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A Saturated Gassy Argument

Filed under: — group @ 26 June 2007 - (Português)

A guest post by Spencer Weart, in collaboration with Raymond T. Pierrehumbert

The simple physics explanations for the greenhouse effect that you find on the internet are often quite wrong. These well-meaning errors can promote confusion about whether humanity is truly causing global warming by adding carbon dioxide to the atmosphere. Some people have been arguing that simple physics shows there is already so much CO2 in the air that its effect on infrared radiation is "saturated"— meaning that adding more gas can make scarcely any difference in how much radiation gets through the atmosphere, since all the radiation is already blocked. And besides, isn’t water vapor already blocking all the infrared rays that CO2 ever would?

The arguments do sound good, so good that in fact they helped to suppress research on the greenhouse effect for half a century. In 1900, shortly after Svante Arrhenius published his pathbreaking argument that our use of fossil fuels will eventually warm the planet, another scientist, Knut Ångström, asked an assistant, Herr J. Koch, to do a simple experiment. He sent infrared radiation through a tube filled with carbon dioxide, containing somewhat less gas in total then would be found in a column of air reaching to the top of the atmosphere. That’s not much, since the concentration in air is only a few hundred parts per million. Herr Koch did his experiments in a 30cm long tube, though 250cm would have been closer to the right length to use to represent the amount of CO2 in the atmosphere. Herr Koch reported that when he cut the amount of gas in the tube by one-third, the amount of radiation that got through scarcely changed. The American meteorological community was alerted to Ångström’s result in a commentary appearing in the June, 1901 issue of Monthly Weather Review, which used the result to caution "geologists" against adhering to Arrhenius’ wild ideas.

Still more persuasive to scientists of the day was the fact that water vapor, which is far more abundant in the air than carbon dioxide, also intercepts infrared radiation. In the infrared spectrum, the main bands where each gas blocked radiation overlapped one another. How could adding CO2 affect radiation in bands of the spectrum that H2O (not to mention CO2 itself) already made opaque? As these ideas spread, even scientists who had been enthusiastic about Arrhenius’s work decided it was in error. Work on the question stagnated. If there was ever an “establishment” view about the greenhouse effect, it was confidence that the CO2 emitted by humans could not affect anything so grand as the Earth’s climate.

Nobody was interested in thinking about the matter deeply enough to notice the flaw in the argument. The scientists were looking at warming from ground level, so to speak, asking about the radiation that reaches and leaves the surface of the Earth. Like Ångström, they tended to treat the atmosphere overhead as a unit, as if it were a single sheet of glass. (Thus the “greenhouse” analogy.) But this is not how global warming actually works.

What happens to infrared radiation emitted by the Earth’s surface? As it moves up layer by layer through the atmosphere, some is stopped in each layer. To be specific: a molecule of carbon dioxide, water vapor or some other greenhouse gas absorbs a bit of energy from the radiation. The molecule may radiate the energy back out again in a random direction. Or it may transfer the energy into velocity in collisions with other air molecules, so that the layer of air where it sits gets warmer. The layer of air radiates some of the energy it has absorbed back toward the ground, and some upwards to higher layers. As you go higher, the atmosphere gets thinner and colder. Eventually the energy reaches a layer so thin that radiation can escape into space.

What happens if we add more carbon dioxide? In the layers so high and thin that much of the heat radiation from lower down slips through, adding more greenhouse gas molecules means the layer will absorb more of the rays. So the place from which most of the heat energy finally leaves the Earth will shift to higher layers. Those are colder layers, so they do not radiate heat as well. The planet as a whole is now taking in more energy than it radiates (which is in fact our current situation). As the higher levels radiate some of the excess downwards, all the lower levels down to the surface warm up. The imbalance must continue until the high levels get hot enough to radiate as much energy back out as the planet is receiving.

Any saturation at lower levels would not change this, since it is the layers from which radiation does escape that determine the planet’s heat balance. The basic logic was neatly explained by John Tyndall 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."

Even a simple explanation can be hard to grasp in all its implications, and scientists only worked those out piecewise. First they had to understand that it was worth the trouble to think about carbon dioxide at all. Didn’t the fact that water vapor thoroughly blocks infrared radiation mean that any changes in CO2 are meaningless? Again, the scientists of the day got caught in the trap of thinking of the atmosphere as a single slab. Although they knew that the higher you went, the drier the air got, they only considered the total water vapor in the column.

The breakthroughs that finally set the field back on the right track came from research during the 1940s. Military officers lavishly funded research on the high layers of the air where their bombers operated, layers traversed by the infrared radiation they might use to detect enemies. Theoretical analysis of absorption leaped forward, with results confirmed by laboratory studies using techniques orders of magnitude better than Ångström could deploy. The resulting developments stimulated new and clearer thinking about atmospheric radiation.

Among other things, the new studies showed that in the frigid and rarified upper atmosphere where the crucial infrared absorption takes place, the nature of the absorption is different from what scientists had assumed from the old sea-level measurements. Take a single molecule of CO2 or H2O. It will absorb light only in a set of specific wavelengths, which show up as thin dark lines in a spectrum. In a gas at sea-level temperature and pressure, the countless molecules colliding with one another at different velocities each absorb at slightly different wavelengths, so the lines are broadened and overlap to a considerable extent. Even at sea level pressure, the absorption is concentrated into discrete spikes, but the gaps between the spikes are fairly narrow and the "valleys" between the spikes are not terribly deep. (see Part II) None of this was known a century ago. With the primitive infrared instruments available in the early 20th century, scientists saw the absorption smeared out into wide bands. And they had no theory to suggest anything different.

Measurements done for the US Air Force drew scientists’ attention to the details of the absorption, and especially at high altitudes. At low pressure the spikes become much more sharply defined, like a picket fence. There are gaps between the H2O lines where radiation can get through unless blocked by CO2 lines. Moreover, researchers had become acutely aware of how very dry the air gets at upper altitudes — indeed the stratosphere has scarcely any water vapor at all. By contrast, CO2 is well mixed all through the atmosphere, so as you look higher it becomes relatively more significant. The main points could have been understood already in the 1930s if scientists had looked at the greenhouse effect closely (in fact one physicist, E.O. Hulbert, did make a pretty good calculation, but the matter was of so little interest that nobody noticed.)

As we have seen, in the higher layers where radiation starts to slip through easily, adding some greenhouse gas must warm the Earth regardless of how the absorption works. The changes in the H2O and CO2 absorption lines with pressure and temperature only shift the layers where the main action takes place. You do need to take it all into account to make an exact calculation of the warming. In the 1950s, after good infrared data and digital computers became available, the physicist Gilbert Plass took time off from what seemed like more important research to work through lengthy calculations of the radiation balance, layer by layer in the atmosphere and point by point in the spectrum. He announced that adding CO2 really could cause a degree or so of global warming. Plass’s calculations were too primitive to account for many important effects. (Heat energy moves up not only by radiation but by convection, some radiation is blocked not by gas but by clouds, etc.) But for the few scientists who paid attention, it was now clear that the question was worth studying. Decades more would pass before scientists began to give the public a clear explanation of what was really going on in these calculations, drawing attention to the high, cold layers of the atmosphere. Even today, many popularizers try to explain the greenhouse effect as if the atmosphere were a single sheet of glass.

