally higher.

    (In short a cool Stratosphere does not a 15um Optical
    Saturation argument make, as at 280 Dobsons, more O3
    there should result in roughly 6-18watts not reaching the tropopause, depending on the season…)

    Okay, leaving that subject, if we examine the total
    estimated annual CO2 respiration it would appear to be,
    according to the old Carbon Cycle cartoons, approximately 202Gt of CO2. Looking at the Mauna Loa graph it would appear that the normal seasonal fluctuation is around 7ppm globally at what, 7km? This change includes all normal seasonal variations forest fires, dead fall, harvesting, anthropogenic influences… (Albeit with a rising trendline.)



    As to the idea of CH4 contributing to an increase in O2
    in the atmosphere we are leaving out the recent examples
    of increased water vapor in the Stratospheric region. In short, it is much more likely that the H4 is combining with the O3 forming water-vapor in the Stratosphere causing the rise in Polar Stratospheric Clouds or the PSC’s that were such an interest 4 years ago.

    Finally the conclusion that chemical weathering has a
    greater impact on the reduction in the atmospheric CO2
    during a Earth Snowball event then biologic functions
    seems slightly humorous to me…; however, if you can
    support the idea I would entertain looking at the data.

    However, the point is we still have not addressed the
    difference between the 255 Deg, K and the global 283/4
    Deg K bottom of the atmospheric column and the role a an
    increasing CO2 level plays. Can we please try to get
    back to this issue as it would help many of us out a lot
    if this could be explained clearly.

    Dave Cooke

    Comment by L, David Cooke — 13 Jul 2010 @ 4:07 PM

  325. Re 303 L. David Cooke – I was reminded by 317 Anonymous Coward that you brought up the inverse square law. Absent emission, absorption, reflection, scattering, and refraction outside of a sphere with radius 1, and assuming steady state, the flux coming out of such a sphere is the same as the flux coming out of any closed surface enveloping that sphere; the area of a sphere is proportional the square of the radius, so the average flux per unit area going through successively larger spheres follows an inverse square law.

    Hence the solar flux/area in space reaching Earth is only about 1366 W/m2.
    (Remember that the Earth’s surface area is about 4 times it’s cross section and it has an albeod of approximately 0.3, so the global time average solar heating of the Earth is approximately (1366/4 * 0.7) W/m2 ~= 239 W/m2 (ignoring significant figures there)).

    The vast majority of the mass of the atmosphere, and hence the vast majority of the optical thickness, is concentrated into a vertical distance that is very small relative to the radius of the Earth. Thus, to a first approximation, the Earth’s curvature and the increasing global area with height can be ignored. It isn’t really important to the Earth’s energy budget what the outgoing flux is at some great distance of the Earth; for the OLR, I think TOA can be approximated as having a radius on the order of 1 % larger – or less – than the radius at the surface. That would make a 2 % difference or less to the global area. Actually, though, most of the OLR originates from below the tropopause (can get up around 18 km in the tropics, generally lower) – with a majority of solar radiation absorbed at the surface, a crude approximation can be made that the area emitting to space is less than 2*(20/6371)*100 % ~= 0.628 % more than the area heated by the sun, so the OLR per unit area should be well within about 0.6 % of the value calculated without the Earth’s curvature (I’m guessing it would actually be closer to if not less than 0.3 % different).

    (Another effect of the Earth’s curvature is that photons emitted downward that manage not to be absorbed first can end up going upward eventually. The refraction by the atmosphere also has effects that tend to counteract the effects of the Earths curvature: it tends to bend radiation downward around the Earth, and it magnifies the lower levels when seen from above, as if the atmosphere were more vertically compressed into a narrower range of radii (blackbody radiation intensity is actually a function of the refractive index; without any reflection/scattering/absorption/emission etc. in between, a blackbody embedded within a material with different refractive index n = n2 from it’s surroundings n1 will appear on the outside (where n = n1) to be emitting the blackbody flux and intensity for the n1 value, and it will appear to come from a larger or smaller object depending on whether n2 is larger or smaller than n1). Because the index of refraction stays very close to 1, and because of the relative thinness of the atmosphere relative to the radius of the Earth, these are all quite minor effects.)

    Comment by Patrick 027 — 13 Jul 2010 @ 4:28 PM

  326. Re 323 simon abingdon -
    the resultant increase/decrease in habitable land area (increased I imagine in Canada, Siberia, Antarctica etc).

    If there were any significant increase in habitable land in Antarctica, it would come at a horrific price (where are you going to put that ice? – just removing ice isn’t enough, it will still be cold and often dark, and there’s not going to be much soil.

    How are you going to move the soil? The infrastructure? Moving has a cost. Some species are photoperiod sensitive. Civilization was built around things being roughly the way they are. Don’t forget ecosystem services.

    I don’t think mass migrations have ever been a problem for the human race. When flying along the eastern seaboard of the USA I was always amazed that the cities I saw had been there for barely 200 years.

    It’s easy to migrate if there are no people in your way (or if you are willing to remove those people). It’s easy to move when you aren’t used to modern comforts.

    Comment by Patrick 027 — 13 Jul 2010 @ 4:40 PM

  327. Re 323 simon abingdon

    It’s not the “human race” that will suffer, but individual humans. Where will the people who live in places like Bangladesh go when they are forced to abandon their homes?

    Comment by Mal Adapted — 13 Jul 2010 @ 5:07 PM

  328. simon abingdon @323

    I don’t think mass migrations have ever been a problem for the human race.

    It’s not the “human race” that will suffer, but individual humans. Where will the people who live in places like Bangladesh go when they are forced to abandon their homes?

    Comment by Mal Adapted — 13 Jul 2010 @ 5:10 PM

  329. Hey Patrick,

    Again thanks for your input; however, I still fail to see how the points you elicit explain the 32 Deg. C related to GHGs and other warming contributors as well as support the 4 Deg. C doubling potential between 280 and 560ppm of CO2. In your calculations please remember to consider that the area of the disk has two sides, one for collection, the other for emission.

    As it seems I am encountering a few “bugs” from this site I accept that it may be that I am being asked to refrain from further participation. To that end, “Good Bye and Thanx for all the Fishes….”

    Dave cooke

    Comment by L. David Cooke — 13 Jul 2010 @ 6:00 PM

  330. “increase in habitable land in Antarctica”…. A lot of Antarctica’s rock surface is below sea level – the present sea level, that is. If all the ice melted, then – well – even more of it would be below sea level, wouldn’t it?

    The good news? The tiny remaining human population of Earth would be able to survive happily by exploiting all the coal and oil previously trapped under the ice.

    (Joke. Ha ha.)

    Comment by Didactylos — 13 Jul 2010 @ 6:02 PM

  331. Re 323 simon abingdon – let me put that last part another way: it may seem easier to leave everything behind when there isn’t much to leave behind.

    Comment by Patrick 027 — 13 Jul 2010 @ 6:07 PM

  332. Dave Cooke,
    You seem preoccupied about the relationship between the 32C and CO2 but that’s a waste of time. Again, these 32C are not explained by CO2 alone but by the total greenhouse effect (including clouds). An Earth without atmospheric CO2 would likely be more than 32C colder than now. The 255K theoretical value depends on the albedo and is an upper limit which can only be reached with constant temperatures across the globe and the day/night cycle.
    Your calculation in #322 is erroneous as it neglects the logarithmic aspect.

    Comment by Anonymous Coward — 13 Jul 2010 @ 6:16 PM

  333. Stratospsheric Cooling Redux

    I’ve been involved in some provocative discussions of the stratospheric cooling issue on Chris Colose’s Climate Change blog – with both Chris and Patrick, two well-informed contributors. It has helped me to refine my own perspective. Without belaboring the process, I thought it might be worthwhile to summarize that perspective here, because stratospheric cooling continues to fascinate and bedevil those who hear about it. We are now far down in the thread, but I expect that at least a few of the expert and knowledgeable readers and bloggers may read it, offer responses, identify flaws, and perhaps take account of these ideas in arriving at their own perspective.

    Stratospheric Cooling by CO2 as a Mechanism Based on Ozone

    The first point, made earlier, is that a plausible explanation exists involving the presence in the stratosphere of a powerful absorber of solar UV radiation – ozone. Ozone is also present in small quantities above the stratosphere, but there, other solar absorbers such as O2 and N2 may be more important. The essence of the argument is simple: much stratospheric warmth is derived from ozone-mediated UV absorption. Added CO2 contributes to the dissipation of this heat to space while contributing less to additional heat absorption in the stratosphere because it absorbs only in the infrared, whereas much of the heat comes from absorbed UV, and CO2 can dissipate that heat as well as heat it absorbs from upwelling IR. The imbalance is responsible for cooling.

    This analysis is discussed more quantitatively by Raymond Pierrehumbert in his upcoming book, “Principles of Planetary Climate”, but Raypierre also mentioned it in a 2007 RC thread, and it was mentioned in an RC thread in 2005 by IBM mathematician James B. Shearer. In Raypierre’s analysis, added CO2 in the absence of ozone should warm rather than cool the stratosphere.

    Although an adequate explanation involving ozone might suffice, it must compete with alternative explanations for cooling that do not involve ozone. One of these asserts that cooling results from the reduced flux of IR into the stratosphere due to trapping in the troposphere from the increased CO2. This explanation fails, because models show that under equilibrium conditions, with OLR restored to its level prior to the extra CO2, the stratosphere persists in a cooler state when the CO2 concentration is higher.

    The Spectral Shift, Pivot Point Argument

    A second alternative acknowledges an unchanging OLR, but posits that less is now entering the stratosphere in wavelengths absorbable by CO2 because a heated surface is now radiating more IR to space in wavelengths where CO2 does not absorb (“window regions”). This “spectral shift” argument, along with other arguments for a cooling in the stratosphere associated with an enhanced greenhouse effect in the troposphere, requires that there must be a transition layer of the atmosphere – a “pivot point” – where warming below is associated with cooling above.

    The spectral shift argument is superficially plausible, because it acknowledges cooling despite an unchanging OLR, and because theory, models, and observations all demonstrate that a spectral shift does occur. The argument appears to fail on a more subtle level.

    WHY THE PIVOT POINT ARGUMENT IS PROBABLY UNTENABLE – subtitle, “Why You Can’t Cool An Object By Heating It.”

    My analysis requires some simplifying assumptions, but the pivot point argument doesn’t posit a mechanism that depends on these being wrong, so we can proceed with them, at least until we need to abandon them.

    1. Cooling occurs even if ozone is absent or plays no role.

    2. Stratospheric cooling is a strictly radiative phenomenon, with no significant influence of non-radiative factors such as convection, turbulence, etc.

    3. At a given insolation and albedo, CO2 and other absorbers, such as water, that obey the same principles, are the determinants of atmospheric temperatures. I will confine the discussion to CO2 as though it alone determined temperature, but including the other absorbers should not contradict the conclusions. Increases in water consequent to CO2 increases should in fact reinforce the point. In actuality, if we get rid of ozone, CO2 will be by far the predominant radiative component in the stratosphere.

    4. Absorption of solar radiation by CO2 is minimal, and increasing CO2 should not change it in a way to mediate cooling. Therefore, for practical purposes, the sole source of excess heat if we increase CO2 is IR emitted by the surface from absorbed solar radiation,. Because of atmospheric absorption and emission, IR at any level will not be coming only from the surface, but that is where it will all originate. (I neglect here atmospheric absorption of IR by water, but that should not mediate cooling at any level. Aerosols exert complex effects, but they have not been incorporated into these arguments, and so I won’t include them).

    5. The heat sink for atmospheric emissions is space, and is unchanging.

    Armed with these assumption, let’s examine the claim for a pivot point altitude in the atmosphere. We will confine the discussion to changes within the CO2 absorption wavelengths, because regardless of how much or how little OLR is emanating within these wavelengths, if the principles of radiative physics are violated there, the argument fails. We can divide the atmosphere into a lower part (LP), which includes the surface and is the source of IR, and an upper part (UP), which we are asked to assume will cool when CO2 increases, in conjunction with the expected warming of LP from the enhanced greenhouse effect. By established principles of radiative physics, a warmer LP should emit more IR within the CO2 wavelengths, including IR upward into the UP. Some of the excess upward IR will escape to space, but some will be absorbed within the UP. We are now asked to conclude that the UP, which was cooler to start with, will now cool still further. (If the heat sink, space, were changing, this might provide a cooling outlet, but it’s not). How can a warmer object, warming further and transmitting some of that increased heat to a cooling object, cause the latter to cool even more? It can’t.

    At this point, a clever reader will say, “Aha, you’ve omitted an important new element. The UP is not only absorbing more heat from below, but we’ve added an IR emitter, CO2, to the UP layers, and so it can rid itself of more heat.” That argument fails also, as long as we make assumption #3 above, that UP temperatures are determined by CO2 and other moieties that will act in the same direction. If CO2 determines temperature, adding more CO2 increases a layer’s emissivity, but it also increases its absorptivity by the same fractional increment, and so the effects cancel out. We are still left then, with the requirement that a warming object transmitting more heat to a cooler object somehow causes it to cool.

    I’m too hot. Put more wood on the fire!

    It may be worthwhile to pursue a simple analogy – a room with a fireplace and an open window – the fireplace equivalent to the Earth’s surface as a source of IR and the window the equivalent of space as a fixed heat sink. We are being asked to believe that if we turn up the heat in the fireplace, the room will cool, which is to say it will increase its heat loss more than its heat gain from the fire. In a real room with a real fireplace and a real window with a fixed opening, would that happen? We can also bring in the absorptivity/emissivity argument here, by asking whether we can help the room to cool by increasing its absorptivitiy and emissivity. One way to do that would be to paint the walls black. Will this make the room cooler? Note that black walls would absorb over a broad spectrum of wavelengths, whereas CO2 absorbs in the IR. In the IR, though, it acts like a black body.

    We can extend the same reductio ad absurdum logic to show that the involved principle – a warm object causing a cooler object to emit even more heat than it gains – is a Second Law violation. Let’s keep the principle but change the scenario slightly. Imagine an isolated chamber filled with air and having a small container at one end. We position a thermometer in the container and another to measure air temperature. We start out by placing a warm object – say a heated piece of iron – in the chamber, and then sealing the chamber, Our principle tells us that the heat from the iron will cause the air to cool by emitting even more heat than it receives. However, in the isolated chamber, that heat can only flow back to the iron. Since we are claiming that the iron is therefore receiving more heat than it emitted, it will warm further, thereby allowing it to cool the air further – a cool object heating up a hot one in violation of the Second Law. (Notice a bit of sleight of hand here. I’m applying the ability to emit excess heat to the air on cooling and to the iron on warming, which converts a Second Law violation into a combined Second/First Law violation. If we omit the claim that the iron will heat further, only the Second Law is violated.)

    Endless Electricity Without Fossil Fuels

    We can vary this theme to create a perpetual motion (or at least perpetual energy) device by not allowing the iron to continue heating further, but rather siphoning off some of the heat to a boiler creating steam to generate electricity. We do this just enough to keep the iron temperature constant. We end up with an endless stream of electricity sufficient to power the world’s growing energy demand, with no need for any more fossil fuels.

    Obviously, the atmosphere is different from a room with a fireplace and a window. It seems to me, though, that the burden falls on those who predict a different outcome for the atmosphere to show why the differences obviate the need to postulate that a warmer system, upon further warming, will cause a cooler system to cool further. Because of the many assumptions made here, I may have overlooked subtle flaws, but that’s the purpose of inviting comment.

    Comment by Fred Moolten — 13 Jul 2010 @ 6:45 PM

  334. Re 324 L, David Cooke – Come again? Perhaps there is a language barrier between us, because I can’t make out much of what I actually intended to say in the way you describe what I said. Judging from the terminology I get the impression you might be an electical engineer or work with fiber optics perhaps? The same terms (band widenning) may have different implications in different fields of study.

    (You also misunderstood my points regarding oxygen and H escape, etc, but I’ll leave that for later.)

    (Sorry, I’ve heard of decibels but I haven’t worked with them much. Is a db supposed to be 1/2 of a power of ten? By the way, the symbol db could be mistaken in the atmospheric sciences to be 1/10 of a bar).

    I think of a waveguide as being a guide of waves through space. The flow of radiation at different frequencies (wavelengths) don’t follow waveguides in that sense, though they can be thought of as different channels of communication. No ‘waveguide’ is necessary to keep a photon from changing its frequency; absent doppler and relativistic effects and certain kinds of scattering like Raman and Compton scattering, photons conserve their frequency while they propagate. Something specific has to happen in order to change a photon’s frequency, and that isn’t a big player in radiative fluxes through the Earth’s climate system.

    (Photons also tend to conserve their wavelength, except as changes are required to conserve frequency while propagating through variations in the index of refraction n. Often we speak of photons as if their wavelengths are unchanging – this is approximately true for radiation flowing though the atmosphere because n is very very close to 1, but in case the issue becomes significant, often when I’ve refered to the wavelength of radiation, I’ve been refering to the wavelength that a photon would have in a vacuum.)

    So I think I need to start over and explain some basics:

    2. The global average solar heating of the Earth is approximately 240 W/m2 (or maybe 235 W/m2 ?). This is about 0.7 * 1/4 of the solar flux incident on a unit area facing the sun at the position of Earth. The reason for this is that the area of a circle is π*radius^2, while the area of a sphere with the same radius is 4 times that value. The Earth is approximately spherical, but it intercepts solar radiation through an area facing the sun (recieving the approx. 1366 W/m2 solar flux per unit area) equal to it’s circular cross section. For at least near present-day conditions, it reflects about 30 % of the solar radiation it intercepts.

    Intensity is the amount of radiant power going in a direction, per unit area facing that direction, per unit solid angle (a range of directions).

    Flux per unit area in direction Q2
    = integral over solid angle of [intensity in direction Q1 * cos(θ)],
    where θ is the angle between Q1 and Q2.

    (The unit area that the flux goes through is perpendicular to Q2, while intensity in direction Q1 is given per unit area perpendicular to Q1; a unit area facing Q2 will appear to have a smaller area in direction Q1 in proportion to cos(θ))

    A flux per unit area can be found by integrating the intensity over a hemisphere of directions that all pass through the unit area in the same direction (in the sense of being from one side of the unit area to the other side, even though they do so at different angles).

    A net flux is the difference between a pair of fluxes in opposite directions. A net flux through a unit area can also be found by integrating the net intensity over a hemisphere of directions.

    Examples of units (sr = steradian = a meaure of solid angle; a solid angle of directions is equal to the surface area of a unit sphere onto which those directions project, where those directions are from the center of the sphere. There are 2*π steradians in a hemisphere of directions; all directions over a whole sphere occupy 4*π steradians.

    Intensity: W/(m^2 * sr)
    Flux per unit area: W/m^2

    A flux or intensity can be for the whole spectrum of frequencies, or some part of that spectrum (LW or SW, for example), or for a smaller band. One can also refer to monochromatic (spectral) fluxes and intensities, which is the flux or intensity at a particular frequency ν (or wavelength λ, or photon energy E) per unit of the spectrum (per interval of ν or λ or E, or even per unit log(ν), etc.). Integrating these values over ν or λ gives the flux or intensity for the whole spectrum or some subset of the spectrum.

    When one refers to a flux or intensity at some ν or λ, etc, it is implied that this is a flux or intensity per unit of the spectrum:

    at a particular ν (units of Hertz, Hz)
    Intensity: W/(m^2 * sr * Hz)
    Flux per unit area: W/(m^2 * Hz)

    at a particular λ (units of microns, μm)
    Intensity: W/(m^2 * sr * μm)
    Flux per unit area: W/(m^2 * μm)


    Often the term flux is used when one is actually refering to a flux per unit area (I caught myself doing this below in a few spots, but it is too cumbersome to fix now; usually one can distinguish what is meant by context).

    If polarization ever matters, one could refer to flux or intensity for some subset of the ‘polarization spectrum’, or to a flux or intensity at a particular polarization – if I ever do this, assume it is per unit of the polarization spectrum. I wouldn’t know how to express that formally but the concept is easy to understand – you would have to integrate such values over the polarization spectrum to find a total for all polarizations. If I use the Planck function in the context of polarized radiation, assume if I don’t otherwise specify it, that it is the original Planck function (monochromatic blackbody intensity as a function of temprature) divided by some value that represents the range of polarizations, so that it is an intensity per unit of the polarization spectrum.

    The following assumes LTE**. Refraction and some other complexities (Raman and Compton scattering, other…) are set aside for now.

    4. At a particular frequency ν and polarization P:

    Along a path with optical thickness τ, if intensity going into one end of the path is I0, the intensity coming out the other end of that path that is of the same photons that were going in is I0*exp(-τ). exp(-τ) is the fraction of intensity that is transmitted. This must be the same in both directions, So τ is the same in both directions along the same path. τ can include absorption and scattering of the original photons out of the path. Note that I0*exp(-τ) does not include contributions from emission of photons within the path or scattering of photons into the path from other directions.

    Different contributions to τ of different types (absorption, scattering) from different sources (different gases, particles, and different segments of the total path length) add linearly. τ per unit length is equal to the extinction cross section per unit volume. Cross sections of different types from different sources also add linearly. The absorption cross section density for radiation coming from a direction = emission cross section density for emission of radiaton into that direction; this is a form of Kirchhoff’s Law. Absorption cross section density is the fraction of radiation absorbed per unit distance. Emission cross section density is the fraction of Bν(ν,T) emitted into a direction per unit distance. Bν(ν,T) is the Planck function for frequency ν and temperature T and is the monochromatic intensity (intensity per unit frequency) that would be emitted by a perfect blackbody at temperature T. Notice that if the intensity coming from a direction is equal to Bν(ν,T), then the emitted intensity into that direction by a small length of path with temperature T is equal to the intensity from that direction absorbed by that same length of path. Scattering cross section density is the fraction of intensity that is scattered out of a path per unit path length.

    There is an ‘I can see you as well as you can see me’ rule. If I have this correctly *** For the same frequency, the fraction of photons at a location r1 going into a direction Q1 with polarization P1 that reach location r2 from direction Q2 with polarization P2 is the same as the fraction of photons at r2 doing into Q2 with polarization P2 that reach r1 from Q1 with polarization P1. Combined with Kirchhoff’s law, this ensures that the net flux of photon energy, from emission to absorption, between two volumes, is from higher to lower temperature, thus satisfying the second law of thermodynamics.

    (If I have this correctly: for a frequency ν, for an intensity I1 of polarization P1 from direction Q1 incident either on some scattering agents or a partially reflecting surface, a fraction f of that is scattered/reflected/transmitted into direction Q2 with polarization P2. The same fraction f of an intensity I2 reaching the same location from direction Q2 with polarizaton P2 is scattered/reflected/transmitted (respectively) into direction Q1 with polarization P1.)

    Note that if the extent to which you can ‘see’ is proportional to your absoptivity and the extent to which you can be seen is proportional to your emissivity, the ‘I can see you as well as you can see me’ rule includes Kirchhoff’s Law.

    Note that the ‘I can see you as well as you can see me’ rule is not violated by one-way mirrors (the room on one side of such a window is relatively dark, so what people on the other side see of that room is darkness, and any details tend to be drowned out by the reflection of the brightly lit room.)

    —— ——– ——–

    Combining Kirchoff’s Law with everything else: EWF: Consider an unit intensity of photons (of a particular frequency, and if necessary, polarization) directed in some direction from some location. The absorption of photons is distributed as a density over space in some way (along a path, exponentially decaying with distance if the absorption cross section density is constant over distance; if their is (partial reflection), it may be along a bent or branching path; if there is scattering, the distribution may fill a volume. If there is a lack of absorption nearby, the distribution is projected onto where it could be absorbed; scattering and reflection will redirect that projection. This distribution is equal to the emission weighting function. Locally multiplying the EWF by Bν(ν,T), and then integrating over the distribution over space (along a path or over a volume) gives the value of the intensity of the radiation coming from that direction and reaching the same location. EWF can be integrated over directions the same way intensity is integrated to find a flux per unit area; the result is an EWF for the flux per unit area (which I’ll refer to as EWFf). EWFf is also equal to the distribution of absorption of a flux per unit area, through the same area, going in an opposite direction, provided that the flux is isotropic (constant intensity) over the whole hemisphere of directions, with intensity = 1.

    Increasing optical thickess of the absorption type compresses the EWF and EWFf into a smaller volume closer to the location considered; increasing scattering optical thickness does the same if absorption is significant, and also can cause the EWF and EWFf to surround the location considered. Otherwise, scattering redistributes the EWF and EWFf so that they may be more evenly distributed around the location, though possibly at some distance away.

    When absorption is a signficant contributor to optical thickness, increasing the optical thickness (increasing the cross section densities) shortens the distances that photons can travel from where they are emitted, and to where they are absorbed. If the optical thickness and temperature distributions are such that the dominant spatial tendency in temperature is to either increase or decrease (as opposed to fluctuate) from a location out to a substantial optical thickness away, then farther increases in optical thickness will bring the flux and intensities coming from that direction toward the values they would have for a blackbody with a temperature equal to the temperature at that location. This approach to a particular asymptotic value is called saturation.

    When there aren’t any gaps in space with zero optical thickness (there is approximately a gap above TOA) and temperature varies continously over space (at sufficient spatial resolution, this is generally true everywhere within the climate system), increasing optical thickness eventually saturates the fluxes going in opposite directions, at which point they become equal, so that the net flux is zero. Saturation at TOA still leaves a nonzero net LW flux into space.


    For LW radiation in the Earth’s climate system, scattering is a minor issue and to a first approximation one can assume only absorption and emission occur. For SW (solar) radiation, there is generally no significant emission (volcanoes and lighting don’t cover enough space and aurora are too weak) within the Earth’s climate system, but scattering is important.


    (PS when refraction occurs, the intensity in the absence of scattering, absorption, emission, or reflection, changes because the same amount of radiation is compressed or expanded to different solid angles as the real component of the refractive index n changes. The blackbody intensity varies as a function of n in the same way. So one can take the actual value of intensity I and divided it by some function of n to find I#, which is conserved in the absence of other processes (specifically, at least in the case of isotropic n, I# = I/n^2);

    then, if I’m not mistaken, for a particular ν, the I# scattered/reflected/transmitted into a direction Q2 with polarization P2 from an incident I#1 from direction Q1 with polarization P1 is the same fraction of I#1 as the fraction of I#2 is the I# scattered/reflected/transmitted, repectively, into direction Q1 with polarization P1 from an incident I#2 from direction Q2 and polarization P2. And I# is emitted and absorbed by emission and absorption cross sections and emissivities and absorptivities that are equal for emission into a direction and absorption from that direction at the same location or over the same path length for the same frequency and polarization. The net flux of radiant energy (from emission to absorption) is from higher to lower temperature. I at any location is determined by I# reaching that location and the n at that location.)


    For the CO2 absorption band (the one of greatets importance in Earthlike conditions) centered at 15 microns (the corresponding frequency ν at this peak is νpeak), the shape of the band can be roughly***** described as per unit mass path of CO2 (mass per unit area along a path length), the optical thickness decays approximately exponentially moving away from the center of the band. As a function of frequency ν, log(τ) ~= τpeak – M1*(νpeak-ν) for ν νpeak.

    The τ from CO2 increases in proportion to the amount of CO2 at all ν; this includes τ = τpeak at ν = ν0. Thus, for all τ smaller than the initial τpeakν value, after increasing the amount of CO2 by a factor of 10, the same τ value can be found at a different ν that is farther out from the center of the band by an amount equal to 1/M1 or 1/M2, depending on which side of the center is being considered. Thus the CO2 absorption band effectively widens by an amount equal to 1/M1 + 1/M2. This has an effect on radiative fluxes by increasing the range of frequencies for which the EWFf’s are compressed by more than some amount. It also has an additional effect by compressing the EWFf’s near the center of the band. Eventually, the fluxes approache asymptotic values – the effect saturates. But when this first happens in the center of the CO2 band, there is still the band widenning effect; the CO2 effect is not saturated at the ‘edges’ of the band, which shift outward over the spectrum with increasing CO2. This pattern continues until there is so much CO2 that other parts of the absorption spectrum with different shapes become important.

    Note that I am refering to the effect of a change in CO2 amount on radiative fluxes while holding the climate steady. In some conditions, saturation can occur while holding temperatures steady, but the climate response can still change the fluxes – this won’t generally add a significant net flux where optical thickness has brought the net flux to zero, but it can change the net flux at TOA even if the effect of optical thickness has been saturated at TOA, and the climatic response could ‘unsaturate’ the effect at TOA by creating a thinner layer of different temperature. If the tropopause level LW flux were ever saturated over the whole LW portion of the spectrum, and there were still significant solar heating below that level, then the tropopause would tend to shift upward to where the LW flux is not saturated at some frequencies; in an equilibrium climate, the net LW flux out of the tropopause has to balance SW heating below the tropopause (in the approximation of zero non-radiative flux out of the tropopause), and thus cannot be zero.

    The effect of CO2 is to cause some sort of a valley or hill*&* in the monochromatic flux graphed over the spectrum (*&*depending on vertical level relative to temperature variations and whether one is considering upward or downward fluxes or the net upward flux). Consider the values of ν on either side of the band where the monochromatic flux is roughly halfway up or down the height or depth of that hill or valley; call these ν1 (lower than νpeak) and ν2 (higher than νpeak).

    To a first approximation, the CO2 radiative forcing can be approximated by taking the net upward monochromatic flux Fνup in the vicinity (in terms of position in the spectrum) of the CO2 band.
    Fνup(no CO2) be the value if there were no CO2 (holding climate steady),
    Fνup(peak) is the value at the peak of the CO2 band.

    The height or depth (as a negative height) of the hill/valley is equal to

    Fνup(peak)-Fνup(no CO2) = Fνup(CO2).

    The effect of band widenning is a reduction in net upward LW flux (this is called the radiative forcing), which is proportional to a change in area under the curve (a graph of flux over the spectrum); the contribution from band widenning is equal to the amount by which the band widens (in units ν) multiplied by -Fνup(CO2). For a doubling, that would be:

    forcing from band widenning, per doubling = -log(2)*(1/M1+1/M2) * Fνup(CO2)

    (the negative sign is there because Fνup(CO2) is positive if CO2 increases the net upward flux, while positive forcing is a decrease in a net upward flux.)

    When the band is saturated at the center, Fνup(CO2) reaches an asymptotic value Fνup(CO2saturated), the difference in the net upward monochromatic flux between a saturating amount of CO2 at that frequency, and no CO2 (notice that Fνup(CO2saturated) can be defined for any particular frequency).

    When the band is not saturated at the center, there will be an additional contribution to radiative forcing per doubling of CO2, that will be on the order of

    -1/2 * log(2) * (1/M1+1/M2) * 1/2 * [Fνup(CO2saturated)-Fνup(CO2)] if the peak is close to saturated

    (ie the area may be approximated as a triangle with a height that is half the difference between the net flux at the peak of the CO2 band and the net flux at saturation, though it will tend to be distorted a bit from that shape),


    -1/2 * log(2) * (1/M1+1/M2) * Fνup(CO2) if the CO2 effect at the center of the band is still quite small,

    though the exact values will vary depending on how the temperature varies over height as measured in terms proportional to optical thicknesses.

    That is sufficient so long as Fνup(CO2) doesn’t reverse it’s tendency at some point. If it reverses, we can treat the value at the point of reversal (marking a maximum height or depth of the hill or valley in the net upward flux spectrum) as the saturation value, and then include some additional effect at the center of the band for additional increases in CO2 that have the opposite sign as the band widenning in their contributions to radiative forcing. This can happen for radiative forcing at TOA because the upper stratosphere, directly heated by the sun, is warmer than the lower stratosphere and tropopause. It tends not to happen within the atmosphere because the net flux saturates at zero and won’t increase again after saturation – although it is hypothetically possible to set up a situation where increasing CO2 would result in one or more ‘pseudosaturations’ (*%* can I use that term?) (where the trend in net monochromatic flux reverses) before reaching the ultimate saturation; if this situation came up, after each ‘pseudosaturation’, the radiative forcing can still be estimated with a band-widenning effect outside the central region where the last ‘pseudosaturation’ has taken effect, minus the contribution from whatever is happenning in the center (think in terms of positive and negative areas on the graph). But the spectrum of net upward flux at the tropopause for Earth is approximately a valley (Fνup(CO2) is negative) with a continual downward slope toward the center on each side (this is an approximation, though*****).

    Note that this approximation assumes that the same optical thickness from CO2 will make the same change to the net upward monochromatic flux at each ν. This can be true to a first approximation. Variations are due to variations in the optical thicknesses already provided by water vapor and clouds, and variation of the Planck function over the spectrum. To deal with such variations, to a first approximation, one can use different values of monochromatic flux (in place of a single Fνup(CO2) value) for the widenning effects at each side of the band and for the the center of the band. For example, once the band is saturated at the center, the forcing from the band widenning could be estimated as:

    forcing from band widenning, per doubling = -log(2)*[ 1/M1 * Fνup(CO2saturated)ν1 + 1/M2 * Fνup(CO2saturated)ν2),


    Fνup(CO2saturated)ν1 and Fνup(CO2saturated)ν2 are the differences between the net upward fluxes with CO2 saturated at ν1 and ν2 and with no CO2, evaluated at ν1 and ν2, respectively; they could be considered the ‘potential’ monochromatic forcing for CO2 at those frequencies.


