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Filed under: — stefan @ 4 May 2010

The new novel Solar by Ian McEwan, Britain’s “national author” (as many call him) tackles the issue of climate change. I should perhaps start my review with a disclosure: I’m a long-standing fan of McEwan and have read all of his novels, and I am also mentioned in the acknowledgements of Solar. I met McEwan in Potsdam and we had some correspondence while he wrote his novel. Our recent book The Climate Crisis quotes a page of McEwan as its Epilogue. And of course I’m not a literature critic but a scientist. So don’t expect a detached professional review.

In interviews McEwan describes his difficulties in approaching the topic of climate change: “I couldn’t quite see how a novel would work without falling flat with moral intent.”

One solution is that he makes his protagonist who tries to “save the world”, the Nobel laureate physicist Michael Beard, thoroughly pathetic and unlikeable. (Actually quite unlike any scientist I know, but certainly less boring than us at Realclimate.) The only redeeming feature of Beard is his sarcastic humor. When his business partner is worried that claims of global warming having stopped will ruin their grand solar energy scheme, Beard (after expertly refuting the “no warming since 1998” myth) retorts:

Here’s the good news. The UN estimates that already a third of a million people a year are dying from climate change. Even as we speak, the inhabitants of the island of Carteret in the South Pacific are being evacuated because the oceans are warming and expanding and rising. Malarial mosquitoes are advancing northwards across Europe… Toby, listen. It’s a catastrophe. Relax!

This is McEwan’s funniest book. The humour in it is another way around the moral gravity of the subject. In an interview he said:

The thing that would have killed the book for me, I’m sure, is if I’d taken up any sort of moral position, I needed a get-out clause. And the get-out clause is, this is an investigation of human nature, with some of the latitude thrown in by comedy.

Half-way through the novel Beard gives a riveting speech on climate change to an auditorium full of pension-fund managers (representing 400 billion dollars of investments) – a speech that I’d be almost tempted to steal and use verbatim myself at some occasion. But what could have been tedious – a whole lecture embedded in a novel – is turned into a hilarious scene where Beard is engaged in a losing battle with his bowels, trying to continue speaking while swallowing down “a fishy reflux rising from his gorge, like salted anchovies, with a dash of bile”.

McEwan showing off that he can write such a speech better than a scientist is reminiscent of his novel Enduring Love, to which he appended an entire scientific paper about a psychological disorder (De Clerambault’s Syndrome) that allegedly inspired the book. Later he admitted this “paper” was part of the fiction. He’d even submitted it to a journal, but one of the reviewers smelled a rat.

McEwan’s deep (and often playful) affinity to science is one of the hallmarks of his writing and of course one reason why I like his novels. The other is his stunning power of observation; he seems to be reading people’s minds, cutting right through their delusions to get to the deeper truths. In that, his analytic work as a writer resembles that of a scientist.

McEwan is a forceful rationalist and well-versed in science culture, and his witty observations on that are a big part of the fun of his books. In Solar, for example, he pokes some hilarious fun at the social constructivists. Beard chairs a government committee to bring more women into physics, and a social scientist on his committee introduces herself with a speech on how a particular gene is not discovered by scientists, but is rather a social construct.

Beard had heard rumours that strange ideas were commonplace among liberal arts departments. It was said that humanities students were routinely taught that science was just one more belief system, no more or less truthful than religion or astrology. He had always thought that this must be a slur against his colleagues on the arts side. The results surely spoke for themselves. Who was going to submit to a vaccine designed by a priest?

This develops into my favourite subplot. At a press conference of his committee, the journalists are “slumped over their recorders and notebooks” and “depressed by the seriousness of their assignment, its scandalous lack of controversy”, as “the whole project was lamentably worthy”. Beard makes some fairly harmless remarks about the efforts of bringing more women into physics perhaps reaching a ceiling one day, because they may have a preference for other branches of science. The social constructivist explodes (“Before I go outside to be sick, and I mean violently sick because of what I’ve just heard, I wish to announce my resignation from Professor Beard’s committee.”) Predictably, that makes the predatory journalists spring to life, and in the following McEwan spins a completely credible story how Beard’s remarks turn into a media storm where Beard’s love life is dragged into the tabloids and his “genetic determinist” views are linked to Third Reich race theories. One journalist, “more in the spirit of playful diary-page spite”, calls him a neo-Nazi.

No one took the charge seriously for a moment, but it became possible for other papers to take up the term even as they dismissed it, carefully bracketing and legalising the insult with quotation marks. Beard became the ‘neo-Nazi’ professor.

McEwan knows what he is writing about: he became subject to a media storm about his Islam-critical views a few years ago. I read Solar in February (thanks to an advance copy that the author had sent me), in parallel with the unfolding surreal, but real-world media campaign against IPCC, and found that McEwan dissects the mechanisms beautifully.

McEwan says that the idea to make a Nobel laureate the main character of his new book came to him in Potsdam, when attending the Nobel Cause Symposium organised by our institute in October 2007 (and on page 179 his hero Beard returns from a conference in Potsdam). At the time I discussed with him whether this wouldn’t be a good topic for a novel: humanity facing an existential threat that is well-understood by its scientists, but largely ignored by a population who prefers to delude itself in creative ways about the gradually unfolding disaster. McEwan responded: everything there is to say about this situation has already been said by Thomas Mann in his novel Death in Venice.

I’m glad he tackled the topic of climate change nevertheless. It’s McEwan at his best. Intelligent, funny, and full of insights. Read for yourself!

Link: Here is McEwan speaking about Solar (and about his views on climate change) in a TV interview.

726 Responses to “Solar”

  1. 401

    Kate 390,

    You have it exactly. The meaning of “democracy” in the US has been stretched far beyond the political sphere where it applies. Most Americans really think anyone’s opinion on any subject is as good as any other–training and education is irrelevant. The example I like to use is a guy who’s never worked with his hands or even read about construction going up to a 20-year union stonemason putting a wall together and telling him “You’re doing that all wrong”–and expecting to be taken seriously. And getting outraged when the guy tells him to bugger off.

  2. 402
    Completely Fed Up says:

    “FCH says, “All appeals to authority are fallacies.”

    I do not agree–it is merely when you assert that the authority of the source automatically confers truth that it becomes a fallacy.”

    Ray has it right, FCH.

    In much the same way as an ad hominem attack is where you take a priori the idiocy of the speaker to prove their argument false, yet you can say that the idiocy of the speakers’ argument is concordant with their past idiocies.