In sum, the way radiation is absorbed only matters if you want to calculate the exact degree of warming — adding carbon dioxide will make the greenhouse effect stronger regardless of saturation in the lower atmosphere. But in fact, the Earth’s atmosphere is not even close to being in a state of saturation. With the primitive techniques of his day, Ångström got a bad result, as explained in the Part II . Actually, it’s not clear that he would have appreciated the significance of his result even if he had gotten the correct answer for the way absorption varies with CO2 amount. From his writing, it’s a pretty good guess that he’d think a change of absorption of a percent or so upon doubling CO2 would be insignificant. In reality, that mere percent increase, when combined properly with the "thinning and cooling" argument, adds 4 Watts per square meter to the planets radiation balance for doubled CO2. That’s only about a percent of the solar energy absorbed by the Earth, but it’s a highly important percent to us! After all, a mere one percent change in the 280 Kelvin surface temperature of the Earth is 2.8 Kelvin (which is also 2.8 Celsius). And that’s without even taking into account the radiative forcing from all those amplifying feedbacks, like those due to water vapor and ice-albedo.

In any event, modern measurements show that there is not nearly enough CO2 in the atmosphere to block most of the infrared radiation in the bands of the spectrum where the gas absorbs. That’s even the case for water vapor in places where the air is very dry. (When night falls in a desert, the temperature can quickly drop from warm to freezing. Radiation from the surface escapes directly into space unless there are clouds to block it.)

So, if a skeptical friend hits you with the "saturation argument" against global warming, here’s all you need to say: (a) You’d still get an increase in greenhouse warming even if the atmosphere were saturated, because it’s the absorption in the thin upper atmosphere (which is unsaturated) that counts (b) It’s not even true that the atmosphere is actually saturated with respect to absorption by CO2, (c) Water vapor doesn’t overwhelm the effects of CO2 because there’s little water vapor in the high, cold regions from which infrared escapes, and at the low pressures there water vapor absorption is like a leaky sieve, which would let a lot more radiation through were it not for CO2, and (d) These issues were satisfactorily addressed by physicists 50 years ago, and the necessary physics is included in all climate models.

Then you can heave a sigh, and wonder how much different the world would be today if these arguments were understood in the 1920’s, as they could well have been if anybody had thought it important enough to think through.

For Further Reading

References and a more detailed history can be found here and here.

Some aspects of the "thinning and cooling" argument, and the importance of the radiating level are found in the post A Busy Week for Water Vapor, which also contains a discussion of water vapor radiative effects on the top-of-atmosphere vs. surface radiation budget. A general discussion of the relative roles of water vapor and CO2 is given in Gavin’s post on ths subject.

You can get a good feel for the way CO2 and water vapor affect the spectrum of radiation escaping the Earth by playing around with Dave Archer’s online radiation model here. It would help, of course, to read through the explanation of radiating levels in Archer’s book, Understanding the Forecast. A discussion of radiating levels for real and idealized cases, at a more advance level, can be found in the draft of Pierrehumbert’s ClimateBook; see Chapters 3 and 4.

The Monthly Weather Review article commenting on Ångström’s work is here, and Ångström’s original article is here.

281 Responses to “A Saturated Gassy Argument”

  1. 201

    For anyone interested, I have some summaries of basic climate concepts on my climatology page:

    http://members.aol.com/bpl1960/Climatology.html

    Recently I’ve been adding rebuttals of denialists. So far I’ve got John Dodds and Viscount Monckton. I’m thinking of doing Rush Limbaugh, although it would take a really long web page just to list all his deliberate lies about the subject (e.g. “one volcano puts more pollution in the air than all human emissions since the Industrial Revolution began”).

  2. 202
    Ignacio Mosqueira says:

    I’ve just begun to review the science of greenhouse warming. I’ve already gathered that GCM’s have a real issue with how they handle the effects of clouds for a number of reasons. But let me try to phrase a question in the spirit of the post of gas saturation and single layer models. The first part of my question seems straightforward to me. That is, given that lower levels of the atmosphere the main greenhouse gas is water vapor it would seem that most of the cooling takes place through dry portions of the troposphere. Then the question is what will warming do to the wet/dry tropospheric distribution, as supposed to overall increase in water vapor due to the increased temperature. Is this taken into account in GCM’s? If so, how? Somewhat in the same vein, I’ve heard Tapio Schneider argue that global warming would likely make tropical regions more humid and extratropical latitudes drier (in an average sense), while increasing the overall water vapor content.

  3. 203
    Lynn Vincentnathan says:

    RE #96 & 86, I couldn’t respond sooner, since I was off-line for a long time.

    I specificially chose the word “denialist” in my entry. I consider anthropogenic global warming “skeptics,” “contrarians,” and “denialists” to be somewhat different from each other. These are the meanings I give:

    SKEPTIC: a person who has some doubts based on some good evidence or theory, or bec of a lack of good evidence or theory. This kind of person does not have any agenda, except they seek scientific validity (which usually requires high confidence, such as 95%). I do not believe there are a whole lot of climate scientist skeptics left; most have come to believe AGW is real, though they might debate the details of it. Skeptics are needed to keep science honest.

    CONTRARIAN: a person who just likes to be contrary. It’s in our Western culture, our rugged individualist ethos, and in some people’s personality make-up. Perhaps Crichton could be considered one. Maybe society needs a few of these, as a gene pool could use diversity and some mutations, but they could also be counterproductive and harmful, as when a problem is real and dangerous, and they convince others to do nothing about it.

    DENIALIST: a person who has some agenda re AGW and its policy implications. They might be tied into fossil fuels, or they might fear economic harm or totalitarianism if we address AGW, or the loss of their world view. I think these people might actually believe or suspect AGW is real, but fear they or society has something great to lose if they do admit to it and to addressing it. These types will probably never change their mind, no matter how much evidence comes in.

    It’s the denialists and contrarians (not the skeptics) who might make contradictory arguments against AGW. And it is ususally people who are not in the spotlight, but people you meet at parties or on blogs, who have heard arguments against AGW from various sources, and are simply relaying them, without concern about inconsistences….sort of like a shotgun approach, with the idea that at least one bullet will knock out the feared thing…but for a discerning person, such an approach lacks credibility.

    So, PHE, you seem to be a skeptic and not a denalist.