    **At LTE (local thermodynamic equilibrium) within a small volume of material (small enough to be isothermal) that is still large enough to contain a large enough population of molecules/atoms/electrons/etc, each population of a type of particle has the same temperature, and the distribution of energy among all particles and all forms it can take (translational, vibrational, rotational, potential, electronic, latent, etc) is an equilibrium distribution).

    (This is not a full thermodynamic equilibrium – it doesn’t require chemical mixtures to be at equilibrium, or for the radiative intensities to be in equilibrium with the non-photon matter. As long as the chemical and physical (and nuclear, etc.) reactions that do occur are occuring slowly enough for energy to be redistributed among particles, LTE can be approximately maintained. In some non-LTE conditions, a subset of particles may act as if they have a particular temperatue with respect to radiation but actually have a different temperature with respect to something else (applicable to photovoltaic devices; quasi-thermodynamic equilibrium). It is hypothetically possible to have populations of different temperatures within the same volume; as long as each seperate population is at LTE within itself, the radiative physics as described above can apply in a modified way – for example, the density distribution of an EWF would have to be distributed over space and over the different populations within that space.)

    (In full thermodynamic equilibrium, all photon-non-photon interactions, including Raman and Compton scattering, would sustain that equilibrium; all such interactions tend to eventually bring a system towards such equilibrium provided that photons (as well as other particles) are not entering or leaving the system from other systems with different conditions.)

    The vast majority of the mass of the atmosphere and surface material is approximately at LTE. LTE can be approximately maintained by redistributions of energy by molecular collisions or other such microscopic interactions among atoms, electrons, etc, as long as these occur rapidly relative to other processes that would selectively add or remove energy from a subset of the particles or forms of energy. Effective maintenance of LTE allows a subset of molecules to absorb radiation or emit radiation with the temperature of the emitting and absorbing population being nearly the same as the temperature of all the local matter, and with any net absorption or emission of radiant energy changing the temperature or physical or chemical state according to the heat capacity or latent heat of all the matter.


    ***** The CO2 spectrum deviates from the simple shape described above in some ways. There are some bumps, and there is also some finer-scale texture associated with the individual lines that make up the absorption band. To the extent that this fine-scale texture is self-similar over intervals of the spectrum that are narrow enough to resolve the band-widenning, they don’t affect the overall behavior so much; one can break up the spectrum into intervals sufficiently small to resolve the overall shape, and assign fractions of each interval to different absorption bands with different peak values but with the same shape and same slope when optical thickness is graphed on a logarithmic scale. The effect is a continuum of different absorption spectra that all have the same band-widenning per doubling and same effects at the center at various stages between no effect and saturation, though they are at different stages in that process for any given amount of CO2; the radiative forcing is a weighted average of the effects of each of those absorption spectra; once the center of the band is saturated for all of the spectra, the band widenning effect is the same for each and thus the forcing from the band widenning is the same as it is in the original simplified picture.

    However, their are other deviations from the simple picture that still render the logarithmic proportionality an approximation.

    There could also be some such complexity in the radiative flux per unit area absent CO2, which would affect the relationship between changes in CO2 and radiative forcing; for sufficient self-similarity of finer scale texture, the effect might be treated the same way as the texture of the CO2 spectrum (?).

    Still, the logarithmic proportionality works as an approximation for the radiative forcing of changes in CO2 amount once the center of the band has become saturated.


    Comment by Patrick 027 — 14 Jul 2010 @ 12:16 AM

  335. Part of this paragraph got cut-off:

    For the CO2 absorption band (the one of greatets importance in Earthlike conditions) centered at 15 microns (the corresponding frequency ν at this peak is νpeak), the shape of the band can be roughly***** described as per unit mass path of CO2 (mass per unit area along a path length), the optical thickness decays approximately exponentially moving away from the center of the band. As a function of frequency ν, log(τ) ~= τpeak – M1*(νpeak-ν) for ν smaller than νpeak, and τpeak – M2*(ν-νpeak) for ν larger than νpeak.

    The τ from CO2 increases in proportion to the amount of CO2 at all ν; this includes τ = τpeak at ν = ν0. …

    Comment by Patrick 027 — 14 Jul 2010 @ 12:23 AM

  336. sa 323: I don’t think mass migrations have ever been a problem for the human race.

    BPL: Or abandoning trillions of dollars worth of coastal infrastructure? And consider how the US has reacted to 10 million illegal aliens from Mexico. How will the red states respond to 100 million refugees from California, New York, and Florida? Or India to 100 million refugees from Bangladesh? Then there’s the fact that agriculture is likely to collapse if GW continues. Any of this concern you?

    Comment by Barton Paul Levenson — 14 Jul 2010 @ 4:50 AM

  337. Fred (#333),
    Your LP/UP model doesn’t take the lapse rate into account. I’m no atmospheric scientist and haven’t really considered the stratospheric cooling issue but, if an increase in the amount of atmospheric CO2 raised the average altitude from which the stratosphere receives radiation in the CO2 bands, wouldn’t it receive less radiation in those bands? It wouldn’t be the warming of the troposphere which cools the stratosphere but the lapse rate combined with the increased opacity in the CO2 bands. Does this explanation hold up?

    Comment by Anonymous Coward — 14 Jul 2010 @ 6:11 AM

  338. To 337 (Anonymous Coward): For clarity, we are discussing the explanation that discounts a role for ozone, in which case I argue the atmosphere would warm at every level if CO2 is added. If we compare a given level with the same altitude prior to the extra CO2, we will find it is receiving more IR from below, because the Earth and troposphere below that level are warmer, and it will be emitting more than before, because having received more IR, it is warmer itself. However, less of that IR will escape, because of the increased optical thickness above it. The result is that the effective radiating altitude rises until it reaches a higher altitude than before, optically thin enough to permit adequate IR to escape. That altitude is cooler than was the earlier radiating altitude (hence the reduced escape via the CO2 wavelengths), but it is warmer than the new altitude was before the CO2 addition, since previously, the new altitude was not the radiating altitude but above it.

    Replying to you also gives me a chance to clarify assumption #1 in my comment #333. That particular assumption is limited to proponents of explanations that discount the role of ozone. It is probably incorrect, but I was using their assumption for a reductio ad absurdum analysis of their explanation.

    Comment by Fred Moolten — 14 Jul 2010 @ 10:10 AM

  339. #321 Jacob
    #323 simon monckton

    In addition to sea level considerations for a warmer world there are myriad other considerations. Sea level is catastrophic because of infrastructure near the water and the costs associated with sea level rise. How much would it cost to move or rebuild all the infrastructure of New York City?

    Also, you need to consider the reality that all our current food infrastructure has been built during the relative radiative forcing of the Holocene and now we have altered that forcing.

    How much will in cost to reestablish the global food infrastructure at new latitudes? Consider this also though: how much will it cost to move that infrastructure multiple times? The climate system and the warming is non linear, so how much will it cost to do this multiple times?

    There are many other costs associated with climate change as well. So it all depends on what you consider catastrophic. Personally I think the economy is under enough stress already. But this is just the tip of the iceberg, so to speak.

    Think about it this way, we are already seeing economic impacts at 389ppm. so how much stress is okay? 540ppm is a lot of stress from pretty much every reasoned view that has examined it.

    As to simon’s question, well, infrastructure cost. Hundreds of thousands of years ago, no one had invested billions of dollars of investment in Manhattan. Consider also the economic strains of human migration.

    I do disagree with the perspective that this will only affect individuals. This is a global affect that unfolds and gets increasingly more expensive for the entire human race, but also we must consider the costs to the economic system itself, oceans, land, air.

    It’s the whole nine yards.

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    Comment by John P. Reisman (OSS Foundation) — 14 Jul 2010 @ 11:04 AM

  340. Re 333,338 Fred Moolten

    That particular assumption is limited to proponents of explanations that discount the role of ozone.

    I don’t think that’s necessarily the intent. I think at least some fraction of the equilibrium and also transient stratospheric cooling depends on the solar heating of the stratosphere; the question is whether there is some amount of cooling that would would still occur in the absence of that solar heating.

    Because of atmospheric absorption and emission, IR at any level will not be coming only from the surface, but that is where it will all originate.

    Actually there can be convection from the surface that is balanced by some of the radiation from within the troposphere, but in the approximation of zero non-radiative transfer above the tropopause, all the flux into the stratosphere must be from below (absent solar heating).

    How can a warmer object, warming further and transmitting some of that increased heat to a cooling object, cause the latter to cool even more? It can’t.

    True, but reducing the transmission to the cooler object can cause the cooler object to cool even more.

    Re 337 Anonymous Coward re Fred Moolten Your LP/UP model doesn’t take the lapse rate into account.

    Actually it does. I had forgotten something about the lapse rate when I earlier argued that there was some equilibrium stratospheric cooling that would occur absent direct solar heating of the stratosphere.

    I think it’s easier to look at this as a function of lapse rates. The lapse rate within the troposphere is largely determined by convection, which redistributes any changes in radiative heating or cooling within the troposphere+surface so that all levels tend to shift temperature similarly (with some regional/latitudinal, diurnal, and seasonal exceptions, and some exceptions for various transient weather events).

    When there is no solar heating above some level, the net non-SW heat flux must be upward and constant at all levels from the tropopause to TOA in equilibrium, to balance solar heating below that level. Radiation transfers heat across different scales at different optical thicknesses for different frequencies; the net radiant flux depends more on temperature variations that occur over distances on the order of a unit of optical thickness, so the net flux can be through smaller-scale temperature variations. However, there is no way to cause vertical fluctuations in equilibrium temperature if the total net LW flux is upward at every level, with all that energy ultimately coming from below, and there is no solar heating. So the lapse rate, though smaller than in the troposphere, will still be positive in the stratosphere; it might approach zero but it will not quite reach zero and will never be negative.

    Much of the absorption of fluxes going into the stratosphere and emission of fluxes going out from within the stratosphere may actually be due to stratospheric water vapor, because it has moderate optical thickness (on the order of unit optical thickness) over a wide band of wavlengths (though it is transparent in the vicinity of the 15-micron-centered CO2 band); the optical thickness is much greater in the CO2 band, but it covers a narrow range of wavelengths.

    However, for any sufficiently thin slice of the stratosphere, the water vapor will be almost transparent everywhere, while the CO2 still has a significant effect near 15 microns; thus, the fluxes among thin layers are mediated more by CO2 and occur near 15 microns.

    Thus, a very thin layer near the top of the stratosphere will essentially only be heated (absent solar heating) by radiation from below at the peak of the CO2 band near 15 microns. At equilibrium, it will have a temperature at which the blackbody flux at 15 microns would be half of the actual OLR at 15 microns. Thus, adding an infinite amount of CO2 would reduce the 15-micron OLR by 50 % (before the climatic response). This is the very important detail I forgot to consider earlier.

    to be cont…

    Comment by Patrick 027 — 14 Jul 2010 @ 1:30 PM

  341. A simple recipe for GHE is both good and useful. Better still would be to also make sure that accurate definitions and concepts are included as part of the GHE recipe.

    For example, the distance light travels before being absorbed is the mean-free-path for absorption, and not the optical depth. The mean-free-path is not typically utilized in radiative transfer calculations. On the other hand, the optical depth is a direct measure of absorber amount (with a distinction to be drawn between absorption optical depth and extinction optical depth to account for the scattering part of the total optical depth, or optical thickness). For greenhouse gases in the IR, since scattering is negligible, the extinction optical depth is essentially equal to the absorption optical depth. More important, the optical depth is a dimensionless quantity, being the ratio of the total absorption cross-section per unit area, to the unit area itself.

    The optical depth, TAU, can also be expressed as the negative of the logarithm of the transmission, i.e., TAU = – log [ exp(–TAU) ]. For greenhouse gases, TAU is a highly variable function of wavelength, ranging from near-zero in the far-wing areas of absorption lines, to many thousands within the core regions of strong absorption lines. TAU = 1 is the amount of absorber that if laid side by side without overlapping would just cover the unit reference area, implying 100% absorption of the incident light beam. But the gaseous absorbers are very small, very numerous, and randomly distributed. The transmission by one such particle is (1 – TAU/N). The transmission by all N particles is (1 – TAU/N)**N, which in the limit of large N, gives the transmission as being equal to exp(–TAU).

    It is noted that the stratosphere is expected to cool, while the troposphere and surface warm in response to GHG increases, as shown by GCMs, but that the picture might be more complicated.

    First, the Earth has a stratosphere because of the local heating due to solar radiation being absorbed by ozone. Without such absorption of solar radiation high in the atmosphere there would be no stratosphere, and the temperature would decrease monotonically with height.

    Second, that GCMs produce stratospheric cooling in response to GHG increases is and indication that the radiative transfer modeling is being done reasonably correctly, i.e., the spectral nature of IR absorption is being modeled, rather than using spectrally grey absorption. Spectrally grey absorption and spectrally integrated fluxes (sigmaT**4) cannot reproduce the stratospheric cooling.

    The explanation for the stratospheric cooling is actually straightforward. Stratospheric cooling arises because the IR window region allows radiation emitted by the ground to go directly out to space, and thus allows a combination of surface temperature change and stratospheric temperature change to contribute to defining the effective temperature, rather than forcing the stratospheric temperature alone to define the effective temperature. Consider a somewhat extreme example where half of the spectral outgoing LW flux is within the window region (emitted by the ground surface), with the other half being emitted within the radiatively opaque part of the spectrum from regions high near the top of atmosphere. In equilibrium we would have that:

    (Te)**4 = 0.5 * [(Ts)**4 + (Tt)**4 ]

    where Te is the effective temperature (as defined by the absorbed solar radiation), Ts is the surface temperature, and Tt represents the stratospheric temperature that is being defined by the opaque spectral region.

    With a GHG increase, say doubling of CO2, upon reaching equilibrium there will be a surface temperature increase by dTs, and a change in the stratospheric temperature by an amount dTt. The effective temperature Te will remain fixed, since we are not allowing changes in absorbed solar radiation (for simplicity). In the new equilibrium,

    (Te)**4 = 0.5 * [(Ts + dTs)**4 + (Tt + dTt)**4 ].

    Expanding the terms gives

    (Te)**4 = 0.5 * [(Ts )**4 + (Tt)**4 + 4dTs (Ts)**3 + 4dTt (Tt)**3].

    Since Te does not change, it then follows that the stratospheric temperature change has to be a cooling effect in order to maintain SW / LW energy balance and to conserve energy. Thus

    dTt = – dTs (Ts/Tt)**3

    In the above, the slight spectral shift of the Planck spectral radiation distribution has been neglected. Note that since Ts is substantially larger than Tt, it follows that the magnitude of the stratospheric cooling dTt will be larger that the surface warming dTs.

    Note also that the added LW opacity due to the CO2 increase will have little effect in the troposphere where convective energy transport is active. But the added opacity will have its full effect in the stratosphere (which is in radiative equilibrium). Opacity added to a radiative layer increases the temperature differential across the layer. The lower stratosphere will warm, and will communicate this warming to the troposphere and ground, while the upper stratosphere will cool because of reduced upwelling radiation.

    Comment by Andy Lacis — 14 Jul 2010 @ 3:12 PM

  342. Andy (#341)

    In my earlier comment (333), I described the reasoning behind the conclusion that increased CO2 only cools the stratosphere in the presence of ozone. Without ozone, the stratosphere should warm. I also attempted to demonstrate that a warming troposphere can’t cool the stratosphere by itself (e.g., without ozone). That rationale holds, I believe, until demonstrated false.

    I have some significant reservations about your analysis. You state:

    With a GHG increase, say doubling of CO2, upon reaching equilibrium there will be a surface temperature increase by dTs, and a change in the stratospheric temperature by an amount dTt. The effective temperature Te will remain fixed, since we are not allowing changes in absorbed solar radiation (for simplicity). In the new equilibrium,

    (Te)**4 = 0.5 * [(Ts + dTs)**4 + (Tt + dTt)**4 ].

    You appear to be adding the new Ts to the new Tt as though their sum were Te, but Te is a radiating level temperature, not an average temperature in either stratosphere or below. In fact, with increased CO2 (absent ozone), the radiating temperature will rise to a higher altitude. In the presence of a spectral shift, the stratospheric radiating temperature in the CO2 wavelengths will decline, but the overall stratospheric temperature will rise. As I mentioned in 333, I see no way for the increased emissions emanating from a warmer surface and troposphere to cool the stratosphere.

    Along the same lines, you also state:

    The lower stratosphere will warm, and will communicate this warming to the troposphere and ground, while the upper stratosphere will cool because of reduced upwelling radiation.

    There is an increase rather than a decrease in upwelling radiation, because the radiation is coming from a warmer surface and troposphere. Note that the radiation escaping from the stratosphere will decline because of the spectral shift, but the radiation entering the stratosphere will increase because more radiation is coming from below. The reduction in the escaping radiation is due to the fact that it would be coming from a higher, cooler layer. Within the stratosphere, each layer will warm (to a declining extent with altitude) because of the increased opacity combined with the increase in the upwelling radiation.

    Not to belabor the point, but as I suggested in 333, for one part of the atmosphere to warm, transmitting that extra warmth to a second, higher part, can’t lead to a cooling of the higher part through any known thermodynamic mechanism

    Comment by Fred Moolten — 14 Jul 2010 @ 4:24 PM

  343. Thanks Dr. Lacis…

    Fred– I still believe you misunderstood the section in Dr. Pierrehumbert’s book which specifically deals with the grey gas model and ignores the fact that a sensor from space will see the stratosphere at the opaque regions (~15 microns). This is where temperature increases with height resulting in an increase in the 15 micron irradiance (decreases in the 15 micron spectral flux into the stratosphere), and increased emission to space in the window region from the lower atmosphere and surface. In the weaker “wing” regions between 14 and 17 um the sensor is seeing the troposphere where irradiance decrease as CO2 is increased.

    In a grey atmosphere, then I would no longer agree with Dr. Lacis to the extent that there is an upper-level absorber present. This is because if you increase the GHG then you can get more cooling (at a given temperature) balancing the same solar heating. If we take a thin slice of isothermal stratosphere being heated by UV radiation (S_ozone)and outgoing longwave radiation from below (εσTe**4) and the stratosphere radiates up and down at εσTt**4 (assuming the emissivity to be constant over all wavelengths, and a factor of two for up and down direction), then the energy balance for that layer is

    (1-ε)S_ozone + εσTe**4 = 2εσTt**4

    From which it follows that

    Tt**4=[S_ozone/ε - S_ozone + σTe**4]/2σ

    If the OLR and absorbed UV are the same for heightened CO2 (at equilibrium), then the only change comes from ε which appears in the denominator of a term forcing the whole expression to become smaller with higher CO2. Thus the stratosphere can cool even in a grey model, although if S_ozone is zero then this term no longer matters. This is obviously not a realistic model through for real atmospheres.

    The fact that the mesosphere/thermosphere cools with higher CO2 (where the temperature declines in the mesosphere), and indeed that the high atmosphere of Venus is even colder than Earth, should also be independent validation that ozone is not a pre-requisite for upper atmosphere cooling.

    Comment by Chris Colose — 14 Jul 2010 @ 4:48 PM

  344. Re Andy Lacis -
    Spectrally grey absorption and spectrally integrated fluxes (sigmaT**4) cannot reproduce the stratospheric cooling.

    Unless there is sufficient solar heating in the upper atmosphere, specifically within the layer that can emit significantly directly to space.

    What if, in addition to increasing optical thickness within a band, you also add some optical thickness in a new band (CO2 is a bit like that because of the shape of the absorption spectrum)?

    The stratosphere can have a positive lapse rate, just so long as it is not large enough to make it part of the troposphere.


    It almost seems like whether the stratosphere or parts thereof would cool from increased GHGs in the absense of direct solar heat is a question balanced on a knife’s edge, and could go either way depending on specifics…

    Comment by Patrick 027 — 14 Jul 2010 @ 5:11 PM

  345. Hi Chris – Let’s take things one at a time. If you read Raypierre’s chapter, you’ll see that he was not invoking a grey gas model to require the presence of ozone for stratospheric cooling. He was explicitly using that mechanism to explain stratospheric cooling observed here on Earth during recent decades (or rather that part of cooling not attributable to ozone depletion). He added that in our own, non-grey gas atmosphere, increased CO2 should raise stratospheric temperatures in the absence of ozone. In that sense, if you disagree, you should probably take it up with him as someone best qualified to defend his assertions.

    Let’s next consider Andy’s equation that he believes requires the stratosphere to cool if the surface warms., presumably without invoking ozone. In his example split between a transparent window region and a very opaque region, he averaged (using the appropriate fourth powers) the surface temperature with the radiating temperature of emissions from the opaque region, calling the latter “the stratospheric temperature”. It isn’t. Rather, as opacity increases due to increased CO2 or other ghgs, the stratospheric temperature deviates more and more from the radiating temperature in the stratosphere for the opaque region. That is because the radiating layer risis to a higher altitude. In essence, the stratosphere warms, while the radiating temperature remains constant if there is no spectral shift, and declines if there is (as one would expect to happen). The latter is what we should see on Earth, with its spectral shift – a warmer stratosphere at all levels with increasing CO2, combined with a reduced temperature at which the stratosphere radiates to space.

    Here is where the grey gas model does help illustrate my point. Assume we increase the ghg responsible for the greyness. If insolation and albedo don’t change, the radiating temperature won’t, but clearly both the surface temperature and atmospheric temperature will rise. The radiating temperature will remain constant because its altitude is elevated.

    What appears to be a prerequisite for cooling is not ozone per se, but a UV absorber – ozone in the stratosphere, but more likely O2 and N2 in higher levels.

    Finally, the laws of thermodynamics must apply. As I discussed in #333, requiring a warmer lower part of the atmosphere, on warming further and emitting more IR, to cause a cooler part receiving the excess IR to cool further, violates radiative transfer principles and/or the Second Law. For anyone following this discussion, I would urge them to find my own conclusions best described in #333, but they should also visit #14, for Raypierre’s perspective on the topic.

    Comment by Fred Moolten — 14 Jul 2010 @ 6:45 PM

  346. this a great analysis but I will also echo something said earlier. the laymen just want to know, how can high altitude areas be cooler than than at sea level yet the energy is coming from above[ the sun].
    granted, over-simplification would merely serve to mislead scientists. my suggestion: two replies side by side, one to the laymen and another about photons, wavelengths, frequencies, planck, einstein.
    good article nevertheless.

    Comment by ziarra — 14 Jul 2010 @ 7:17 PM

  347. Fred, are you distinguishing the stratosphere temperature
    –during the period of nonequilibrium from
    –during the new equilibrium period after CO2 stops increasing and the warming has leveled off at a higher temperature?

    Comment by Hank Roberts — 14 Jul 2010 @ 7:28 PM

  348. Re Chris Colose, Andy Lacis, Fred Moolten – Okay, I’ve figured it out. (I now agree with Chris Colose and Andy Lacis). I wouldn’t have taken so long if I hadn’t been flipping between different ways of picturing the problem:

    The forcing of a doubling of CO2, in the approximation of a band where optical thickness halves over a spectral interval of BW (BW1 or BW2 depending on the side of the peak) going away from the peak

    and in the approximation that other sources of optical thickness and the Planck function don’t vary much over the width of the CO2 band so – or their combination of variations is such – that the baseline spectral flux for no CO2 as well as the value at any given optical thickness from CO2 is approximatly constant over wavlength – or else so that the baseline and other levels of spectral flux for a given additional optical thickness, or at least the differences among them, vary over the band is such that as the band widens, decreasing effect on one side is balanced by increasing effect on the other – but for now I’ll just use the simplification of a constant baseline and additional optical thickness effect on spectral flux over the width of the band:

    Consider a graph of the spectal flux (per unit area, of course) over wavelength, with some baseline flux for the absence of CO2, and some saturation value when CO2 optical thickness is very large. The effect of CO2 is a hill or valley that has some height or depth from the baseline; it’s maximum height or depth is achieved when the central portion of the band saturates. The magnitude of the radiative forcing per doubling is equal to the effect of band widenning, which is (BW1+BW2)*depth of valley or height of hill, plus some additional effect in the center of the band, which is on the order of 1/2 * (BW1+BW2) * increase in height or depth of hill or valley; the central contribution could be more or less than that, but it will be less than double (because the shape of the absorption spectrum won’t allow a square shape in the graph of the spectral flux). This last part becomes insignificant when the center of the band becomes saturated; however, if the temperature fluctuatuates over thin vertical layers near the level for which this flux is evaluated, an initial saturation effect can be reversed. Hypothetically it could reverse multiple times; each time, the height or depth of the hill/valley at the point of the the most recent ‘saturation’ can be multiplied by the BW1+BW2 to find the magnitude of the radiative forcing from band widenning, with the only remaining part to consider being the reversal of the trend in the flux near the center since the most recent ‘saturation’.

    At the tropopause, there is a baseline net upward spectral flux, which is the upward – downward baseline fluxes. Absent CO2, the stratosphere is essentially transparent near the CO2 band, so the net upward baseline flux is equal to the upward baseline flux from below, and it is equal to the baseline OLR spectral flux at TOA. Thus the baseline of the net upward spectral flux is the same at the tropopause, TOA, and everywhere in between.

    The radiative forcing is the decrease in net upward flux.

    CO2 puts a valley in the upward flux; at the tropopause it puts a hill in the downward flux, which combine to form a valley in the net upward flux. The generally positive lapse rate in the troposphere down to the surface means that the valley in the upward flux at the tropopause (I’m going to say TRPP, for short) has no reversals in the depth of the valley until ultimate saturation. Depending on the lapse rate in the stratosphere, the hill in the downward flux could reverse at some point, particularly if their is a large negative lapse rate in the base of the stratosphere – but I don’t think this tends to be the case; anyway, let’s assume that the CO2 valley in the TRPP net upward flux only deepens until it saturates at zero (it saturates at zero because at that point the upward and downward spectral fluxes at the center of the band are equal to the blackbody value for the temperature at TRPP).

    There is thus a greater maximum depth that the CO2 valley can achieve at TRPP (or within the stratosphere) than at TOA because the baseline net upward flux is the same but the net flux can be brought all the way to zero except at TOA, where there is no source of downward flux. Thus, if the CO2 band center is sufficiently close to saturation at TRPP, the forcing per doubling will be smaller at TOA, implying some cooling of the space in between (equal to the difference in forcing between TRPP and TOA; the climatic response will, via cooling, reduce the fluxes out of the stratosphere by the same amount; some fraction of this can go into the troposphere, and since it is a reduced downward flux, it cancels out some of the initial TRPP forcing, resulting in a smaller TRPP forcing (the forcing with stratospheric adjustment) that the surface+troposphere must respond to. When the troposphere+stratosphere respond by warming, an increase in the net upward flux at TRPP occurs that is equal to the TRPP forcing with stratospheric adjustment – the stratosphere is warmed by this, but only by the fraction of that which it absorbs; if that is sufficiently small, than the stratospheric warming is smaller than than the initial cooling, so some cooling remains (there will be feedback from this stratospheric warming that results in some additional warming of the troposphere+surface, which adds some more stratospheric warming, but an infinite number of iterations will converge to a small finite effect if the stratospheric absorption of the changes in upward fluxes from below is small enough). Depending (?) on how the temperature varies with height and how other gases, etc, within the troposphere that lower the baseline, are distributed relative to temperature, it may in general be the case that the valley at TRPP will be deeper than the valley at TOA even if it is not saturated at TRPP (?).

    With solar heating, particularly of the upper stratosphere, the upper stratosphere is warmer than otherwise; with sufficient heating (as it is now on Earth), the upper stratosphere is warmer than the lower stratosphere. The valley in net flux at TOA can, at sufficient CO2 amounts, develops a hill at the bottom. The effect of the growth of this central region partly cancels the band-widenning (which is itself proportional to the depth of the valley, which may tend to be less than the depth of the valley at TRPP). Thus, a given amount of solar heating results in increased stratospheric cooling for a doubling of CO2.

    But without direct solar heating of the stratosphere (and in the approximation of no non-radiative energy fluxes throught the stratosphere), while the temperature should decline through the stratosphere, it will not go to zero. The CO2 valley for the OLR at TOA still cannot get as deep as it can at TRPP, although it won’t reverse after saturation (lack of reversal would also be true for an isothermal stratosphere).

    Approaching TOA, the temperature falls toward a skin temperature (see last paragraph of my 340, see Chris Colose’s comment for the reason why), which is lower than the brightness temperature of the OLR at the wavelengths at which the skin layer absorbs OLR from below; specifically, the skin temperature is such that, were the skin layer to become very optically thick, the OLR at those wavelengths would drop to half of what they are. Let’s assume that it is the 15 micron OLR that controls the skin temperature; the blackbody OLR (at 15 microns) for the skin temperature will be half of the actual OLR. In a linear approximation (that the blackbody spectral flux as a function of local temperature changes linearly over optical thickness going down from TOA, down to a sufficient optical depth), a doubling of CO2 will bring the depth of the valley halfway towards half of the OLR (the OLR at 15 microns will decrease by 25 % per doubling – remember this is before the temperature responds).

    So, assuming the same baseline net upward flux (transparent (except for CO2) stratosphere in the vicinity of the CO2 band), if the CO2 valley in net upward flux is saturated (at the center) at TRPP, the depth of the TRPP valley is deeper than the valley at TOA both before doubling, after doubling, and even at TOA saturation. The forcing for an unsaturated valley, per doubling of CO2, is more than the (BW1+BW2) * initial valley depth, but it is less than the (BW1+BW2) * final valley depth, which will be less than the (BW1+BW2) * saturated valley depth at TOA, which is still less than (BW1+BW2) * saturated valley depth at TRPP.

    Thus, at least if the CO2 band is sufficiently close to saturated at it’s center at TRPP, and maybe even if it is not, the TRPP radiative forcing will be greater than the TOA radiative forcing for a doubling of CO2, so their will still be initial stratospheric cooling. It will be, as in the case with direct solar heating, larger than the final equibrium cooling, but it could still be a cooling even after surface+tropospheric warming, though both the initial and final cooling will be smaller than in the case with direct solar heating.

    (PS to deal with the shift in the tropopause, we could take TRPP to be the higher final tropopause position.)

    (the other approach I was thinking of involved considering how the lapse rate equilibrates so that the net flux is constant over some thickness for the whole LW spectrum (approximately true for equilibrium above the tropopause). This won’t generally be the case at every LW frequency. Thus, at some frequencies, there will be layers with net radiative heating; which means at others, there will be net radiative cooling of the same layers. So what happens when optical thickness is changed at one or the other of those sets of frequencies?

    Of course, though some of the flux up at the tropopause escapes directly to space, and some is absorbed by CO2 (over the whole stratosphere in the wings of the CO2 band, concentrated towards the base of the stratosphere for larger optical thicknesses), some is absorbed by ozone (with variable concentration), and some by water vapor. The troposphere+surface have to warm up enough so that the upward flux at TRPP balances both the TRPP forcing and TRPP feedbacks from changes below TRPP. That doens’t affect the equilibrium increase in the upward flux at TRPP in response, though it may change how much of that is absorbed by the stratosphere (perhaps a reduction due to shielding of water vapor and CO2 wings in the stratosphere by increased tropospheric water vapor (as it would by an increase in clouds, particularly higher clouds) – PS feedbacks also change the baseline spectral flux in the vicinity of the CO2 band.

    But then there’s feedbacks within the stratosphere (water vapor), which would increase the stratospheric heating by upward radiation from below, as well as add some feedback to the downward flux at TRPP that the upward flux at TRPP would have to respond to via warming below TRPP. (In general, the troposphere+surface have to warm to balance the TRPP forcing and feedbacks (in terms of net flux, thus depending on stratospheric feedbacks), and the stratospheric temperature has to respond to both forcing and feedbacks in the TOA net flux – TRPP net flux.)

    PS what if their where a substance within the stratosphere that provided significant optical thickness in the vicinity of the CO2 band. This would tend to reduce the potential for TOA forcing even more, leading to more stratospheric cooling in response to an increase in CO2; however, the presence of such a substance would itself make the inital stratospheric temperature warmer than otherwise.

    Comment by Patrick 027 — 14 Jul 2010 @ 8:31 PM

  349. Patrick27, 340, 344–

    I hesitate to comment on a discussion I am not prepared (for the most part) to understand in any depth; however, perhaps others will be confused, as I was, by your comments WRT the stratospheric lapse rate.