  3. 403
    Geoff Wexler says:

    RealClimate avoids writing down equations because most people are highly allergic to math

    Counter-example :

    For the equations try Open Mind e.g.

    [I see that Michael Mann is still being harassed :

  4. 404
    Dappledwater says:

    Shirley @ 347 – some useful reading here:

  5. 405
    John E. Pearson says:

    Steckis: On Venusian temperatures: I found this.

    which you might want to read. (The book should pop open to about page 230-231). ALthough I am certain what you call “Motl’s analysis” (and I think of as Motl’s incoherent jabber) is wrong, I don’t know this stuff well enough to put my finger directly on where he is wrong. In the link Hansen writes down this nice little formula:

    T_s = T_e + \Gamma H

    where T_s is the surface temperature, T_e is the top if atmosphere temperature (which can be calculated easily by flux balancing) , \Gamma is the lapse rate ~ 7C/km on venus and H is the altitude of emission to space. Hansen et al remark that this formula gives a nice estimate of the greenhouse effect on a given planet. In essence it all boils down to where the atmosphere emits. i.e. What is H?

    On Earth H is about 6 km. On venus it is about 70 km. My guess is that on earth the dependence of H on CO2 is logarithmic and that on Venus it isn’t. On earth, CO2 is a trace gas and on Venus it is the primary constituent of the atmosphere. I would guess that there is a regime in a pure CO2 atmosphere in which H is linear with the total amount of CO2.

  6. 406

    CFU @ 399:

    I could care less what you think, or who you agree with — you might want to consider “Ray says so”‘s relevance in a discussion about whether or not appeals to authority are or aren’t valid. “Appeal to Authority” is an invalid form of an argument. Period. As another poster pointed out, it may help you with the confidence that the remainder of the argument is valid, but the use of an authority in an argument has zero relevance, whatsoever, on the validity of the argument.

    If you can’t grasp this, I’d suggest you construct an argument supporting CO2 as a cause of global warming. Which part of the physical science requires inserting “Ray says so”? If Ray makes a mistake, and Ray still says so, is Ray right, even though he’s wrong?

    Study formal logic. It isn’t that hard.

  7. 407
    John E. Pearson says:

    402: oops.

    H on earth isn’t exactly logarithmic with CO2. It is logarithmic with a constant offset.

    If T_s(CO2) = k Log(CO2) = T_e + \Gamma H then

    H = [k log(CO2) – T_e]/\Gamma

    If k is 2C and \Gamma is 5C/km then one expects H to increase by 2/5 km with a doubling of CO2 on earth. As I said before though, there is no particular reason to assume such a relationship holds on a planet in which CO2 is the primary atmospheric constituent. Note also that the logarithmic dependence of of T_s on CO2 can’t possibly hold all the way to [CO2]=0. Somewhere it must rollover to something that is sensible at [CO2]=0. Presumably it is linear at small [CO2]. My guess is that in a pure CO2 atmosphere (Like on Venus) the linear regime lasts far longer than it does when CO2 is a trace gas (like on Earth). My guess also is that this stuff is all pretty well understood and that the right person could point us to a reference that explains it all. That person isn’t me.

  8. 408
    Completely Fed Up says:

    FCH you may want to consider evidence given as being evidence given and rather than knock yourself out with your own knee, read something.

    Or is this a bad time for you..?

  9. 409
    Completely Fed Up says:

    “you might want to consider “Ray says so”’s”

    You might want to get a better pres cription.

    “Ray has it right” is not “Ray says so”. It’s saying that what Ray is saying is right.

    You may want to consider a softer science to work in if you’re not really happy with logical reasoning.

  10. 410
    Hank Roberts says:

    Oh, lordy lord lord lord. More people who’ve never looked at the visible-light pictures of the surface of Venus:

    Gerlich and Tscheuschner, On The Barometric Formulas

    “… another popular but incorrect idea communicated by some proponents of the global warming hypothesis …. since the venusian atmosphere is opaque to visible light, the central assumption of the greenhouse hypotheses is not obeyed…..”

    You’d think they’d bother to look this stuff up, rather than simply asserting a belief without citing any source for it.

    Here, for example.

    Pictures in black-and-white:

    Spectral measurements:
    Venera-12 landed on Venus on December 21, 1978, and Venera-11 landed on December 25. All of the color panoramic cameras failed, due to atmospheric pressure.

    V.I. Moroz and his team at IKI designed the IOAV spectrometer which measured the sky at 20 nanometer wavelength intervals and in multiple directions. Below is displayed the zenith sky color as measured during the descent of Venera-11. The small images show the form of the spectrum from 360 to 830 nm, with the area under the curve filled in with the corresponding sRGB standard value. Actual spectral data extended well into the infrared, to identify gas absorption bands. …
    The increasingly orange color is due to rayleigh scattering by the thick atmosphere, and possibly an additional unknown blue-absorbing gas component. Brightness is normalized. The text color for these web pages was chosen to approximate the Venera-11 sky color.”

  11. 411
    Ray Ladbury says:

    Whether an appeal to authority is valid or not depends on the argument. If I want to know how a word is spelled, I will appeal to a dictionary–that is, an accepted authority. If I want to know the approximate population of Costa Rica in 2006, I will look in an almanac–and accepted authority.

    Not all arguments can be reduced to logic (even in arithmetic, as Kurt Godel showed). Some require a)empirical input, or b)an agreed upon standard (no one spells “fish” ghoti except G. B. Shaw).

    The fallacy of appeal to authority only comes into play if I claim the authority’s advocacy of necessity implies the truth of the statement. That I have not done.

  12. 412
    greyfox says:

    Sorry to bother again…just ran across a scad of articles attacking surface temperature (various weather stations and their locales etc.) accuracy…basically a wholesale ixnay. Of course, Cato and Heartland figured significantly, but can someone direct me to a simple rebuttal? Thanks.

  13. 413

    CFU @ 408 & 409:

    “Evidence given” is not Not NOT “Appeal to Authority”. “Appeal to Authority” is a very specific fallacy, and it’s a fallacy because “Ray has it right” or “Ray says so” or “CFU is a f*cking id1ot!” is irrelevant to whatever is being proven.

    And frankly, Ray still has it wrong, and why he (and you) took the stance he did boggles my mind. “Appeal to Authority” is used all over the place here, though more often than not it’s “Appeal to has a blog” or “Appeal to has an unrelated Science degree” or “Appeal to not being Algore.”

    But hey — I liked the ad homme, though I suspect it was more an ad menstruatum.