  4. 204
  5. 205
    Roger William Chamberlin says:

    I just wanted to point at the slowly-emerging fact that getting the right answers at last requires a highly interdisciplinary approach that has not yet quite evolved… as a pertinent example of what I mean, consider that many phytoplankton, which hav been on the earth as a species for vastly more time than mankind, have evolved both methods of cloud control and the means to elevate themselves into the atmosphere where they live [AND SO ALTER GAS BALANCES] and have UV protection [AFFECTING both UV and heat] whilst dispersing themselves over vast distances throughout the atmosphere…

    These ‘clever’ little creatures kept the earth in favourable balance of temperature way different than what it would have been by Physics alone , something which made it possible for mankind to eventually appear and begin killing them off in enormous numbers by acidifying the sea with XS CO2 as we now see today …

    Phytoplankton manufacture and release Dimethyl Sulphide when under stress of iron deficiency , a gas which rises through the atmosphere to form potent sulphate aerosols and create clouds [thus provoking storms by means of the instability of the atmosphere and providing themselves with the means to spread to other areas of sea where there may be more iron]

    The implication then , due to the massive contribution of the sea to the atmosphere and the vast numbers of phytoplankton and their ability to populate any ammount of ocean in but three days given travces of iron, is that one cannot ignore the biological DYNAMICS … one needs to consider the input of iron to the ocean surface in CO2 modelling ! … the main sources are from dust blown from the land [wind and drought dependent] , overflow of water from acidic soils and peat bogs [dependent on heavy rainfall to wash out iron chelates of humic acids and fulmic acid] , from heavy storms stirring deep waters to the surface, and from changes in ocean currents causing upturn at suitable coastlines and ocean ridges/mountains/volcanoes …

    The models will thus fail in necessary extreme accuracy [since there are many instabilities through positive feedback effects] without taking into account all disciplines in science , notably the massive [and pre-historical] biological offsetting effects and indeed the disastrous positive feedback in CO2 release AND less absorption by the oceans as we continue our already insane killing of the base of the food webs in the oceans with simply too much CO2 …

    It seems then that we sit o a much-unrecognised knife-edge between a world that could be a paradise and one which more resmbles the common misunderstanding about ‘hell’

    Ironically, work in the last 15 years has revealed that the oceans are largely dead simply because of lack of only trace elements [typically iron] required in the tiniest ammounts only to turn dead oceans into thriving eco-systems which could absorb a vast ammount of CO2 back into biomass [where it came from!] rather rapidly [and so perhaps save our skins from our short-sighted ‘convenience’ living which will apparently shortly prove most inconvenient in extreme]…

    The irony is that we are already killing off perhaps the only, and certainly the cheapest and safest, method of restoring the balance which we have upset by our extremely short-sighted methods of industrialisation , faulty methods of assessing value in ‘economics’, and consequently rather inadequate governance and leadership …

    The sea could save us only if we stop almost immediately from killing it off and introduce international co-operation in place of competition [since the sea is international and ‘farming’ the sea would have to be controlled in interests of all, else the power of this new potential blessing , food for all mankind from ‘waste’ CO2 that would otherwise possibly destroy us , could end up making things far worse for some, many or all…

    I think then that the CO2 crisis , when finally unravelled from the short-sighted vested interests of the few who think they like wars, hoardes of money, control of others , and think complacently that they have the means to face any crisis, has enormous potential to re-unite mankind , just as man was united no doubt by the crisis that limited our genetics so many millenia ago … not without first a period of extreme stress caused by inertia to acting wisely – but the prize might be mankind as one species , coming to realise we have but one home , and worthy of respect from us, not the abuse we deal out today in our ignorance and complacency…

    I thus applaud loudly the work of this site, it is awesome in the way it translates complex interactions into words that folks who are not specialists can come to grips with , a massive resource that surely must break down interdisciplinary barriers holding up the uniting of the people into demanding an end to the wars, inequalities, injustices, and sheer inadequate caring of nations with ‘power’ … aprocess which must start with establishing the TRUTH first and then disseminating it worldwide to unite men in facing the massive problem we all have , but which is struggling to be acknowledged amongst a mass of false propaganda and much misunderstanding and misinterpretation…

    Awesome my friends, so much ‘uphill’ work in perhaps the greatest challenge to mankind yet …. becoming one species again and saving our planet [from our division] by means of coming nearer to the truth :) !

  6. 206
    Dean says:

    Re #24:

    The 2.8C temperature increase due to global warming seems to be an exaggeration. Compare the average temperature of a non-greenhouse gas body (the moon) to a greenhouse gas body (the earth). The average temperature of the moon is 238K The average temperature of the earth is 288K. The difference is 50K. Therefore, the 1% should be measured off of 50K instead of 285K. That results in a 0.5K increase in temperature, not 2.8K.

    Also, the stratospheric cooling effect has me confused. If the stratosphere is cooling, then that causes the troposphere to warm, right? well, the troposphere greenhouse gas composition is dominated by water vapor, not CO2. So why would such a small increase in overall greenhouse gases make a big difference?

  7. 207
    David B. Benson says:

    Re #206: Dean — There is a feedback effect. This is described, in fairly simple terms, in earlier threads. I also encourage looking at the AIP history site, linked on the sidebar, and some of the highlight threads, also linked on the sidebar, here on RealClimate.

  8. 208
    ray ladbury says:

    Dean, no, the 1% is of the total incident sunlight–not the radiation that causes the greenhouse effect.

  9. 209

    [[The 2.8C temperature increase due to global warming seems to be an exaggeration. Compare the average temperature of a non-greenhouse gas body (the moon) to a greenhouse gas body (the earth). The average temperature of the moon is 238K The average temperature of the earth is 288K. The difference is 50K. Therefore, the 1% should be measured off of 50K instead of 285K. That results in a 0.5K increase in temperature, not 2.8K.]]

    What in the world do you mean here? I’ve read this paragraph several times now and I still cannot figure out what you’re saying. (Your average temperature figure for the Moon is way too low, by the way.)

  10. 210

    Okay, Dave, I think I see where you went wrong. You’re assuming the Earth’s temperature would be 238 K without an atmosphere, and that the 50 K difference is due directly to carbon dioxide and is linear, so that a 1% increase in CO2 would yield a 0.5 K increase in temperature. Do I have that right?

    The Earth’s equilibrium temperature is actually 255 K, not 238 K, and the net greenhouse effect amounts to 33 K. But the relation between CO2 and the greenhouse increment is not linear. All kinds of factors combine to set the temperature of the Earth. For instance, the greenhouse effect from Earth’s atmosphere would actually be about 77 K, raising the surface temperature to 332 K, were it not for the fact that evaporation of seawater, convection and conduction cool the surface considerably.

    With all other factors being equal, a doubling of CO2 causes a surface temperature increase on Earth of about 1.2 K (Houghton 2004). Factoring in the known climate-system positive feedbacks, especially the increase in water vapor with ambient temperature, a doubling in practice will be closer to 2.8 K.

  11. 211
    Hank Roberts says:

    Measuring the temperature of the moon is done from the top of Mauna Kea, by infrared astronomers, who have to account for the immediate and variable water vapor along their line of sight as well as much else, so asking the temperature of the moon has some direct relation to the topic. I know I’m stretching (grin).

    This describes that effort and makes clear how complicated the work is: http://hera.ph1.uni-koeln.de/~wiedner/publications/lunareclipse.pdf
    “… The magnitude of the temperature drop observed during the eclipse at 265 GHz (central frequency of the band covered) was about â�¼70 K, in very good agreement with previous millimeter-wave measurements of other lunar eclipses. We detected, in addition, a clear frequency trend in the temperature drop that has been compared to a thermal and microwave emission model of the lunar regolith, with the result of a good match of the relative flux drop at different frequencies between model and measurements.”