    Surely the stratospheric lapse rate is in fact negative, as every “general science”-level discussion of the matter I’ve ever read states? After all, the stratopause is what, about -3C?

    Comment by Kevin McKinney — 14 Jul 2010 @ 8:35 PM

  350. Re 346 ziarra – the flow of heat (between adjacent layers of material via conduction, convection, or mass diffusion, or potentially across larger distances via emission and absorption of photons) will be from hot to cold (or from higher to lower concentrations of a substance carrying heat, which might end up being from cold to hot in some conditions, such as a wet surface cooling by evaporation into warm dry air).

    But this flow of heat is spontaneous because the energy (or matter than embodies it) tends to spread out from whereever it is. It is spreading out even from cooler regions; but because the concentration is less, the flow of energy out of lower concentrations is less than the flow out of higher concentrations (other things being equal). Thus the flow of heat, which is a net flow of energy, is from higher to lower concentrations of that type of energy.

    The radiation from a cooler upper atmosphere can warm the surface because it counteracts the even greater amount of radiation in the other direction, thus reducing the net flow of heat.

    Comment by Patrick 027 — 14 Jul 2010 @ 8:39 PM

  351. “Thus the flow of heat, which is a net flow of energy, is from higher to lower concentrations of that type of energy.”

    Although one may refer to the individual flows of that type of energy as flows of heat, but they aren’t *THE* (net/total) flow of heat.

    Comment by Patrick 027 — 14 Jul 2010 @ 8:41 PM

  352. Hank (347) – I’ve restricted my discussion to equilibrium conditions. While I’m commenting, I want to agree with Patrick above that as long as there is a solar absorber, there will be conditions permitting increased opacity in a grey gas atmosphere to result in stratospheric cooling. I also agree that if complicating factors are introduced that invalidate my assumptions in #333 about an explanation excluding ozone, one might see cooling without ozone, but I’m not aware of any factor that would actually change the assumptions sufficiently to do that. I therefore must stick with the conclusion that a solar warmer is needed for increasing CO2 to cool the stratosphere.

    Chris C – In reviewing Raypierre’s chapter, I note that he introduced his equations using a grey gas model, but my point was that he then applied the results to our own atmosphere. Regarding Venus, it appears that the solar absorber is CO2, primarily in the near infrared.

    To all – now that we’re airing some disagreements, I want to restate my respect for all those participating. I present the logic of my conclusions as convincingly as I can, but that doesn’t diminish my respect for those who disagree as thoughtfully as is the case here.

    Comment by Fred Moolten — 14 Jul 2010 @ 8:48 PM

  353. Re 346 ziarra, again:
    “The radiation from a cooler upper atmosphere can warm the surface because it counteracts the even greater amount of radiation in the other direction, thus reducing the net flow of heat.”

    In other words, the greenhouse effect reduces the radiative heat loss of the surface, which is being heated by the sun; the surface has to warm up enough so that it can lose heat at the same rate that it gains heat from the sun (though changes in radiative heating at the surface can be made up for by convection, which is why we tend to focus on the effect of net heat loss at the tropopause, which is approximately an upper boundary to convection; the surface and troposphere together are cooled by the net radiative heat loss at the tropopause, which can be reduced both by greenhouse gases and clouds within the troposphere (reducing the upward flow of radiation because they are cooler than the surface and block the greater flow of radiation from the surface) as well as by the greenhouse gases within the stratosphere (by increasing the downward flow of radiation; withoug the greenhouse gases, the stratosphere would not emit any radiation).

    The surface and troposphere are linked by convection so that they tend to warm up and cool down together in response to changes in either the greenhouse effect or in solar heating.

    Air expands and cools as it rises (to lower pressure) and does the opposite when it sinks (to higher pressure), which is why convection cannot make the troposphere as warm as the surface. Convection tends to occur where radiative processes alone would make the temperature drop with height faster than the rate that air cools as it rises (the greenhouse effect is important for that, too).

    Comment by Patrick 027 — 14 Jul 2010 @ 9:08 PM

  354. Since you’ve taken it upon yourself to explain climate science to us, there’s one subject that has always confused me. If the atmosphere is a big window to space, it seems not to be transparent to very many wavelengths of infra red light. What is particularly bad about CO2? Does it block one of the few open pathways? How about methane, SF6, and others – do they block the same wavelengths as CO2, or do they stake out other wavelengths. I find it amazing that CO2, present in such tiny amounts, can cause such mayhem.

    Comment by Pete Baldo — 14 Jul 2010 @ 9:19 PM

  355. ref. #10

    Neaaaaa….what’s up Doc?

    Sorry Edward…I could not help myself.

    Great lecture Gavin…


    Comment by lucien locke — 14 Jul 2010 @ 9:52 PM

  356. In the grey gas case with no solar heating above the stratosphere, the equilibrium temperature at TOA is fixed by the equilibrium OLR (such that the blackbody flux for T(TOA) is half of actual OLR; by the way, for some purposes it may be easier to refer to values of temperature in terms of the corresponding blackbody or Planck function value – ie the surface has warmed up to 390 W/m2, etc…).

    The temperature from the tropopause to TOA drops in such a way as to keep the net upward LW flux constant. For large optical thicknesses, this can be achieved (within limits – see below) by having T^4 decrease linearly over distance measured in terms of optical thickness, so that the corresponding blackbody flux changes linearly over optical thickness – in that case, an evenly distributed increase in optical thickness reduces the net upward flux by the same amount at different vertical positions, so that no layer experiences an initial heating or cooling (this is before temperatures change elsewhere, such as at the surface and troposphere).

    However, if the temperature outside some region breaks from this pattern (in the troposphere or at the surface, above TOA in effect), this changes LW fluxes entering the region where the pattern holds, requiring some compensating deviation from that pattern in those locations. Both the deviations from such a pattern outside the stratosphere and the deviations necessary within the stratosphere may allow an increase in optical thickness to cause some initial warming or cooling within the stratosphere.

    Effect of additional optical thickness on the skin layer: The OLR is reduced, which cools the skin layer. This is entirely transient since the OLR has to return to the same equilibrium value when the full climatic equilibrium response occurs (absent SW feedbacks, of course). For an optically thick stratosphere, for full equilibrium, the same temperature profile is compressed towards TOA, except where the flux from the troposphere+surface requires some deviation.

    Comment by Patrick 027 — 14 Jul 2010 @ 10:19 PM

  357. Patrick (348) – I wonder whether you’re using the terms “upward flux” and “net upward flux” interchangeably. They are very different. With a warming troposphere due to increased CO2, the upward flux must inevitably increase via the Planck function. This warms any atmosphere above it. In the absence of ozone, there would be no well-defined stratosphere, but what we now call the stratosphere would also warm due to its increased opacity, and an increased upward flux from below in the CO2 wavelengths. This is why, barring some unusual extraneous factors, we would predict “stratospheric” warming rather than cooling from a CO2 increase.

    I feel like I’m belaboring the point, but I would refer anyone interested to go back to #333 for the thermodynamic/radiative transfer analysis. Despite the fact that I see the logic there as sound in its own right, my confidence is reinforced by the explanation I quoted from Raypierre in #14.

    Comment by Fred Moolten — 14 Jul 2010 @ 10:54 PM

  358. Pete Baldo (354):

    Please refer to this diagram which will be helpful for your question

    For the top part of the figure: The “window” regions are those levels where radiation from the surface and lower troposphere can easily escape to space, and so the blue squiggly curve tracks the blackbody spectrum for hotter temperatures (between 280 and 300 K). This can be found primarily between 800 and 1200 cm**-1 except for the ditch caused by ozone (the units here are wavenumbers, which is the inverse of wavelength). CO2 absorbs between the 600-800 cm**-1 region, a very important part of the spectrum for planets or moons which radiate at Earth-like temperatures, and so yes, this substantially reduces the outgoing radiation of the planet for a given temperature.

    By the way, how effective a new greenhouse will be for altering the global climate depends very much on whether another absorber is present at those wave numbers of strong absorption. Introducing a greenhouse gas that absorbs in the window regions would have a much larger effect than introducing a new greenhouse gas that absorbed where CO2 already did. This is why CFC’s have a stronger molecule-by-molecule impact than CO2.

    Comment by Chris Colose — 14 Jul 2010 @ 11:01 PM

  359. To Patrick, Fred, and other interested in this discussion on the technical details of stratospheric cooling. I have just had a brief e-mail correspondence with Ray Pierrehumbert asking for clarification on the relevant section in his book; he is currently in New Zealand and busy with work and so he cannot explore our conversation here. Having his permission, I am posting his remarks from two emails here (psst…I am dubbing this ‘raypierre-gate’ but don’t tell anyone). He didn’t seem to directly answer the question of whether you get upper-atmosphere cooling with no UV-absorbers at all, which my impression from his message goes beyond a simple thought experiment. He is also leaving us with work exercises for the readers:


    Email 1

    Hi, Chris,

    [irrelevant discussion]
    I’m glad the analytic grey gas solution
    has gotten people thinking. It’s what it’s for.

    The grey gas version doesn’t actually do the complete job of accounting
    for what is going on regarding stratospheric cooling/tropospheric warming.
    The main points of that solution are to show that (1) for making
    temperature increase with height, it’s not enough
    to have a stratospheric absorber; you need one with the right vertical
    profile, and (2) you can get stratospheric cooling in response to
    increased IR opacity because you get rid of more of the absorbed solar
    locally. The tricky part is getting stratospheric cooling together with
    tropospheric warming. My analytic solution doesn’t even try to do the
    whole problem, since the analytic solution is just pure radiative
    equilibrium. In the pure radiative equilibrium, you can get it into a
    range where the grey model gives you surface warming and stratospheric
    cooling (that’s in one of the problems), but you have to work at it a bit,
    and also remember to plot things in pressure coord, not optical depth
    coordinates. That’s still
    not the whole story, though, since the full story involves
    radiative-convective equilibrium. I’m pretty sure you can get the grey
    version of that into a strat-cooling/trop-warming situation if you pick
    the strat absorbers right, but Andy is certainly right that non-grey
    effects play a crucial role in explaining quantitatively what is going on
    in the real atmosphere (that’s connected with the non-grey explanation for
    the anomalously cold tropopause which I have in Chapter 4, and also with
    the reason that aerosols do not produce stratospheric cooling, and
    everything depends a lot on what level you are looking at). Remember,
    too, that ozone changes are part of the observed stratospheric cooling.

    I hope those remarks help to set things in the right direction. The book
    is in production, and will go to the printers in August if I return the
    proofs on time. Still takes until December for it to get distributed and
    go on sale. I have started cleaning up the web site and online materials.
    A complete set of data sets and scripts is now available at the new
    web site (still embryonic, but growing):

    [irrelevant discussion]


    Email 2



    I see what the discussion is centered on. These are interesting and
    thought provoking issues. Certainly, it is true that you can’t get the
    stratospheric cooling in a grey model without shortwave absorbers, not if
    you keep the OLR fixed (i.e. constrain things to satisfy the TOA radiation
    budget). In the full radiative-convective case, it’s rather tedious to
    work that out analytically (though you can, in the optically thick limit),
    but exploring it numerically is fairly simple. The basic idea, though, is
    that the stratosphere temperature scales with the skin temperature, and
    that doesn’t change if you hold OLR fixed.

    For a real gas it’s a lot harder to do the reasoning analytically,
    especially since you have to keep in mind the effects of changing the
    tropopause height. It would be instructive to work this out for the
    window-grey atmosphere, which has a lot of the basic features of the real
    gas in this regard. I don’t really have a suitable plot in Chapter 4 to
    address this question, since the real-gas results in Chapter 4 are
    computed holding the surface temperature fixed while you make the
    atmosphere more optically thick (in which case you do get stratospheric
    cooling, but that’s not the same thing you’re talking about). I’d suggest
    doing a simple CO2 plus dry air radiative-convective calculation for
    either the NCAR model or my homebrew radiation code, using the Python
    scripts I have provided for the purpose. There are always more questions
    than can be covered by an static set of graphs, which is why I worked so
    hard to provide software so people can explore this sort of thing on their



    Hopefully these help for the discussion we’re having, of which I don’t know if I can add anything more


    Comment by Chris Colose — 15 Jul 2010 @ 2:32 AM

  360. Re: #354

    What is particularly bad about CO2?

    The main reason is that your phrase “present in such tiny amounts” has led you astray. If you see such a remark in science ask yourself tiny compared to what ?> The concentration of CO2 is the wrong measure for deciding whether it is ‘tiny’, because it compares the amount of CO2 with the amounts of oxygen and nitrogen which don’t absorb infra-red at normal pressures.

    Thus CO2 is important because

    (a) There is a lot of it compared to all the other greenhouse gases except water vapour.
    (b) If we increase the amount , the increase will stay around for an unusually long time.
    (c) The level of water vapour depends on the global temperature , so it is roughly fixed until something else warms the atmosphere when it increases in amount producing more warming. The CO2 is often the something else, especially during the last few decades i.e. the CO2 has been acting as a driver for the water vapour.

    Comment by Geoff Wexler — 15 Jul 2010 @ 4:23 AM

  361. Ray’s answer makes it obvious (for me) that reality is very complex and far from being explainable by simple, hand-made arguments for the general audience; that’s why I think that trying to explain “simply” the very complex phenomena involved in radiation transfer is just lost time- and in my opinion the REAL issues associated with social impacts of GW are not primarily associated with the detailed physics of the phenomenon.

    Concerning the stratospheric cooling, I have the impression that they’re two different explanations that are often mixed and confused.
    * increasing CO2 concentration of the opaque (lower) layer of the troposphere absorbs more LWR , which decreases the heating of the upper layers and eventually produces a cooling.
    * increasing CO2 concentration in the optically thin (upper) layer in the stratosphere increases the LWR emissivity and hence increases the cooling.

    Correct me if I’m wrong, but I think that the first effect can only be a transient effect, because it holds only during the warming phase of the Earth surface. Actually to reach a new, higher equilibrium temperature, the Earth surface (including oceans) must warm and thus the radiative budget MUST be unbalanced, less radiation must be emitted in space compared to the (unchanged) incoming solar radiation. So during this phase, the increased absorption actually lowers the temperature of TOA. But eventually, this will be exactly compensated by the increased emission from the surface (because it’s getting warmer and warmer), until by definition both fluxes compensate exactly and a new steady state is reached. But the the radiation emitted in space is again exactly the same, and so the “photosphere ” (TOA defined by IR optical depth around one) , what I understand being the “skin”, is the same. And ABOVE this skin, there is no reason why the stratosphere should cool – IMHO the argument that the temperature gradient must still be larger is INCORRECT, because in the transparent regime, the heat flux is no more linked to temperature gradient (hence the temperature increase with altitude…)

    so once the new equilibrium temperature is reached, the increased absorption of the lower level is compensated by the increased emission from the ground, and this shouldn’t change the stratosphere temperature. That’s how I understand Ray’s assertion “The basic idea, though, is that the stratosphere temperature scales with the skin temperature, and that doesn’t change if you hold OLR fixed.”

    So the ONLY permanent effect is the second one : stratosphere temperature (which is NOT related to heat flux but is the result of heating and cooling process far from LTE) is mainly dominated by heating from the incident UV flux and cooling by the IR emissivity from (optically thin) GES. Increasing GES concentration increases the cooling and hence lowers the equilibrium temperature.

    Comment by Gilles — 15 Jul 2010 @ 5:38 AM

  362. #354 Pete Baldo

    “I find it amazing that CO2, present in such tiny amounts, can cause such mayhem.”

    Pete, probably the best way to explain how much mayhem such a tiny amount of CO2 can cause, is to consider what the earth would be like without that ‘tiny’ amount.


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    Comment by John P. Reisman (OSS Foundation) — 15 Jul 2010 @ 6:21 AM

  363. Andy Lacis 341,

    your equation should read

    T = exp(-tau)

    where T is transmissivity. Having tau on both sides of the equation just overcomplicates things.

    Comment by Barton Paul Levenson — 15 Jul 2010 @ 6:32 AM

  364. Kevin McKinney 349,

    The stratosphere is isothermal in its lower altitudes and has a negative lapse rate in the upper part.

    Comment by Barton Paul Levenson — 15 Jul 2010 @ 6:34 AM

  365. #360, Geoff Wexler:

    An additional point:
    - H2O vapor quits at about 10 km altitude
    - CO2 goes on strong until about 90 km

    Since the cooling due to radiation at a frequency is controlled by the temperature at the photosphere (optical depth = 1) at that frequency, the gas on top is most important for the 15-micron band.

    (Numbers are from

    Comment by Neal J. King — 15 Jul 2010 @ 10:54 AM

  366. The stratospheric cooling that takes place when GHG concentrations are increased is independent of the ozone heating. As I was suggesting in my earlier (341) post, UV absorption by ozone is responsible for creating a stratosphere that is substantially warmer than the tropopause point. With no ozone, the atmospheric temperature would decrease monotonically, and we would instead have to speak of cooling of the “upper atmosphere” in conjunction with the surface warming due to increasing GHGs. The key factor for this model work as the real atmosphere is having a transparent window in the spectrum.

    To help illustrate what is happening, it is useful to consider a simple radiative system consisting of a fixed-temperature ground surface (Ts), and a homogeneous, isothermal, single layer atmosphere (of temperature Ta) with spectrally grey absorption. I follows that the ground will it emit Planck radiation according to Bs = sigma (Ts)**4. The atmospheric layer will absorb the amount Bs*[1 – exp(–TAU)], where TAU is the optical depth of the atmospheric layer. By Kirchhoff’s radiation law, the layer emissivity is also equal to the layer absorptivity. Thus the atmospheric layer must emit radiation according to Ba*[1 – exp(–TAU)], where Ba = sigma (Ta)**4, in both the upward, as well as the downward directions. Radiative energy balance for this atmospheric layer requires that

    Bs * [1 – exp(–TAU) ] = 2 * Ba * [1 – exp(–TAU) ].

    Interestingly, this means that the temperature of this isothermal layer will be independent of the LW optical depth TAU, and is equal to Ta = (1/2)**0.25 Ts, or Ta = 0.84 Ts. This solution is robust for an optically very thin layer, since both the top section of the layer (Tt), and the bottom section of the layer (Tb) will see the same surface temperature. Note that both the top and bottom sections of the atmospheric layer will absorb a tiny fraction Bs*[1 – exp(–dTAU)], and they will similarly radiate the essentially equal amounts of energy 2*Ba*[1 – exp(–dTAU)]. Thus, the temperature gradient that is established within the layer will indeed be close to isothermal. Isothermal layers as such are unphysical for finite optical depths since there is no infinitely fast acting physical process to redistribute the absorbed heat uniformly within the layer. Accordingly, as the optical depth is cranked up, a temperature gradient will be established within the atmospheric layer as the layer bottom temperature Tb becomes hotter than the layer mean temperature, and the layer top temperature Tt becomes colder than the layer mean.

    This seems like an ideal problem to assign in a physics class. Given a homogenous spectrally grey slab sitting on a hotplate of fixed temperature, what will be the equilibrium temperature gradient that is established within the homogenous slab?

    While an analytic solution is possible, is is anything but straightforward. This is because the analytic solution requires integration over all angles and the evaluation of fredholm integrals of the second kind. Thus, it is preferable to simply solve the problem numerically. Numerical calculations show that the equilibrium temperature gradient within the homogeneous atmospheric slab will be essentially linear in Planck, i.e., a straight line in TAU space can be drawn between Bt = sigma (Tt)**4 at the top of the layer, and Bb = sigma (Tb)**4 at the bottom. We derived analytic formulas for expressing the emitted radiance in the upward and downward directions from such an atmospheric layer in our correlated k-distribution paper (Lacis and Oinas, 1991, JGR).

    Now, in this particular example with the fixed surface temperature (assuming the heat capacity of the ground to be infinite, or that there is some thermostat regulating the energy input to the ground to maintain the fixed temperature), as the optical depth is cranked up to infinity, the layer bottom temperature Tb will approach the surface temperature Ts, while the layer top temperature will approach zero. A small temperature discontinuity must remain between the ground and atmosphere in order to transfer heat energy to the atmosphere to maintain the temperature gradient. (If the heat source at the ground were set equal to zero, the only heat source would be the 3K cosmic background input at the top of the atmosphere. The temperature gradient would then collapse, and the laws of thermodynamics would only permit an isothermal (3K) atmosphere to exist.) This simple radiative example (convective transport is not being allowed) shows that any finite surface temperature Ts can be supported in radiative equilibrium with any arbitrarily cold “upper atmosphere” temperature Tt, by prescribing the appropriate LW opacity TAU for the atmospheric layer, with the energy required to maintain a fixed Ts adjusted accordingly.

    Note that the above example with the fixed surface temperature is not descriptive of the operation of the terrestrial greenhouse effect. The terrestrial greenhouse effect requires that there is significant solar energy deposition at the ground surface. Then, if the atmosphere were to consist of opaque isothermal layers, each layer of the atmosphere (as in the above example) would be colder by 0.84 than the layer below, thus establishing a decreasing temperature trend with height. As it is, atmospheric layers are not really totally opaque, nor are they isothermal. Moreover, the atmospheric temperature gradient is mitigated by the absorption of solar radiation within the atmosphere (also latent heat deposition), thus a more moderate temperature gradient is established within the ral atmosphere.

    Furthermore, the key global energy balance consideration for the terrestrial greenhouse that is in hydrostatic and thermal equilibrium, is that the solar energy that is absorbed by the ground surface and atmosphere must be balanced by the outgoing LW emission to space. This means that for a spectrally grey atmosphere, the “upper atmosphere” represented by the temperature Tt (more specifically the TAU = 1 level as measured from the top of the atmosphere), must be at such a temperature (Te) as to be able to radiate away the absorbed solar energy. Thus, in the spectrally grey atmosphere, Tt is constrained to be equal to the effective temperature Te. Then as atmospheric opacity TAU is increased (doubled CO2, and beyond), the surface temperature Ts can increase essentially without bound as LW TAU is increased (assuming no change in SW albedo, Te will stay fixed). As a result, for this grey opacity model, the surface temperature can continue increasing (as LW TAU is increased) until the Planck surface radiation starts spilling into the solar part of the spectrum. But the “stratosphere”, or “upper atmosphere”, will not able to cool since Tt is constrained to be equal to Te.

    From this it is clear that the transparent spectral window is the key factor in limiting and constraining the radiative behavior of the terrestrial greenhouse. As in my earlier (341) post, where half of the spectral outgoing LW flux is assumed to be within the window region (and thus emitted by the ground surface), with the other half being emitted within the radiatively absorbing part of the spectrum, it follows that:

    (Te)**4 = 0.5 * [(Ts)**4 + (Tt)**4 ].

    Note that in this situation, Tt can vary just as in the fixed surface temperature example described above. But with the transparent window, Tt is now decoupled from being constrained to maintain the planetary energy balance requirement as set by Te. In the case where the LW opacity is negligibly small, Tt will approach the value of the surface temperature Ts. If LW TAU is increased toward infinity, Tt will approach zero, independent of the value of Ts, in which case we will have Ts = Te. Since the absorbed solar radiation is deemed to be 240 W/m2, it follows that Te = 255K, and Ts = 255K will represent the no-greenhouse surface temperature (again assuming there are no changes in solar albedo). With the LW opacity of the atmosphere increased to infinity, we then have [(Ts)**4 = 2*(Te)**4, so that Ts = 303K. This limiting situation represents the maximum possible greenhouse effect that is achievable with an atmosphere that has a spectral window that covers half of the spectrum.

    The real world spectral window is of course significantly smaller than half of the spectrum, which would allow the surface temperature to go significantly higher than 303K. Also, the real world spectral window is not spectrally contiguous, nor is it fully transparent for the entire atmospheric column. Nevertheless, the contrasting behavior of the spectrally grey atmosphere, and of the atmosphere with the transparent spectral window, provides a clear indication of how the existence of a transparent spectral window decouples the stratospheric temperature from having to maintain (all by itself) the global energy balance set by the effective temperature Te. That is why it is important to accurately model the radiative transfer within the climate system.

    Comment by Andy Lacis — 15 Jul 2010 @ 12:32 PM

  367. Giles (361)

    But a substantial amount of increased emission at the surface (to reach equilibrium) is in the window region (e.g. 10 microns) where CO2 is pretty transparent.

    Comment by Chris Colose — 15 Jul 2010 @ 12:45 PM

  368. Re 349 Kevin McKinney

    On Earth, because of solar heating of the ozone layer (PS the maximum solar heating density will be above the maximum ozone density because the heating is proportional to the solar flux (of relevant wavelengths), which decreases through an absorbing medium), the upper stratosphere is warmer than the lower stratosphere and tropopause. This would actually not be true at sufficiently high latitudes in the winter hemisphere, except that some circulation in the upper atmosphere is driven by kinetic energy generated within the troposphere (small amount of energy involved) which, so far as I know, doesn’t result in much of a global time average non-radiative energy flux above the tropopause, but it does have important regional effects, and the result is that the top of the stratosphere is warmer than the tropopause at all latitudes in all seasons so far as I know.

    However, away from lower latitudes, the lower stratosphere is nearly isothermal, and at higher winter latitudes, it has a positive lapse rate.

    Because of conditions on Earth, we may think of the stratosphere as being defined by temperature increasing with height (or at least not decreasing by much), but in general, the stratosphere is just the region above the tropopause, and the lapse rate can be positive, just as long as it isn’t large enough to become part of the troposphere.

    (PS I had once read that without an ozone layer, the atmosphere could be divided into two layers (by temperature trends – of course there is also compositional and electromagnetic distinctions (homosphere, turbopause, heterosphere; ?electrosphere?, ionosphere, magnetosphere) – the troposphere and the thermosphere. There might be different conventions in labeling in cases where there is no mesosphere?)

    Re 357 Fred Moolten (and Gilles)
    Patrick (348) – I wonder whether you’re using the terms “upward flux” and “net upward flux” interchangeably. They are very different. With a warming troposphere due to increased CO2, the upward flux must inevitably increase via the Planck function. This warms any atmosphere above it. In the absence of ozone, there would be no well-defined stratosphere, but what we now call the stratosphere would also warm due to its increased opacity, and an increased upward flux from below in the CO2 wavelengths. This is why, barring some unusual extraneous factors, we would predict “stratospheric” warming rather than cooling from a CO2 increase.

    I agree with all that, regarding the stratospheric response to the increased upward flux from below.

    I am very aware aware of the distinction between upward and net upward fluxes; if I slipped up and called one the other, it was a typo – except maybe in my 224 – it’s been a while so I don’t remember whether I slipped up or not in that one; I kept the concepts distinct in my more recent 340,344,348 comments.

    What you didn’t include just now, though, is that the increased upward flux at the tropopause is in response to a decreased net upward flux from the tropopause. Before allowing the temperature to respond, we can consider the forcing at the tropopause (TRPP) and at TOA, both reductions in net upward fluxes (though at TOA, the net upward LW flux is simply the OLR); my point is that even without direct solar heating above the tropopause, the forcing at TOA can be less than the forcing at TRPP (as explained in detail for CO2 in my 348, but in general, it is possible to bring the net upward flux at TRPP toward zero but even with saturation at TOA, the nonzero skin temperature requires some nonzero net upward flux to remain – now it just depends on what the net fluxes were before we made the changes, and whether the proportionality of forcings at TRPP and TOA is similar if the effect has not approached saturation at TRPP); the forcing at TRPP is the forcing on the surface+troposphere, which they must warm up to balance, while the forcing difference between TOA and TRPP is the forcing on the stratosphere; if the forcing at TRPP is larger than at TOA, the stratosphere must cool, reducing outward fluxes from the stratosphere by the same total amount as the difference in forcings between TRPP and TOA. Some fraction of that may (depending on the distribution of temperature change within the stratosphere and the optical thicknesses) be transferred to the TRPP forcing, reducing the TRPP forcing that the surface+troposphere must respond to. Some fraction of the increase in upward flux at TRPP can also be transferred to the stratosphere, requiring it to warm again (if that is a small fraction, or if the fraction of that which is transferred to the TRPP flux again is small), then the resulting iteration of additional warming will converge relative quickly so that this feedback is a small effect. In the end, there is some increase in upward flux at TRPP, which is equal to a value between the TRPP forcing before stratospheric cooling and the TRPP forcing with initial stratospheric adjustment (unless … *&&*); if the fraction of that which is absorbed by the stratosphere is sufficiently small (which it may be if the stratosphere is nearly transparent over a sufficient portion of the spectrum), then some net stratospheric cooling will remain.

    Given the much more rapid respons time of the stratosphere to radiative forcings, there is(can be) some initial stratospheric cooling (or at least some cooling somewhere in the stratosphere), which consists of a transient component, and a component that remains at full equilibrium. Solar heating of the stratosphere, properly distributed as pointed out above, will increase both, but it is possible to have some cooling, even at full equilibration of the climate system, even with direct solar heating above the tropopause.

    Re 361 Gilles

    The skin is not the Earth’s effective photosphere (in analogy to the sun); it is above that layer. This is why (absent sufficient solar or other non-LW heating) the skin temperature is lower than the effective radiating temperature of the planet (in analogy to the sun, the SW radiation from the sun is like the LW radiation, and the direct ‘solar heating’ of the part of the atmosphere above the photosphere may have to due with electromagnetic effects (as in macroscopic plasmas and fields, not so much radiation emitted as a function of temperature). The skin layer planet is optically very thin, so it doesn’t affect the OLR significantly, but (absent direct solar heating) the little bit of the radiant flux (approximatly equal to the OLR) from below that it absorbs must be (at equilibrium) balanced by emission, which will be both downward and upward, so the flux emitted in either direction is only half of what was absorbed from below; via Kirchhoff’s Law, the temperature must be smaller than the brightness temperature of the OLR (for a grey gas, Tskin^4 ~= (Te^4)/2, where Te is the effective radiating temperature for the planet, equal to the brightness temperature of the OLR – ***HOWEVER, see below***).

    *&&* – if the stratosphere were optically thick and warmed at the bottom even if the whole experiences net cooling, then the stratospheric feedback adds to the initial TRPP forcing, and the end result could require warming below TRPP to change the flux at TRPP to an amount greater than the TRPP after stratospheric adjustment, because of the additional warming that would occur in the (lower) stratosphere.

    *** – will get back to that.

    Comment by Patrick 027 — 15 Jul 2010 @ 1:41 PM

  369. Re #366 (Andy Lacis) – Although we appeared to have concluded the stratospheric cooling discussion earlier, you have brought it up again, and so perhaps a response is appropriate. Based on the entire previous discussions over several pages, it now seems reasonable to conclude that solar absorption is a critical element needed for stratospheric cooling, but whether any cooling at all can occur without solar absorption was left unsettled. I would argue that if we use a simple radiative model with a variety of assumptions, no upper atmosphere cooling but only warming will occur with increased CO2 (see #333), based on the radiative transfer equations and the Second Law of thermodynamics, but when other complexities are introduced, this might change.

    Regarding your most recent comment, I believe you are making the same mistake you made earlier by confusing Tt with the temperature of the upper atmosphere (without ozone, it would be hard to call it a “stratosphere” so I’ll use that term in quotes). Tt is not the temperature of the “stratosphere” but rather the effective temperature at which radiation is emitted to space from the “stratosphere”, and the two diverge more and more as opacity is increased. In the absence of a solar absorber, the “stratosphere” won’t be isothermal, but will be cooler at higher altitudes until it asymptotes to the skin temperature, which won’t change. In essence, all parts of the “stratosphere” below that limit will be warmer. Basically, what happens, I would argue, is that increased opacity raises the height of the “stratospheric” radiating layer. In the absence of a spectral shift, its former temperature would be restored, at that higher altitude. Because a spectral shift would occur, the radiating layer of the “stratosphere” will be cooler than before, but the rest of the “stratosphere” would be warmer. To conclude otherwise would be to assert that a warmer body, the troposphere, on warming further and transmitting some of that heat to a cooler body, the “stratosphere”, could cause the latter to cool further, in what would seem to be a Second Law violation.

    I have a sense that we are all repeating ourselves at this point, but I’ll look forward to any new insights.

    Comment by Fred Moolten — 15 Jul 2010 @ 3:44 PM

  370. *&&* – if the stratosphere were optically thick and warmed at the bottom even if the whole experiences net cooling, then the stratospheric feedback adds to the initial TRPP forcing, and the end result could require warming below TRPP to change the flux at TRPP to an amount greater than the TRPP after stratospheric adjustment, because of the additional warming that would occur in the (lower) stratosphere. … there could be other ways to make the full response of the stratosphere+troposphere greater than the largest of these – initial (instantaneous) TRPP forcing, TRPP forcing after initial stratospheric adjustment … OF course, here and in my last comment, I am not including any non-Planck feedbacks.

    Comment by Patrick 027 — 15 Jul 2010 @ 4:29 PM

  371. Re my own comment #369 above, a correction: Not only will the effective radiating temperature of the “stratosphere” described there decrease when opacity increases, as stated, but so will the skin temperature, with both now located at higher altitudes. At any given altitude, temperatures will be warmer.