  14. 414
    Kevin Stanley says:

    Appeals to authority don’t _prove_ anything, but they can be _persuasive_. Slightly different animals, unless you will only be persuaded about something that can be proved…in which case you’re headed for an existential crisis, my friend.

    As for judging the quality of an argument–i.e., whether to be persuaded by it–I find it useful to think in terms of a hierarchy of evidence. So for instance: a large set of scientific studies > a single scientific study > a coherent but untested theory > the opinion of a knowledgeable person (lacking a specific theory) > the opinion of a non-knowledgeable person. The “appeal to authority” is at worst the second-to-last item on that list…which is just fine when it’s competing with the last item on that list.

    In climate change conversations, the pro-science side (or “warmists,” “alarmists,” or whatever) always have that first item sewed up. The body of the scientific evidence is highly partisan in these arguments. And so, often, I believe that what looks like an appeal to authority is kind of a proxy for that fact, as in “person A, who can reasonably be assumed to understand the evidence better than person B for the following reasons (XYZ) says Q.” The real “authority” there is, in fact, the evidence….

  15. 415
    Patrick 027 says:

    Re 391 Richard Steckis – do you have an equation showing another realistic way to keep Venus’s surface warmer without a greenhouse effect?

    Re 398 CFU – I think you left out that CO2 is only (preindustrial) ~ 0.3 mb partial pressure on Earth – but that itself is misleading because partial pressure results from the total weight of the overlying air being distributed among molecules according to molar fraction. The molar mass of CO2 is roughly 1.5 times that of the air, so removing all CO2 would reduce total pressure by 1.5 times the partial pressure of CO2 – or removing all other material from the air, the surface pressure of a pure CO2 atmosphere would be roughly ~ 0.45 mb, which would require about 11 doublings to reach nearly 1 bar and then between another 6 to 7 to get near 90 bar, with a little extra mass to produce the same pressure with the somewhat lower gravitational acceleration of Venus.

  16. 416
    Richard Steckis says:

    John E. Pearson says:
    10 May 2010 at 9:02 AM

    “Steckis: On Venusian temperatures: I found this.”

    Thanks for your information John. Actually the DALR (Dry Adiabatic Lapse Rate) is about 10.4 C/km for Venus. I think in the case of the density of CO2, the relationship remains logarithmic regardless of the density. That is covered by Beer-Lamberts law. Some say that the law breaks down at high concentration, but that is not true. What becomes erroneous is the failure of the measuring equipment to to adhere to the condition under which the law is derived (

  17. 417
    Jacob Mack says:

    FCH: So, next time we “appeal to authority” from Einstein, Gibbs, Darwin, ad infinitum, I will remember that some philosopher said that it is just a fallacy.

  18. 418
    Richard Steckis says:

    “Response: So my inability to fit a line-by-line radiative transfer model in a comment on a blog is proof to you that no such calculation exists? Hmmm… (really, please look at a textbook on planetary atmospheres – nothing I can possibly put in a comment will satisfy you). -gavin”

    Not at all Gavin. That is not what I am implying. Also I never said that there was NO greenhouse effect on Venus, just that the GE is not the primary source of heat in the Venusian atmosphere. I will do some more research on planetary atmospheres (but access to such works is difficult for me as our work library is mainly stocked with biological texts). Maybe I should do a degree in Physics……Nah. I might end up like Ray.

  19. 419
    Hank Roberts says:

    Folks, don’t squabble about “authority” — cite to references.
    Kate has it right! Please read her posts again, briefly taking yer teeth out of each others’ throats and ankles– start with her post she points to:
    and also

  20. 420
    John E. Pearson says:

    Stekis: If you’re actually interested in learning the scientific consensus regarding Venusian temperatures here are some more references.

    GreenhouseModelsof Venus’High SurfaceTemperature,asConstrained by PioneerVenus Measurements

    The atmosphere of Venus

    Schubert, G.; Covey, C. C.
    Scientific American, vol. 245, July 1981, p. 66-74.…66S

    The Planet Venus:

  21. 421
    Doug Bostrom says:

    Jim Eaton says: 9 May 2010 at 1:46 AM

    Your sad experience with your first system was typical of the main flaw w/draindown systems, namely that they involved too many moving parts to work reliably without excessive attention on the part of owners. Drainback systems of the type Actually Thoughtful has mentioned and which appear to be one of the only things he and I agree on solve that problem nicely. A failure means water stays safely in the drainback tank where it can’t cause problems.

    Your point about the size of your first system’s storage makes me realize that I’ve failed to express myself properly on this topic. My fundamental point is rather simple: for a vast portion of the potential market for solar DHW and given a realistic deployment of time, material and money, producing finished hot water ready for a showerhead or automatic dishwasher is incompatible with maximizing energy gain from a solar hot water system. If one is off-grid, finished water is a necessary goal worth sacrificing total gain, but if one is connected to a grid the most energy and hence money can be saved by preheating water.

    Aiming for finished hot water automatically reduces the total potential net gain of any given collector system and will always degrade the economics of a given collector system. This is a matter of pretty basic thermodynamics.

    That’s not to say there’s no room or reason for systems producing finished hot water.

    If you’re off-grid and intend to take comfortable showers, etc., you need a system that allows collector temperature to exceed the temperature of your target finish temperature. Unfortunately for a given level of resource inputs that design objective necessarily increases losses throughout the system meaning less energy is captured for a given amount of resource input. Full autonomy of this kind also makes inclement weather more of a challenge, requiring additional expense to surmount.

    If you’re on-grid and are interested in maximizing energy gain, your somewhat counterintuitive goal is to keep collector temperature as low as possible, which is done by providing a large mass of water into which to dump heat. This brings other benefits in terms of less stringent engineering requirements for insulation, etc. In fact, the entire engineering bar is lowered by choosing the objective of maximizing energy gain for a given resource input, a happy circumstance.

    Regarding AT’s remarks about controller costs, although the kind of feedback he speaks of is important to hobbyists and other aficionados I don’t think AT can produce anything more than anecdotes to justify the expense of elaborate controller displays and the like. On the other hand, arithmetic tells an unambiguous and quantified story. As an example, in my particular case the increased cost of the controller he insists is necessary for marketing solar DHW would push my economic break-even point out by some two years. It only takes a few decisions of this kind to make systems unaffordable for the vast bulk of potential customers, choices that so far have confined solar DHW in the U.S. to a boutique market. Sad and frustrating, leaving uncounted clean kWh unrealized, not to mention savings.

  22. 422
    SecularAnimist says:

    FCH wrote: “I’d suggest you construct an argument supporting CO2 as a cause of global warming. Which part of the physical science requires inserting ‘Ray says so’?”