    For simple statements, there’s:

    http://www.iop.org/EJ/article/0031-9120/26/3/008/pe910308.pdf
    Physics in the global greenhouse –S Ross – Physics Education, 1991 – iop.org
    “… solar energy) that the Moonâ��s â��effcctive radiating temperatureâ�� should be roughly -18°C. This is indeed the average temperature of the Moon ….”

    and a more recent number:
    Five times more water on Moon? – P BALL – Virus, 2003 – nature.com
    “… the Moon. Dark arts. The average temperature of the Moon’s surface is -23ºC. It gets much warmer in direct sunlight. But in permanently … ” [No working link for that, it’s just a Google Scholar hit]

  12. 212

    The Solar constant for the moon is the same as for the Earth, 1367.6 W m-2. (This figure is overprecise and probably a bit high, but it’s canonical, so I like to use it.) The moon’s bolometric Bond albedo, according to Bonnie Buratti’s team, is about 0.11. So the flux absorbed by the moon is (1367.6 / 4) x (1 – 0.11) or 304.3 W m-2. This corresponds to an equilibrium temperature of 270.7 degrees K. But the moon rotates very slowly (27.3 days sidereal), so in effect it only radiates from the dayside, 2 π R2 instead of 4 π R2. This would make its dayside temperature, at least, higher by a factor of 20.25, or 321.8 degrees K. I believe Langley in 1890 reported the measured temperature of the Moon as 318 degrees K. Does anyone have a later figure from the primary literature?

  13. 213
    Dave Embody says:

    Very good presentation and excellent follow-up q&a!

    One thing I would like to see better treated is the concept of convective heat transport. The concept that molecules of water absorb heat and become water vapor, the water vapor rises and cools through adiabatic lapse, releases the absorbed energy, condenses and falls as liquid water is well known by most people. But the parallel process which works with other greenhouse gasses is less understood.

    CO2 gas is opaque to various spectra of long wave infra red and absorbs energy at those frequencies. The absorbed heat makes the gas expand and rise. As the gas rises the pressure decreases with altitude and the gas expands and cools, without the loss of absorbed energy, through dry adiabatic lapse. The infrared frequency at which the gas radiates becomes gradually longer as it rises, expands, and cools. At some point the wavelength will hit a frequency where the gas is relatively transparent and the gas loses the absorbed energy through infrared radiation.

    Between the point where the infrared energy was absorbed near the surface and where it is released at altitude we effectively have convective heat transport. I would be interested in knowing how the rate of convective heat transport is affected by the saturation level of the various greenhouse gasses. I also wonder if we could see CO2, and other greenhouse gasses visibly in the atmosphere, how well defined the bases and tops of the transport cells would be.

  14. 214
    Hank Roberts says:

    >Moon
    I found these here: http://www.solarviews.com/eng/moon.htm
    Mean surface temperature (day) 107°C
    Mean surface temperature (night) -153°C
    Maximum surface temperature 123°C
    Minimum surface temperature -233°C

    Handy conversion tool: http://www.csgnetwork.com/temp2conv.html

    And this: http://www.space.com/scienceastronomy/051207_moon_storms.html: “a few hours after every lunar sunrise, the experiment’s temperature rocketed so high–near that of boiling water–that ‘LEAM had to be turned off because it was overheating.’ — apparently duststorms follow the sunrise on the Moon.

    And, very topical, this:
    “NASA acquired 41 monthsâ��worth of records of the Moons surface temperature…..On the near side of the
    airless moon, where Apollo 15 landed, surface temperature is controlled by solar radiation
    during daytime and energy radiated from Earth at night. Huang showed that due to an amplifying effect, even
    weak radiation from Earth produces measurable temperature changes in the regolith. Further, his revisit of the
    data revealed distinctly different characteristics in daytime and nighttime lunar surface temperature variations.
    This allowed him to uncover a lunar night�time warming trend from mid�1972 to late 1975, which was consistent
    with a global dimming of Earth that occurred over the same period and was due to a general decrease of sunlight
    over land surfaces. (Widespread ground�based radiation records from that period show that solar radiation
    reaching Earths surface during that period decreased significantly, for reasons that are not completely
    understood.)
    Huang’s study demonstrated that signals from the energy budget of Earths climate system are detectable on the
    Moon and can be useful in monitoring and predicting climate change…..
    http://www.astrobio.net/cgi-bin/h2ps.cgi?sid=2354&ext=.ps

  15. 215
    llewelly says:

    Dave Embody:

    I also wonder if we could see CO2, and other greenhouse gasses visibly in the atmosphere,

    CO2 concentrations at the mid-tropospheric level (roughly 8km) )at least can be detected by AIRS (via Eli Rabett, which also has many other interesting CO2 links.)

  16. 216
    AEBanner says:

    With reference to the piece which started this thread, fifth paragraph, please can somebody tell me the altitude corresponding to “a layer so thin that radiation can escape into space”.

  17. 217
    Hank Roberts says:

    The original post, including for clarity the full sentence, said:
    “Eventually the energy reaches a layer so thin that radiation can escape into space.”

    That isn’t talking about “all energy” — it’s talking about any given particular bundle, and its chances of escaping.

    They’re following any particular example of a chunk of energy, bouncing around after coming to Earth, in various forms.

    Any chunkj of energy can only leave the planet as radiation (an infrared photon) if it doesn’t first run into another molecule.

    So they’re not specifying a number for altitude — not a single fixed “layer” or a specific height or thinness that applies to each and every photon, not a glass ceiling kind of thing.

    The “altitude corresponding” would be, approximately, “way way up there where the air is very thin” on average.

    Of course if the emitted photon happened to be pointed downward, it would nevertheless hit another molecule — so even at the very “top of the atmosphere” half the photons are not going to escape into space.

    Your altitude will vary for each individual occurrence, of course — but the odds are better the thinner the air is.

    There’ s no Maxwell’s Demon at 90,000 Feet or any other specific altitude.

  18. 218
    AEBanner says:

    Thank you, Hank Roberts, for your poetic description of the altitude discussed in paragraph 5 of “A Saturated Gassy Argument”, which started this thread. However, I was asking for some idea of the altitude, not a precise figure.

    In his book “Global Warming – The Complete Briefing”, page19, Fig 2.3, Houghton gives a value of about 6Km for the average altitude at which outgoing radiation occurs. So what value should I take for “way, way up there where the atmosphere is very thin”? 8 Km, 10 Km, 20 Km, or perhaps even 100 Km?

    This could be rather important, because there is a negative effect which depends upon altitude. The greater the altitude, the smaller is the proportion of photons returned to the Earth’s surface, because of the solid angle subtended at any given emitting point by the circle on the Earth’s horizon, as seen from that altitude.

    The following table shows the reduction in the returned proportion for the given altitudes compared with the proportion for zero altitude.