    Comment by Fred Moolten — 15 Jul 2010 @ 4:45 PM

  372. Re 366 Andy Lacis –

    I agree that the non-grey nature of atmospheric optical properties is important to the issue of stratospheric cooling and that an increase in a greenhouse gas like CO2 can cause stratospheric cooling even without solar heating of the stratosphere.

    However, I think, given some solar heating of the stratosphere, stratospheric cooling from an increased GHE can be enhanced, and that it could happen for a grey gas GHE as well – maybe not for the whole stratosphere, but for part of it.

    As pointed out by Ray Pierrehumbert via 359 Chris Colose, the distribution of solar heating is important. Without going into detail of how, I’ll just point out that the temperature profile is what determines how LW fluxes respond to a change in optical thickness at the relevant wavelengths. The solar heating affects the equilibrium temperature profile of the stratosphere. Before the response of the surface+troposphere, what allows stratospheric cooling is the TOA forcing being less than the tropopause-level forcing; both are affected by the stratospheric temperature profile.

    For a grey gas, the skin layer temperature is such that the corresponding blackbody flux is 1/2 of the OLR, absent solar heating of the skin layer. If there is solar heating of the skin layer, the temperature will be larger so that the skin layer’s emission balances it’s heat gain from both absorption of LW radiation from below and SW radiation. Doubling the optical thickness effectively halves the thickness of the skin layer, removing (if the solar heating had been evenly distributed over the skin layer) half of the solar heating. It is true that this lost solar heating now adds to the LW flux coming from below, but the skin layer only absorbs a tiny fraction of that, so the increase in absorped LW flux from below is less than the decrease in the absorbed SW radiation. So the skin layer will cool.

    Comment by Patrick 027 — 15 Jul 2010 @ 5:04 PM

  373. Re 366 Andy Lacis

    Numerical calculations show that the equilibrium temperature gradient within the homogeneous atmospheric slab will be essentially linear in Planck, i.e., a straight line in TAU space can be drawn between Bt = sigma (Tt)**4 at the top of the layer, and Bb = sigma (Tb)**4 at the bottom.

    That makes some intuitive sense to me (as allowed by optical thickness, photons moving out of a region in proportion to concentration; constant photon concentration gradient can be sustained with constant T^4 gradient, etc.), though then I have to correct something I said earlier – within the region where T^4 varies linearly (over optical distance), the radiation will be anisotropic. The surface and space are both analogous to infinite optical thicknesses that are isothermal; the flux originating from them (in the case of space, in this approximation, zero) will be isotropic. If not for the temperature discontinuity, then the radiation coming from the surface would be less than what fits the linear T^4 pattern, with the biggest difference at angles near vertical. With the temperature discontinuity, the intensity of radiation could still be smaller than what would fit the T^4 pattern at nearly vertical angles; but that could be balanced by intensities larger than what would fit the T^4 pattern at greater angles from vertical (the same intensity would be larger than the T^4 anisotropic pattern at greater angles from vertical and smaller than the T^4 pattern closer to vertical) – so the flux per unit area could fit the T^4 pattern, but now, this would lead to (relative to the T^4 pattern) anomalous heating next to the surface and anomalous cooling just above that, because the anomalously larger intensities would be absorbed closer to the surface (being at greater angles from vertical) while the anomalously smaller intensities would be absorbed over a thicker vertical extent. And for the lack of downward radiation at TOA … etc. So I’m wondering how that works out… is there any way to explain besides the number crunching?

    Comment by Patrick 027 — 15 Jul 2010 @ 6:44 PM

  374. … interestingly in the grey gas case with no solar heating of the stratosphere, increasing the optical thickness of the atmosphere would result in an initial cooling of and in the vicinity of the skin layer (reduced OLR), and an initial radiative warming of the air just above the surface (increased backradiation) – of course, the first of those dissappears at full equilibrium.

    PS where I said earlier that direct solar heating (properly distributed) can enhance both the transient and full equilibrium cooling of the stratosphere, or portions of the stratosphere, I did not mean – or should not have meant – that the solar heating enhanced the transient component of the response – the component that dissapears at full equilibrium. It may or may not, I haven’t made any general arguments for it. What I did mean was that the initial cooling, which is the sum of the transient and full equilibrium cooling components, can be enhanced, as well as the full equilibrium cooling.

    Comment by Patrick 027 — 15 Jul 2010 @ 9:25 PM

  375. About skin temperature – *** – will get back to that. -

    The OLR will not generally be isotropic unless the whole atmosphere is optically quite thin (entirely within the skin layer except for the troposphere) or if an optically thick upper portion is isothermal.

    The skin layer will absorb a larger fraction of the intensity coming from closer to horizontal than from closer to vertical. Depending on optical thicknesses and lapse rates, the skin layer may preferentially absorb the OLR intensities with lower brightness temperature than the whole OLR flux/area.

    If either the skin layer’s absorptivity were isotropic or the OLR were isotropic, the skin layer would have the temperature with the corresponding blackbody flux of half of the OLR. But if the skin layer’s absorptivity is greater at angles where the OLR intensity is less, then the equilibrium skin temperature will be colder.

    So far so good, but then, what about the top part of the skin layer where absorptivity is small at large angles from vertical and essentially zero everywhere else. This skin of the skin layer would be absorbing radiation mostly emitted from layers above where the OLR is emitted. The temperature would be even colder. The skin of the skin of the skin of the skin might be absorbing radiation primarily emitted from the first skin. Etc. (I have to say, I don’t like where this is going (toward absolute zero – PS this wouldn’t completely change the argument about CO2 causing cooling; the nature of the skin temperature is such that at equilbrium, the center of the CO2 band can never be saturated at TOA absent solar heating.).) I would guess something is wrong with this argument, since I’ve never heard of this. And it would seem to apply to cases where the OLR would otherwise be isotropic.

    Comment by Patrick 027 — 15 Jul 2010 @ 9:58 PM

  376. Re my 348 last paragraph:
    PS what if their where a substance within the stratosphere that provided significant optical thickness in the vicinity of the CO2 band. This would tend to reduce the potential for TOA forcing even more, leading to more stratospheric cooling in response to an increase in CO2;

    Depending on the temperature where that substance is. If it is in an isothermal layer, it will radiate upward as much as downward; it will decrease the baseline TRPP net flux and increase the baseline TOA flux by the same amount, but it will decrease the baseline TOA flux by a greater amount if it is absorbing radiation with a higher brightness temperature from below (the baseline upward flux at TRPP), so it will increase the amount by which the baseline net flux at TRPP is greater than that at TOA. If the lapse rate is positive, the effect will be reduced; if it is negative, the effect will be increased.

    CORRECTION however, the presence of such a substance would itself make the inital stratospheric temperature warmer than otherwise.

    No. By absorbing radiation from below; but it would radiate both upward and downward, thus making the layer cooler; but if it is optically thick, it could make the lower part warmer.


    In general: even if the stratosphere as a whole cools (in terms of a decrease in total flux going out, to balance radiative forcings + radiative response from below), this doesn’t necessarily mean cooling occurs throughout; there could be some portions that warm. And vice vera – with stratospheric warming as a whole there could still be cooling in places. As with forcings and responses in fluxes at TOA and TRPP, one could consider them at TOA and some other level to find the effect for an upper portion of the stratosphere, etc.

    Comment by Patrick 027 — 15 Jul 2010 @ 11:04 PM

  377. First part of last comment: If the lapse rate is positive, the effect will be reduced; if it is negative, the effect will be increased.

    reverse that.

    Comment by Patrick 027 — 15 Jul 2010 @ 11:11 PM

  378. Patrick, I don’t know if anybody but you can follow what you’re explaining. I can’t – and as far as I can judge, some of the things you’re saying are erroneous.

    In the wavelengths where the atmosphere is opaque, the radiation field is almost isotropic, because photons are constantly absorbed and reemitted. As I mentioned before, the fact that a CO2 molecule absorbing a photon will preferentially loose its energy by collisions doesn’t mean that the total photon density in the line strongly decreases, because it’s compensated almost exactly by the opposite effect : the very large number of collisions will excite also CO2 molecules, a small part of them reemitting a photon, which almost cancel the number of absorptions. So basically thinking of a “global absorption ” exp(-tau) throughout the atmosphere is not particularly relevant : it holds for the initial photons emitted for the ground, but not for the total amount of photons. In the absorption lines, the atmosphere is mostly like fog : you can’t see the sun, but you see light all around you. Actually the radiation is not absorbed but scattered and thermalized.

    In all what I said before, the “almost” refers to the fact that the atmosphere is not isothermal , but there is a temperature gradient. So the radiation field is not perfectly isotropic, it’s a little bit brighter (hotter ) from below and a liitle bit colder from above; this insures a small anisotropy responsible for the outwards flux in the line. It makes also the total number of photons slightly decrease with distance, following the blackbody temperature, until the photosphere is reached, then we have basically only the 1/r^2 law.

    This holds only in the opaque lines. In transparent windows, the radiation field basically tracks the source : the sun in the sky and the ground, and is strongly anisotropic, and not thermalized : it keeps the spectrum of the source, not of the local BB temperature.

    This is the main reason why the effective temperature is different from the local temperature : because the radiation field is only partly thermalized. Effective temperature is defined such as the emergent power is sigma Teff^4 whatever the spectrum is. But in the transparent windows, the radiation field is “hotter” (being a combination of reflected SWR and emitted “hot” ground LWR) , so in the lines, it is “colder” : the lines appear thus as absorption lines from the space, with a lower brightness temperature than the continuum.

    So actually the local radiation field is much simpler that what you’re trying to describe : in the transparent windows, it’s just the emitted intensity from the source (sun + ground), and in the opaque lines, it is nearly isotropic with the excitation temperature of the molecules close to the local kinetic temperature if collisions are numerous enough, with a small anisotropy linked to the net radiation flux. All “memory ” of where the photons come from has almost be forgotten, except this small anisotropy.

    Comment by Gilles — 16 Jul 2010 @ 12:17 AM

  379. Our climate changes are accompanied by storms li “KYrill” with 202 km/h and more (re: research-eu No. 63)will get an do so constantly more strengh. Aren’t those cyvlones not only steadily tugging more on the earth’s surface on our seas (e. g. the so-called monsterwaves) but pulling also on our firm crust in certain places, thereby provoking unusual outbreaks of volcanoes, like in Iceland, and with that maybe also causing every more a little change on the polar axis of our planet? Research and forecast in this direction?

    [Response: No. Far too small. - gavin]

    Comment by Herbert — 16 Jul 2010 @ 7:16 AM

  380. RE: 332

    Hey Anonymous Coward,

    The central theme of the relationship between GHG and the non-GHG planetoid I see as crucial in the understanding of how a change in GHG can effect surface temperatures. You asked why this is important it is only so that I and other less educated people can understand the principles better.

    As to the issue of the formula I think I got it right. If as the 2006 basis suggested that the doubling of the 1750 level should have been near 280ppm. (I believe there was a 2005 paper suggesting the pre-anthropogenic emission should have balanced around 240ppm.) If the total change between 1750 and the doubling of the density value should occur somewhere between 2075 and 2125, the percentage change in the temperature offered by the increase in CO2 today should be roughly 40% of 4 Deg. C. As the IPCC has suggested that the contribution of total Global Warmth contributors both positive and negative CO2 should average out to be approximately 40%. Hence, the total temperature potential of the current temperature rise due to the change to the current CO2 levels should be approximately 3.7 Deg of the total potential change of roughly 10 Deg. C if all other things remained proportionally similar.

    That the trend in GAT surface temperatures we are seeing demonstrate roughly a 0.65 Deg. C change suggests that much of the rest of the change has to be radiated elsewhere. Hence, given the idea of 360 Deg. radiation would suggest that 1/2 of the estimated 1.48 Deg C. suggested should be roughly a net gain at the surface of around 0.74 Deg. C while at the same time the net gain at 560ppm of CO2 should be approximately 1/2 of 10 Deg. C or roughly 5 Deg. C.

    Now back to the original issue, to get a surface temperature differential of 32 Deg. C at 280ppm of CO2 would seem to require that the net Warming gain would have to of been roughly 64 Deg. C. Of which, if the proportions were the same, CO2 should have been responsible for 25.6 Deg. C. From here we then would need to determine the rough amount of doubling cycles between the CO2 voided planetoid and the suggested pre-anthropogenic 240ppm content.

    All I am asking is for the value of change required to achieve the current doubling potential of 4 Deg. C at 280ppm from the estimate of the 2006 paper and the total potential change of 25.6 Deg C above the 0ppm theoretical baseline. So far no one has stepped up with the logarithmic value and the estimated doubling points. (Note: You may have missed my suggestion that the systematic change would likely be linear or proportional while the CO2 level was logarithmic.)

    Dave Cooke

    Comment by L. David Cooke — 16 Jul 2010 @ 9:08 AM

  381. Thanks to Barton & Patrick for responses to my #349–helpful, and appreciated.

    An additional response to Pete Baldo @ #354:

    IMO, the “but 390 ppm is so small” theme comes from failing to think quantitatively. That’s ironic coming from me, as I’m an artsy whose eyes tend to glaze (or, in extreme cases, cross) when confronted with actual equations. . . however, sometimes you gotta do what you gotta do.

    And what you gotta do in this case (IMO) is look at the actual numbers of molecules involved, in a rough back-of-the-envelope sort of way.

    So, by Avogadro’s number you’ve got about 6 x 10e23 molecules per mole of air, and that’s about 22 liters (according, at least, to some random website I once consulted–corrections welcomed.) (For perspective, an average human male has a lung capacity of around 6 liters.) 390 ppm is .00039; multiply that by Avogadro’s number (or my lazy approximation of it, rather) and you get 2.34 X 10e20 (unless I dropped a decimal or something.) But the point is that there is still, at 390 ppm, a whole bunch of CO2 molecules per unit of atmosphere.

    People go wrong about this, I think, because their everyday experience doesn’t lead to a gut-level understanding of just how numerous molecules actually are. (A point made with a vivid irony by Arthur C. Clarke at the end of one of his “Tales From The White Hart” (paraphrased): “It’s quite probable that even now, molecules of the late professor are passing through the very seawater filter that he devised. . .”)

    Hence, they focus on that .00039 with a tacit assumption that 1 x .00039 is always neglible. But if you think of .00039 x 6 x 10e23, as we have just done, that doesn’t seem quite so negligible after all!

    Comment by Kevin McKinney — 16 Jul 2010 @ 9:31 AM

  382. “neglible”–ugh! Sorry. . .

    Comment by Kevin McKinney — 16 Jul 2010 @ 9:33 AM

  383. Gilles (378), in following this discussion I have a number of sidebar questions. But for fear of hijacking or deviating the main topic let me try just one… for now. I was under the impression that in a collision the tendency to transfer CO2 excitation energy to other kinetic energy is much greater than for kinetic energy to transfer to the excited levels of CO2, at least at low altitudes. You seem to say otherwise. Further you say that the kinetic-to-excitation transfer is great enough to cause the now re-excited CO2 molecules to relax with emission at near the same level as the original absorption, instead of collision-to-kinetic transfer, which normally greatly exceeds the emission type relaxation as I asked about above. This sounds like the radiation energy field at the absorption frequencies (say 15um, e.g.) would not vary nor diminish, other than for same short transient, as the total emissions (primary and after-collisions secondary) “almost exactly” matches the absorption. This strikes me as incorrect.

    Can you further explain this? Or did I miss the point?

    Comment by Rod B — 16 Jul 2010 @ 10:25 AM

  384. Great article for those of us who have had a physics education years ago and have left physics for other careers. I will suggest that for engineering/science graduates (at least a master’s level) it ought to be used.

    I see little chance a journalist will read and understand it — but who knows? Worh a shot.

    An exception to the first statement may be oilfield engineers. Here in Houston, so many jobs depend on oil that global warming is a gnat to be swatted away. I can have a reasoned discussion with an oil engineer of some topic we disagee on — not on climate change.

    Thanks again.


    Comment by John (Burgy) Burgeson — 16 Jul 2010 @ 10:43 AM

  385. Kevin McKinney (381), smarter guys than I can reply: your math is pretty good. The interesting part of this has been pointed out by others (Ray Ladbury comes to mind) and relates to the number of acceptable photons that are shot into the air. This math requires some very sensitive assumptions which can result in a wide range of answers, but one is: your 22.4 liters of atmosphere that has 2.34x10e20 CO2 molecules can be put in a cylinder 100m high with a 2.24cm^2 base. At 290 degrees between 14.3 and 15.6um (one of the highly variable assumptions) the 2.24cm^2 base area emits (I think) 0.0056watts = 0.0056joules/sec. Based on harmonics physics and math (something down a musician’s alley I suspect ;-) ) the center frequency of CO2 absorption is 15um and equates to 1.325x10e-20 joules/photon. That means the base area is emitting 4.26x10e17 absorbable photons each second with a total of 2.34x10e20 CO2 molecules to absorb them — roughly 500 molecules to absorb a photon every second within a 100 meter path. This can vary by magnitudes depending on the assumptions, but it describes the main idea within a ballpark: there may be a tiny number of CO2 molecules but — though depending on a bunch of stuff!! — there are probably much fewer photons for them to absorb.

    Comment by Rod B — 16 Jul 2010 @ 11:40 AM

  386. Rod ” This sounds like the radiation energy field at the absorption frequencies (say 15um, e.g.) would not vary nor diminish, other than for same short transient, as the total emissions (primary and after-collisions secondary) “almost exactly” matches the absorption. This strikes me as incorrect.”
    sorry but it is correct : close to the thermal equilibrium, emission and absorption “almost” cancel : actually AT the thermal equilibrium, the photon density must remain constant and equal to the Planck law density – this means of course that any absorbed photon is exactly compensated by an emitted photon. Now consider a single molecule that is supposed to loose more rapidly its energy by collision after absorption of a single photon. Just after the absorption, this molecule has no idea if it is in a thermal bath and if the photon density is the Planck law or not , so it will transfer its energy by collision in any case. So IF the thermal equilibrium is reached, the absorbed photon must be exactly offset by an emitted one – and of course the source of energy can be nothing but a inelastic collision if the photon has to been created. So the Planck photon density is exactly the value for which absorption and emission rates cancel.

    Now the matching is just “almost perfect” if there is a temperature gradient, because the photon density must slowly decrease to match the local excitation temperature. So actually there is a small warming term from the lower layers, exactly compensated by a cooling towards the upper layer. This is neither a net absorption , or a warming (in the sense that the atmosphere tends to reach an equilibrium local temperature, but an energy transfer . )


    Comment by Gilles — 16 Jul 2010 @ 12:19 PM

  387. Re 378 Gilles – yes at least one comment I have made is erroneous, but I wouldn’t disagree with any of what you just posted (of course the T^4 relationship is for a grey gas; when you get into different parts of the spectrum you have to follow the Planck function’s temperature dependence. But yes, as optical thickness gets large on the spatial scale of temperature variation, the anisotropy in the radiation field gets smaller (assuming isotropic optical properties, of course, although if there were a direction with minimum optical thickness, increasing the optical thickness in all directions with constant proportionality would eventually bring all directions towards an ultimate saturation), and the brightness temperature in all directions approaches the actual local temperature (this happens faster toward more isothermal directions – ie typically nearly horizontal in the atmosphere) – which is the situation at the ultimate saturation.

    However, the skin layer, absent solar heating, has an equilibrium temperature that is smaller than the brightness temperature of the radiation from below at those wavelengths where the skin layer absorbs. That means saturation will not have occured; the OLR brightness temperature will be larger than the skin temperature, though the difference will be smaller for intensities in nearly horizontal directions – not just because the skin layer is colder but because some portion of the atmosphere below that is colder (the temperature will gradually approach the skin temperature going upward from the ‘photosphere’ (effective emitting level) as you would call it in analogy with the sun).

    Comment by Patrick 027 — 16 Jul 2010 @ 4:24 PM

  388. Re my 376,377 – go ahead and ignore that as well as the last paragraph of my 348; I made one or more silly algebraic errors (if you could call it that; I was doing it in my head and apparently flipped some things around and maybe left out a couple of ‘terms’).

    I’ll post the correct version later.

    Comment by Patrick 027 — 16 Jul 2010 @ 4:28 PM

  389. #385, Rod B.:

    The “fewness” of IR photons is not relevant. What is relevant is the probability that such a photon will be absorbed by (or more generally interact with) a susceptible molecule (CO2) within the given length. So the argument does not hang on the rate of emission of IR photons.

    In accordance with the original posting: the issue is whether you have enough added CO2 to move the level of the IR photosphere (the point at which optical depth, as measured from outer space inward, = 1) significantly.

    As I noted earlier, CO2 is quite pervasive in the atmosphere up to 90 km, whereas H2O seems to quit at about 10 km. That means that CO2 is in a leveraged position (near the top) to influence the altitude of the photosphere. If the CO2/H2O ratio of concentrations were constant, I believe the skeptics would have a valid point that “CO2 can’t be important, compared to water vapor”.

    (It’s true that CO2 absorbs more IR in the window around 15-micron than H2O, but by eye, the difference is not that impressive, maybe a factor of 2; whereas the ratio of total H2O to CO2 is quite large.)

    In other words, if the ratio of local CO2 concentration to H2O concentration were constant throughout the atmosphere, I believe the enhanced greenhouse effect would be indeed be negligible at current levels.

    If someone sees an error in this analysis, I would be pleased to be corrected.

    Comment by Neal J. King — 16 Jul 2010 @ 5:21 PM

  390. Re 383 Rod B – That is all taken care of by the LTE approximation. The frequency at which photons are emitted or absorbed is small relative to the rate of energy redistribution among molecules and their modes, so the fraction of some molecules that are excited in some way is only slightly more or less than the characteristic fraction for that temperature (depending on whether photons absorption to generate that particular state is greater than photon emission from that state or vice versa, which depends on the brightness temperature of the incident radiation relative to the local temperature).

    I think the LTE approximation is still valid through the stratosphere; where it does break down, there can still be a greenhouse effect still works, but to the extent that atoms and molecules are emitting photons of the same frequencies that they absorb without redistribution of energy to other states/molecules in between absorption and emission, it would be analogous to scattering; the mathematical relationships will be a bit different. Hypothetically, you could even have a greenhouse effect with fluorescence or phosphorescence.

    Comment by Patrick 027 — 16 Jul 2010 @ 10:57 PM

  391. Re 380 L. David Cooke -

    If you want to see how the total GHE can be approximately calculated, see, for example, Kiehl and Trenberth 1997, from links here:
    - Kiehl and Trenberth 1997:
    - see also the link for K

    In Kiehl and Trenberth 1997, they find a 155 W/m2 total greenhouse effect for approximately present-day Earth conditions (among the approximations: surface is a perfect (isothermal**) blackbody, and the use a representative 1-dimensional atmospheric column (instead of seperate calculations for each location over the globe at each time over the course of a period of time sufficient to describe a climatic state – but note righthand side of p. 200, just past halfway down the column) … a few other things).

    **(the nonlinearity of blackbody flux/area relative to temperature means that for the same emitted flux, one can have a lower average temperature if there is more temperature variation. In spite of the temperature difference from Antarctic winter to Saharan midday summer, this effect is actually rather small for the Earth (PS horizontal and temporal temperature variations within most of the mass of the atmosphere are of the same order of magnitude or smaller than at the surface), so a global average flux computed from global time average temperature will not have a large error; more extreme temperature variations that occur on bodies like the moon or Mercury would be more important.)

    **(the existence of some correlation between variable gases and clouds and different surface temperatures and vertical temperature distributions could affect the average effects – though at least for water vapor, I’d guess this tends to even out the OLR distribution over the globe (?). There would also be some correlation between local/regional climate and surface emissivity (I think sea ice is different than open ocean, for example).)


    See Fig 1 which shows the spectrum of OLR (outgoing LW radiation) – the smooth curve is the Planck function for 288 K, approximate surface temperature, scaled (by a factor of pi steradians) to be in terms of flux per unit area per unit of the spectrum.

    The other curve is a calculated actual OLR for the amount and distribution of water vapor, CO2, CH4, etc, and clouds, for a vertical temperature profile, representative of the global atmoosphere.

    The area between the two curves is the TOA radiative forcing of the total greenhouse effect, calculated to be about 155 W/m2 …

    (Since the net upward LW flux balances the net downward SW flux in equilibrium, and without a GHE, the same net upward flux would be found at all vertical levels, one could add the solar heating of the stratosphere (roughly, 3 % * 342 W/m2 ~= 10 W/m2) to find the tropopause-level total GHE forcing.) (PS don’t mistake this dependence on solar heating in this context to equate to an argument that all full-equilibrium stratospheric cooling in the increase of a GHE requires stratospheric solar heating; also, this additional 10 W/m2 doesn’t include any stratospheric adjustment effect.)

    This area is shown (upside down) in Fig 2; the contribution made by clouds after the rest is shown in Fig 3. Why ‘after the rest’? Because there are overlaps – clouds alone could accomplish more; the presence of the gases reduces the additional radiative forcing caused by the addition of clouds. These overlap issues are summarized in table 3.

    (Note that radiative forcing is not necessarily proportional to reduction in atmospheric transparency, because relatively opaque layers in the lower warmer troposphere (water vapor, and for the fractional area they occupy, low level clouds) can reduce atmospheric transparency a lot on their own while only reducing the net upward LW flux above them by a small amount; colder, higher-level clouds will have a bigger effect on the net upward LW flux above them (per fraction of areal coverage), though they will have a smaller effect on the net upward LW flux below them. (Water vapor and low-level clouds can have a big effect on the radiative balance of the surface.)

    (Because convection can balance imbalances in radiative fluxes, and the troposphere+surface will tend to respond (to a first approximation) about the same in response to changes in radiative inputs and outputs of their whole, it is the tropopause-level forcing which is really key.)

    Look at Fig 1 again – keeping all the other greenhouse agents, removing CO2 would remove the valley in OLR between roughly 13 and 17 microns (or 13 and 18?) – you could draw in a line across the top of that valley to approximate what water vapor and clouds, etc, would do without CO2; the area of the valley created by adding CO2, given everything else, is 22 W/m2 (from table 3).

    What does this mean for CO2 forcing? A doubling of CO2 in present conditions would add a forcing of about 3.7 W/m2 (+/- ? mabye 0.5 W/m2, I don’t remember exactly offhand, but the error bar is not very large). This is for the tropopause level with stratospheric adjustment. A halving of CO2 would do about the same in reverse, -3.7 W/m2. Removing all CO2 would result in a radiative forcing of -22 W/m2, TOA – I don’t know the tropopause level with stratospheric adjustment value; assuming it is similar to in proportion to the TOA forcing as for doubling CO2, removing all CO2 might have a tropopause level with stratospheric adjustment forcing somewhere roughly around -30 W/m2, though that proportionality may break down as we get to a point where CO2 is not saturated… But using 22/3.7 and 30/3.7, it appears for a rough estimate that the logarithmic proportionality for CO2 may break down before about 6 to 8 halvings of CO2. The proportion of forcing to CO2 amount eventually becomes linear as the amount of CO2 goes to zero – this is nothing special; any continuous smooth function can be approximated by a straight line over a sufficiently short interval; adding a sufficiently small amount of any greenhouse gas will have about half the effect as adding twice as much.

    What does this mean for climate sensitivity? If a doubling of CO2 resulted in a temperature increase of approximately 1 K before any non-Planck feedbacks (before water vapor, etc.), then assuming the same climate sensitivity to the total GHE, removing the whole GHE would result in about a (setting the TOA/tropopause distinction aside, as it is relatively small relative to the 155 W/m2 value) 155/3.7 * 1 K ~= 42 K. Which is a bit more than 32 or 33 K, though I’m not surprised by the difference. (This doesn’t include any solar-heating (albedo, etc.) feedbacks, which is necessary for a direct comparison; the GHE warming of about 33 K is only the effect of the atmopheric LW optical thickness, and thus doesn’t include any feedbacks on solar heating)

    Climate sensitivity, even excluding non-Planck feedbacks, can’t be expected to be constant over all climates – we can start, if not knowing otherwise, with an assumption that it will be nearly constant for a sufficiently small range of temperatures (ie the same forcing that causes 2 K warming may be about half the forcing that would cause a 4 K warming) – for the same reason that any sufficiently small addition of a greenhouse gas will have about half the forcing as double that addition – linear approximations are generally valid for sufficiently small intervals.

    … to be cont.

    Comment by Patrick 027 — 17 Jul 2010 @ 12:32 AM

  392. Andy (#366),

    Actually, in the totally optically thick case it is easy to calculate the temperature gradient. Each layer must transport the same energy as the layer below and its emissivity is perfect (optically thick) so it transports according to R^2T^4 where R is the radius from the center of the planet and T is absolute temperature. T is thus proportional to sqrt(R). Your factor of 0.84 gets washed out by this surface area limit on energy transport. This is the temperature gradient throughout most of the Sun, for example.

    Comment by Chris Dudley — 17 Jul 2010 @ 8:47 AM

  393. Nice article. Different articles are needed for different audiences; this one fills a need. If technically interested audiences get an understanding, their less technical friends notice. Regular people rely on various kinds of authorities, including their technically minded friends.

    What regular people should hear most often is this: “I am a scientist, and I am concerned. I think the future looks very worrisome.” Give the public hundred such statements, preferably with a photograph of the scientist.

    Next level would be simple statements like “I assure you that I am not conspiring just to get research grants. If I were not worried about the future climate, I would be applying for other grants and researching other things. The reason I win grants for climate research is that the guardians of the research funds are feeling worried too by the climate prospects.” and “The attacks on the climate research are very unfair, trust me. They are often like saying car engines are not possible because the spark plug would expand in the heat and crack the engine block. Sounds plausible if you have heard about thermal expansion, but in reality there are millions of cars running just fine.”

    So the emphasis has to be on the “trust me” part. That is how people decide must issues. How many have verified in any serious way that the Earth is really round, not flat? People pick their beliefs through social mechanisms. Use them.

    But some people struggle to make the various pieces they know about fit together. This article helps doing that, but mostly for people that already wanted to know how Planck’s law fit in the big picture.

    There is still a lack of good, convincing, and correct descriptions at a simpler level. The “Start here” articles in RC deserve much wider dissemination. I would have preferred a big “Beginners Click Here” button centered prominently below the banner picture on the home page.

    But even those could improve. Consider the water bucket model. It shows buckets with different inflows. It should have been buckets with different size stones lodged in the outlet hole, as the GHE acts to impede the outflow of energy while the solar irradiation is essentially constant. And the outflow water rays should have been made to show more prominently the difference in pressure, with the trickle ray going almost straight down, and the strongest ray flowing farther horizontally. Forces are not directly visible, make them more so using a playbook from Walt Disney comics.

    In the end, I think that public relations is a non-trivial science, and this science should be brought to bear on this problem. I have no background in it, so in the above paragraphs I am just another “idiot with an opinion”. It’s my best effort, though, for whatever it is worth.

    Comment by Enrique P — 17 Jul 2010 @ 11:38 AM

  394. Neal J. King, you’re right of course. I just thought that was one level deeper into the science that would complicate rather than help McKinney’s ballpark query.

    Comment by Rod B — 17 Jul 2010 @ 12:17 PM

  395. Re 392 Chris Dudley – I don’t understand what you mean by R^2T^4 – and there should be something about how optical depth is proportional to R, and also, if you’re going a significant distance toward the center of such an object, there is the issue of spherical geometry; if the optical thickness is large enough across small changes in radius, then you don’t need to account for the spherical geometry in the calculation of the flux per unit area as a function of the temperature profile and optical thickness; however, the flux per unit area outward will drop as an inverse square, except of course within the layers that are being heated through a different process (SW heating for a planet, radioactivity, latent and sensible heat loss associated with a cooling interior, gravitational potential energy conversion to enthalpy via compression (adiabatic warming) and settling of denser material under gravity (the later both leads to compression via increased pressure via increased gravity within the interior, and also is a source of kinetic energy which can be converted to heat)…

    (Kinetic energy in a molten metal core or plasma can under the right conditions sustain a magnetic field (dynamo); this process extracts energy but can return some of that energy via electrical resistance heating; PS off on a tangent here but I actually came across a study of the possibility of a process of sustaining a dynamo via motions induced by such things as precession (precession being caused by tidal torques on the Earth’s equatorial bulge) when thermal or chemical buoyancy wouldn’t be sufficient to drive motions (possibly before an inner core forms and grows, releasing latent heat and rejecting some less dense liquid) (PS the differential heating/cooling available to drive convection can be reduced by thermal conduction withint the liquid metal core)

    … and nuclear fusion within the core of a star).