    Well, every part of the physical science requires making assertions of fact, e.g. “CO2 is a greenhouse gas” or “Human activities have released X gigatons of carbon into the atmosphere during the 20th century”.

    So, I construct my “argument” and when I get to the part about CO2 being a greenhouse gas, the person I’m arguing with retorts, “Yeah? Says who? You?”

    How do I respond, if not with an “appeal to authority”? I can regale him with the whole 150-year history of scientific understanding of the role of CO2 in the atmosphere, but isn’t that really just an elaborate “appeal to authority”?

    I suppose I could give him instructions for performing an appropriate experiment, and tell him that I’ll continue with the rest of my “argument” after he performs the experiment himself and verifies that CO2 does what I’m claiming it does. Assuming that he agrees that the experiment shows what I say it shows.

    FCH wrote: “Study formal logic. It isn’t that hard.”

    I have studied formal logic. I found it very beautiful. It also has no content other than pure abstractions, and as such has limited applicability to actual discourse about actual things, which at times, as a practical matter, would seem to require “appealing to the authority” of experts who we can agree know what they are talking about.

    Formal logic can tell us whether logical structures are valid, e.g. “If A is true then …”

    But formal logic cannot tell us whether A is, in fact, true. And we are not always in a position to look for ourselves and determine first hand whether A is true. Sometimes, we have to consult an expert.

  23. 423
    Hank Roberts says:

    From the original post:
    > humanity facing an existential threat that is well-understood by its
    > scientists, but largely ignored by a population who prefers to delude
    > itself in creative ways about the gradually unfolding disaster. McEwan
    > responded: everything there is to say about this situation has already
    > been said by Thomas Mann in his novel Death in Venice.

    The book is available online (links at Wikipedia).
    Read it and you can see why that was McEwan’s first response.
    It rings true–though it’s about a far smaller disaster than
    climate change, the human motivations are nailed.


    “… In early June the quarantine barracks of the hospital had been filling silently, in the two orphanages there was no longer enough room, and a horrific traffic developed between the city and San Michele, the cemetery island. But the fear of general damage, regard for the recently opened exhibition of paintings in the municipal gardens, for the enormous financial losses that threatened the tourist industry in case of a panic, had more impact in the city than love of truth and observation of international agreements; it made feasible the official policy of secrecy and denial. The highest medical official had resigned, filled with indignation, and had been replaced with a more docile person. The people were aware of that ….

    … In febrile excitement, triumphantly in possession of the truth, with a taste of disgust on his tongue and fantastic horror in heart, the loner paced up and down on the flags of the square. He considered a cathartic and decent deed. He could approach the pearl-wearing woman after dinner and talk to her like this: “Please allow this stranger, madam, to give you advice and warning, kept from you by selfishness. Depart, depart right now, with Tadzio and your daughters! Venice is diseased!” Then he could place his hand upon the crown of that tool of a taunting god, turn around and flee from this swamp. But he immediately felt he did not really want to take that step. It would lead him back, give his soul back to himself; but when one is frantic, the last thing one desires is to be oneself again…. and the thought of returning home, of prudence, of austerity, hardship and mastery seemed so repulsive to him that his face took on a grimace of bodily nauseousness. “One should keep silent!” he whispered impetuously. And: “I will keep silent!” The knowledge of his complicity intoxicated him, like a small amount of liquor intoxicates an old and faded brain. The image of the afflicted and derelict city caused him to hope for things that were unreasonable and of unspeakable sweetness. What was that little bit of happiness of which he had just dreamed in comparison to this? What was art and virtue to him compared to the advantages of disorder? He kept silent and stayed….”

  24. 424
    Marcus says:

    “Note also that the logarithmic dependence of of T_s on CO2 can’t possibly hold all the way to [CO2]=0. Somewhere it must rollover to something that is sensible at [CO2]=0. Presumably it is linear at small [CO2]. My guess is that in a pure CO2 atmosphere (Like on Venus) the linear regime lasts far longer than it does when CO2 is a trace gas (like on Earth).”

    A GHG introduced into an IR transparent atmosphere will always add to forcing linearly at low concentrations. As the concentration rises, some wavelengths will begin to saturate. Then the forcing increases as the SQRT (methane and N2O) or the log (CO2) of the concentration. However, as concentration rises even higher, weak bands (which are still in the linear regime) will become more important than the strong bands. (eg, any linear function will eventually overwhelm a logarithmic function). This was posted at WUWT but it went right over Goddard’s head. The reference therein which shows the linear and logarithmic compoments side by side was:

    Though I would love to see a better reference somewhere that actually shows radiative forcing over the full spectrum from 0 ppm to Venus-type concentrations (presumably on a log scale).

    (also, presumably, add enough gas and even the weak bands will begin to saturate, so radiative forcing will return to a SQRT and then a log dependence on concentration again).

  25. 425
    Ike Solem says:

    A novel on global warming should probably cover at least a hundred year period – and the same is true for a novel on species extinction. That’s the timescale over which significant changes become glaringly obvious. Maybe McEwan should have modeled his book on “One Hundred Years of Solitude.” As it is, McEwan’s effort seems like a effort to recast Upton Sinclair’s “Oil!”, replacing the independent oilman/priest figure of Joe Ross with the independent solar entrepreneur/scientist figure of Michael Beard, who is apparently obsessed with making a fortune off of energy patents he manages to corral while serving as director of the NREL labs, before having a major personal breakdown? Seems like a collection of caricatures, in other words… as in “Ecowarriors spewing noxious emissions from their vehicles as they tour the pristine snowscapes they are keen to protect…”, etc.

    Increased solar energy production will not directly halt the growth of atmospheric CO2, however – to do that, you’d have to eliminate fossil fuel combustion entirely, and then wait and see how the global carbon cycle feedback responded to the new global temperature….

    P.S. Why are people rehashing radiative transfer theory again? That work was done in the 1950s and 1960s –
    For a more comprehensive view, see Moller & Manabe 1961:

    It is a very challenging problem, however, to simulate the latitudinal distribution of the height of the tropopause, that of the temperature in the stratosphere, and the polar inversion in the lower troposphere. In order to do this it is necessary to build a model which has a high resolution (many levels) in the vertical direction and which includes the various thermal processes acting in the atmosphere, i.e., radiation, condensation, and the eddy flux of sensible and latent heat from the earth’s surface.