    Altitude___Proportion of total___Reduction in
    Km _______returning to Earth ___proportion

    0___________0.50______________0%
    6___________0.48______________4%
    10__________0.47______________6%
    20__________0.46______________8%
    50__________0.44_____________12%
    100_________0.41_____________18%

    It follows that if the altitude “way, way up there” in order to achieve the required “thinness” is significantly higher than Houghton’s 6 Km, then the reduction in proportion may well exceed the postulated increase in energy returned from doubling carbon dioxide. This would mean that the Saturated Gassy Argument fails or, at least, is significantly diminished.

    AEB

  19. 219
    Hank Roberts says:

    You’re making the mistake of assuming no atmosphere, calculating angles subtended by the solid planet.
    The number you want is how far a photon on average will go before it interacts with a molecule.

  20. 220
    Timothy Chase says:

    AEBanner (#217) wrote:

    In his book “Global Warming – The Complete Briefing”, page19, Fig 2.3, Houghton gives a value of about 6Km for the average altitude at which outgoing radiation occurs. So what value should I take for “way, way up there where the atmosphere is very thin”? 8 Km, 10 Km, 20 Km, or perhaps even 100 Km?

    It follows that if the altitude “way, way up there” in order to achieve the required “thinness” is significantly higher than Houghton’s 6 Km, then the reduction in proportion may well exceed the postulated increase in energy returned from doubling carbon dioxide. This would mean that the Saturated Gassy Argument fails or, at least, is significantly diminished.

    The troposphere extends from 8 km to 14.5 km. As I understand it, water vapor dominates from the ground only to about 4 km, if I am not mistaken. Carbon dioxide (and ozone) dominate after that. But the stratosphere itself constitutes approximately 25% of the earth’s atmosphere. So I wouldn’t assume that the greenhouse effect ends at the tropopause, or that the atmosphere becomes so thin at this point that it no longer matters – although I would certainly defer to someone who I regarded as more knowledgable than myself.

    From what I understand, Local Thermodynamic Equilibrium is a fair approximation for most of the relevant wavelengths except when one gets to the outer reaches of the stratosphere – and I would regard this as relevant. And it is worth keeping in mind the fact that as more carbon dioxide is added to the atmosphere, this tends to raise the both the tropopause and the effective radiating layer, the latter of which is that which emits radiation at the temperature which the earth would radiate in the absence of an atmosphere.

    Additionally, as I see things, it makes little sense to whatsoever to argue that there is an exact boundary at which carbon dioxide has no effect because it is “completely saturated” (it never is) to suddenly being unable to absorb any radiation at all. In fact, there is no point that it is completely saturated – although its effects are quite insignificant at ground level given the moisture in the air. There is the diminishing spreading due to pressure and temperature as one ascends, but assuming the atmosphere becomes dry before this, carbon dioxide can and will play a role that grows with higher partial pressures. Additionally, it is my understanding that carbon dioxide is directly responsible for roughly a third of the marginal greenhouse effect and that this is a conclusion which has a fair amount of empirical support.

    In any case, I believe that Houghton was refering not to the point at which outgoing radiation last encounters molecules but rather what known as the effective radiating layer. This is the point at which the net effect of carbon dioxide is to cool the atmosphere at that altitude, radiating thermal more thermal energy in the direction of space than it radiates towards the ground. However, much of the radiation which it radiates will still be in the direction of the ground.

    Additionally, as more carbon dioxide is added to the atmosphere, this will tend to raise the effective radiating altitude, and holding the lapse rate constant (not entirely accurate, but a fair approximation – see Tamino’s post “Lapse Rate” at Open Mind), this will result in more greenhouse gas prior to the effective radiating layer, increasing the greenhouse effect experienced at the surface.

    I hope this helps…

  21. 221
    AEBanner says:

    Thank you, Hank Roberts, for your contribution #219, but I find it difficult to see your point. Atmosphere or not, there will only be extra surface warming from additional CO2 if the photons return to the surface in line with the standard explanation of the GH effect, and to do this they must be confined to the solid angle governed by the altitude as in the table in my #218. Hence, there will be a reduction, or even a cancellation, of the extra warming from additional CO2 at “high” altitudes.

    The amount of this negative effect depends on the altitude, and hence my interest in it. Surely, some expert in these matters must know, at least, a rough figure for this. Please help.

  22. 222
    Timothy Chase says:

    AEBanner (#221) wrote:

    Thank you, Hank Roberts, for your contribution #219, but I find it difficult to see your point. Atmosphere or not, there will only be extra surface warming from additional CO2 if the photons return to the surface in line with the standard explanation of the GH effect, and to do this they must be confined to the solid angle governed by the altitude as in the table in my #218. Hence, there will be a reduction, or even a cancellation, of the extra warming from additional CO2 at “high” altitudes.

    At the very least, I believe you are making a number of mistakes. One of the lesser mistakes would appear to be the belief that a photon gets absorbed only once.

    And as I pointed out in the second to last paragraph of #220, I believe you are misinterpretting Houghton, specifically by assuming that when he speaks of the altitude at which thermal energy escapes, he means that photons never get absorbed after that. As I stated, I believe that he is refering to the effective radiating altitude – which is the height at which the greenhouse effect begins to radiate more energy towards space than it does towards the ground. This is the height at which the atmosphere has the effective radiating temperature – which is what the temperature of the earth would be in the absence of an atmosphere (holding the albedo the constant).

    However, much of the radiation which is re-emitted above this altitude will still be re-emitted towards the ground and be absorbed by the ground, increasing the greenhouse effect as it is experience at ground level. Likewise, raising the level of carbon dioxide will tend to raise the altitude of the effective radiating layer. Holding the lapse rate constant, this will increase the height of the air column prior to the effective radiating layer resulting in an increase in the greenhouse effect and consequent warming at ground level.

    I could say more, but I believe I already have.

  23. 223
    Ron Taylor says:

    Re 221: I think Hank’s point is that a photon which returns to earth will typically be the result of many absorptions and readmissions following the emission of the original photon from the surface of the earth. Thus, an interaction at high altitude will not necessarily require that the emitted photon be within the solid angle subtended by the earth. Even if it is emitted upward, it may encounter a molecule that, in effect, redirects it toward the earth. Have I got this right?

  24. 224
    Timothy Chase says:

    Ron Taylor (#223) wrote:

    Re 221: I think Hank’s point is that a photon which returns to earth will typically be the result of many absorptions and readmissions following the emission of the original photon from the surface of the earth. Thus, an interaction at high altitude will not necessarily require that the emitted photon be within the solid angle subtended by the earth. Even if it is emitted upward, it may encounter a molecule that, in effect, redirects it toward the earth. Have I got this right?