    Comment by Patrick 027 — 17 Jul 2010 @ 12:19 PM

  396. Re 392 Chris Dudley – while it makes intuitive sense that a spatially-invariant net photon flux could be sustained by a constant gradient in local equilibrium photon concentration (proportional to T^4 for a grey gas, assuming constant real component of index of refraction), the calculation of what that gradient should actually be is made a bit more complicated by the fact that photons travelling in different directions will on average be absorbed over longer or shorter vertical distances.

    But so long as T^4 (for a grey gas – use Planck function for a particular wavelength) has a constant gradient over vertial optical depth out to a sufficient distance beyond a level being considered, (and assuming isotropic optical properties, and assuming only absorption and emission – no scattering, etc.) the intensity in each direction will,

    being the average of T^4

    weighted by the emission weighting function

    which will decay exponentially (over optical depth in that direction) away from the point of view, with an e-folding scale of unit optical depth in that direction,

    and given that T^4 varies linearly over optical depth in all directions (but at different rates),

    … the intensity will thus be the blackbody intensity for the temperature found at unit optical depth distance from the point of view.

    With a vertical local blackbody intensity (B_wholespectrum = σ/(π sr) * T^4) gradient, varying over vertical optical depth such that d(B_wholespectrum)/d(optical depth, positive downward) = BVGRAD, then the intensity I’ in the vertical direction, relative to the blackbody value at the point of view, will be +/- BVGRAD (+looking down, -up); the intensity at an angle θ from vertical will be +/- BVGRAD/sec(θ) = +/- BVGRAD*cos(θ), because optical depth per unit vertical distance is proportional to sec(θ).

    The flux F’ (relative to the blackbody value, σ*T^4, for T at the point of view) will then be the integral over solid angle of the intensity (relative to blackbody intensity for T at the point of view) * cos(θ) (this other factor of cos(θ) is due to the way a unit area facing vertical projects onto a smaller area in other directions), which will be

    = integral (θ = 0 to π/2) of (I’ * area projection factor * d(solid angle) )

    = integral (θ = 0 to π/2) of (I’ * cos(θ) * 2*π*sin(θ)*dθ )

    = integral (θ = 0 to π/2) of (+/- BVGRAD*cos(θ) * cos(θ) * 2*π*sin(θ)*dθ )

    = +/- π * integral (θ = 0 to π/2) of (BVGRAD*cos(θ) * sin(2*θ) * dθ )

    = +/- π/2 * integral (θ = 0 to π/2) of (BVGRAD * [sin(θ) + sin(3*θ)] * dθ )

    = +/- π/2 * BVGRAD * [-cos(θ) + -cos(3*θ)/3](difference from θ = 0 to π/2)

    = +/- π/2 * BVGRAD * [0 - -1 + 0 - -1/3]

    = +/- π/2 * BVGRAD * 4/3

    = +/- 2/3 * π * BVGRAD

    Comment by Patrick 027 — 17 Jul 2010 @ 1:56 PM

  397. Gilles (386) and a bit of Patrick 027, I still can’t get a grasp of the practicalities of it all. The simple conclusion from your analysis would seem to say that the radiation intensity of say the 15um band through the atmosphere would not diminish (other than by the inverse square.) Maybe it’s the LTE that is a bother (the atmos is nor really in LTV..??, as Ray said), or that “brightness temperature” is confusing me (what is your exact definition and use of the term?) Or maybe I simplify too much (though I think complex things ought to pass the simple aspects, too….)

    Although molecular energy transfer is excruciatingly complex, I think it is reasonably understood that in at least the lower atmosphere the probability of a collision transferring CO2 vibration energy to translation energy is much greater than the other direction. But this is at odds with your assertion.

    What am I (or maybe you??) missing?

    Comment by Rod B — 17 Jul 2010 @ 2:38 PM

  398. F’
    = +/- 2/3 * π * BVGRAD
    = +/- 2/3 * π * d(B_wholespectrum)/d(optical depth)
    = +/- 2/3 * d(σ*T^4)/d(optical depth)

    The net upward flux would be 2*|F’| = 4/3 * d(σ*T^4)/d(optical depth)

    Which means that, if modelled as a series of isothermal layers that each radiate up and down as blackbodies, each layer would correspond to a layer of atmosphere with 4/3 vertical optical depth.

    Comment by Patrick 027 — 17 Jul 2010 @ 3:26 PM

  399. Re 397 Rod B -

    Brightness temperature = the temperature that a blackbody would need to have to emit the same intensity of radiation (or if applied to a flux per unit area, the temperature of a blackbody emitting the same flux per unit area).

    Inverse square law – see my 325
    - you don’t really need it much in the context of the atmospheres of terrestrial planets regarding most of the mass of those atmospheres.

    Going in a direction, The intensity in that direction decreases if it’s brightness temperature is higher than the local temperature, and increases if it is smaller than the local temperature (because the material emits less or more than it absorbs depending on whether it’s temperature is lower or higher than the brightness temperature of the incident radiation) – this assuming no scattering or reflection, only absorption and emission.

    Comment by Patrick 027 — 17 Jul 2010 @ 5:06 PM

  400. Re 392 Chris Dudley (cont. from 396,398) – … The net upward flux would be 2*|F’| = 4/3 * d(σ*T^4)/d(optical depth)

    Notice that in order for this to hold at some level, the gradient in σ*T^4 has to be constant out to some large optical depth up and down from that level, to ‘insulate’ the level from the perturbation radiative fluxes from perturbations to the pattern.

    For the context of atmospheric radiation, the surface (assuming a perferct blackbody) and space can be considered isothermal regions of infinite optical depth (surface at T = Ts, space at T ~= 0 K). This necessarily breaks the pattern. (see also my comment 373)

    Let d(T^4)/d(optical depth downward) = T4grad,
    Tsa = surface air temperature
    T_TOA = air temperature at TOA

    The downward radiation at the surface would be σ*(Tsa^4 – 2/3*T4grad)
    The upward radiation would have to be σ*(Tsa^4 + 2/3*T4grad) in order for the net upward flux to be constant through the air, which requires
    Ts^4 = Tsa^4 + 2/3*T4grad. So the surface is warmer than the air immediately above it, with T^4 larger by the same amount as it is smaller at a unit optical depth above the surface. But the upward flux from the surface (assuming a perfect blackbody) is isotropic, which means that in order for the upward flux per unit area to fit the T^4 pattern, the intensity will be anomalously small (relative to the T^4 pattern) in a range of directions near vertical, and anomalously large in a range of directions closer to horizontal. Because intensities at different angles are absorbed over shorter or longer vertical distances, this leads to anomalous warming in the air just above the surface and anomalous cooling in a layer above that (the anomalous cooling would taper off with height but never quite go to zero). If the air just above the surface were anomalously warmer, the increased emission from that layer would reduce the anomalous warming and decrease the anomalous cooling higher up – however, that would also reduce the net flux at the surface, so the surface would also have to be warmer (also helping to reduce the cooling higher up). I’m not sure exactly what the shape of the resulting pattern would be, but it should a perturbation from the T^4 pattern that gradually decays with height (although a temperature discontinuity at the surface would still be required, as stated by Andy Lacis in 366).

    Likewise a perturbation to the T^4 pattern that gradually decays downward into the atmosphere may be necessary to balance the anomolous cooling near TOA and some anomalous warming below that due to the darkness of space (the anomalous warming would be from the intensity in all directions downward from space not only being not more than 0 but also being not less than 0 – continuation of the T^4 pattern would after all require negative values at some point).

    Suppose the T^4 held up all the way to TOA.

    The upward radiation at TOA would be σ*(T_TOA^4 + 2/3*T4grad) = OLR flux per unit area. But that is supposed to be equal to the net flux within the atmosphere, so

    σ*(T_TOA^4 + 2/3*T4grad) = σ*(4/3*T4grad)

    which implies

    σ*T_TOA^4 = 2/3*T4grad

    And notice this fits the skin temperature (the blackbody flux for the skin temperature is half of the OLR).

    Given the upward flux/area is the net flux/areat at TOA, the downward radiation would be zero, but let’s consider the formula for the downward flux: it has to be σ*(T_TOA^4 – 2/3*T4grad) in order for the net upward flux to be constant through the air. Letting this equal zero fits the above solution for T_TOA.

    But if the T^4 pattern actually continued upward to produce the same zero downward flux, the downward intensity at nearly horizontal angles would be positive, while the downward intensity closer to vertical directions would be negative (at the vertical direction, the brightness T^4 would be the T at a unit optical distance above, which would be T_TOA^4 – T4grad = – 1/3 * T4grad). So the downward intensities are anomalously large near vertical and anomalously small near horizontal, leading to anomalous cooling at and near TOA and anomalous warming below that, tapering off to zero at infinite optical depth below.

    Cooling the temperature at and near TOA would help restore balance. There would have to be some warming below to keep the same OLR. Or maybe only warming of the rest of the atmopshere relative to the old T^4 pattern would keep the same OLR and maybe allow the same skin temperature (although the anisotropy in the OLR suggests there should be a colder skin temperature)- this might be equivalent to shifting the T^4 pattern upward toward TOA and compressing it near TOA ?

    Or is the same net upward flux maitained by a larger T4grad when the thickness of the atmosphere is reduced?

    Comment by Patrick 027 — 17 Jul 2010 @ 7:21 PM

  401. All of that (396,398, and my last comment) are of course for pure radiative equilibrium, with the particular case studied being a grey gas, though the same principles could be applied to radiation at a particular set of frequencies, provided that the equilibrium is established only at those frequencies (transparency or purely scattering at all other wavelengths).

    Interesting aside: The brightness temperature of the downward intensity at TOA that would fit the T^4 pattern would actually be complex (square root of -1 is +/- i, square roots of +/- i are half of each of i+1, -i-1, i-1, -i+1)

    Comment by Patrick 027 — 17 Jul 2010 @ 7:32 PM

  402. Patrick 027 (399), I’m still scratching. If any absorbed radiation is eventually exactly matched by collision caused emission, the radiation field has to remain constant (again after transients). On average the radiant energy in joules absorbed equals the radiant energy in joules later “re”-emitted. Except that the re-emission can go up or down which would make the upward field half of the original and the field between the wrecked molecule and the surface 50% greater — but this is giving me a headache.

    Something is amiss. If the emissivity of the earth is 1.0, its brightness temperature is the same as its Planck blackbody temperature. More to the point though, CO2 (or H2O or whatever) absorption of IR radiation does not depend on the earth’s blackbody or brightness temperature being higher than the mean temperature of the atmosphere (and the CO2). Likewise, CO2 at a mean temperature less than the earth’s brightness temperature still absorbs radiation. It seems like you might be confusing Planck function radiation (absorption and emission) with internal molecular energy (vibration and rotation) absorption and emission, which only requires, within certain quantum ground rules, a compatible or synchronized optical collision. The temperature of the molecule(s) is only a minor secondary factor.. Though Planck’s function is used, with some specific gyrations and limits, to analyze and asses vibrotation emission and absorption (and mathematically it does a very good job IMO) the physical processes are not the same and do not follow the same unfettered rules. Or so I maintain (Ray Ladbury’s et al protests not withstanding ;-) )

    Am I wrong? Can CO2 at ~1km, ~ 6C colder than the surface and the earth’s brightness temperature, not absorb any of the earth’s IR radiation? Or am I still missing what you are trying to say?

    Comment by Rod B — 17 Jul 2010 @ 8:08 PM

  403. Patrick 027, ps. In reading your post #400 (and I apologized if I missed this in earlier posts or am not reading your posts with sufficient care) it seems you are referring to physical planck-type radiation from atmospheric layers. If that is the case then your analysis sounds correct. But, to be clear, atmospheric planck function radiation (absorption and emission) is still not physically the same as vibrotation internal energy absorption and emission. Even though, as I said above, the mathematics of the planck and associated functions are used to assess the latter. For example, though temperature is a secondary factor, higher temperature CO2 is somewhat less likely to relax through emission than cooled CO2 — the opposite of Planck function.

    BTW, and I don’t wish to restart it now, there is major disputes as to how much or even if the atmosphere radiates ala Planck functions, i.e. in proportion to T^4 mitigated with emissivity. I believe it does (but have little clue how much); others (and some with good bona fides) vehemently oppose.

    Comment by Rod B — 17 Jul 2010 @ 8:29 PM

  404. Re 380 L. David Cooke, PART II. – cont. from 391 Patrick 027

    It generally makes sense that climate sensitivity, defined per unit radiative forcing (limiting ourselves only to the Planck response, wherein emission of radiation stays proportional the the Planck function as temperature changes, holding optical properties constant) should be larger at smaller temperatures, because of the nonlinear dependence of blackbody radiation on Temperature …

    (PS we are considering the climate sensitivity to be in terms of changes in global-time average surface temperature per unit global-time average radiative forcing, though one could also define other sensitivities for other measures of climate).

    A 1 % change in T leads to a

    4 % change in whole-spectrum blackbody flux per unit area, with larger % changes occuring at higher frequencies (shorter wavelengths):

    5 % change in spectral blackbody intensity ( = Planck function) at peak per unit vacuum wavelength (which occurs at a vacuum wavelength λpeak = 2897 μm*K / T; see Wien’s displacement law)

    4 % change in the Planck function at peak per unit log(frequency or vacuum wavelength) (which occurs at a vacuum wavelength λ = 5/3 * λpeak)

    3 % change in the Planck function at peak per unit frequency (which occurs at a vacuum wavelength λ = 5/4 * λpeak)

    approx. 1 % change in the Planck function at very large wavelengths (very low frequencies).

    HUGE % changes at much shorter wavelengths (much higher frequencies)


    … The GHE TOA forcing of 155 W/m2 is approximatly the difference between the blackbody fluxes at 255 K and 288 K; thus if maitaining 288 K surface temperature, removing it …

    (and not allowing surface temperature variation to increase so much that the average temperature drops significantly relative to global average OLR)

    (while maintaining solar heating, which is actually a hypothetical excercise in part because removing clouds would change the albedo, though albedo could be artificially maintained by other means for the sake of this thought experiment)

    …requires the surface temperature to drop to 255 K in order to restore balance between solar heating and OLR. The difference in radiant flux will be smaller between 222 K and 255 K, and larger between 288 K and 321 K, and it will take a greater GHE TOA forcing to reduce the effective radiating temperature (the temperature of a blackbody that would emit a radiative flux) at TOA from 288 K to 277 K as it would to reduce it from 277 K to 266 K, etc.

    As to the other (non-Planck) feedbacks: these are temperature dependent as well. First, for changing just CO2 forcing (or CH4, etc, or for a non-GHE forcing, such as a change in incident solar radiation, volcanic aerosols, etc.) , there will be other GHE radiative ‘forcings’ (feedbacks, though in the context of measuring their radiative effect, they can be described as having radiative forcings of x W/m2 per change in surface T), such as water vapor feedback, LW cloud feedback, and also, because GHE depends on the vertical temperature distribution, the lapse rate feedback (this generally refers to the tropospheric lapse rate, though changes in the position of the tropopause and changes in the stratospheric temperature could also be considered lapse-rate feedbacks for forcing at TOA; forcing at the tropopause with stratospheric adjustment takes some of that into account; sensitivity to forcing at the tropopause with stratospheric adjustment will generally be different from sensitivity to forcing without stratospheric adjustment and both will generally be different from forcing at TOA before stratospheric adjustment; forcing at TOA after stratospehric adjustment is identical to forcing at the tropopause after stratospheric adjustment). global-time average GHE will also depend on horizontal and temporal variations in temperature, so there is a potential for feedback from that as well (that should be small for small changes for the present-day Earth, but they might become significant for a very large cooling.

    Then there are also non-GHE feedbacks, such as albedo feedbacks (cloud albedo, snow, ice, vegetation, dust/aerosols).

    The snow and ice feedback is generally positive and becomes very large at very cold temperatures; obviously it approaches zero when the temperature is sufficiently warm that very little snow or ice remain and when they occur when and where there is little solar radiation to reflect.

    The water vapor feedback (a generally positive feedback) – there is an roughly exponential increase in saturation water vapor pressure with increasing temperature, and the relative humidity (at a given vertical level) overall tends not to change a lot globally, though there will be different regional trends associated with shifting precipitation patterns. However, the mixing ratio of water vapor decreases roughly exponentially with height (in global time-average effect; locally it may vary step-wise or irregularly). So the water vapor profile might simply shift upward by some amount with each unit temperature increase. But the boundary layer of the atmosphere can be moist with dry air above it, and how does the thickness of the boundary layer change, if it does, etc… Anyway, from Hartmann, “Global Physical Climatology”, 1994, p.233, modeling by Manabe and Wetherald (1967) suggests that at least some feedbacks cancel out the nonlinear effect of the Planck response at least betweeen about 250 K and 315 K, and Hartmann states that with some reasonable assumptions and approximations (constant relative humidity, radiative-convective equilibrium, 1-dimensional model), OLR varies linearly with surface temperature just including the Planck response and the water vapor feedback. This seems to imply the water vapor feedback gets stronger at higher temperatures so that the climate sensitivity does not decrease.

    At sufficiently high temperatures, the water vapor feedback can get so large that climate sensitivity becomes infinite – this is the runaway water vapor feedback. Unlike the snowball Earth case, there isn’t the same hysteresis following equilibrium climate (not including biogeochemical evolution); the process is reversable so long as water vapor is not lost via H escape to space, etc. When all the water available has gone into the atmosphere, the runaway process stops, and it requires additional external forcing to cause additional climate change. (Within the range where water vapor feedback is runaway, zero change in external forcing ’causes’ a large change in climate; the equilibrium surface temperature, graphed over some measure of external forcing, takes a step at some particular value.) Maintanence of such hot conditions still require an external forcing; if the external forcing is changed to cause cooling and the amount of water vapor in the atmosphere starts to decline via conversion to liquid, the runaway feedback starts again, and doesn’t stop until the climate has cooled back to the value where the runaway would start upon warming.


    to be cont.

    Comment by Patrick 027 — 17 Jul 2010 @ 9:20 PM

  405. CORRECTION Re my 404: in discussing % changes in spectral intensity per % 1 change in temperature:

    The 4 % change at peak spectral intensity in terms of per unit log(frequency or wavelength) occurs at λ = 5/4 * λpeak, while the 3 % change at the peak spectral intensity in terms of per unit frequency occurs at λ = 5/3 * λpeak ; I had switched the 5/4 and 5/3 earlier.

    Comment by Patrick 027 — 17 Jul 2010 @ 11:19 PM

  406. Patrick (#395),

    Sorry, I was only paying attention to exponents. Each layer transfers 4piR^2sigmaT^4 of power. The transfered power is the same at each layer so we can write T2 at some layer 2 at R2 in terms of T1 at layer 1 at R1 as T2=T1sqrt(R1/R2) so it is really a 1/sqrt(R) dependence rather that sqrt(R) as I originally stated.

    At an actual solid gas boundary, the change in opacity will usually lead to convective rather than radiative energy transport so that this will not often be encountered.

    One place where this situation does arise is in protostars where pressureless dust provides the opacity and all energy transport is thus radiative as in the original example.

    Comment by Chris Dudley — 18 Jul 2010 @ 12:15 AM

  407. Patrick :”We are considering the climate sensitivity to be in terms of changes in global-time average surface temperature per unit global-time average radiative forcing,”

    the problem is that this definition implicitly assumes that the global, time average surface temperature is a definite single valued function of the radiative average forcing, which is far from being true since there are considerable horizontal heat transfer modifying the latitudinal repartition of temperature: the local vertical radiative budget is NOT verified. So of course one could think that the climatic engine will have a complex but definite answer to any variation of the forcing, and that it would define a complicated, but single-valued response of the “average temperature” to the “average forcing” (which is what I understand to be the “fundamental assumption” of climatology). But this is only an assumption since in principle, highly complex systems can have complicated non linear variability at all time scales (for instance through oceanic circulation that needs one millenium to complete a cycle). The time average makes sense only if you are sure to have caught all variability time-scale in the average (i.e., that they are all smaller than 30 years, say) – I’ve never seen clearly where this assumption comes from, apart from computer simulations, which are NOT reliable for this kind of physics.

    Comment by Gilles — 18 Jul 2010 @ 12:39 AM

  408. ” But, to be clear, atmospheric planck function radiation (absorption and emission) is still not physically the same as vibrotation internal energy absorption and emission. ”

    Rod, absorption and emission always tend to fix the photon density to the Planck value at the excitation temperature of the relevant process. This a general rule that links emission and absorption probabilities, based on the Second Principle (so a very very stringent law ! ) So for a saturated line, the photon density will be close the local excitation temperature if the medium is thermalized. If the medium is transparent, then the radiation temperature is approximately that of the last scattering surface – generally the ground for the transparent windows. The overall spectrum emitted by the Earth is far from a planck distribution basically because the last diffusion surface varies with wavelength, opaque lines being emitted from the TOA, at its local temperature, much lower than the ground.

    Comment by Gilles — 18 Jul 2010 @ 12:47 AM

  409. Re Gilles 407 – I was going to get to that… (but 1. For the benifit of L. David Cooke and/or others at his level, I was starting with the total GHE (global time average) in the approximation of an isothermal blackbody surface. In that context the surface temperature is fixed for a given OLR when the GHE is a given TOA forcing. 2. I never asserted that sensitivity in terms of equilibrium time-average surface temperature change per unit change in TOA or even tropopause-level forcing (with or without stratospheric adjustment) would be the same for each type of forcing for each climatic state and the external forcings that maintain it (or for that matter, for each of those different of forcings (TOA vs tropopause, etc.) with everything held constant. 3. Nonetheless, there is a tendency for similar equilibrium climate sensitivity ECS, especially using a Charney ECS defined as equilibrium global time average surface temperature change per unit tropopause-level forcing with stratospheric adjustment, for different types of forcings (CO2, CH4, solar) if the forcings are not too idiosyncratic. Variations among different climate sensitivies for different agents of forcings are due to their differences and at least in principle can be understood as a consequence of their idiosyncracies (solar forcing causes the same sign of change in stratosphere and troposphere, volcanic aerosol forcing may cause high latitude temperature responses of opposite sign); if their idiosyncracies are outweighed by the similar feedback pattern for a given global average temperature change, then there will be some robust patterns common to ECS change from different kinds of forcings (polar amplification at the surface; enhnaced tropical warming in the upper troposphere, perhaps also the changes in convective heat loss at the surface that balance the surface radiative forcing from water vapor feedback) associated regional changes in storm tracks, precipitation, etc.)… It is specific idiosyncracies in forcings that cause deviations from that, both global average and regional ECS effects.

    Comment by Patrick 027 — 18 Jul 2010 @ 1:24 PM

  410. Gilles (408), the problem might be in part semantics and symbols getting confused with reality. I’m not sure how you define “excitation temperature.” Excited molecules can be ascribed a “temperature of rotation” and a “temperature of vibration” but these are constructs and symbolic to help scientists make comparisons (though as defined may have mathematical units of “temperature.”) They are not temperature in the kinetic and Planck function context — which is real honest-to goodness ‘feels hot’ temperature. Planck radiation is a direct function of the “real” temperature, the radiation intensity or flux being in direct proportion to T^4 (or T^5 depending how you slice it). Vibrotation emission is not directly a function of T^4 or even T. Its connection to temperature is indirect and a function only of the Boltzmann distribution which tells the probability of a molecule within a population of molecules being in an excited state (rotation or vibration for our purposes) within its background temperature. For example, the higher the background temperature the less likely an excited molecule will relax; meaning it is less likely to emit (all else being equal) — the opposite of the Planck function. Secondly, vibrational relaxation is discontinuous in time, staccato if you will; Planck radiation is continuous in time. Thirdly Planck function has more or less a continuous spectrum; the relaxation emission is more or less a single unchanging frequency. Lastly assigning “temperature” to a vibrationally excited CO2 molecule by equating the vibration energy to 1/2kT (as a rule of thumb) gives it a temperature of about 2000K which fits nowhere in this discussion.

    Comment by Rod B — 18 Jul 2010 @ 2:55 PM

  411. Re 402 Rod B

    Part of the confusion may be between temporal and spatial variation.

    Planck function/blackbody radiation vs radiation from molecules, matter: the physical processes are not the same and do not follow the same unfettered rules.

    They are exactly the same because the Planck function and blackbody flux formulas describe something that applies to all radiation. They describe the intensity and flux that would be in thermodynamic equilibrium with matter at a given temperature; which would imply that a population of photons of some frequency and direction which have that particular intensity would have that temperature – their brightness temperature.

    Their is no subset of processes on the molecular level that gives rise to ‘Planck type’ radiation. There are processes that emit and absorb photons. The details on a molecular level determine how likely a given transition is likely to occur – in other words, the fraction of photons of some frequency, polarization, and direction, that are absorbed over some path through an amount of material, and the number of photons of the same type which are emitted per unit time. But in full thermodynamic equilibrium, with equilibrium among all photons and non-photons, the rate of emission into a direction and absorption from that direction at some location, of each type of photon, will be equal.

    Temporal variation – the tendency toward thermodynamic equilibrium in a closed isolated system

    Suppose a bunch of photons and non-photons are thrown into an isolated closed chamber, perfectly mirrored and insulated (or otherwise assume an infinite expanse which is self-similar on a large scale). Whatever the amount of photon energy and other energy, however distributed, over time, absent kinetic barriers, the system will tend to approach equilibrium. The extent to which matter interacts in various ways determines how quickly this occurs. Absent interactions with photons, non-photons will come to a thermodynamic equilibrium wherein there is some equilibrium energy distribution characteristic of that type of material at some particular temperature, and the non-photons will thus have that temperature. Absent interactions with non-photons, the photons have no way of equilibrating amongst themselves, but scattering which preserves photon energy would at least over time redistribute the photons toward an equilibrium distribution over directions, which will be isotropic so long as the real component of the index of refraction is isotropic. Scattering may also drive the distribution over polarizations toward an equilibrium (which would be, at any given frequency and direction, constant over polarizations so long as the real component of the index of refraction is independent of polarization) Interactions wherein photons are scattered by matter with some exchange of energy will eventually redistribute photons toward a Planck-function distribution – a blackbody spectrum – characteristic of some temperature, and because the exchange involves some other type of matter, the photon gas temperature (brightness temperature) will approach the temperature of the material it is interacting with (? unless there is a problem due to scattering preserving the number of photons – in that case, there would be a quasi-equilibrium, analogous to the quasi-equilibrium that can occur when electrons and holes interact with non-photons rapidly to be redistributed within a band while tending to remain within each band so that they are not at equilibrium with each other across bands at the temperature that they have within their bands). Notice that all of these processes involve populations of photons with different brightness temperatures (which are the temperatures of those populations) exchanging energy with a net flux of energy from higher to lower brightness temperatures, bringing larger populations of photons (either all the photons at some frequency, or … etc.) towards the same temperature. Some of these mechanisms preserve the number of photons and the total energy of the photons. An effective way to bring all populations towards the same temperature involves emission and absorption of photons combined with interactions among non-photons; populations of non-photons come to equilibrium with photons of various frequencies, polarizations, and directions, or larger groups of photons depending on how specific the non-photon optical properties are; different populations of non-photons interact to achieve LTE among them, and scattering can drive different populations of photons towards equilibrium with each other, though it is only necessary that the non-photons tend toward LTE to cause different populations of photons to come to the same equilibrium temperature.

    Spatial variation – the tendency of photon intensity brightness temperature to approach the temperature of material over a path through that material

    Now consider what happens if the photons travel among different systems of non-photons with different temperatures. If there is scattering with photon energy changes – Raman or Compton (or for that matter if there is significant stimulated emission?), then the interaction gets complicated, but if we stick to purely complete emission and absorption of photons, with any scattering preserving photon energy, then, if the non-photons within each local system are at LTE, then they will emit into a direction as much as they absorb from a direction of the same type of photons if their temperature is the same as the brightness temperature of the incident photons. This is because they would be in thermodynamic equilibrium with those photons. As long as LTE is maintained, the fraction of photons in some direction of some type that are absorbed will be the same regardless of the intensity of photons. As long as LTE is maintained and assuming stimulated emission is insignificant, the non-photons would be emitting at the same rate regardless of photon absorbption.

    So for a particular type of photon, emitted intensity (I.emitted) into a direction = absorbed intensity (I.absorbed) from that direction if the temperature of the non-photons is equal to the brightness temperature of the incident radiant intensity (I.incident). I.absorbed/I.incident = absorptivity; I.absorbed = I.emitted; I.incident = B.emitted (because they have the same brightness temperature, where B.emitted is what would be emitted by a blackbody, and is what would be in equilibrium with matter at that temperature), emissivity = I.emitted/B.emitted; therefore, given that absorptivity is independent of incident intensity but is fixed for that material at that temperature at LTE, and the emitted intensity is also independent of incident intensity but is fixed for that material at that temperature, emissivity (into a direction) = absorptivity (from a direction). For other reasons, at LTE, the transmission (of a given type of photon) is the same in a pair of opposite directions, so in the absence of scattering, emissivity and absorptivity must each be the same for opposite directions across the same path of material, and thus they will be the same for absorption of photons from a direction and emission of photons into the opposite direction. Even with scattering, if the properties have 2-fold rotational symmetry or are isotropic, emissivity and absorptivity will be the same for the same and opposite directions.

    In that case, while holding temperatures constant and non-photon material at LTE, along a path, absent scattering and reflection, the intensity is always tending to approach the local blackbody value; it will not actually reach the blackbody value if the temperature varies along the path with the same tendency. The brightness temperature of the intensity, over distance, is always changing toward the local temperature, at a rate proportional to the absorption cross section density, which is equal to the optical thickness per unit distance, which is equal to absorbtivity per unit distance in the limit of zero distance …

    (absorptivity doesn’t increase linearly over distance; optical thickness does;
    absorptivity = 1-exp(-optical thickness) (when there is no scattering, etc.);
    if we have finite-length path segments that are isothermal, we can use absorptivity and Planck function (for the temperature of the segment) of each segment to determine the change in intensity from one end point to the other, but if temperature is varying continuously over distance, we need to look at a change in intensity over differential lengths ds; where
    absorption optical thickness = s* (absorption cross section) density,
    absorptivity = 1-exp(-s * absorption cross section density),

    d(absorptivity)/ds = (absorption cross section density) *exp(-s * (absorption cross section density))
    = absorption cross section density * transmitted fraction over distance s
    = fraction of intensity from s=0 that reaches s and is absorbed per distance ds;

    the absorptivity of ds itself is just the fraction of intensity incident at ds that is absorbed, which is equal to the absorption cross section density)

    So the intensity of radiation (at some frequency and polarization) changes over distance, such that, in the direction the intensity is going, it is always approaching the blackbody value (Planck function) for the local temperature; it approaches this quickly if the absorption cross section density is high; if the cross section density is very high and the temperature doesn’t vary much over distance, the intensity may be nearly equal to the Planck function for that location; otherwise its value is a weighted average of the Planck function of local temperature extending back over the path in the direction it came from. (if there is scattering and absorption, then the intensity at some location will be a weighted average of the Planck function over some volume that may to some extent surround the location; if there is only scattering, then the intensity will be a weighted average of the Planck function at the emitting surfaces (surface, space) depending on how much is scattered from where.)

    The intensities from all directions, weighted by the cosine of the angle from vertical, add up over solid angle to equal a flux per unit horizontal area. Summing over a hemisphere upward and hemisphere downward give the downard and upward fluxes, the difference between them being a net (upward or downward) flux (per unit area), which can also be found by summing (Weighted by the cosine of the angle from vertical) the net intensity over a hemisphere, or the intensity over a whole sphere.

    Back to time evolution
    The difference in net upward flux between the top and bottom of a layer (a flux convergence or divergence) is a net energy absorption/accumulation or emission/depletion of that layer, indicating energy is being gained or lost. This leads to temperature changes (and/or changes of physical or chemical state, of course). In radiative-convective equilibrium, the convergence of different energy fluxes (solar and LW radiation, summed over all frequencies, and convection/conduction/etc.) sum to zero for each layer, so the net upward LW flux plus the net upward non-radiative flux is equal to the net downward solar flux.

    Back to Planck function

    The Planck function describes an equilibrium intensity for a type of photon, as a function of temperature. Assuming an LTE approximation, setting aside stimulated emission and scattering that changes photon energy (Raman, Compton), how rapidly over space or time the equilibrium may be approached depends on optical properties, which are the aggregate effect of the microscopic processess which themselves are not described by the Planck function, but do obey certain rules (regarding a proportion between likelihood of emission and likelihood of absorption) such that, at LTE, in aggregate, they emit a fraction of the Planck function and absorb the same fraction of incident intensity. (Raman and Compton scattering and, I would assume, stimulated emission, also obey the laws of thermodynamics but if the material is not already in equilibrium with the incident radiation from all directions, the emitted radiation will depend on both the incident radiation and the temperature of the material, etc.)