    Yes, that was fifty years ago, before computers & satellites and more comprehensive data collection – but it’s all been upheld, hasn’t it? Here’s more from the same paper:

    Gowan computed the distribution of radiative equilibrium temperature of the stratosphere and obtained an increase of temperature with altitude by taking into consideration the heating due to the absorption of solar ultraviolet radiation by ozone as well as the effect of long wave radiation by water vapor. In the improved version of his computation, he also includes the effects of the the 15u band of carbon dioxide, the 9.6u band of ozone, and the absorption of solar radiation by water vapor. The equilibrium temperature of the stratosphere thus obtained increases with altitude and qualitatively coincides with observed features. Quantitatively, however, the temperatures are much warmer than those observed. This computation could be further improved by adopting recent observations of the extraterrestrial solar spectrum and the distributions of gases in the stratosphere as well as the absorptivities recently obtained in the laboratory.

    As far as the specific role of carbon dioxide, and the pressure-temperature dependence of the effect?

    Although the mixing ratio of carbon dioxide is approximately constant with height, pressure as well as temperature vary with altitude. Therefore, the estimation of effective temperature involves cumbersome computations… However, according to Goody, the 15u band of carbon dioxide has a rather strong heating effect at the tropopause. The reason for this strong heating could be found from a careful examination of Plass’ results of the temperature change due to this band.

    Plass (1956) “The Influence of the 15u Carbon Dioxide Band on the Atmospheric Infra-Red Cooling Rate.”

    Moller & Manabe (1961) “On the Radiative Equilibrium and Heat Balance of the Atmosphere.”

    Rehash it if you like…

  26. 426
    Brian Dodge says:

    Does the transient ionization of Nitrogen in the atmosphere by GCR and high energy radiation from the sun cause the development of dipole moments and allow conversion of thermal energy to IR emission? In other words, does N2 plus an extra electron (or minus one of its normal electrons, i.e. plus a hole) behave like a wierd triatomic molecule with vibrational absorption bands?

    “Is an actual surface made of dirt-like material (with a clear boundary between gaseous atmosphere and solid) actually required?” Jaime Frontero — 7 May 2010 @ 11:02 AM
    Nope – consider that the absorption of visible radiation in the oceans is a volume process – light penetrates some tens of meters into the oceans. The details of absorption of visible light affect “how much” but not “how” the energy gets redistributed into the absorbing mass and into other masses. The main pathways for the energy are transmission(including scattering and reflection), absorption, radiation, conduction, evaporation, and convection.
    The atmosphere mostly transmits visible; dark aerosols absorb some light, and that energy is quickly conducted into the surrounding gas and convected through the atmosphere. Dirt absorbs between ~60 and 90 percent of the visible radiation within a wavelength or less of the solid surface; if the soil is moist, some of the energy goes into evaporation, directly or through vegetation; some of the energy gets conducted down into the earth(see borehole thermometry), Energy is carried away by atmospheric convection of sensible and the latent heat in the evaporated water, and a lot of the energy is reradiated as IR.
    Most of the energy the ocean absorbs is far enough below the surface that the energy must be conducted or convected(wind->waves->surface layer mixing) deeper into the ocean, or to the surface, where it can be radiated, carried away as latent heat of evaporation, or convected into the atmosphere. Although the ocean is somewhat transparent to visible, it is essentially opaque to IR, so only a very thin layer at the surface can radiate. In the real world, sometimes the scale of some pathways is so small that they can be treated as zero – not much energy gets convected by air flow through porous solids like dirt or snow.
    Imagine if the Vogons showed up with their Molecular Matter Transmuter and replaced the solid bits of Venus with an equal volume of water at the current surface temperature and a chunk of neutron star so the gravitational field remained the same. There wouldn’t be any surface, since the temperature is above the critical point of water. Water clouds would occur above where the lapse rate cooled the atmosphere below the critical point and the humidity was high enough. CO2 would diffuse from the atmosphere into the supercritical water, and the greenhouse effect and surface temperatures would decrease. If the Vogons provide enough CO2 in the water that the equilibrium atmospheric CO2 is about where it is today, and suspend enough colloidal crap in the supercritical water so that the visible radiation gets absorbed near where the surface used to be, it would get hotter where the surface used to be, because of the additional greenhouse effect of the added water vapor. Convection would carry some of this additional heat into the mass of supercritical water, since it starts out at the old surface temperature, and is fluid instead of solid.
    There is also an analogous greenhouse effect without a gaseous atmosphere – in solar ponds. Solar ponds use salt density gradients in water to suppress convection: visible light is absorbed at the bottom of the pond, heating it. IR from the bottom is rapidly absorbed in the water, and thermalized or reradiated up and down. At wavelengths where the mean free path is on the order of or less than a wavelength, math describing radiative transfer breaks down, so it doesn’t make sense to try to describe “emission” and “absorption”; the main transfer of energy is through conduction. Because the radiative and convective heat transfer is suppressed, large temperature gradients with low energy transfer is supported -80 degree centigrade in a three meter deep pond. No gas laws & no adiabatic processes involved.

  27. 427
    Patrick 027 says:

    Re 392 David Russell

    “The adiabatic lapse rate can be derived from gravity. Total molecular energy is the sum of kinetic energy and potential energy. Temperature is a measure of molecular kinetic energy. If the Earth’s surface at sea level is taken as the reference point, molecules at a higher elevation have higher potential energy. Therefore molecules with a lower temperature at higher elevations have equal total energy to those with a higher temperature at lower elevations.”

    That’s one way to look at it, although this would suggest that any dry adiabat eventually reaches 0 K at some finite height. When air is raised or lowered, it loses or gains enthalpy by doing work or having work done on it by expanding or compressing at the pressure it is at. Some thermodyamics and calculus shows that for an ideal gas undergoing adiabatic pressure change,

    T = T0 * (p/p0)^(R/cp) where R is the gas constant and cp is the specific heat at constant pressure (cp * change in T = change in enthalpy; enthalpy = internal energy + work done by expanding at pressure; change in internal energy = cv * change in T, where cv is specific heat at constant volume; cv + R = cp)

    where T0 is the temperature where p = p0; if p0 is at a standard pressure, 1000 mb, T0 is then the potential temperature.

    (PS for the expansion of air being heated, the change in enthalpy – change in internal energy = work done in expanding, and since the pressure is (in the hydrostatic approximation) from the weight of overlying air, the work is equal to an increase in gravitational potential energy of the overlying air.

    (During an adiabatic process where equal masses of warmer air and cool air (of same composition) sink past the same pressure level, undergoing the same pressure change, it can be shown that there is a net loss in enthalpy (the adiabatic temperature decline of the warmer air is greater than the adiabatic temperature increase of the cooler air), and this corresponds to a net conversion of enthalpy to kinetic energy…)

    “How does the greenhouse effect explain why the daytime high temperature atop Mt. Everest never exceed -15°C?”