    That is exactly what Hank Roberts (#219) is arguing – and that is really the most essential point. But what would seem to be the central problem is a misunderstanding of Houghton, namely that he holds that photons tend to escape without interacting with the atmosphere at 6 km or above. What I believe Houghton holds is that this is the altitude of the effective radiating layer, and as a matter of fact, Gavin mentions that the altitude of the effective radiating layer is roughly 6 km in an earlier essay:

    In the case of the Earth, the solar input (and therefore long wave output) are roughly constant. This implies that there is a level in the atmosphere (called the effective radiating level) that must be at the effective radiating temperature (around 252K). This is around the mid-troposphere ~ 6km. Since increasing GHGs implies an increasing temperature gradient, the temperatures must therefore ‘pivot’ around this (fixed) level. i.e. everything below that level will warm, and everything above that level will cool.

    Why does the stratosphere cool when the troposphere warms?
    7 December 2004
    http://www.realclimate.org/index.php?p=58&langswitch_lang=en

    Some of the energy re-emitted at this level and above will still be redirected towards the surface thereby increasing the surface temperature. However, the net effect of carbon dioxide at this level and above will be to cool the layer which is in. In contrast ozone will tend to absorb ultraviolet, warming that layer of the atmosphere.

    PS

    Correction to my earlier post: the net effect of carbon dioxide somewhat below the effective radiating level is no doubt to cool those layers. The effective radiating level is simply the level at which the temperature is equal to what it would be in the absence of any greenhouse effect.

  25. 225
    Timothy Chase says:

    PS to 224

    It should be noted that despite what I quoted from Gavin, the effective radiating level isn’t fixed. He later acknowledges as much in the discussion which comes afterwards, but had been relying upon someone else’s calculations. However, he left it in partly because it preserved the continuity of the discussion. As is later noted, the effective radiating level rises with increased levels of carbon dioxide. This is something which is also dealt with Tamino’s “Lapse Rate” and Archer’s book.

    Interestingly, another point which comes during the discussion which follows Tamino’s essay is that the tropopause rises as well as the result of increased levels of carbon dioxide. This is something which was predicted by the models but which has also been observed.

  26. 226
    Hank Roberts says:

    > extra warming if photons return to the surface
    Nope, the extra warming persists because the photons, or the energy they represent in other forms, are staying in play in the atmosphere. A photon emitted at 6km may be more likely than not to escape the planet if it’s emitted upward, which I believe is the point being made about that altitude. But as mentioned, this is changin, as was predicted by modelers
    http://adsabs.harvard.edu/abs/1987JGR….9210897C
    and later observed http://www.sciencemag.org/cgi/content/abstract/301/5632/479

    Hmmm, I miss the “preview” function, which was useful to check whether the links actually work. That first one should take you to:
    On the depletion of ozone by a height increase of the tropical tropopause
    Chimonas, George
    Journal of Geophysical Research, Volume 92, Issue D9, p. 10897-10902 09/1987
    1987JGR….9210897C

  27. 227
    Hank Roberts says:

    >tropopause rises, predicted and observed
    http://www.llnl.gov/str/March04/Santer.html
    http://www.sciencemag.org/cgi/content/abstract/301/5632/479

    Mr. Banner wrote, I believe incorrectly:
    “there will only be extra surface warming from additional CO2 if the photons return to the surface …”
    Nope. The photon may exist only for a fraction of a second before it gets absorbed. The molecule that absorbed it may be bumping and grinding before some other molecule gets enough energy for long enough to emit another photon. That’s all the same energy.
    The energy takes many forms, it doesn’t stay as a photon or have to hit the surface to be contributing to surface warming. As long as the energy hasn’t escaped to space it is still here in one form or another.

  28. 228

    [[Atmosphere or not, there will only be extra surface warming from additional CO2 if the photons return to the surface in line with the standard explanation of the GH effect,]]

    Not true. Warming at any level affects all the other levels, even if not directly. Let me know if you want a mathematical example.

  29. 229
    Capell Aris says:

    Although we know about the increased absorbtion of energy by CO2, it still remains the case that this varies logarithmically with CO2 concentration; what this article explores is a change in the constant in front of the logarithm of CO2 concentrations in our calculation of energy absorbtion.
    And that means that I still can’t buy the global warming scare.
    We’ve been experiemnting with CO2 in the atmsophere for a long time now, we don’t need fancy models. Let’s assume that we’ve observed 0.7 C of warming since 1940, during which time CO2 levels have risen from 290 to 380 ppm. The IPCC claims ’90 % certainty that 50 % of the warming observed to date has been caused by emissions of CO2′. Fine, let’s accept that, so that’s 0.35 C warming due to CO2. Since CO2 is a logarithmic effect, we can now predict what would happen if we doubled up the CO2 to 780 ppm (a prodigous amount, probably not even possible with our current oil reserves). The amount of warming would then be given by
    0.35*ln(760/380)/ln(380/290)
    The proportionallity constants drop out.
    That works out at 0.9 C. Not 6 C, not 4 C, not even 2 C. But less than 1 C.
    But what about the feedback mechanisms? Well, they all apply as of now, and have done since 1940, so they’re built into the calculation I’ve just done.
    What about thermal inertia – perhaps we haven’t seen the full effects of the 380 ppm we’ve already dumped in the atmosphere. Perhaps we haven’t. although 60 years is a long time. But whatever inertia we’ve experienced in the past will apply to the future as well, so we can say that within 60 years from now, the max temperature rise will be less than a degree.

    [Response: The statement from the IPCC is not correct; the planet is responding to the net forcing, not just CO2; thermal inertia implies that a transient result can’t be extrapolated to equilibrium responses, etc. Bottom line: you are attempting to calculate cliamte sensitivity from the 20th Century trend, but as we’ve discussed many times, that is not much of a constraint because of the uncertain influence of aerosols and the ocean uptake of heat. It would be nice if it was that easy, but the reality is that it isn’t. – gavin]

  30. 230
    Hank Roberts says:

    Capell Aris — where do you find this statement you say you are quoting from the IPCC? Gavin says it’s not correct; I wonder if it’s even from the IPCC at all. Cite please?

  31. 231
    Capell Aris says:

    I have to admit that I’m struggling to find the IPCC reference. I thought it came from the briefing for the latest report, but I can no longer find that on their website. I would therefore be quite willing to accept a corrected percentage figure.

    However, I cannot agree with Gavin
    (i) I believe I’m extrapolating a trend of over sixty years that gives us ample time to see all the effects, to date, of aerosols and the uptake of ocean heat. There may be changes in how some of these variables behave in the future, but those chnages should be second order. (The world temperature is only changing by a fraction of a percent. I agree, that if we confine our scope of interest to the temperature/pressure range for water then the percentage is higher, but it’s still only about a percent). This simple analysis demonstrates VERY powerfully, that predictions of temperature rises of 6 C are absurd, simple scaremongering.
    (ii) thermal inertia remains a constant. If it applies to the observations over the past 60 years, it will apply with equal force in the future.
    (iii) I appreciate that we’re adding a series of stimulii each of which will create an exponential temperature rises, but again, the accuracy of the simple calculation will not be greatly affected by considering them as two step changes. Yes, I agree it may not be ‘this’ simple, but at the same time we cannot postualte changes as high as 6 C merely on the grounds of complexity.