    Comment by Patrick 027 — 18 Jul 2010 @ 8:10 PM

  412. Re 407 Gilles – it might help to consider what sustains internal variability

    There are externally imposed horizontal and vertical differential heating patterns. Temperature tends to respond so that, depending on optical properties, LW emission will tend to reduce the vertical differential heating by cooling warmer parts more than cooler parts (for the surface and atmosphere); also (not significant within the atmosphere and ocean in general, but significant at the interface betwen the surface and the air, and also significant (in part due to the small heat fluxes involved, viscosity in the crust and somewhat in the mantle (where there are thick boundary layers with superadiabatic lapse rates) and thermal conductivity of the core) in parts of the Earth’s interior) temperature changes will cause conduction/diffusion of heat that partly balances the differential heating. It is the remaining differential heating that is available to drive convection, if any is available.

    Convection could assume steady state motion to steadily balance, along with LW radiation, etc, the imposed differential heating. In that case the optical property feedbacks, etc, could also be steady. In the absence of horizontal differential heating to anchor convection cells, cells could tend to maintain themselves via the inflow to updrafts and downdrafts being warmed and coolded along the way so that the cells reinforce horizontal temperature variations that organize them. Latent heating would play a role in that in the atmosphere. The kinetic energy produced by thermally-direct overturning would be steadily viscously dissipated. Transport of momentum (linear and angular) within the atmosphere and ocean would be balanced by transfer via pressure gradient and coriolis and viscous forces and by gains or losses at interfaces with each other and the solid Earth.

    The pattern would respond to externally forced diurnal and seasonal and orbital-scale cycles with some lag time from thermal and mechanical and compositional, etc, inertia, but with a constant pattern of heat accumulation and depletion over each cycle.

    (PS For a given temperature profile within the layer, the layer’s average temperature (and optical properties, etc.) determines whether the fluxes into and out of the layer as a whole are balanced – hence the importance of tropopause-level forcing, but that’s not really the point here.)

    But depending on how much differential heating is available, and the underlying physics, such a steady state flow (except for externally imposed cycles) may become unstable to other flow patterns which cannot be steady.

    I’ve read that for simple cellular convection in a homogeneous fluid, turning up the differential heating can eventually cause wobbling and more complext behavior and eventually chaotic turbulence; I won’t go into exactly why because I haven’t studied it, I’d guess it has to do with the steady state cell circulation being unable to balance the heat flux via convection while at the same time preventing smaller scale convective instability in the boundary layers where a superadiabatic lapse rate may be required for the transport of heat into and out of the circulating fluid (PS viscosity more effectively impedes convection on smaller scales).

    Cumulus convection tends to occur episodically with individual updrafts. Because precipitation removes water, sinking air is often dry, and lapse rates up to dry adiabatic can be sustained even though they would be unstable to moist convection; heat and humidity build up until conditions favor convection, until something triggers it, and then it can sustain itself until the energy is drained.

    Hadley cell-type overturning leaves a large horizontal temperature gradient (which has available potential energy, APE) that can be unstable to baroclinic instability (a Rossby-wave instability). Small perturbations on the synoptic scale grow into midlatitude storms; they take APE from the ‘basic state’ and put it into the waves, take some of it and convert it to kinetic energy, which allows them to pull out even more APE, but in the process, they use up some of their energy source; some of the kinetic energy gets put into the ‘basic state’ via a Ferrel cell, some is lost to friction. Storm-track activity patterns are shaped by the momentum distribution and affect the momentum distribution (I think they may tend to reinforce the average momentum distribution).

    There is also barotropic instability (also a Rossby-wave instability). Eddies can grow by extracting kinetic energy from a steady-state flow pattern, if there is an elongated horizontal maximum or minimum in potential vorticity; however, the shear can tilt those eddies in such a way that the eddies give back their kinetic energy.

    Something very similar to that, tilted on it’s side, can allow vertical wind shear to produce eddies (if the wind shear is strong enough, it can overcome static stabiltiy to do this); on this scale, the eddies lose kinetic energy to smaller scale motions and viscosity more effectively so they tend not to give their energy back to the smooth flow pattern. Momentum can be transfered by the resulting ‘eddy viscosity’ more effectively than by molecular viscosity.

    There are some positive momentum feedbacks that can reinforce a momentum redistribution, such as associated with storm track activity, or also (I think this is a good example), with feedback from SST rearrangment, ENSO.

    There is an interesting process in the equatorial stratosphere wherein upward transport of momentum and energy by waves is absorbed depending on the wind structure in such a way as to cause the wind to oscillate from easterly to westerly on a timescale that has no direct dependence on the timescales of any forcing – a bit like an internal clock (QBO).

    Some of this internal variability can have affect the global average radiative energy balance. For example, episodic deviations in cloud and snow cover, dust and smoke, etc, will have some radiative effect that could cause some global average temperature change. Redistribution of heat (such as vertical transport between the surface and the deeper ocean) could cause some surface and atmospheric temperature change that causes some global average warming or cooling. But these will tend to average out over sufficient time.

    The point is, turbulent chaotic episodic motions can develop on various timescales. They do so not because the system is being perturbed from outside, but because (at least on shorter timescales) a steady-state flow is unstable – but the activity is still anchored to external forcing, still relies on a finite imposed energy supply and thus the behavior tends to stay within limits with a predictable overall texture, though the butterfly effect renders prediction of specific events essentially impossible beyond some time horizon (and also means that tiny fluctuations in external forcings (the odd cosmic ray here or there) can affect weather significantly given time, even though they are insignificant to climate). Some low-frequency variability can exist because more slowly evolving internal variability in the oceans may anchor atmospheric patterns, and because of positive feedbacks (not radiative per se – momentum rearrangements may have positive feedbacks while radiative feedbacks may be negative**) within the atmosphere (just as some atmospheric patterns may anchor patterns in smaller scale rapid processes); there can be some positive or reinforcing feedbacks (as in momentum, moisture, snow cover?…), but if internally-generated perturbations that could trigger a shift occur with some frequency, other such perturbations that could trigger a different shift, perhaps the opposite shift, may also occur with some frequency. If they did not, then the climate would, sooner or later, end up stuck in the new state, and thus that would be the equilibrium climatic state.

    Comment by Patrick 027 — 18 Jul 2010 @ 10:45 PM

  413. Re 380 L. David Cooke, PART III (actually it may be part VI, but oh well…)

    In addition to climate sensitivity being depenent on climatic state, there is also the fact that radiative forcing, for the same change in optical properties/composition, is dependent on climatic state.

    For example, climate affects albedo (and it’s distribution), which affects how much a change in incident solar radiation (globally or regionally as in orbital forcing) forces a change in solar heating. Climate can also affects the vertical distribution of solar heating.

    Different climates have different vertical temperature profiles (aside from horizontal and temporal temperature variations), which affects the radiative forcing that an amount and arrangement of greenhouse agents (CO2, CH4, etc, also, water vapor and clouds) will have.

    So while, in the isothermal blackbody surface approximation, if the starting surface temperature is 288 K and we know the OLR is reduced from surface emission by 150 W/m2 via GHE, we know that removing all greenhouse agents will have a TOA forcing of -150 W/m2, (and some forcing at the tropopause, etc.) which will cool the surface temperature to about 255 K at equilibrium , absent non-Planck feedbacks. And we know that adding the same greenhouse agents back will (absent hysteresis among equilibria – which should be avoidable if we limit ourselves to considering only the Planck response) warm the climate back up to a surface temperature of 288 K.

    But the forcing will be different. In fact, if there is any significant solar heating of the atmosphere, the TOA forcing from adding all GH agents back should tend to be negative! This is because the equilibrium climate without any GHE requires the OLR, which must balance the solar heating of the surface and atmosphere, must be emitted from the surface, requiring heat from solar heating of the air to flow downward to the surface. There could be some weak, shallow overturning due to horizontal differential heating (cooling of sinking air would have to occur via downward diffusion of heat), but to a first approximation, the tropopause level may actually rest near or at the surface. The addition of GH agents will have a positive forcing at the surface and also the tropopause, because, even with stratospheric adjustment, the atmosphere will still be cooler than zero K, and will emit some radiation downward to the surface, which is more than zero (no GHE requires no backradiation to the surface). This highlights the importance of tropopause-level forcing (in this case, at or near the surface) to the surface and tropospheric temperature responses, but we still can’t expect that the tropopause-level forcing would be 150 W/m2.

    The same externally-forced change to composition will have the same magnitude of effect on equilibrium climate in the forward and reverse directions provided no hysteresis, but if the change is quite large, the radiative forcing, and the feedback, and the climate sensitivity to the forcing, will be significantly different. The forcing and feedback (including the vertical temperature profile feedback) will be different in complimentary ways to result in the same magnitude of shift in equilibrium climate.

    One way in which this works – consider the overlap between CO2 and water vapor and clouds. To isolate this effect, hold the lapse rate (at all levels) steady. Removing CO2 will have some forcing, and their will be a water vapor feedback. Now adding back the CO2 will have a larger magnitude of forcing than the initial removal because there is much less water vapor, and the water vapor feedback in terms of W/m2 will be smaller in magnitude because of the overlap with CO2.

    Comment by Patrick 027 — 18 Jul 2010 @ 11:09 PM

  414. CORRECTION: “because, even with stratospheric adjustment, the atmosphere will still be cooler than zero K,”

    Obviously that should be “warmer than zero K”

    PS the TOA forcing would be negative initially; after stratospheric adjustment it would be less negative – it could be positive, but that depends on the distribution of solar heating.

    Comment by Patrick 027 — 18 Jul 2010 @ 11:14 PM

  415. Rod : the temperature is not associated with a single state of a system, but with a statistical distribution. A single excited CO2 molecule has no temperature. A large set of CO2 molecules, or the time averaged distribution of the states of one molecule, can often be described by a Boltzmann distribution P \propto exp(-E/kB Texc) where Texc is the “excitation temperature”. If the true thermodynamical equilibrium is achieved, all temperatures will be equal to the temperature of photons (Planck distr.) and the kinetic one (Maxwell distr.). But very often, the temperature will be different and the energy transfer is due to this difference.

    Concerning “For example, the higher the background temperature the less likely an excited molecule will relax; meaning it is less likely to emit (all else being equal) — the opposite of the Planck function. ” I don’t know what you means by “the opposite of the PLanck function” (it doesn’t “emit” anything), but your first assertion is wrong. Neglecting coherent (stimulated) emission process, the relaxation of an excited molecule doesn’t depend on the background. Stimulated emission INCREASES the relaxation rate (because the background photon density increases). What happens is that for higher temperature, the absorption rate of ground state molecules increases and the relaxation rate is almost constant – so the density of excited molecules increases.

    Comment by Gilles — 19 Jul 2010 @ 1:39 AM

  416. Patrick 027, a quick response to the first of your 411 post (I’ll get to the rest of it later): In a few words, they ARE NOT the same. The fact that similar math and equations can be applied to different things does not make those things identical. Many of the equations, such as from Beer-Lambert and Kirchhoff laws, can be (are) applied to Planck radiation and to molecular relaxation radiation — provided one puts the proper limits, coefficients and boundaries on the equation. But, the actual Planck Radiation Law and its follow-ons Wien’s Displacement and Stefan-Boltzmann Laws has no relation whatsoever and can not determine the result of any molecular de-excitation radiation. So, I repeat, ARE NOT! Using Planck’s Law along with Beer-Lambert and Kirchhoff and dividing the atmosphere into some number of slabs at the physicist’s choosing is a very convenient way to assess global climate change actions even though greenhouse gases have no actual physical relation with Planck’s Law, and just as the atmosphere is not actually divided up into umpteen slabs, we think that we none-the-less get a very good approximation of what’s happening with the GHGs. But, for these reasons and my earlier post, still ARE NOT the same physical process. In a large ballpark view, it is probably close enough. But in the specific details as to what’s happening at the molecular view, it is NOT close enough; assuming you can analyze this level with inappropriate physics often leads to seriously wrong answers.

    What is the brightness temperature of the source of a photon at 2x10E4 gigahertz with an energy of 1.35x10E-20 joules? [And as long as I'm digging, photon sources have temperature; photons do not.]

    Comment by Rod B — 19 Jul 2010 @ 12:05 PM

  417. Gilles, thanks. My understanding is that excitation temperature is a construct more commonly used to describe internal energy levels, especially electronic. I was thinking elsewhere when I asked for the definition.

    What I meant was that Planck radiation increases with body or amb ient temperature, but higher temperature, per the Boltzmann distribution, makes it more probable that rotation, vibration, and/or electronic levels will be excited, and therefore less likely to emit relaxation energy, though as you point out this may not be exactly what happens physically — emission radiation is more flat than anything with increasing temperatures. But is sure ain’t increasing in proportion to T^4, as Planck radiation would. This is not talking of stimulated emission.

    Comment by Rod B — 19 Jul 2010 @ 12:48 PM

  418. Patrick 027, PS: While my quip about photon temperature may be true, it’s not very helpful. There is much insight to be gained (as per your post #411) by ascribing a characteristic temperature to an EM field based on the brightness temp and Planck distribution, etc, and there is not much to lose. So, what the hay!

    Comment by Rod B — 19 Jul 2010 @ 2:46 PM

  419. Re Rod B – yes, a single photon has no brightness temperature; a population of photons (via their combined intensity) does have a brightness temperature.

    Okay, the Planck function is not the same as the molecular-scale processes that emit radiation, but the Planck function is applicable to describing that radiation in aggregate. (We approximate the atmosphere as some number of layers for the purposes of numerical integration/computer modelling; this is an approximation to a continuum (on scales larger than individual molecules), and we know the approximation gets better at higher resolution. The approximation is not fundamentally different from reality, it will just have some (small) error).

    Comment by Patrick 027 — 19 Jul 2010 @ 5:18 PM

  420. Re my 414,413
    PS the TOA forcing would be negative initially; after stratospheric adjustment it would be less negative – it could be positive, but that depends on the distribution of solar heating

    Oh, no, that’s not true.

    The TOA forcing will be equal to tropopause-level forcing after stratospheric adjustment (their can’t be a net forcing on the stratosphere after it reaches equilibrium).

    What I should have said is that the stratosphere will cool – whether it gets cooler than the surface or tropopause or remains warmer (remember this is the case where we started with zero GHE and had some solar heating within the atmosphere) depends on specifics.

    Comment by Patrick 027 — 19 Jul 2010 @ 6:36 PM

  421. Re 380 L. David Cooke ,

    Re my 413 (PART III) – and of course, in the case of removing all GH agents and then adding them back and considering only the Planck response – actually, it’s the Planck response plus the vertical temperature profile feedback – which is actually essentially the same as the Planck response except for the troposphere:

    1. That was holding the distribution of solar heating steady, which would require removing water vapor, cloud, and ozone LW optical thickness but still leaving behind their SW (solar) optical properties.

    2. In that case what makes up the difference in forcing magnitude between the forward and reverse directions is the difference in the temperature-profile feedback. In the case of removing all greenhouse agents, there is no temperature profile feedback to the surface temperature change, because after all greenhouse agents are removed, the vertical temperature profile, while it will respond to the change, will not affect the equilibrium surface temperature. That is not the case when there are greenhoug agents (of the absorbing/emitting kind, as opposed to scattering).

    For some reason I kept refering to a 150 W/m2 GHE when I should have been refering to a 155 W/m2 GHE (TOA).


    Refraction, specifically the real component of refraction n (describes bending of rays, wavelength changes relative to a vacuum, affects blackbody fluxes and intensities – as opposed to the imaginary component, which is related to absorption and emission) is relatively unimportant to shaping radiant fluxes through the atmosphere on Earth (except on the small scale processes where it (along with difraction, reflection) gives rise to scattering, particularly of solar radiation – in that case, the effect on the larger scale can be described by scattering properties, the emergent behavior).

    But I mentioned it earlier and just wanted to clarify: I# is I scaled by n such that I# is conserved over distance in the direction I propagates absent scattering, reflection, absorption; The fraction of I that is absorbed, or scattered, or reflected at a given point is proportional to the fraction of I# that is absorbed, scattered, or reflected. Also, I think the fraction of I# that is scattered from one direction to another is the same as the fraction of I that is scattered from one direction to another. So long as I# is that for the same side of a reflecting interface or the same direction as I – the amount of I that is transmitted or goes in a different direction may be more or less than what was actually taken from another path because of the variation of n, but the amount of I# that is transmitted or goes in a different direction will be equal to the amount that was taken from another path. The emission cross section multiplied by the Planck function for a vacuum will equal the emitted I# per unit distance; multiplying instead by the Planck function for that medium with that refractive index will equal the emitted I per unit distance.

    I spreads out or is compressed into a larger or smaller differential solid angle as it moves along a path through variations in n. The total amount of solid angle is always 4*π sr (a whole sphere), so as rays covering some solid angle, such as 2*π sr, spread out going toward smaller n, some have to exit that solid angle to make room as they spread out; thus, if all the rays fill a 2*π sr hemisphere before n declines, some rays have to bend around and go back toward the other hemisphere of directions as n declines, and a smaller fraction of rays will reach a smaller n, as the rest ‘return’ before reaching that n. The rays that get sent back join rays going the other way as more rays get compressed into the same solid angle going back toward larger n. This is the basis for total internal reflection (TIR) – it can occur at an interface between different media, but it can also occur over a continuous distribution of n. A continuous distribution tends not to reflect much radiation (TIR in that case just involves rays taking curved paths).

    Comment by Patrick 027 — 19 Jul 2010 @ 7:15 PM

  422. Patrick 027, O.K., just for fun, what is the brightness temperature of a large pile of photons all at 2×10E4 gigahertz with an energy of 1.35×10E-20 joules having been just emitted from a large pile of relaxing CO2 molecules?

    Comment by Rod B — 19 Jul 2010 @ 11:16 PM

  423. I got called away before finishing my thoughts. Not sure anyone is still following this thread, but for my own piece of mind.

    317 by Anonymous Coward,
    “…the UK is not close to being on either top 5 list.”
    ‘Either’? There are a more than two ways to define the top emitters. Where would you put the UK if you measured its cumulative emissions over the last hundred years, total or per capita? Why 100 years? Well, I just picked it; longest period when someone alive today could have benefited from their country’s use of fossil fuels and within the time that most of any additional CO2 would still have an effect.

    Patrick 027,
    I think I finally came upon a way to properly express my doubt about your comment at #172, my #258.

    Pick some density d-saturated moles/m^3 that effectively means the gas is saturated as far as radiative transfer is concerned.
    Pick some density d-toa moles/m^3 that effectively corresponds to TOA, near zero I presume.

    Not sure how to handle temperature, but if you assume temps close to real world conditions, you’ll stay close enough to what is realistic. You can adjust for a translation between density/partial pressure of your GHG to density/total pressure if you like, but as long as the same partial/total is used on both sides, I don’t think it will matter as far as the conclusion is concerned. Then, you can use the formulas at

    to find the difference between h-saturated and h-toa. I don’t think you can create conditions where the height difference is anywhere near zero and still maintain a pressure/density curve that would occur in reality.

    Comment by Chris G — 20 Jul 2010 @ 2:04 AM

  424. Re 422 Rod B – assuming index of refraction is 1 (otherwise an adjustment has to be made to the Planck function):

    If either the photons have precisely the same energy, and/or are emitted at precisely the same time from precisely the same location in precisely the same direction, or otherwise are emitted so that they end up in the same direction passing the same point at the same time, then the brightness temperature would be infinity. Of course, photons don’t occupy zero space, … (quantum uncertainty, …) – but the point is, we have to specify the solid angle over which the photons are distributed, and the time period over which the photons pass a given location, and the interval of frequencies over which the photons are distributed, as well as the total number of photons (that’s what gives us the spectral intensity).

    PS the complete absence of photons (in a given direction over a given time period at a given frequency, over a given frequency interval) also has a brightness temperature (absolute zero).

    Comment by Patrick 027 — 20 Jul 2010 @ 12:29 PM

  425. Re 423 Chris G – whether the effect saturates at a given density depends on the way the temperature is distributed; if the temperature from TOA downward is isothermal for a sufficient thickness, than the effect could be saturated at TOA (if starting from a large enough optical thickness per unit atmospheric mass path, a change in the density of the gas/etc that contributes optical thickness would then have little to no effect on the flux at TOA, which is what is meant by saturation. Of course, this doesn’t necessarily mean that the resulting temperature response to the forcing (zero forcing at TOA does not mean zero forcing everywhere) can’t ‘unsaturate’ the effect at TOA so that there might be a forcing at TOA for some additional change in the composition of the atmosphere).

    Any realistic temperature distribution would allow a sufficient increase in optical thickness per unit atmospheric mass path to approach saturation at TOA (before the temperature response); the realistic limitation to that is that the optical thickness per unit atmospheric mass path can never get to be more than the optical thickness per unit mass path for the ‘strongest’ gas (or whatever material is involved), since the atmosphere can’t be more than 10^6 ppm of anything.

    (You could have a more than 10^6 ppm increase in CO2 relative to a reference atmosphere such as the initial atmosphere, but the result would only be an atmosphere that is more than 50 % CO2 and never more than 100 % CO2.)

    Comment by Patrick 027 — 20 Jul 2010 @ 1:01 PM

  426. Re 380 L. David Cooke -

    The point of Part III was that there are complexities to very large climate changes, wherein the same change in forcing agent will tend to cause the same magnitude of change in forward and reverse if everything is is held constant, but the change will be a different combination of forcing and feedback, with different climate sensitivity.

    For smaller changes, this may not be so apparent or important (a doubling of CO2 from 280 to 560 ppm may have about the same magnitude of forcing and result in the same magnitude of feedback as halving CO2 from 560 to 280 ppm).

    Since the 155 W/m2 GHE is the GHE forcing based on the present climate (in the sense that removing all GH agents (only their LW opacity, keeping solar radiation properties constant) results in a forcing of -155 W/m2 at TOA for the present climate, and we know that without any GHE, in the isothermal blackbody surface approximation, the temperature will fall approximately 33 K without any non-Planck feedbacks), it can be compared to smaller climate forcings made in the context of the present climate (such as a doubling CO2.) However, direct comparisons require either only considering the Planck response with radiative-convective equilibrium (maybe also allowing the lapse rate feedback within the troposphere since that is not a change in optical properties – although that is in reality somewhat of a packaged deal with the water vapor feedback), or else including the feedbacks to consider some total W/m2 amount that the climate will be adjusting to. There is also the matter of forcing at TOA vs tropopause level vs tropopause level with stratospheric adjustment.


    I had been preparing comments to explain – how LW radiative forcing (greenhouse effect) works, why forcing from CO2 is approximately linearly proportional to CO2 at sufficiently small amounts of CO2 and approximately logarithmically proportional to CO2 within a range of larger amounts, and then how the climate responds to forcings, but that got very very long and so I’m going to hold off on that.

    Here’s what I’ll post for now:

    The climate system behavior, including its internal variability (see my 412 above, and also ** below), is anchored to externally-imposed conditions – things that don’t change as a function of climate.

    For example, the optical thickness of the CO2 in the atmosphere (if you see an error in this list of things independent of climate, see below), the incident solar radiation and it’s distribution over time and space (latitude), variations in surface albedo between ocean, rock, vegetation, etc.). While the amounts and distribution of water vapor and clouds are feedbacks, the intrinsic properties are ‘externally-imposed’ by the physics, as is the case with snow and ice, etc. These all don’t affect energy fluxes or their spatial-temporal distribution so directly: there’s the heat capacity and viscosity, gravity, the coriolis effect (rotation of the Earth), the distribution of continents and oceans and their topography/bathymetry (aside from albedo, there’s an obvious mechanical forcing to circulation patterns, which, as with the coriolis effect, etc, can have an effect on the radiative feedbacks and sensitivity to radiative forcings (example: changes to geography affect sensitivity to orbital forcing; the coriolis effect (and mountain ranges and ocean geometry) has an affect on horizontal heat transport, which may affect sensitivity by affecting how snow and ice change for the same global average temperature change by affecting temperature gradients).

    In hypothetical experiments (modelling), we can pick anything we want to be an externally-imposed condition, alter it and hold it fixed at will and consider how the climate responds.

    In reality, the distinction between forcing and feedback depends on perspective; in particular, the time frame.

    Over a short-enough time frame, the ocean SST distribution may anchor atmospheric weather patterns, but over longer periods, there is important two-way interaction (the components are more strongly coupled).

    There are some things (water vapor, clouds, seasonal snow) that respond rapidly to climate change. Sea ice can also respond relatively quickly.

    It is convenient to use a climate sensitivity using predictable rapid feedbacks and holding other things (natural CH4 emissions, ice sheets, vegetation?) fixed. Charney sensitivity is such a concept. If something is expected to change in response to climate change, but there is uncertainty, or maybe just uncertainty in the timing of the response (slow or fast, maybe irregular jumps), we can at least use Charney sensitivity, and treating the left-out feedbacks as a forcing, use Charney senstivity to that forcing to consider what may happen.

    Obviously, sensitivity to radiative forcing of greenhouse gases (not water vapor, but CO2 and CH4) can’t include feedbacks of those same gases – those are defined as forcings in such a sensitivity. To consider such feedback, the forcing has to be the actual action that is disturbing the amount of CO2 and CH4 (anthropogenic emissions), and a good description of the response may be time-dependent (trajectory of climate as a function of trajectory of anthropogenic emissions).

    Over longer time scales, there is CO2 feedback. There is positive CO2 feedback on the scale of orbitally-forced ice ages and interglacials; this isn’t a general fact – it depends on how the system is set-up (the same is actually true of the ice sheet feedback. With a different overall climatic state or geography, the system might be considerably less sensitive to orbital forcing (obviously it has been less sensitive; orbital forcing has been going on throughout Earth’s history (modulated by tidally-induced changes in Earth’s rotation and the moon’s orbit)). Althoug absent ice age-integlacial response, orbital forcing still affects low-latitude circulation patterns (monsoons).

    (Orbital forcing doesn’t have much of a global annual average forcing, and it’s even concievable that the sensitivity to orbital forcing as measured in terms of global averages and the long-term response (temporal scale of ice sheet response) might be approaching infinity or even be negative (if more sunlight is directed onto an ice sheet, the global average albedo might increase, but the ice sheet would be more likely to decay, with a global average albedo feedback that causes warming). Orbital forcing causes ice ages or ends them by redistributing incoming solar radiation over seasons and latitudes so that ice sheet growth or decay is more or less favorable on a regional basis, with a resulting global average albedo feedback.)


    The equilbrium global time average response (on a time scale sufficient to characterize externally-forced cycles (day, year) and internal varibility) to an imposed global time average radiative forcing is a change that balances the externally imposed forcing plus any non-Planck feedbacks (where the Planck response is part of the response to the other feedbacks. Within a convecting layer, convective fluxes can also be part of the response, but where convection is bounded within a layer, the layer as a whole must respond with radiation to radiative forcings and feedbacks.)

    Patterns in feedbacks can shape the 4-dimensional structure of the climate response; so can patterns in the externally imposed (or just external) forcing, but among external forcings that are not too idiosyncratic, the feedback distribution may dominate so that the climate response is similar in structure. The climate sensitivity to the external forcing will also tend to be similar. Idiosyncracies in the forcings may alter the 4-dimension structure of the climate response so as to change the global average feedback. The climate sensitivity to a forcing divided by climate sensitivity to some reference forcing is called efficacy. Among forcings which have opposite effects on the stratosphere for the same sign of effect on the troposphere+surface, efficacy will tend to be more similar if in terms of tropopause-level forcing with stratospheric adjustment (although there can be mechanical effects on the troposphere+surface from stratospheric changes (and vice versa)).

    Anthropogenic aerosols are somewhat more idiosyncratic because of their regional distribution.

    Orbital forcing is very idiosyncratic.


    ** example of internal variability: sound produced by wind blowing through a tree. There is no external forcing with cycles in the frequencies of sound waves; the sound is produced by internal variability. The system is forced by the speed of wind and the type of tree. The energy flux of the sound will tend to increase with greater wind speed. Interestingly, the texture of the internal variability is strongly affected by the type of tree. You can hear the difference between a quaking aspen (rustling-clapping) and a pine-tree (whooshing/rushing/shhhh).

    Comment by Patrick 027 — 23 Jul 2010 @ 8:44 PM

  427. Also, CO2 has non-radiative effects (fertilization (not the panacea it is sometimes assumed to be), acidification), which might somehow feedback on climate (regionally, changes in evapotranspiration, for example – not a tropopause level forcing, but it would have some effects).

    Over longer periods of time, there is a negative CO2 feedback (see prior comments)(depending on geography (relative to circulation patterns) and CO2 amount, warming can cause enhanced chemical weathering, which supplies ions that can combine with CO2 to form carbonates. In the absence of that ion supply, abiotic CO2 uptake in the ocean as a function of CO2 in air is at least somewhat limited by ions already present; acification can (over time) dissolve carbonate minerals that supply cations and carbonate ions, buffering pH and reacting with CO2 to form bicarbonate ions; new cations from chemical weathering have to be supplied to actually remove C from the oceans while keeping pH from dropping and without releasing as much CO2 from bicarbonate ions).

    (Re L. David Cooke

    PS What I meant about H escape – I was refering to a process that could have been important in the Archean eon – it’s importance now would be the leftover oxidized environment, not so much ongoing H escape.

    You had mentioned a CO2 – O2 balance; the larger point I should make is that while the organic C cycle affects the CO2 and O2 oppositely, the fluxes are largely balanced (organic C burial is a small term and not all geologic CO2 emissions come from inorganic C in the crust and mantle -some of that organic C returns to the atmosphere+ocean+biota eventually), and there are other processes that affect CO2 and O2 seperately (I think organic C burial is typically ~ 1/5 (?) of the total geologic sequestration; the rest being in the form of carbonate minerals; oxygen reacts with ferrous Fe to form ferric Fe, and there’s H escape to space – these things (so far as I know) might not be so important now but they were at one time).


    Okay, I’m just going to go ahead and post what I came up with – 4 parts, sorry for the length and poor organization in parts; don’t worry about my time being wasted, because it’s good excercise and whenever I try to explain something, it gives me insight into how I could explain it, and now they’ll be a bunch of paragraphs I might recycle in other discussions rather than reproducing from scratch…

    Comment by Patrick 027 — 23 Jul 2010 @ 10:16 PM

  428. How CO2 changes are related to radiative forcing (I’ve covered this before but it always goes long; I want to try to summarize it neatly).

    Part IV. First, reviewing how optical properties shape radiative processes:
    ———- ————
    Note optical thickness of any type, per unit distance = that type of cross section per unit volume. In this context we’ll generally only consider absorption and emission (except for occasional mentions of what other types of CSD can do), and so I will just refer to a cross section density, CSD.

    The below generally applies seperately for each frequency (and if necessary, polarization).

    In this discussion, we hold temperature constant. (This is how a radiative forcing for a change in optical properties is determined. Starting from an old equilbrium, a change in radiative forcing results in a radiative imbalance, which results in energy accumulation or depletion, which causes a temperature response that approahes equilibrium when the remaining imbalance approaches zero – thus the equilibrium climatic response, in the global-time average (for a time period long enough to characterize the climatic state, including externally imposed cycles (day, year) and internal variability), causes an opposite change in radiative fluxes (via Planck function) (plus convective fluxes, etc, where they occur) equal in magnitude to the sum of the (externally) imposed forcing plus any ‘forcings’ caused by non-Planck feedbacks (in particular, climate-dependent changes in optical properties, + etc.). )

    Consider any preexisting (baseline) CSD (of the absorbing/emitting type) that exists at some frequency, with some temperature variation over vertical distance. In that case, at a given level L, there is some upward and downward intensity, and net upward intensity at each angle from vertical, and they can be integrated over directions (weighted by the cosine of the angle from vertical) to find an upward, downward, and net upward flux per unit horizontal area.

    The intensity that comes from some direction, reaching a given location L, is emitted from a spatial distribution that can be called the emission weighting function (EWF). EWF is a density over distance along a line (in the absence of scattering, etc.) or lines (when partial specular reflection occurs), or a density over volume (when scattering contributes to the CSD), where the sum over all space = 1; it matches the distribution over space of the absorption of a unit amount of radiation incident at L from the opposite direction. The effective spatial extent of the bulk of an EWF is on the order of the average distance between photon emission and photon absorption.

    If at every point in space, EWF is multiplied by the Planck function for the temperature at that point, the product can be integrated over space (over the extent of the EWF), and the result is the intensity found for the given direction for the given location L. Thus the brightness temperature of the intensity is within the range of temperatures within the EWF; it would be the EWF-averaged temperature were it not for the nonlinearity of the Planck function; but it can be the EWF-averaged temperature for certain temperature distributions; if the temperature varies continously over space and if, over most of the EWF, it varies approximately linearly over space with a small percent change so that the Planck function over that range can be approximated as linearly over that range of temperatures, then the brightness temperature of the intensity can be approximated as being the temperature of the centroid of the EWF.

    Greater CSD will compress the EWF into a smaller region, towards the location L.