    Elevated surfaces have less air above them and thus have less of a greenhouse effect (setting aside clouds, etc.). Mixing of the air will tend to bring temperatures towards an adiabat (dry or moist, depending) and thus can’t bring elevated surface temperatures to be as warm as at lower elevations. However, solar heating of elevated surfaces can be greater; even if that is not the case, when the temperature over an elevated surface is warmer than the air at lower elevations brought adiabatically to the same pressure level would be, then this can tend to drive upslope motion. Elevated regions can have larger diurnal temperature ranges than lower elevations because of the reduced greenhouse effect.

  28. 428
    David B. Benson says:

    From, for example, Wally Broecker’s new book, the water from the deep ocean rises mainly near Antarctica, due to the acftion of the circumpolar voretx there.

  29. 429
    Pete Dunkelberg says:

    Venus: greenhouse clearly but what wavelenghts do depart and cool Venus?

  30. 430
    Eli Rabett says:

    Another view about the dry adiabatic lapse rate. The key is that it is dry and adiabatic, meaning the net heat flow into/out of any air packet is zero, so gravitational compression and the specific heat of the air determine the lapse rate.

  31. 431
    Patrick 027 says:

    Re 398 CFU – …”which would require about 11 doublings to reach nearly 1 bar and then between another 6 to 7 to get near 90 bar, with a little extra mass to produce the same pressure with the somewhat lower gravitational acceleration of Venus.”

    Discussing mass – actually refering to mass per unit area, of course.

    Re 392 David Russell
    – “Elevated surfaces have less air above them and thus have less of a greenhouse effect” –

    There is less mass between the surface and space, and also tends to be less mass between the surface and tropopause; a larger fraction of radiation from the surface can escape to space; the back radiation from the atmosphere is less because 1. there is less air above 2. their is an absence of higher pressure layers that have greater line-broadenning 3. the temperature itself is lower. The backradiation is particularly important in influencing the diurnal temperature range. If the whole global surface were ‘elevated’ to lower pressure levels, then there would tend to be cooling via reduction of the greenhouse effect via the tropopause level forcing.

    “then this can tend to drive upslope motion”

    Not necessarily – if the air at the surface is at a higher temperature than air at the same pressure over a lower-lying surface, that will tend to drive upslope motion.

    Re myself 393 – about the prospects of a feeble troposphere when the greenhouse effect is zero.

    a some mixing against stable stratification that would tend to bring the lapse rate closer to a convective lapse rate could be forced by kinetic energy that is supplied from spontaneous thermally-direct overturning via the potential energy associated with horizontal temperature variations; however, that kind of overturning itself tends to increase the stable stratification, and if their is net radiative cooling increasing downward, that tends to remove the available potential energy by increasing vertical stability (vertical stability reduces the available potential energy of horizontal temperature variation). If there is no emission of radiation by the atmosphere, then, while any rising air may adiabatically cool by rising to lower pressure, the atmosphere would be unable to lose any heat it picks up from the surface except by way of returning it to the surface. Lack of radiative cooling aloft inhibits a troposphere. Maybe there could be some very thin layer of overturning air where there is sinking over colder regions; the cooling of the air that drives the sinking would have to be by conduction of heat downward.

  32. 432
    Patrick 027 says:

    Re John E. Pearson – the idea of an effective emmitting level is quite useful.

    The level will be a function of wavelength. The effective emitting level can be near the surface at some wavelengths (8-12 microns, interupted by the ozone band somewhere around 9-10 microns) if there are no clouds and the water vapor concentration is small. Starting without any CO2 and adding some, the effective emitting level for upward LW flux at the tropopause and at the top of the atmosphere (TOA) rises up from whereever it would be given the clouds and water vapor present, starting around 15 microns. Uplift of the emitting level occurs at similar wavelengths, lagging behind farther away from 15 microns, with some finer scale texture associated with individual absorption lines. Eventually the level near 15 microns approaches the tropopause level. The elevated region of the emitting level continues to spread out over a larger interval of the spectrum, tending to spread by a particular amount per each doubling of CO2. The emitting level of downward radiation from the stratosphere falls from space following the same pattern; as the two levels approach each other near the tropopause, the net LW radiation at the tropopause approaches zero and the tropopause-level effect becomes saturated. This occurs first near 15 microns and then spreads out. Initially the tropopause level forcing is approximately linearly proportional to increases in CO2; when the central part of the absorption band is saturated, the interval of the spectrum where CO2 aborption is significant continues to spread out by approximately some amount per doubling, and that is why the forcing at that point is approximately logarithmically proportional to changes in CO2 amount. At some very large amount of CO2, other absorption bands become significant, changing the proportionality.

  33. 433
  34. 434

    JF 394,

    Well, you could work out the contribution from conduction.

  35. 435
    dhogaza says:


    And frankly, Ray still has it wrong, and why he (and you) took the stance he did boggles my mind.

    Because without reliance on authority we’d constantly be trying to individually prove everything individually, from first principles.

    Your own argument is circular, since your citation of the definition of the fallacy of the appeal to authority is, in itself …

    an appeal to authority.

  36. 436

    Gilles 395: We don’t know why supernovae explode

    BPL: Actually, we do.

    A Type I supernova happens in a close red-giant/white-dwarf binary when enough hydrogen blowoff from the giant accumulates on the dwarf to initiate a fusion explosion.

    A Type II supernova happens in a very massive star at the end of its life, after hydrogen was depleted in the core, and the core contracted until helium ignited-“helium flash.” The same thing happened when the helium ran out, so you end with the star having an “onion-ring” structure–an outer layer of hydrogen, helium inside that, then carbon, then a mix of neon, oxygen and magnesium, then silicon, then iron. But iron can’t fuse, since Fe-56 is near the bottom of the packing fraction curve. The entire star therefore collapses, everything becomes fusion fuel, and the whole thing blows up. What’s left at the center is a neutron star, or if the star was massive enough, a black hole.

  37. 437
    Jerry Steffens says:

    Re: Appeals to authority, etc.

    There is a difference between an appeal to authority and an appeal to a vast body of previous work WITH REFERENCES. Who would you want to do your heart surgery, a cardiologist with a long track record of successful surgeries, or some guy who just read an article about the heart on Wikipedia?

  38. 438
    Xyrus says:

    RE: 443 FCH

    All that aside, it’s fallacious to apply formal logic to the real world, where everything is subject to some level of uncertainty.