    [Response: You misunderstand the nature of the problem. The key is to define ‘climate sensitivity’ so that, given estimates of future GHG levels, we can estimate the resulting temperature change. This is not a question of linear extrapolation! So from the 20th C (or the last 60 years), do we have enough information to constrain sensitivity? The answer is no. See this post for a more worked out example for why uncertainties in aerosols and ocean heat uptake matter. However, other constraints on sensitivity put it around 3 +/- 1 deg C for a doubling of CO2. Future temperatures are a convolution of this sensitivity, the actual amount of CO2 rise and the delay due to thermal inertia. 6 deg is only if we max out on both the sensitivity and we end up with high emissions. I don’t think it would be describable as a best guess – more a worst case scenario. -gavin]

  32. 232
    Marcus says:

    Capell Aris: I’m interested in how you decide that aerosols and ocean heat uptake changes in the future should be “second order”? If, hypothetically, we posit a world in which CO2 concentration is increasing linearly and aerosol emissions are increasing linearly such that they exactly cancel out, and then one day aerosol emissions flatten out, then you go from having _zero_ increase in forcing to continual increase in forcing.

    Now, in our world, CO2 has been increasing linearly, whereas aerosol loading first increased, then flattened out, and we don’t know what it is going to do in the future. I think that’s a first order effect.

    Ocean heat uptake similarly can do odd things: if increased atmospheric heat leads to increased stratification of the top layers of the ocean as they heat up, then that will reduce ocean heat uptake and suddenly you get accelerated heating as the sink disappears (and the ocean sink is important for carbon uptake too).

    Basically, just picking 2 examples can show how flawed your “simple analysis” is. You may want to consider in the future that when a large number of experts overlook what you think is “simple” that perhaps they know something you don’t know. (And we haven’t even addressed other GHGs, volcanoes, and all sorts of other complicating effects)

    ps. We don’t reach 780 ppm with oil reserves alone: that takes coal reserves too, of which there are plenty. Or ecological disaster in the amazonian rainforest, permafrost carbon release, or other such natural event potentially caused by climate change…

  33. 233
    Hank Roberts says:

    Interesting, from: http://www.agu.org/pubs/crossref/2007/2006GL028668.shtml

    “For every 1% decrease in SO2 emissions over Europe and the USA the modelled sulfate column burden decreased by 0.65%, while over Asia a 1% increase in SO2 resulted in a 0.88% increase in sulfate. The different responses can be explained by the availability of oxidant in cloud. We find that because emissions have moved southward to latitudes where in-cloud oxidation is less oxidant limited, the 12% reduction in global SO2 emissions between 1985 and 2000 caused only a 3% decrease in global sulfate.”

  34. 234
    AEBanner says:

    Firstly, I wish to thank the several contributors for their helpful replies to my #218. Unfortunately, I seem to have caused confusion about my thoughts on this matter by my reference to Houghton’s figure of 6 Km altitude. I mentioned this figure simply for comparison with the requested values for “way, way up there where the air is very thin” in the “Saturated Gassy Argument”. Sorry for misleading anyone.

    Secondly, please remember that, while fully accepting that global warming is occurring, I am sceptical about increased carbon dioxide being the cause. However, I am ready to be persuaded to this view by appropriate arguments. All I want is the truth of the matter.

    With reference to my argument about the solid angle subtended by the Earth at points emitting at high altitudes, Mr Roberts, supported by others, seems to say, if I have correctly understood, that the energy reaching the Earth’s surface from any given emitting point need not be considered as being constantly within the cone of the solid angle, because the emitted energy, initially electromagnetic, can be transferred to other molecules as kinetic energy, and these molecules can enter the cone by random molecular collisions. Have I got this right?

    However, by the same process in reverse, an equal amount of energy can leave the cone, so cancelling the argument. So we are back to my original point that the amount of energy reaching the surface within the cone reduces as the altitude increases, and the excess escapes into space.

  35. 235
    Hank Roberts says:

    > the cone of the solid angle …

    No, as I understand it this isn’t a line of sight issue.

    For any emitted photon, what happens to that packet of energy is some probability of being absorbed by a gas molecule.

    That probability changes with elevation/temperature/density and gas mixture at least, probably with other factors too. What else adds and subtracts energy from bond angles, bond vibration, and so forth?

    We know the molecules at the top of the atmosphere are higher and colder recently, as the atmosphere below them expands (observed as predicted). That’s what’s changed in the region from which infrared is effectively leaving the planet — the gas doing the emitting is colder.

  36. 236
    Hank Roberts says:

    Abuse? I believe he’s attempting argument. Let’s check:
    http://www.ibras.dk/montypython/finalripoff.htm#Argument

  37. 237
    David B. Benson says:

    Re #324: AEBanner — Have you read the AIP history of climatology, linked on the sidebar?

  38. 238
    AEBanner says:

    Re #237

    Yes. What do you think I’ve missed?

  39. 239
    Hank Roberts says:

    Well, the AIP history explicitly does not cover developments since the 1980s, which this topic and the associated topic do address. It seems to me what you may be missing is the source of the information used for the work being described:

    “The discussion here is based on CO2 absorption data found in the HITRAN spectroscopic archive. This is the main infrared database used by atmospheric radiation modellers. This database is a legacy of the military work on infrared described in Part I , and descends from a spectroscopic archive compiled by the Air Force Geophysics Laboratory at Hanscom Field, MA (referred to in some early editions of radiative transfer textbooks as the “AFGL Tape”).”
    http://www.realclimate.org/index.php/archives/2007/06/a-saturated-gassy-argument-part-ii

  40. 240
    David B. Benson says:

    Re #238: AEBanner — The page entitled “The Carbon Dioxide Greenhouse Effect”, perhaps?

  41. 241
  42. 242
    Timothy Chase says:

    AEBanner (#238) wrote:

    With reference to my argument about the solid angle subtended by the Earth at points emitting at high altitudes, Mr Roberts, supported by others, seems to say, if I have correctly understood, that the energy reaching the Earth’s surface from any given emitting point need not be considered as being constantly within the cone of the solid angle, because the emitted energy, initially electromagnetic, can be transferred to other molecules as kinetic energy, and these molecules can enter the cone by random molecular collisions. Have I got this right?

    However, by the same process in reverse, an equal amount of energy can leave the cone, so cancelling the argument. So we are back to my original point that the amount of energy reaching the surface within the cone reduces as the altitude increases, and the excess escapes into space.

    Here are some of my thoughts regarding your cone argument.