    (This is true for a mixture of absorption and scattering CSD contributions as well as for purely absorbing CSD; it is not true for purely scattering CSD, which tends to redistribute the EWF so that it surrounds L more evenly (partial reflection off a surface can also do the same thing), but the EWF must be found where absorption can occur. Pockets of dense CSD of either type may cast shadows in the disribution of EWF. Aside from the compression or redirection of EWF by CSD, EWF is locally proportional to the CSD from absorption.)

    Thus, as CSD increases to large values relative to the spatial scale of temperature variations, the brightness temperature of the intensity at L will approach the local temperature at L (then the effect approaches saturation). If the location L is embedded in a continuous temperature distribution with a continuous CSD distribution, the same will happen for intensities in opposite directions when CSD is large enough, so that the net intensity goes to zero; unless CSD is purely scattering near TOA, this won’t happen at TOA because of the lack of radiation from space (except for solar radiation, or for very tiny solid angles directed at specific objects, which can be ignored for our purposes here)

    ———— ————-
    For the rest of this section:
    We’ll assume CSD is horizontally homogeneous. Also we’ll assume each vertical level is approximately isothermal over horizontal distances. We’ll assume CSD is isotropic (same for all directions at any location).

    Trends as a function of CSD, Saturation: If the temperature varies monotonically over the distance from which most of the radiation reaching that level is emitted, then increasing the CSD will bring the upward and downward fluxes and intensities (at a given angle) toward the same value, reducing the net intensities and fluxes, until eventually they approach zero (or a nonzero saturation value at TOA). If the temperature fluctuates over shorter distances near that level, then the upward/downward/net intensities and fluxes may fluctuate – let’s say whenever they reach a maximum or minimum before reversing tendency, this is a temporary saturation

    (I’m coining a term here because it makes sense to introduce some term, but I’m unaware of a term specifically used for this concept; obviously if another term already exists for this concept, it should be used)

    …, but once the optical thickness becomes large over the spatial scale of the nearest maximum or minimum temperature on either side, the net fluxes and intensities will reach a final peak if they have not yet done so, and then decline toward zero (or another value at TOA) – an ultimate saturation (see note about temporary saturation).

    Trends as a function of CSD, different directions: There are larger optical thicknesses over the same vertical distance at larger angles from vertical for the same CSD (assuming isotropic (constant over direction) CSD, which we’ll do here); the intensities at these angles at one value of CSD will be the intensities at smaller angles from vertical at larger values of CSD; thus the intensities are larger angles from vertical lead and the intensities closer to vertical up or down will lag the trends as CSD is increased. If there is some CSD for which the vertical intensity (up, down, net) reaches a maximum or minimum, then the flux (up, down, net, respectively) per unit area, having contributions from intensities in all directions, each in proportion to the cosine of the angle from vertical, will reach a maximum or minimum at a somewhat smaller CSD, while intensities at sufficiently large angles will reach a maximum or minimum at even smaller CSD.

    12b. – notice the analogy to how sufficiently self-similar fine-scale texture in an absorption band can be treated.

    ——– ——–

    The exact way that intensities and fluxes vary as a function of CSD depends on the spatial temperature distribution as well as the Planck function, or in combination, it depends on the spatial distribution of the Planck function (for local temperature).

    However, it is possible to point out some generalities:

    Any smooth continuous function can be approximated as linear over a sufficiently short interval.

    Thus, for a sufficiently small change in CSD, double that change will result in approximately double the change in intensity at every angle, and thus the same applies to the change in flux per unit area; thus the radiative forcing is linearly proportional to changes in CSD for sufficiently small changes. (This also applies to absorption + scattering CSD, or pure scattering.)

    For a particular frequency and a given continuous smooth Planck function distribution, a large enough CSD compresses most of the EWF’s for intensities in all directions to a smaller enough region such that the Planck function can be approximated as following a linear spatial trend within the EWF’s. In that case, for a given direction, a doubling of CSD will halve the difference between the intensity at L and the Planck function for the temperature at L. This occurs for all directions and so occurs for the flux per unit area as well. Thus there will be an approach to an ultimate saturation asymptotic value, with the shape of the flux as a function of CSD being a hyperbola. When this is occuring for upward and downward fluxes, the asymptotic value for the net flux per unit area is zero (provided the Planck function is continuous through the level L, as opposed to what happens in effect at TOA), so that the net flux per unit area halves for each doubling in CSD.

    (This actually applies to a doubling of total CSD, and assumes any variations of CSD over vertical position will be held in constant proportionality (CSD changes by the same percent everywhere within most of the EWF’s), but when the additional amount of CSD, relative to a given baseline amount of CSD, is relatively large, the total can be approximated as the additional amount so that doubling the additional amount is approximately the same as doubling the total amount, and also, it will only be necessary to keep the vertical variations in the additional amount of CSD in constant proportionality for the same reason, while the baseline CSD could be distributed differently.)

    (I think this should also tend to apply if the CSD comes from a mix of absorption and scattering, provided that the proportionalities among different kinds of CSD are kept constant as CSD is doubled. However, if the CSD around L is purely scattering, the mathematics changes; as EWF’s are redistributed but not compressed toward L).

    The largest effects of a doubling of CSD, or a doubling of some additional CSD (given some baseline amount of CSD) will tend to occur somewhere between the ‘linear regime’ and the ‘hyperbolic regime’.


    At a given frequency, if the Planck function B varies over a CSD-weighted distance ztau (using an initial value of CSD so that temperature remains fixed at each ztau) (where ztau = 0 at the level L) in such a way that it can be approximated as a hyperbola

    B = a + b/|ztau|^c, with c = 1,

    then the linear proportionality of changes in intensity and flux over changes in CSD (provided that total CSD changes by the same percent everywhere) can hold for all CSD.

    (If c is larger than 1, then each additional unit increase in total CSD would result in a greater change in the intensities and flux than the previous unit increase of the same size. If c is less than 1, then each incremental change in CSD has a smaller effect at larger CSD.)

    If such a distribution occurs on both sides over similar CSD-weighted spatial scales, then the same type of behavior will be true for the net fluxes and intensities.

    However, in order for the temperature to remain finite (and if b is negative, in order for the temperature to not be negative), such a Planck function distribution cannot hold at the smallest ztau values (regions close to L), in which case, the linear proportionality must break down at sufficiently large CSD, when the region near L with the different Planck function distribution becomes a significant portion of the EWF’s.

    In the case where this happens on both sides of L, the Planck function could have a sharp peak or dip at L or else follow an S-shape going through L, with an approximate B = a + b/|ztau|^c on both sides of L except at small ztau (a and b could be different on each side of L, but for simplicity of behavior of net intensities and flux, keep the same c on each side of L.)

    (If there is a mix of scattering and absorption contributions to CSD, then, holding the proportionalities constant while increasing the total CSD can, **I think**, have the same effect for that type of a Planck function distribution, provided that the distribution can be approximated as such a hyperbola on both sides of the location, as described in the last paragraph of 15.3a (because scattering can cause the EWF’s to wrap around the location L)).

    ———- ———- ———— ———–

    Comment by Patrick 027 — 23 Jul 2010 @ 10:50 PM

  429. PART V.

    The CO2 band with a peak CSD near 15 microns (15 microns vacuum ~= 667 per cm (the inverse of wavelength is often used as a measure of frequency), though I’m not sure how close the peak is to that specific wavenumber. ):

    The shape of the CO2 absorption band, in terms of CSD per unit CO2 concentration, can be approximated as having a peak at some frequency (designated ν0) or wavelength (about 15 microns for CO2) with, on each side of that peak, a halving of that optical thickness for each amount BW1 or BW2 that one moves away from the center (toward lower or higher frequency, respectively)

    (This can be either in frequency or wavelength; since they are inversely proportional, the absorption band can’t have precisely this shape in both, but it may be approximated this way in whichever unit of the spectrum we decide to use (one might be better than another, though) – if we use wavelength, then we need to use the Planck function for intensity per unit wavelength; if we use frequency, then we need to use the Planck function for intensity per unit frequency. I’ll go by frequency here.)

    Linear approximation for small changes:

    Starting at any baseline amount of CSD, which may vary over space in some different way from what we will add to it:

    For a sufficiently small amount of CO2, adding double the amount would have approximately double the effect on radiant intensities and fluxes – at all frequencies, at all directions. This would be true for a sufficiently small amount of any greenhouse agent.


    Now consider a baseline amount of CSD from non-CO2 (which needn’t be mixed with the CSD of CO2 in the same ratio everywhere). Let’s assume it is constant over frequency in the vicinity of the CO2 band.

    Consider graphs of upward, downward, and net (spectral/monochromatic) fluxes F or intensities I, as a function of frequency, at some given vertical level. The area under the function is the total for all frequencies.

    Let’s measure the amounts in terms of brightness temperature BT, in which case the area is not proportional to the total intensity or flux over all frequencies, but there is an approximate proportionality over small regions of that area. What is convenient is that the baseline CDS will be a flat line on such a graph, and any particular distribution and amount of CDS will produce the same BT at any frequency.

    For consideration of net fluxes or intensities, the BT on the graph will be a difference between upward flux/intensity BT and downward flux/intensity BT.

    Some amount of CO2 creates a hill or valley in the BT spectrum. Let the difference from the baseline be BTc; BTc at ν0 is BTc0.

    The specific shape of the BTc hill or valley depends on the temperature distribution, but there are some generalities due to the convenient shape of the CO2 spectrum.

    Doubling the amount of CO2 will change the area under the BT graph in a way that can be divided into two components:

    Band-widening effect – because on either side of ν = ν0, the CDS halves over an interval BW1 or BW2, in doubling the CO2, the same value of CDS will now be found shifted outward from ν0 by a change in ν equal to BW1 or BW2, respectively. This is true for the entire set of CDS values that were initially found along the graph, and it is true for all directions and thus the band widening effect applies to all intensities and thus to the fluxes per unit area as well.

    The change in area from band-widening is equal to
    BW1 * BTc0i
    BW2 * BTc0i
    on each side, where BTc0i is the initial value of BTc0, the value before the CO2 was doubled.

    Band center contribution: change in BTc0: Where the change in BTc0 = ΔBTc0, there will be some additional change in the area that will be on the order of
    ~ 1/2 * (BW1+BW2) * ΔBTc0 .
    It could be smaller than that or larger, depending on the way that temperature varies with height; but it will not be larger than twice that, provided that a temporary saturation doesn’t happen and then significantly reverse in the span of a single doubling – in other words, provided that the process of any temporary saturation and following reversal (wherein BTc0 increases, halts, and then decreases, or in the opposite order) can be sufficiently resolved by the fractional change in CO2.

    If we need to, we can use a series of smaller changes than a doubling – for example, we could multiply the CO2 concentration by 2^b, with b between 1 and 0, in which case,

    the band widening effect would be
    b * BW1 * BTc0i and 1/5 * BW1 * BTc0i,
    where BTc0i is the value of BTc0 after the prior 2^(1/5) change and before the next.

    The band center contribution would be on the order of
    ~ b * 1/2 * (BW1+BW2) * ΔBTc0,
    where this time, ΔBTc0 is the change in BTc0 for a 2^(1/5) change. The smaller the change (the smaller b is), the better this formula will approximate the actual change.

    As long as the changes are small enough that we can stop between increases in CO2 whenever BTc0 reaches a maximum or minimum, this works.

    Notice that (for changes small enough to resolve any temporary saturations) as long as ΔBTc0 is not more than BTc0i …

    (a condition which tends to be satisfied for a doubling of CO2, unless the temperature variation is sufficiently compressed toward L, analogous the cases discussed in 15.3a with c larger than 1 except for the nonlinear relationship between the intensity or flux and the BT– and preexisting non-CO2 CDS will actually make it harder for ΔBTc0 to be larger relative to BTc0i),

    …the band-widening effect will be greater than this band center contribution.

    Note that, for sufficiently small changes that b * 1/2 * (BW1+BW2) * ΔBTc0 is a good approximation for the band center contribution, ΔBTc0 would have to be more than 2*BTc0i for the band center contribution to be more than the band widening effect.

    There is no need for special treatment of temporary saturations that might occur due to temperature fluctuations of sufficiently limited spatial extent. If the shape of the hill or valley in BTc has undulations, the band-widening involves positive and negative changes in area on the graph at different points, which are all neatly accounted for by using the BTc0 value at the peak frequency to multiply by the band widening intervals BW1 and BW2.


    With a sufficiently small amount of CO2 to start with, a doubling will approximately double BTc0 (and do the same at all other frequencies).

    With a sufficiently large amount of CO2, each doubling will approximately halve the difference between BTc0 and the ultimate saturation value BTcsat (which will be the same at all frequencies for the given vertical level, equal to the temperature at that level minus the baseline BT value, or if we are considering net fluxes and intensities, it will be zero except at TOA).

    But the band-widening effect is actually at its strongest (assuming any temporary saturations did not take BT outside the range of baseline BT and T at the level L) when ultimate saturation has been reached at the center of the band. When the band center approaches saturation, the forcing by farther changes in CO2 becomes approximately logarithmically proportional to CO2, because there is a certain amount of band-widening per doubling while the height/depth of the hill/valley in BT stays constant (for the simplifying conditions we’ve used).


    There is still the matter that the intensity or flux per unit area…

    (given by the Planck function or spectral blackbody flux/area, respectively, for T = BT, except when BT is the difference between upward and downward brightness temperatures, in which case the differences between Planck functions or blackbody fluxes must be used)

    … is not linearly proportional to BT. Also, the baseline BT value may not be constant over the width of the band.

    Changes in the intensity will be approximately linearly proportional to changes in BT if they are sufficiently small, and intensity for a given BT can be approximated as constant over sufficiently short intervals of the spectrum.

    If the difference between baseline intensities or fluxes and ultimate saturation intensities or fluxes varies approximately linearly over the vicinity of the CO2, with slopes in inverse proportion to BW1 and BW2 on either side of the peak frequency, then the effect can average out and the radiative forcing for the whole band will be proportional to the area changes on the BT graph.

    Otherwise, an approximation can be made by using, in place of BTc0i and ΔBTc0, three corresponding values of upward/downward/net fluxes per unit area, two values for frequencies ν1 and ν2 on either side of the band near the centroids of the areas on the graph for the band-widening effect (works unless there are temporary saturations leaving positive and negative areas, in which case more different values for different frequencies would work better) to multiply by b*BW1 and b*BW2, respectively, to find the band-widenning effect, and one value for the peak frequency ν0, to multiply by something on the order of b* ½ * (BW1+BW2) to find the band center contribution.

    But given the narrowness of BW1 and BW2, relative to the scale of the spectral intervals over which the Planck function changes substantially, and given the way water vapor and cloud CDS vary over the spectrum in the vicinity of CO2 (clouds being nearly independent of frequency over much of the LW spectrum as I understand it; water vapor gets stronger over the span of the CO2 band from higher to lower frequencies, but not with big jumps (glossing over some of the finer-scale texture)), the logarithmic approximation is still a good approximation for CO2 forcing (in which the radiative forcing changes by some amount per doubling of CO2 concentration) when the center of the band is saturated.

    **(Of course, the above logic was based on an approximation to the CO2 absorption spectrum – but the linear/logarithmic approximation still works and more exact answers can be found with more detailed calculations.

    ——– ——- ——– ——– ——-

    Comment by Patrick 027 — 23 Jul 2010 @ 10:54 PM

  430. PART VI.
    Considering the case where LW scattering and reflection is minor (as it is on Earth):

    The temperature generally decreases with height (positive lapse rate) in the troposphere (see 46,47), so increasing the optical thickness (via increasing CSD) of the troposphere tends to reduce the upward LW flux at the tropopause.

    Space is dark, and increasing the the optical thickness (increasing CSD) of the stratosphere tends to increase the downward LW flux at the tropopause. An exception can occur if the stratospheric temperature increases with height, especially if it does so immediately above the tropopause, in which case, if there is already sufficient optical thickness, the downward flux can be decreased by adding more (this effect is reduced if the temperature increase is concentrated toward the upper stratosphere). (On Earth, the stratosphere is transparent in the vicinity of the CO2 band, so that, given the shape of the CO2 band, increases in CO2 will increase the total LW downward flux at the tropopause for a wide variety of stratospheric temperature profiles.)

    (By similar logic, increasing atmospheric optical thickness tends to increase the downward flux at the surface or any other level, and reduce the upward flux at TOA or any other level, but with exceptions due to inversions (layers with increasing temperature with height).

    There can/will be local and regional, latitudinal, diurnal and seasonal, and internal variability-related deviations to the pattern (in temperature and in optical properties (LW and SW) from components (water vapor, clouds, snow, etc.) that vary with weather and climate), but the global average effect is at least somewhat constrained by the global average vertical distribution of solar heating, which requires the equilibrium net convective + LW fluxes, in the global average, to be sizable and upward at all levels from the surface to TOA, thus tending to limit the extent and magnitude of inversions.)

    Solar heating is distributed in a certain way; heat must flow from where solar heating occurs to space. With zero LW absorbing optical thickness within the atmosphere, the heat must get to surface (if not already there) before escaping to space. With some LW absorbing optical thickness, the atmosphere can emit radiation to space, so some heat will flow into the atmosphere from where solar heating occurs to get to space. With more LW opacity with some of it being from absorption, more heat must get into the atmosphere before escaping to space, and with more LW opacity, the more heat has to get higher into the atmosphere before escaping to space, with some of that radiant heat taking multiple steps (emission to absorption) to get from solar or convective heating to where it leaves for space (note this refers to the net LW fluxes; photons will generally go back and forth, with the larger flux from higher to lower temperatures). Temperature gradients are generally (see next paragraph) required to drive these flows of heat (continually through layers with convection/conduction/diffusion driven by differential heating, on the scale of distances from emission to absorption for radiant flows), so the temperature tends to decline from where solar heating occurs to where heat escapes to space.

    (In the global time average, diffusion of latent heat is in the same direction as sensible heat transport, but latent heat will tend to flow from higher to lower concentrations of water vapor (or equilibrium vapor pressure at the liquid/solid water surface), and regionally/locally, conditions can arise where the latent heat and sensible heat fluxes are oppositely directed.)

    (The CSD near a level has the greatest effect on the flux at that level and reduces the effect of CSD at farther distances in the same direction. Thus, the relative concentration of water vapor toward the surface enhances its effect on the surface LW flux and reduces its effect on fluxes at the tropopause and TOA.)


    The combination of decreasing upward flux and increasing downward flux add to a decreasing net upward flux (true for both SW and LW radiation).

    Radiative forcing RF at a level is equal to a decrease in net upward flux (either SW, LW, or both; the greenhouse effect refers to LW forcing) at that given level, due to a change in (optical) properties, while holding temperatures constant.

    The equilibrium response to an addition of RF at a level is an increase in net upward flux consisting of LW radiation (the Planck response, PR) plus a convective flux response CR; CR is approximately zero at and above the tropopause in the global time average.

    (Within a typical atmosphere, as on Earth, heat transport by conduction and molecular mass diffusion are relatively insignificant for bulk transport (there is some role in smaller-scale processes involving particles in the air), except when the net radiative flux and convective flux are very very small (not a condition generally found on Earth). An exception occurs in a very thin layer of air (~ 1 mm for Earthly conditions) next to the surface (and for a thin layer of water underneath the surface, and for a thicker layer of the land surface material). This is because the surface is a boundary to convection; heat flows across the surface require conduction and diffusion, and over short distances, viscosity is more effective at impeding convection. In the context of climate and weather, the term convection often is meant to include the conduction and diffusion at the surface; these fluxes heat a thin layer as convection cools it, thus the tendency is that approximately the same flux continues from the surface through a short distance of air, changing from conduction and diffusion into convection along the way. Sufficiently vigorous convection will tend to maintain an adiabatic (dry or moist, depending) lapse rate; near the surface there can be a superadiabatic lapse rate when the differential radiant heating is strong enough, so the temperature profile diverges from the convective lapse rate; however, the surface temperature still generally tends to follow changes in the troposphere – see 63. below, 47 above.)

    The climate responds to feedbacks from changes in optical properties (at any location above or below the level) in the same general way it responds to externally-imposed radiative forcings, by changing so as to restore balance at a new equilibrium; feedbacks can be described in terms of radiative ‘forcing’ per unit change in climate (such as in terms of surface temperature) . One can consider net PR+CR as a response to externally-imposed RF (external forcing) plus feedback ‘RF’, or one can consider PR + CR – feedback ‘RF’ as the response to the externally imposed RF; the later is perhaps more helpful in picturing the time evolution toward equilibrium (and illustrates why the time it takes for an imbalance,
    equal to: externally imposed RF – climate dependent terms (PR + CR – feedback ‘RF’),
    to decay is proportional to both heat capacity and climate sensitivity (defined per unit externally imposed RF).

    In some contexts, radiative forcing (RF) refers exclusively to externally imposed RF.

    With the approximation of geothermal and tidal (and fossil fuel combustion) heat supplies being zero (valid for at least the inner planets), the net flux at a given level is equal to the energy gain or loss rate for the whole climate system below that level. Thus, forcing at TOA is a forcing on the climate system as a whole, and forcing at the tropopause level is a forcing on the troposphere and surface (see next parenthetical paragraph) as a whole.

    (The climate system of course includes the ocean and some (relatively thin) layer of the crust / land surface that interacts with the climate system on relevant time scales – with respect to energy balances, that pertains to the depth to which heating changes penetrate beneath the surface on the time scales being considered. In equilibrium, all fluxes into the surface will be balanced by fluxes out of the surface (including momentum, etc, as well as energy), so whatever lies beneath the surface gives the surface an effective heat capacity and also (in the oceans) some ability for local/regional imbalances to be balanced globally, with all of that responding to forcings and PR+CR and other feedbacks at the surface. (And momentum beneath the surface respond to momentum fluxes at the surface, etc.))


    The variation of RF over a layer, increasing/decreasing with height, means that there is a forced convergence/divergence of radiative fluxes; the RF acting on a layer is equal to the difference between RF at the top and bottom of the layer and is positive/negative if the RF is greater/smaller at the top.

    The responses of individual layers (smaller than the whole climate system) are complicated by the fact that some of the PR + CR of one layer goes to other parts of the climate system (as opposed to space). The layers can feedback on each in that way, acting like additional RF (not that it should be called RF, though it might be considered an adjustment to the RF – see below) on any given layer from the portion of PR+CR from the other layers that is absorbed in that layer.

    In this way, the response of LW fluxes (PR) and convection (CR) tend to spread the temperature response vertically from where forcings occur – not generally eliminating the effect of RF distribution over height, although in the case with convection driven by differential radiative heating within a layer, CR can to a first approximation evenly distribute a temperature response over such a layer.

    (In the full 4-dimensional climate, responses can also tend spread horizontally by convection (advection) and temporally by heat capacity, though ‘fingerprints’ of horizontal and temporal variations in RF (externally imposed and feedback – snow and ice albedo, for example) can remain – this spreading is somewhat different as it relies in part on the circulation already present as well as circulation changes)

    57c, … – see addendum


    (Regarding PR, the fraction of PR from one layer that is absorbed by another depends on their optical properties (as well as the optical properties of other layers in between, and other layers if scattering/reflection were to occur), including variations over the spectrum and how the temperature change in the layer emitting the PR is distributed, which, along with optical properties, affects how much PR goes out of a layer from the top or bottom, and where it is found in the spectrum. In general, the portion of a layer’s PR emitted at the top needn’t be the same sign as that emitted out the bottom (also true of CR), and thus the equilibrium PR out in one direction can actually be greater than the RF on the layer – what is true is that the sum of equilibrium PR+CR out the top and out the bottom is determined by RF). .

    (The PR from a layer will tend to be more evenly distributed between going out the top and out the bottom if either the change in temperature is evenly distributed within the layer, or if the layer has significant but not large optical thickness over a portion of the spectrum (weighted by the Planck function(s) for the temperature(s) involved) considerably greater than any portion where the optical thickness is large.)

    (The effects of PR+CR from all layers at a given level is a net PR+CR at that level, so the net PR+CR at a level includes the PR+CR type feedbacks among layers.)

    The RF before such interlayer feedback can be called an instantaneous RF.

    How this works, Earth’s climate system as an example:

    For example, consider dividing the climate system into two layers: a surface+tropoposphere layer and a stratosphere…

    (on Earth, the mass of the mesosphere and thermosphere are so small that the effect of the entire upper atmosphere above the tropopause on fluxes at TOA and at the tropopause and below can generally be well-approximated by the effect of the stratosphere. (?)In some contexts the term ‘stratosphere’ may refer to everything between the tropopause and TOA(?).)

    The instantaneous RF difference between the tropopause and TOA is the instantaneous forcing on the stratosphere RFs1; if the TOA forcing is smaller than the tropopause forcing, then the forcing on the stratosphere is negative, which means that the stratosphere will cool (this doesn’t necessarily mean it will cool everywhere, but the equilibrium response to negative stratospheric RF requires a negative PR+CR response – being the stratosphere, at least in the global time average, CR can be approximated as zero).

    Thus, the stratosphere responds to a negative instantaneous RFs1 with an equal negative PRs1. Some fraction, ft1 of that PRs1 is absorbed below (or in this case where ft1*PRs1 is a reduction of flux downward, was absorbed below before it was removed); the fraction of PRs1 that goes to space is then (1-ft1). This adjusts the RF at the tropopause, so that the troposphere+surface must now respond to
    the tropopause RF with stratospheric adjustment (RFt2)
    equal to:
    instantaneous tropopause (RFt1) + ft1*RFs1.

    The differential heating imposed on the troposphere+surface layer is sufficient that LW emissions from within the layer are not able to establish pure radiative equilibrium without having the temperature profile become unstable to convection. Thus there is convection within the troposphere that (to a first approximation) tends to sustain some lapse rate profile within the layer – that itself can vary as a function of climate (and height, location, time), but given any relative temperature distribution within the layer (including horizontal and temporal variations and relationship to variable CSD contributors (water vapor, clouds)), the temperature of the whole layer must shift to balance radiative fluxes into and out of the layer (in the global time averae, and in the approximation of zero global time average convection above the troposphere), producing a PRt2 (in the global time average) equal to RFt2.


    Some fraction of PRt2, fs2, will be absorbed in the stratosphere. The stratospheric response to this will be PRs2, a fraction ft2 will be absorbed by the troposphere-surface layer. Etc. Approximating the fractions of additional PR of one layer absorbed by another as the same after this point, the total PR from the troposphere+surface will then be the sum of RFt2*(fs2*ft2)^n for n=0 to infinity, equal to

    RFt2/[1 - fs2*ft2],

    while the total PR from the stratosphere will then be equal to

    RFs1 + fs2* RFt2/[1 - fs2*ft2]

    (which will be negative if RFs1 is negative and the second term is small enough – even if it is not negative, this wouldn’t necessarily mean that there is no cooling in the stratosphere, but it would mean that such cooling would have to be limited to a portion of the stratosphere with warming in other parts).

    These values represent, in terms of fluxes, the warming of the surface+troposphere and stratosphere, respectively, in response to the instantaneous forcings combined with inter-layer flux changes.

    Notice that the instantaneous TOA forcing is RFt1 + RFs1, and the end result PR at TOA is the PR from the troposphere+surface that is not absorbed by the stratosphere (first term in next line), plus the PR from the stratosphere that is not absorbed by the troposphere+surface (second and third term):

    (1-fs2)* RFt2/[1 - fs2*ft2] + (1-ft2)* fs2* RFt2/[1- fs2*ft2] + (1-ft1)*RFs1
    RFt2/[1 - fs2*ft2] * [1-fs2 + (1-ft2)* fs2 ] + (1-ft1)*RFs1
    (RFt1+ft1*RFs1)/[1 - fs2*ft2] * [1 - fs2*ft2 ] + (1-ft1)*RFs1
    RFt1 + ft1*RFs1 + (1-ft1)*RFs1
    RFt1 + RFs1
    = instantaneous RF at TOA, as expected.

    Also, the net PR at the tropopause is the PR from the troposphere+surface (first term in first line below), minus the downward PR from the stratosphere (other two terms):

    RFt2/[1 - fs2*ft2] – ft2*(fs2* RFt2/[1-(fs2*ft2)]) – ft1*RFs1
    RFt2/[1 - fs2*ft2] * [1 – fs2*ft2] – ft1*RFs1
    RFt2 – ft1*RFs1
    = instantaneous RF at tropopause, as expected.

    Note that ft2 is not necessarily equal to ft1 (the pattern of stratospheric response to changes in fluxes from the troposphere alone could be different from the response to the instantaneous forcing, which involves changes in upward and downward fluxes at the troposphere as well as the flux at TOA) , and also, f1 could be negative (see 15,16 above), though f1 is positive for Earthly conditions.

    There can/will also be a shift in the tropopause (relative to mass – I am not referring to thermal expansion, though that happens; thermal contraction happens in layers that cool), which means that some layer of air is reclassified from stratospheric to tropospheric (for an upward shift). The solar heating and LW absorption and emission of that layer will also be transferred to the troposphere. One way to get around that is to consider the RF at the new tropopause level (for an upward shift) or old (for a downward shift); the shift itself would then be like a lapse rate feedback

    (A lapse rate feedback doesn’t directly change fluxes but it changes the relationships of temperatures between vertical levels, so that for a given temperature at one level, a lapse rate feedback changes temperature at another level and thus affects LW fluxes.)

    Comment by Patrick 027 — 23 Jul 2010 @ 10:56 PM

  431. 57c – .**
    (see 47,63, and second half of , and , note I used LSHO instead of LHSO to refer to the same concept)

    The troposphere is not everywhere at all times locally vertically coupled by convection; in particular, at night and at high latitudes, especially in winter, and where there is warm air advection aloft, some layer of air can become stable to localized convection.

    This locally reduces the convective vertical spreading of the temperature response to forcings.

    (57d) Air near the surface gains latent and sensible heat (convective fluxes) from the surface over some fraction of area and time; sometimes air near the surface loses heat to the surface. Deep localized convection where the troposphere is convectively heated by the surface and lower air occurs over some fraction of area and time (where the surface tends to be warm). Horizontal and temporal heat transport/storage brings that heat into regions stable to convection.

    (57e) Horizontally large scale circulation still connects all parts of the troposphere. The warm air above nocturnal or polar inversions, or even stable air masses with small positive lapse rates, are warmer than otherwise because of heat capacity and radiant+convective heating during daytime and/or because of heating occurring at other latitudes/regions that is transported to higher latitudes/regions. Some of that heat flows to the surface by LW radiation, reducing the net radiant cooling of the surface.

    (57f) When an inversion in the troposphere, in particular near the surface, is sufficiently strong, TOA and tropopause level RF from an increase in LW opacity (with a sufficient amount from absorbing CSD) may actually be negative (blocking radiation from below and replacing it with a larger amount emitted by warmer layers), but it will then be positive at some lower level such as at the surface (increased backradiation), and in such conditions, the temperature response to RF at lower levels (note that surface albedo changes have an RF at the surface) will not be locally vertically spread as much by convection (though there will be some horizontal spreading by advection).

    (57h) There is large horizontal-scale overturning (LHSO) that is driven by a combination of differential horizontal net radiant heating and differential vertical net radiant heating; this overturning may be slowed by smaller lapse rates but it can still occur and actually reduce the lapse rate below adiabatic (moist or dry) lapse rates. Slowing such overturning by reducing the horizontal differential heating could tend to allow heat to build up at lower levels until the lapse rate is more favorable to localized vertical overturning (LVO) (The two forms of overturning are not always completely distinct or separate; for example, the Hadley cell, Walker, and monsoon circulations, as well as extratropical storm track activity (developing from baroclinic instability (Rossby wave phenomena)) are driven and organized in part by horizontal differential heating, but in the ascending portions of these circulations, cumulus-type convection can occur).

    (57i) The LHSO and LVO described above are thermally-direct circulations, wherein differential heating creates available potential energy (APE) (in the form of internal energy and gravitational potential energy) that is then converted to kinetic energy by adiabatic motions (latent heating also can create APE, or the potential for latent heating can be included in APE, as in CAPE). Thus, some heat gets converted to kinetic energy, but that gets converted back to heat, either by viscosity or by thermally-indirect circulations that produce APE while pulling heat downward in the process (LHSO: Ferrel cell (driven by extratropical storm track activity), Planetary-scale overturning in the stratosphere and mesosphere (includes Brewer-Dobson circulation (I’m not sure if the whole thing is the Brewer-Dobson circulation or if only part of it is)), some motions in the ocean; LVO: wind driven mixing of the boundary layer and of the upper ocean (though mixing itself tends to destroy the APE that the kinetic energy would create by forcing heat downward)). APE produced from kinetic energy may take the form of temperature variations that are farther from radiative equilibrium, and thus may be destroyed by differential radiative heating.

    APE can also be due to compositional variations – a generally minor effect in the atmosphere (water vapor makes air less dense; clouds and dust increase the density) but important in the ocean (salinity variations) kinetic energy can be converted from and to this APE as well and this APE can also be destroyed by mixing; within the climate system, it is still ultimately derived from heat (such as via phase changes of water). (Within sufficiently fresh water near the freezing point, the sense of vertical heat flux is reversed between thermally direct and thermally indirect motion.)