    In science you provide evidence. In math you provide proof.


  39. 439


    “In climate change conversations, the pro-science side (or “warmists,” “alarmists,” or whatever). . .”

    I’ve been going with “mainstream” or, occasionally, “mainstreamers.”

  40. 440
    Thomas says:

    407,423: the sqrt and log dependencies depend upon the line shapes. Once line centers are saturated the line wings decay exponentially, so the width (in wavelength space) where the opacity times the density is roughly greater than unity depends logarithmically on the column density (of the GHG). Once the continuum region (between lines) becomes saturated this mechanism would not apply. In reality one needs to do a full radiative analysis, portions of the resulting curve may be reasonably fit by simple functions (such as logarithmically or whatever).

    434: Supernovas have become more problematic of late. In the good old days when only 1-D (radially symmetric) models were used, I think it was thought to be understood. But 3D codes are showing some very messy behavior which I think calls into question a lot of things. Of course those basic instabilities do exist, but how they dynamically evolve I think is still an issue not well pinned down. For example for the core collapse, does the energy/mass get absorbed into the neutronstar/black hole, or is it available to blow the outer layers of the star away. And how assymetric are the explosions. Assymetry creates a kick to the neutron star/black hole……

  41. 441
    Ike Solem says:

    Assuming everyone’s happy with radiative transfer theory to get a realistic projection of long-term and regional climate changes, one has to predict the future response of the oceans. There is less data to go in the oceans:

    However, the general trend is one of ocean warming, with associated side effects:

    The sudden thinning in 1997 of Jakobshavn, one of Greenland’s largest glaciers, was caused by subsurface ocean warming, according to research published in the journal Nature Geoscience.

    Lead author Dr Hamish Pritchard from British Antarctic Survey (BAS) says, “We were surprised to see such a strong pattern of thinning glaciers across such large areas of coastline – it’s widespread and in some cases thinning extends hundreds of kilometres inland. We think that warm ocean currents reaching the coast and melting the glacier front is the most likely cause of faster glacier flow. This kind of ice loss is so poorly understood that it remains the most unpredictable part of future sea level rise.”

    As the polar regions warm, the ability of the oceans and land masses to absorb extra CO2 will decline, and a good fraction of the frozen carbon in permafrost will slowly enter the atmosphere as methane or CO2. If shallow seas with methane hydrates warm, that could become another source of atmospheric forcing. These responses are all pretty uncertain – that is, they’re expected to happen, but the speed of the response? Fairly slow, hopefully.

    Given the situation, a moratorium on drilling for fossil fuels in the newly ice-free polar regions might be a good idea. Even if done “cleanly,” which is unlikely at best, more offshore drilling only exacerbates the overall CO2 problem, at a higher and higher price.

  42. 442
    t_p_hamilton says:

    Steckis said:”I think in the case of the density of CO2, the relationship remains logarithmic regardless of the density. That is covered by Beer-Lamberts law. Some say that the law breaks down at high concentration, but that is not true. What becomes erroneous is the failure of the measuring equipment to to adhere to the condition under which the law is derived (”

    The first half of this is incoherent, the second half is wrong. The Beer-Lambert Law deviates from nonlinearity because of saturation (usually), and also from spectral changes (such as dimers in concentrated samples having a different absorption spectrum). Your reference shows that even when the Beer-Lambert conditions perfectly hold, one cannot assume that instruments are magic devices that give linear curves. You must understand how the instruments operate and how they influence the measured spectrum, hence the tutorial about instrument effects. Instrument effects are irrelevant to CO2 in the atmosphere, as no instrument is involved in the absorption and re-emission of IR.

    Saturation is a problem for the frequency where the absorption coefficient is high (center of the absorption band), but not a problem where the absorption coefficient is low (edges of the band). This is why a line by line code for each gas is needed to do a proper simulation.

  43. 443


    All I’ve said is that an argument based on an Appeal to Authority is not a =valid= argument. I’ve said nothing about the truth or falsehood of the conclusion.

    Jerry Steffens @ 436 got it right — provide references to the underlying material (“science”). Even Einstein got a few things wrong, and it was only because we had his material that we’ve been able to figure out what he did wrong. If people had said “Einstein says the Universe is static, I believe him” and not looked at his equations (which provided his peers with a clue that he’d fudged the science), or ignored Hubble because “Einstein said so”, we’d still be stuck with a static universe — a very wrong model of the universe, as we know today.

  44. 444
    Hank Roberts says:

    Speaking of solar heat capture, finally someone’s testing phase change material for building, a long-promised idea:

    “a phase-change wallboard, ThermalCORE, just announced by National Gypsum…. introduced at Greenbuild (but is not yet on the market) is a micro-encapsulated paraffin … in acrylic shells, and these are mixed with the gypsum in drywall. The paraffin melts at 73°F, plus-or-minus 2°F. The PCM used in ThermalCORE is Micronal, made by the German chemical giant BASF. Micronal was introduced about five years ago ….

    BASF’s Micronal PCM is available in commercial products in Europe ….
    … the ThermalCORE wallboard stores about 22 BTUs of thermal energy per square foot. The idea is that warmth from the sun during the day will be stored in the wallboard, and then released at night to keep the space warm. …. Field trial sites are currently being sought through the California Emerging Technologies Coordinating Council and the U.S. Department of Energy National Renewable Energy Laboratory in Golden, Colorado; most will be in California.”

  45. 445
    Patrick 027 says:

    Re 416 Richard Steckis

    We were not refering to the Beer-Lambert law when we were saying the logarithmic proportionality doesn’t hold beyond some limits. We were refering to the radiative forcing of CO2. The difference?

    Beer-Lambert law, which applies to monochromatic radiation (and could also depend on polarization of radiation) along one particular line of sight:

    I = I0 * exp(- optical thickness)

    where optical thickness = integral over distance of (d(geometric distance) * absorption cross section per unit volume)

    Or more generally, where there is scattering (in which case, the relationship may have a different name),

    optical thickness = integral over distance of (d(geometric distance) * extinction cross section per unit volume)

    where extinction cross section = absorption cross section + scattering cross section, and both are proportional to the amount of material of a particular form that provides the effect.