    1. You are right about a cone being involved, but the point of the cone is not what you “project.” It is not a point at the surface, but at the center of the earth. As such, we are not dealing with a single point on the surface of the earth, or any canceling-out due to photons hopping cones. Given how small the distance is between the earth’s surface and the “surface” of the atmosphere is relative to the distance to the earth’s center, what we are dealing with regarding the volume over which a photon travels is for all intents and purposes a vertical column.
    2. At the time, the column is much taller than you suppose, and the higher the cone the more difficult the difficult the photon will find it to make it from the surface of the earth to space. The photon’s path, given absorption and isotropic re-emission is a random walk and the greater the column height the higher the likelihood that it will make several round trips to the earth’s surface prior to finally escaping to space.
    3. The column height over which carbon dioxide is effective is much higher than you suppose, consisting of all but the last handful of kilometers within the troposphere over which water vapor dominates – and much of the stratosphere.
    4. Adding carbon dioxide to the atmosphere increases the height over which it is effective – largely by raising the tropopause.
    5. You assume that carbon dioxide goes from non-effective due to saturation to non-effective due to being too cold with lines and bands too narrow over a negligible distance. Calculations demonstrate otherwise – the lapse rate is roughly constant. With increased temperatures at the surface of the earth, the distance over which carbon dioxide is effective increases.
    6. Your knowledge of the physics in operation within the atmosphere is minimal and you apparently stand in need of time studying basic and analytic geometry – yet you seem to think that you know more than the vast majority of climatologists spent a fair number of years acquiring a PhD and even more years in the field studying it. Obviously you are quite mistaken.

  43. 243
    AEBanner says:

    Re #242 Timothy Chase

    I’m sorry, Mr Chase, but you have completely mis-understood my “analytic geometry”, as you call it. No doubt it’s my fault for not explaining what I meant more clearly.

    By the “acceptable cone”, if I may coin the phrase, I meant the solid angle subtended at the photon emitting point at very high altitude by the circle on the Earth’s surface at the horizon as seen from the emitting point. I’m afraid I cannot express it more simply or concisely. Nothing to do with a point on the Earth’s surface, or at the centre of the Earth, as you seem to think.

    As a result of this mis-understanding, the comments you have just made, #242, are somewhat irrelevant, and I take exception to the view you have taken in your point 6. How do you know what I know about anything? If you have a PhD, as you imply, it surprises and saddens me that you so misread my post.

    If you refer again, more calmly, to my #218, you will see that I have used my “basic” analytic geometry to calculate what I suggested was the “acceptable cone” for a range of altitudes up into the stratosphere, and beyond. This clearly shows a reduction in the solid angle as height increases. So what we need to know is the altitude and the spread of the absorbing region concerned in the explanation of the “Saturated Gassy Argument”.

    So far, the PhD climatologists you refer to have not deigned to offer any figues for these parameters. Therefore, it is almost impossible to evaluate the proposed effect, or indeed to see if the “acceptable cone” has any significant numerical effect.

    Until we have such information, as Hank Roberts would say, “it’s just poetry”.

  44. 244
    Hank Roberts says:

    Er, no, I’d say it’s just a question of the mean free path on average, and an empirical question how much radiation escapes the planet — and that line of sight doesn’t matter. You’re making much the same argument, I think, that is made by one person who posts here regularly, that the atmosphere has to be transparent to infrared.

    I’ve suggested looking for infrared photographs of the Earth showing the horizon — if the cloud tops mark the top of the atmosphere as photographed in the infrared he’s right. If, however, the upper atmosphere is bright in the infrared above the clouds — which is what the infrared astronomers keep claiming in arguing for funding to put their infrared telescopes on mountaintops, on stratospheric balloons, and in orbit —- then he and you are wrong.

    I’m going with the consensus on this — I think the upper atmosphere is bright (and so foggy) in the infrared, for the reasons explained above, and that line of sight doesn’t constrain where the energy goes.

    Poetry as I use the word here is a serious effort to actually find the best words to explain the math. The math says you’re wrong too.

  45. 245
    AEBanner says:

    The replies to my posts about the solid angle subtended by the Earth at points emitting at high altitudes, seem to say, if I have correctly understood, that the energy reaching the Earth’s surface from any given emitting point is not in line of sight, and need not be considered as being constantly within the cone of the solid angle, because the emitted energy, initially electromagnetic, can be transferred to other molecules outside the cone as kinetic energy, and these molecules can enter the cone by random molecular collisions, as in a random walk. Have I got this right?

    I fully accept these statements, but by the same process in reverse, an equal amount of energy can leave the cone, so cancelling the argument. So we are back to my original point that the amount of energy reaching the surface within the cone reduces as the altitude increases, and the excess escapes into space. I tried to make this point previously, but I believe the replies were not really appropriate.

  46. 246
    Hank Roberts says:

    No. You’re mistaking the solid surface for the Earth.

    The “Earth” is not just the solid part of the planet. The Earth — heating up now — includes everything up to the top of the atmosphere. A photon coming in from outside the system, from the sun, adds to the heat. Energy moving around within the system doesn’t add or subtract, it rearranges. A photon exiting the system into space removes energy, as heat. With a sudden increase in greenhouse gases, this heat flow in and out is out of balance.

  47. 247
    Timothy Chase says:

    AEBanner (#243) wrote:

    Re #242 Timothy Chase

    I’m sorry, Mr Chase, but you have completely mis-understood my “analytic geometry”, as you call it. No doubt it’s my fault for not explaining what I meant more clearly.

    By the “acceptable cone”, if I may coin the phrase, I meant the solid angle subtended at the photon emitting point at very high altitude by the circle on the Earth’s surface at the horizon as seen from the emitting point. I’m afraid I cannot express it more simply or concisely. Nothing to do with a point on the Earth’s surface, or at the centre of the Earth, as you seem to think.

    Agreed.

    I misunderstood you. My apologies. And no, I am not a climatologist.

    I checked, and the figures you’ve given for your line-of-sight “calculation” are accurate. At a hundred kilometers I get 17.51 percent.

    Not that it matters.

    The kind of calculation you’ve made is largely irrelevant. Or to be more precise, it takes into account only one of a variety of factors, not the least of which is the fact that absorption will be increasing along the entire column, not simply at some (somewhat arbitrarily defined) moving endpoint.

    More importantly, I think you misunderstood the point of the two essays: they were not to demonstrate how to perform the specific calculations on paper that climate models perform. They were to demonstrate what was wrong with the view that carbon dioxide is saturated, and therefore increasing the amount of carbon dioxide will have no increased greenhouse effect. In the process of explaining this historical, Ray was able to illustrate the importance of spreading. Simple column calculations are more than enough to get get both points across.

    However, if you seriously wish to claim that increasing the amount of carbon dioxide in the atmosphere will have no increased greenhouse effect, I have a small problem for you: Venus.

  48. 248
    Marcus says:

    AEBanner: Thought experiment: A sphere of CO2 gas floating in space: An infrared light source in the center of the sphere: Does the sphere heat up?

    I think you would agree the answer is yes. And yet… there is _no_ solid object in the middle, so the subtended solid angle would be zero. So this is a problem if you want to argue based on this subtended angle logic that a higher altitude CO2 molecule has a reduced impact on heating up the earth system.

  49. 249
    AEBanner says:

    Thank you, gentlemen, for your posts,#246, #247 and #248, and for your efforts in trying to sort out my ideas on the “cone”. I can see that I shall have to do more thinking about this.

  50. 250
    Timothy Chase says:

    {\Omega}_{e}=2\pi\left[\sqrt[]{\frac{2{R}_{e}h+{h}^{2}}{{({R}_{e}+h)}^{2}}}\right]