    At least in the global time average, the non-radiative fluxes through and above the tropopause can be approximated as zero. Whatever kinetic energy goes into the ocean and is dissipated must come out at the surface as heat. Kinetic energy production is small compared to the fluxes of heat involved.

    (57j) For surface+tropospheric warming in general, there is (given a cold enough start) positive surface albedo feedback, that is concentrated at higher latitudes and in some seasons (though the temperature response to reduced summer sea ice cover tends to be realized more in winter when there is more heat that must be released before ice forms). The moist adiabatic lapse rate declines with increasing temperature. These shape the 4-dimensional pattern of temperature and other changes – the patterns of circulation, latent heating, and precipitation will shift, as can the cycles driven the imposed diurnal and seasonal cycles in incident solar radiation; the texture of internal variability can also shift. Water vapor also tends to reduce net LW cooling at the surface, which would force increased convection from the surface. There will be Regionally/locally and temporal variations; increased temperature and backradiation tend to reduce the diurnal temperature cycle on land, though regional variations in cloud feedbacks and water vapor could cause some regions to have the opposite effect; changes in surface moisture and humidity also changes the amount of convective cooling that can occur for the same temperature distribution. Regionally, changes in relative humidity near the surface would affect the height at which clouds form…

    (57k) When I state that the equilibrium climatic response must balance imposed RF (and feedbacks that occur), I am referring to a global time average RF and global time average response (in terms of radiative and convective fluxes), on a time scale sufficient to characterize the climatic state (including cycles driven by externally-forced cycles (diurnal, annual) and internal variability. Of course, in such a time average, each location’s fluxes (energy, and also momentum and mass) are balanced, with vertical imbalances (generally a net gain in heat at lower latitudes and net loss in higher latitudes, especially in winter) are balanced by horizontal fluxes.

    (57l) It would be possible for changes in externally imposed RF involving horizontal and temporal rearrangement with zero global time average to cause a climate change where there is no global average response (except to global average feedbacks).

    (57m) However, externally imposed forcings with a global average externally imposed RF may tend to cause similar climatic responses both in the global average and in regional/latitudinal and seasonal (modulation of response to external-forcing cycles that themselves are held constant) and internal variability patterns, provided they are not too idiosyncratic. The effects of some variations among different external forcings with the same global time average RF could be smaller than the effects of horizontal and temporal, and maybe even vertical (as in the water vapor feedback’s effect on convection) variations among feedbacks (surface albedo feedback, moist adiabatic lapse rate changes).

    For example, changes in solar brightness (TSI) will have an RF that is largest in the midday at low latitudes with clear skies and dark surfaces (oceans, forests), with a significant amount of RF applying directly to the surface, and some RF of the same sign acting on the stratosphere. In contrast, CO2 forcing by layers changes sign between the surface+troposphere and stratosphere (modulated by the effect of existing solar heating of the stratosphere), and it may have a different distribution of RF over the surface+troposphere layer (which would affect convection) and is more evenly distributed horizontally and temporally. However, there is some similarity: it (or at least the tropopause level forcing) is smallest at high latitudes and greatest in the low latitudes in the absence of at least high-level clouds. But both CO2 and solar-caused surface+tropospheric warming will cause at least some similar latitudinal and seasonal patterns of change within the troposphere+surface via the patterns of albedo feedback and lapse rate feedback.

    The efficacy of a forcing is the climate sensitivity (in terms of global average surface temperature change per unit global average RF) of that forcing relative to a standard type of forcing. Efficacies can vary because different patterns of RF can alter the climate response with some global average effect. Among forcings with RF being of different signs in the stratosphere for the same sign at the tropopause, greater similarity in climate sensitivity should be found using the tropopause-level forcing after stratospheric adjustment (see 61-67). For example, the troposphere+surface response is more directly comparable between CO2 and solar forcing for tropopause-level RF with stratospheric adjustment. (Although change in the stratosphere can interact mechanically with changes below.) Forcings which are not too idiosyncratic should tend to have similar efficacies.

    Comment by Patrick 027 — 23 Jul 2010 @ 10:59 PM

  432. Patrick (#395) and further to my #406.

    I’d forgotten a rather important aspect of the approximation I was describing. It is used for dust in the interstellar medium which has continuous opacity as a function of frequency but it is not really gray but rather has lower opacity at lower frequency, Thus a layer which is opaque in up welling emission may be transparent in down welling absorption so that the next layer out sees its own down welling emission canceled by emission from the opposite side in the approximation of complete transparency at the appropriate frequencies for the inner shells. T~1/sqrt(R) falls out of that. In radiative stellar interiors the temperature gradient is even less steep.

    Comment by Chris Dudley — 24 Jul 2010 @ 11:36 AM

  433. Additions/clarifications:

    Re my 426: Charney Sensitivity – It is convenient to use a climate sensitivity using predictable rapid feedbacks and holding other thingsfixed. Charney sensitivity is such a concept.

    1. part of the utility is that Charney sensitivity, using only relatively rapid feedbacks, describes the climate response to an externally imposed forcing change on a particular timescale related to the heat capacity of the system (if the feedbacks were sufficiniently rapid and the heat capacity independent of time scale (it’s not largely because of oceanic circulation), an imbalance would exponentially decay on the time scale of heat capacity * Charney equilibrium climate sensitivity. I’m not quite sure that all the feedbacks in Charney sensitivity are quite that rapid (?). Feedbacks that act on a longer time scale would leave a residual but more persistent imbalance, with a change in the long term sensitivity. Heat capacity that is ‘used’ over a longer period of time (penetration of temperature change through the depths of the ocean and up to regions of upwelling) would leave a more persistent residual imbalance, but the effect would only just stall the full change to equilibrium climate, not change the long term equilibrium sensitivity.)

    2. I’m not sure that every feedback not included in Charney sensitivity is less-predictable (with present knowledge or in principle – two different things) than every feedback included in Charney sensitivity.

    See also
    “Earth system sensitivity inferred from Pliocene modelling and data”; first paragraph:

    Since the 1979 National Research Council report1, the concept
    of climate sensitivity has been discussed extensively (see, for
    example, refs 24). It is usually defined as the increase in
    global mean temperature owing to a doubling of CO2 after the
    `fast’ short-term feedbacks, typically acting on timescales of years
    to decades, in the atmosphere and upper ocean have had time
    to equilibrate5. These fast feedbacks correspond to the physics
    available in climate models circa 1980 (see, for example, ref. 6), and
    include, for example, water vapour, snow albedo, sea-ice albedo
    and clouds. This sensitivity (described hereafter as the `Charney’
    sensitivity) remains a useful benchmark for comparing different
    climate models in idealized circumstances, and has been one of the
    central concepts used by the Intergovernmental Panel on Climate
    Change in their assessments of future climate change7,8.


    426, 431 (57m) – efficacy:

    Not to be taken as a blank check for deciding on a whim that some tiny forcing might be responsible for most of some change with a larger forcing contributing rather little. (There has to be a reason why.)

    431 (57i): thermally-indirect circulations that produce APE while pulling heat downward in the process (LHSO: Ferrel cell (driven by extratropical storm track activity)

    The flow of energy between different circulation patterns is dependent on fram of reference (Eulerian vs transformed Eulerian); The Ferrel Cell is the result of some average upward motion poleward of some average downward motion with return flows at lower and higher altitudes, superimposed on the average temperature distribution. Some (not all, I think) of that motion actually occurs where the temperature is perturbed from the average in a particular way so it may not be as thermally indirect as the averages would make it appear – at least that’s my understanding of it. The circulation can be divided among components and the temperature advection by the average motion acting on the average temperature distribution would be one component.

    Comment by Patrick 027 — 26 Jul 2010 @ 12:18 AM

  434. Re 430 add items

    The changes in the stratosphere and feedback via Planck response to the troposphere will tend to be more similar for the same tropopause-level forcing after the initial stratospheric adjustment.

    The stratosphere will, absent sustained non-radiative perturbations (see 57i), approach radiative equilibrium on a time scale under a year (Holton, “An Introduction to Dynamic Meteorology”, 1992, p. 410), so taking stratospheric adjustment to instantaneous stratospheric forcing first and then applying the adjusted tropopause-level forcing to the troposphere+surface and stratospheric feedbacks is similar to the actual order of events in reality.

    Comment by Patrick 027 — 26 Jul 2010 @ 4:43 PM

  435. Estimate of radiative relaxation time – for small perturbations, using a linearized approximation, wherein imbalances decay exponentially:

    Stratospheric temperature ~ 220 K, give or take (this is a rough estimate)

    Stratospheric mass ~ 1500 kg/m2 (I recall that being a global average; it’s more in the extratropics, it gets down to ~ 1000 kg/m2 in lower latitudes)
    Specific heat cp of air 1004 J/(kg*K)
    heat capacity of stratosphere ~ 3 (MJ/m2)/K

    From Hartmann, “Global Physical Climatology”, 1994, p.28, stratospheric emission leaving the stratosphere up and down: 11 % (5 % down, 6 % up) of 342 W/m2, or 37.62 W/m2 (ignoring sig.figs).

    Grey approximation: 4 % change in emission per 1 % change in temperature

    (CO2 band is near the peak wavelength, water vapor bands significant in stratosphere for wavelengths longer than ~ 25 microns and between ~ 5.5 and 7 microns, and ozone between ~ 9.5 and 10 microns, and CH4 and N2O between ~ 7.5 and 8 microns – Hartmann p.44 and 48, rough est. from graphs; signficant stratospheric transparency remains in several of those bands except near the peak of the CO2 band, but especially water vapor from 25 to 50 microns.)

    4 * 100 % / 220 K ~= 1.818 %/K,
    1.818 %/K * 37.62 W/m2 = 0.684 (W/m2)/K,
    3 (MJ/m2)/K / 0.684 (W/m2)/K ~= 50.8 days ~= 0.14 year (that’s an e-folding time scale). Thinner slices of the stratosphere will have less emissivity but also less heat capacity, with the later diminishing faster until the limit is reached where emissivity can be approximated as linearly proportional to thickness. Thus the relaxation time will tend to be larger for thinner layers – except for changes in % change in emission per K change in temperature. The thinnest layers would depend mainly on CO2 for emission (and absorption).

    I don’t think there are any significant optical property feedbacks in the stratosphere that don’t require tropospheric+surface changes – except ozone…

    Corresponding time for surface+tropospheric equilibration: given 3 K warming (including feedbacks) per ~ 3.7 W/m2 forcing (this includes the effects of feedbacks):
    10 years per heat capacity of ~ 130 m layer of ocean (~ heat capacity of 92 or 93 m of liquid water spread over the whole globe)

    Comment by Patrick 027 — 26 Jul 2010 @ 7:27 PM

  436. Re my 433 – wow, thanks for the clean up! But to clarify, the block quote should follow “; first paragraph:”, not the RC link.

    Comment by Patrick 027 — 27 Jul 2010 @ 4:56 PM

  437. Back to the matter of stratospheric cooling -

    if at some wavelengths, the stratosphere has already reached radiative equilibrium involving a positive lapse rate, then adding a greenhouse gas with absorption at some wavelengths could cause cooling if those wavelengths are long enough or warming if those wavelengths are short enough, relative to the spectrum of preexisting absorption, I think … more later if time allows.

    Comment by Patrick 027 — 28 Jul 2010 @ 12:17 AM

  438. … I need to think about that some more, but a key point is:

    IF there is some frequency at which absorption and emission occur within the atmosphere, then above the tropopause, in the approximation of zero convection above the tropopause, radiative equilibrium will require some pattern of vertical variation of the Planck function at that frequency.

    With the corresponding temperature variation, and using bandwidths (with constant optical thickness within each band) so that the band-integration of the Planck function is constant at some reference level RL among various possible bands, then, if at some reference frequency, the band-integrated Planck function ‘lapse rate’ crosses 1 W/(m2 sr) at RL and is linear (or in a coordinate system where it becomes linear), then all such band integrated ‘lapse rates’ cross the same value at the same RL, but at shorter wavelengths, the ‘lapse rate’ will be steeper at RL and concave, possibly approaching zero at finite height below TOA, while at longer wavelengths, the ‘lapse rate’ will be less steep at RL and convex.

    Comment by Patrick 027 — 28 Jul 2010 @ 9:00 PM

  439. … Well, some things I’ve come up with (assuming only absorption, no scattering, etc.):

    For simplicity, assume all solar heating at the surface (so that the lapse rate is (1-dimensional climate model, radiative convective equilibrium) positive or approaching zero but never negative) unless otherwise stated:

    1. A band with optical thickess per unit gas decaying exponentially away from a peak: Assuming the peak is saturated at some level within the atmopshere and there are no other absorbers in the same band of wavelengths above that level, increasing the concentration of that gas will result in at least an instantaneous cooling forcing of the layer above (not necessarily all of the layer, but the instantaneous forcing on the layer as a whole will be negative).

    (If there were some prexisting non-CO2 absorption between the level and TOA, than the additional forcing that could be accomplished by doubling CO2 would be reduced, and more so at the lower level than at TOA, thus reducing the cooling effect on the layer from doubling CO2.)

    Question – what about where the band isn’t saturated?

    2a. the saturated portion of the band cannot cause (in instantaneous forcing) cooling and may cause warming of the layer above as a whole (no forcing at the base of the layer, but a reduction in OLR at TOA, thus positive forcing of the layer).

    Therefore the part of the band that causes cooling must be outside the central saturated portion.

    2b. But is it in the far wings? Maybe not. Adding a small amount of absorption at some wavelengths, the each layer of the atmosphere will absorb a fraction of the radiation from the surface (or lower-atmospheric absorbers not found above some level) and emit twice that fraction of the blackbody value at each level. Thus, this would tend to cause cooling in the lower atmosphere and warming in the upper atmopshere, if the temperature decline from the surface (or lower-level emission sources) to TOA is great enough as determined by radiative-convective equilibrium established by preexisting absorption at other wavelengths.


    In general:

    3. Adding optical thickness in any band reduces OLR in that band initially.

    4. Adding a band with some small optical thickness, the atmosphere as a whole cools towards a skin temperature (except where the troposphere forms); the surface warms slightly, and OLR is enhanced at other frequencies. Adding more optical thickness to the same band reduces OLR in that band, cooling at least some portion of the upper atmosphere up to the TOA level, and increases in OLR outside that band results in some portion of that cooling remaining at full equilibrium (as expained by Andy Lacis). This cooling should be larger if the band is at longer wavelengths (see 438).

    5. Increasing the width of a band? Well, if we add atmospheric absorption to wavelengths just outside the first band, there could be initial cooling of lower levels and warming of upper levels as explained in 1b, which will be enhanced if this is added at shorter wavelengths (reduced if addeed at longer wavelengths) relative to where the initial atmopsheric absorption was (see 438). But what happens after that…

    6. What happens if we start from scratch and just add a wider band? The same temperature increase at lower levels and increased OLR outside the band will be accomplished at smaller optical thickness within the band, so the OLR reduction within the band should be smaller and thus there will be a warmer upper atmsopherer near TOA for the same surface temperature.

    7. However, this doesn’t directly address what happens if a band is simply widenned while keeping the optical thickness within the band constant over wavelength.

    Keeping within a sufficiently small range of wavelengths that the effects discussed in 438 can be set aside, What such band widenning would do, without a surface temperature increase, is simply increase the range of wavelengths at which the same temperature variation accomplishes the same spectral fluxes through the band, thus not changing OLR within the band – the warming that results from such band-widenning should thus tend to increase the OLR within the band. So band-widenning would warm the upper atmosphere (note this isn’t the same type of band-widenning as described for a CO2-like band).

    Comment by Patrick 027 — 30 Jul 2010 @ 11:12 PM

  440. RE my 439
    (If there were some prexisting non-CO2 absorption between the level and TOA, than the additional forcing that could be accomplished by doubling CO2 would be reduced, and more so at the lower level than at TOA, thus reducing the cooling effect on the layer from doubling CO2.)

    (Note that this is supposed to concern the effect of adding (more) CO2 to a preexisting equilibrium condition, so the effect of the non-CO2 absorber (with spectral overlap with CO2 within the layer) on temperature is not the issue. Also, this is assuming CO2 is nearly saturated at the peak of the band at the base of this top layer, however thick that layer is supposed to be (it needn’t just be the stratosphere or be the whole stratosphere).)

    Possible exceptions exist. The reduction in CO2-cooling (of a layer between TOA and some other level) assumes the increased downward emission at the base of the layer from the non-CO2 absorber within the layer is greater than the decreased OLR at TOA, which is the absorption of radiation from below the layer minus the emission from the layer reaching TOA (refering to the ‘baseline effects’ that would remain if the preexisting CO2 were removed).

    For a small amount of absorption, the emission upward and downward would be about the same, so if the upward (spectral) flux from below the layer were more than 2* the (average) blackbody value for the layer temperature(s), the OLR at TOA would be reduced more than the net upward flux at the base of the layer, decreasing CO2 TOA forcing more than CO2 forcing at the base, thus increasing the cooling of the base. Interestingly, in that situation, the non-CO2 absorption within that layer would itself be making the layer warmer than otherwise by absorbing more radiation than it emits. If the blackbody flux of the layer were greater than twice the flux from below, the non-CO2 absorption would tend to cool the layer and reduce the cooling that additional CO2 would accomplish.

    If there is some greater amount of non-CO2 absorption, then assuming a positive lapse rate, the decrease in the net upward flux at the base of the layer (from emission from the layer) would be greater than the increase in OLR from TOA from emission from the layer, thus shifting the cutoff between CO2-cooling/non-CO2 warming and the reverse towards a smaller flux from below relative to the average blackbody value for the layer.


    To summarize (with the simplifying assumptions of zero non-Planck feedbacks, a perfect blackbody surface for LW, and that all solar heating is at the surface, or at least beneath the tropopause – which is not to say that none of this applies to all other cases):

    Starting with zero atmospheric LW absorption, adding any small amount cools the whole atmopshere towards a skin temperature and warms the surface – tending to produce a troposphere (the forcing at any level will be positive, and thus will be positive at the tropopause; it will increase downward toward the surface if the atmosphere were not already as cold as the skin temperature, thus resulting in atmospheric cooling toward the skin temperature; cooling within the troposphere will be balanced by convective heating from the surface at equilibrium, with that surface+troposphere layer responding to tropopause-level forcing.)

    In the grey gas(and cloud) case, subsequent addition of absorbing substances reduces OLR initially, but OLR must return to the original value at full equillibrium, so there is a cooling at and near TOA that is temporary. Starting with small amounts of absorption, the transient cooling should extend through most of the atmosphere (except the troposphere) because each layer’s emission and absorption of radiation from the surface would increase equally if not for the increased absorption of radiation from the surface by lower layers, while the increased absorption of radiation from other layers would be a smaller effect due to the small emissivities – this would be true in the troposphere as well except the convective coupling with the surface would prevent it. With larger optical thicknesses, the transient cooling would be more restricted to near TOA.


    Refering to bands where optical thickness is constant over the interval of each band, if the atmospheric LW absorption is limited to some band (that doesn’t cover all LW radiation), than increases in OLR in response to surface warming will occur outside that band, so OLR will drop within the band – there will still be some portion of stratospheric or near-TOA cooling that will be transient, but some will remain at full equilibrium.

    Widening such a band while holding spectral optical thickness constant within the band will tend to warm the surface+troposphere and the stratosphere and TOA in general because the widenning would not have any forcing effect on layers of air (except for the Planck function’s temperature and wavelength dependence) but will have a positive forcing at the surface, and some of increased upward flux from the surface+tropospheric warming will be absorbed within the band and increase emissions farther up, or else directly increase OLR within the band.


    Competing bands

    With one band (along with the convective lapse rate below the tropopause) establishing the atmospheric temperature profile, adding some other band of absorption may result in some different pattern of temperature change.

    In full equilibrium, at any given level, there may be some net radiative heating at some frequencies compensated by some net radiative cooling at other frequencies, with convection balancing the full spectrum radiative cooling of the troposphere and heating of the surface.

    Radiative equilibrium at small LW optical thickness occurs when the whole atmosphere has a temperature such that the Planck function is about half of that of the surface (a skin temperature), whereas at larger LW optical thicknesses, the equilibrium profile has a signficant drop in the Planck function through the atmosphere, approaching half the OLR value at TOA and approaching the surface value towards the surface – of course, convection near the surface will bring a closer match between surface and surface-air temperatures.

    The ability of a band to shape the temperature profile of the whole atmosphere should tend to be maximum at intermediate optical thicknesses (for a given band width), because at small optical thicknesses, the amounts of emission and absorption within any layer will be small relative to what happens in other bands, while at large optical thicknesses, the net fluxes will tend to go to zero (except near TOA and, absent convection, the surface) and will be insensitive to changes in the temperature profile (except near TOA), thus allowing other bands greater control over the temperature profile (depending on wavelength – greater influence for bands with larger bandwidths at wavelengths closer to the peak wavelength – which will depend on temperature and thus vary with height.

    Thus, adding absorption to some new band will initially tend to warm the colder upper atmosphere and radiatively cool the lower atmosphere and warm the surface (The forcing at any level will be positive, so the surface+troposphere will warm; if some of the increased flux escaping in parts of the spectrum where the abover layers have sufficiently small optical thickness, some of the upper-level cooling will persist. This also depends on how stratospheric absorption and the change in upward flux from below are distributed over the spectrum.)

    As more optical thickness is added to a ‘new’ band, it will gain greater control over the temperature profile, but eventually, the equilibrium for that band will shift towards a cold enough upper atmosphere and warm enough lower atmosphere and surface, such that farther increases will cool the upper atmosphere or just that portion near TOA while warming the lower atmosphere and surface – until the optical thickness is so large (relative to other bands) that the band loses influence (except at TOA) and has little farther effect (except at TOA).

    The peak upper level warming that occurs as optical thickness in a ‘new’ band is increased should be larger for a wider band, as it can gain greater dominance over controlling the temperature profile at smaller optical thickness and will have a greater peak in it’s influence.


    The equilibrium profile for each band varies over wavelength at the same optical thickness, with larger temperature variations at longer wavelengths. Thus, among competing bands, there may be net radiative cooling in the upper atmosphere or near TOA at longer wavelengths and net heating and shorter wavelengths. The heating of the upper atmosphere and radiative cooling of the lower atmosphere by introducing some small amount of absorption in a ‘new’ band should be enhanced at shorter wavelengths relative to the bands that are/were controlling the profile, and reduced by the opposite arrangement. Less TOA cooling will occur if bands are placed where, in the upper atmosphere or near TOA, they absorb more of the increases in radiation from below from surface+tropospheric(+lower stratospheric) warming.

    Question: if the bands controlling the profile are at short enough wavelengths, could adding a ‘new’ absorption band at long-enough wavelengths result in initial cooling of the upper atmosphere? AT sufficiently short wavelengths, the temperature of the upper atmosphere and near TOA would have to be a sizable fraction of the surface temperature in order for the Planck function for higher levels to be a small fraction of the that at the surface (example: at 5 microns, relative to T = 250 K and the Planck function at 250 K, a 20 % reduction in temperature reduces the Planck function by about 94.4 %). At much longer wavelengths, given the surface temperature (which won’t change much by introducing a small amount of absorption), the skin temperature would only be a bit more than half of the surface temperature (example: for a surface temperature of 250 K and a small amount of atmospheric absorption at 200 microns, the skin temperature would be about 56 % of the surface temperature) , which could be less than the temperature even at TOA. So yes, if the profile is originally controlled at sufficiently short wavelengths, introducing some optical thickness at sufficiently long wavelengths would tend to cool the entire atmosphere (above the tropopause, of course). Of course, going to extremes of the spectrum reduces the strength of the effect of a band even if band width extends toward infinity.


    Some 1-dimensional radiative-convective equilibrium temperature profiles are shown in Hartmann (Global Physical Climatology) in Chapter 3. Interestingly, going from (among H2O, CO2, and O3) only H2O vapor to H2O+CO2, there is stratospheric warming.

    Perhaps this is because of the band-widenning (of the type refered to above) effect, with the initial introduction of some CO2 causing some upper level warming (enhanced by the shorter wavelengths of the CO2 band relative to stratospheric water vapor given the cold temperatures (lack of importance of the ~ 5 to 7 micron band (?)- The cold upper troposphere affects the flux coming up from the troposphere+surface, so the shorter wavelengths have less influence in both absorption and emission within the stratosphere). This doesn’t contradict the argument that, given present amounts, doubling CO2 should cause stratospheric cooling even without solar heating of the stratosphere (with the effect in the far wings being the opposite, and with the effect at the center of the band being restricted towards TOA).

    Adding O3 causes much more warming, especially of the upper stratosphere. Interestingly, there is a part of the lower stratosphere where (according to the graphs shown in Hartmann) O3 causes more heating by LW absorption than by SW absorption. Because the O3 mixing ratio rises going into the stratosphere, the ozone layer can absorb some radiation coming directly from signficantly lower and warmer layers and the surface. The upper part of the ozone layer contributes to net LW cooling there – of course, this includes the effect of solar heating on the stratospheric lapse rate.

    Comment by Patrick 027 — 1 Aug 2010 @ 12:01 AM

  441. Also, though, CO2 does absorb a little solar radiation, which would also contribute to the stratospheric warming (second to last paragraph of previous comment) and generally reduce the stratospheric cooling of farther increases in CO2.

    Comment by Patrick 027 — 1 Aug 2010 @ 12:07 AM

  442. Patrick 027,

    If you are willing to take a few CO2 questions off forum you can contact me at:

    I would appreciate your response. Thank you

    Comment by burt — 1 Aug 2010 @ 11:37 AM

  443. Re my 441 – competing bands – To clarify, the absorption of each band adds to a warming effect of the surface+troposphere; given those temperatures, there are different equilibrium profiles of the stratosphere (and different radiative heating and cooling rates in the troposphere, etc.) for different amounts of absorption at different wavelengths; the bands with absorption ‘pull’ on the temperature profile toward their equilibria; disequilibrium at individual bands is balanced over the whole spectrum (with zero net LW cooling, or net LW cooling that balances convective and solar heating).

    (Refering to zero direct solar heating of the air, or at least of the stratosphere:)

    The effect where, adding a ‘new’ absorption band and increasing the absorption, there may initially be warming of the colder layers, etc, followed by a stage of upper level or near-TOA cooling – this includes the warming from absorption from increased radiation from the surface+troposphere – which will be greater when more of the spectrum, especially near wavelengths where the emitted spectral flux change is greatest, has a greater amount of absorption. So if more of the spectrum has some amount of absorption, or if absorption is being added to a wider band, etc, it makes sense that the stage of warming of the coldest layers should be prolonged, with greater peak warming of those layers occuring before cooling would take over with farther increases in absorption. If absorption is being added to the most transparent bands, this will eventually bring the situation toward a grey-gas case, and thus cooling of upper levels shouldn’t tend to occur.

    (PS in the grey gas case, the whole atmosphere warms with increases in optical thickness, except at TOA; all the same temperatures are found but they are found at higher levels in the atmosphere closer to TOA.)


    This link may have been given somewhere above but it deserves emphasis and can illustrate the ‘competing bands’ effect.
    See Fig 3 – note that even for well-mixed gases, vertical optical thickness is not proportional to the vertical scale here – it would be proportional to pressure to a first approximation, though there are variations in line broadenning and line strength with height. O3 mixing ratio peaks in the upper atmosphere; water vapor mixing ratio declines from the surface to the tropopause, so that at wavelengths with sufficiently low water vapor optical thickness, LW cooling from water vapor is found at lower levels in the atmosphere.

    It must be kept in mind that solar heating of the air is included in this diagram; their is some net LW cooling that balances solar heating above the tropopause, which peaks around the relatively warm stratopause, in bands with sufficient optical thickness. Radiation from this warmer region can contribute to net heating (or reduce net cooling) above and below.

    There is cooling (from water vapor) at longer wavelengths even in the cooler layers, which can be explained at least in part by the wavelength dependence of the Planck function’s dependence on temperature.

    The most optically thick wavelengths in the upper atmosphere contribute to strong cooling even at 0.1 mb, while less optically thick bands contribute to warming or less cooling at that level.

    The warming effect near the tropopause level from CO2 can be explained by the relatively sharp change in the lapse rate. O3 in the lower stratosphere can of course absorb radiation coming from the lower warmer parts of the troposphere and surface.

    Comment by Patrick 027 — 2 Aug 2010 @ 11:10 PM

  444. Cont. from my 443 above -The warming effect near the tropopause level from CO2 can be explained by the relatively sharp change in the lapse rate.

    Two points on that:

    1. A sharp change in lapse rate will (absent sharp changes in optical thickness per unit distance, which occurs at TOA and at the surface even in wavelength bands dominated by well-mixed gases) tend to differ from radiative equilibrium – the inflection point may correspond to a maximum deviation from radiative equilibrium if the radiative equilibrium profile has some intermediate lapse rate in that vicinity.

    2. When optical thickness is large, the net flux will tend to be small, but the flux will vary with lapse rate (according to the corresponding Planck function ‘lapse rate’) and a sufficiently sharp change in that lapse rate could lead to some significant flux convergence or divergence at that level (net radiant heating or cooling).

    There is a small amount of warming in the short-wavelength wing of the CO2 band in the lower stratosphere. I would expect that absent solar heating of the ozone layer, the positive lapse rate of the stratosphere may displace this warming upward and the coolness of the upper stratosphere would make it extend upward and be stronger, and perhaps also appear on the other wing of the CO2 band. (If solar heating were absent, radiant cooling near 1 mb would be reduced in general.)

    If the CO2 optical thickness in the center of the band is so large, how can there be so much cooling at the 1 mb level in the center of the band, not just in between the peak and wings? Aside from variations in line strength and line broadenning with height, their is the important point that, relative to the mass path of CO2 (distances measured in terms of kg per unit area), temperature variations at those heights occur over small scales.

    Recap and some additional points:

    In the tugging on the temperature profile (by net radiant heating/cooling resulting from radiative disequilibrium at single wavelengths) by the absorption (and emission) by different bands, the larger-scale aspects of the temperature profile will tend to be shaped more by the bands with moderate amounts of absorption, while finer-scale variations will be more influenced by bands with larger optical thicknesses per unit distance (where there can be significant emission and absorption by a thinner layer). Near TOA, the bands with largest optical thickness per unit distance will have greatest control over the the temperature.

    Absent direct solar heating of air and absorption in other bands, when absorption in a band is increased, OLR (at TOA, as well as net upward fluxes at any level (including convection, etc, where that occurs)) would be kept constant following equilibrium if the response were limited to that band; the increased emission at other wavelengths in response to warming at lower levels removes some of upward flux from that band at higher levels (including OLR), thus reducing absorption and leading to cooling near TOA or over some uppermost layer upper in general, depending. But if the optical thickness in that band is sufficiently smaller than in another band (depending on wavelengths), adding some absorption to the optically-thinner band would tend to result in warming of the colder layers (as there would be less temperature variation over height in radiative equilbrium for that band, given the same surface(+tropospheric) temperatures.

    What happens when more optical thickness is added to the thickest bands? Then OLR tends to be displaced toward other bands, which don’t have as much influence on temperature near TOA.

    What happens to OLR when optical thickness is added to other bands? There would fraction of the increase in emission from warmed lower layers that would pass through all bands, and given all other bands have the same absorption as before, the portion of OLR originating from warmed layers would be displaced from the band with added optical thickness to all other bands, though it would cause smaller changes (depending on wavelength) to OLR in optically-thicker bands; nonetheless OLR would not be reduced in the optically thicker bands from that effect along, it would only be reduced in the band where optical thickness was added. However, some of the OLR and upward fluxes in upper levels in general come from other levels, especially in optically-thicker bands. If the addition of optical thickness to some band is able to sufficiently cool the uppermost layers sufficiently, OLR would be reduced in the optically thicker bands as well; if warming occurs in uppermost layers, OLR would increase in the optically thicker bands. OLR increases in the optically thinner bands would lead to atmospheric warming in general, but this has to be accompanied by OLR decreases somewhere, such as in optically thicker bands (and always in the band where optical thickness was added, assuming positive lapse rates everywhere as is the case in a 1-dimensional equilibrium model with zero solar heating above the tropopause, or at least not too much solar heating in some distributions), which will tend to cause cooling of upper levels.

    Comment by Patrick 027 — 3 Aug 2010 @ 10:18 PM

  445. Re 442 burt – it seems like the conversation here is just a trickle now, so would you like to post your questions here?

    Comment by Patrick 027 — 3 Aug 2010 @ 10:20 PM

  446. OLR increases in the optically thinner bands would lead to atmospheric warming in general – bands that are thin but not transparent.

    Comment by Patrick 027 — 3 Aug 2010 @ 10:22 PM

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