    [AT THIS POINT, note that for familiar Earthly conditions, and so far as I know, typical planetary atmospheres around stars similar to the sun that are not caught in a snowball state with dry ice clouds,

    LW radiation (for Earth, wavelengths (n~=1) longer than about 4 microns, dominated by emissions from the climate system of the planet) is mainly affected by absorption and emission and exit to space, with scattering and reflection playing a relatively minor role,

    while SW radiation (for Earth, wavelengths (n~=1) shorter than about 4 microns, dominated by solar (or more generally, stellar) radiation) is significantly affected by scattering and reflection as well as absorption, with emission from within the climate system being very small, approximately zero.

    (Polarization might be ignorable for some purposes… perhaps especially for LW radiation (except for cirrus clouds?) … or even where effects vary with polarization, perhaps the effects average out to nearly the same as if polarization didn’t matter (?) for at least some purposes…)

    Also note that n, the real component of the index of refraction, remains quite close to 1 in the Earth’s atmopshere; to a good first approximation, refraction can be neglected for radiation within the atmosphere (as can, (except in determining the angle of solar radiation entering the system, and maybe some other purposes involving the upper thin portions of the atmopshere), the curvature of the Earth and the increase in area with height, because the optically-significant atmosphere is concentrated into such a thin spherical shell)]

    The relationship describes the fraction of photons along a particular path that are transmitted over some distance along the line of sight. I is intensity; if there is refraction, I must be replaced by, as I have been writing it for lack of knowing customary notation, I#, which is, at least in the case of isotropic refractive index (same in all directions at any given location), I/n^2, where n is the real component of the index of refraction. This scaling by n^2 is because, even when no photons leave the line of sight, changes in n compress or expand the photons into a narrower or wider solid angle; intensity is the flux per unit area per unit solid angle.

    In differential form:

    dI# = -I# * (acsv+scsv) * dx

    acsv = absorption cross section per unit volume
    scsv = scattering cross section per unit volume

    now consider

    ecsv = emission cross section per unit volume
    scsvO = an effective scattering cross section per unit volume that acts on photons in other directions

    and a more general form that includes emission and scattering of photons into the path:

    dI# = sum of these terms:
    -I#*acsv*dx, the absorbed intensity
    U#*ecsv*dx, the emitted intensity
    -I#*scsv*dx, the intensity of phtotons that are scattered out of the line of sight
    I#O*scsvO*dx, the intensity of photons from other directions scattered into the line of sight, where I#O is a function of I# in other directions and of the type of scattering.

    Assuming the non-photon matter is in quasi-LTE (local thermodynamic equilibrium), which is a good approximation for most of the mass of the Earth’s atmosphere and generally the case of planetary atmospheres of significant density,

    ecsv in one direction = acsv in the opposite direction, and U# = blackbody radiation intensity I# (blackbody I (which is proportional to a function of n) divided by a function of n) (for the frequency and polarization considered).

    If radiative properties are isotropic, as they tend to be for randomly oriented particles (gas molecules) or spherically symmetric particles (small cloud droplets), then ecsv, acsv, and scsv will be independent of direction at a given location, and ecsv and acsv will be independent of polarization. Even if that is not the case, it can still be the case that acsv and ecsv are the same in the same direction, and that tends to be the case in typical atmospheric conditions.

    Aside Raman and Compton scattering, and doppler-shifting by scattering, photon frequency is preserved by scattering. Assuming photon frequency conservation by scattering, and quasi-LTE of the non-photons, and setting aside relativistic effects or changes of conditions in time (which can be ignored if changes are small in the time between photon entry or emission and photon exit or absorption), then there is, for monochromatic photons of some polarization, a ‘I can see you as much as you can see me’ rule:

    Along a line of sight over some distance:

    fraction of I# transmitted in one direction is equal to fraction of I# transmitted in the other direction

    absorptivity in the forward direction = emissivity in the reverse direction (which remains true for a surface that with 0 transmission, 0 scattering interface, where the line of sight is bent at the interface and absorptivity and emissivity are given as properties of the surface).

    and I think (though am not completely sure about this part):

    the fraction of I# of one polarization P1 from one directon Q1 scattered into another direction Q2 with polarization P2 is equal to the fraction of I# with P2 coming from direction Q2 scattered toward Q1 with polarization P1.

    (PS interestingly, while the scattering cross section density scvs can be independent of direction and polarization (for randomly oriented or spherically-symmetric particles), the scattered radiation can have a prefered distribution of directions and polarizations, relative to the direction and polarization of incident radiation; see
    and especially, the last frame of )

    And the same is true of reflection off an interface and refraction through an interface.

    To sum up, one can put together, for radiation coming from a direction Q with some polarization P and frequency v, and emission weighting function, which is a distribution over space, that when multiplied by the blackbody I# (a function of local temperature) and integrated over space, gives the the I# coming from that direction. The emission weighting function is equal to the distribution of absorption of photons coming from the opposite direction. If there is only absorption and emission, the weighting function is along a single path. If there is reflection, the path has sharp bends. If there are variations in n, the path curves. If there is partial reflection, the weighting function is distributed along a branched path. If their is scattering, the weighting function may fill a volume, and that volume may wrap around the location for which this is evaluated. However, if there is no absorption or emission within a volume, then the weighting function projects onto absorbing or emitting surfaces (space can, for these purposes, outside contributions from objects in space such as the sun, be treated as a blackbody surface with temperature near zero K); if those surfaces are partially reflecting, then the weighting functions are partially reflected; if there is scattering, the weighting function is scattered towards surfaces in different directions. A high density region of scattering or absorption can cast a shadow in the weighting function; the weighting function will tend to be concentrated in regions of greater absorption cross section density, but if optical properties are constant over space, the weighting function’s density decreases away from the location considered. If there is absorption cross section within a volume enveloping the location, then either increased scattering cross section density or increased absorption cross section density tends to reduce the weighting function density beyond some distance and increase it near the location; the locations at which the weighting function switches from increasing density to decreasing density is itself pulled toward the location considered as opacity is increased.

    A net intensity is the difference in intensities between a pair of weighting functions. Integrating over solid angle – specifically:
    cos(q) * intensity over a hemisphere
    or cos(q) * net intensity over a hemisphere
    or cos(q) * intenisty over a sphere
    the flux,
    or the net flux,
    or the net flux,
    per unit area normal to Q0 (the same as flux per unit area in the direction Q0)
    where q is the angle from Q0

    Weighting functions are a function of direction; For a surface running through a location, where q is the angle from perpendicular to the surface, the integral over solid angle of cos(q) * weighting function (Q) over a hemisphere gives the weighting function for the flux per unit area through the surface (note this could be more complicated if n is a function of Q; I haven’t been through that math), and this done for each hemisphere gives a pair of such weighting functions that can be used for the net flux per unit area through the surface. The flux per unit area F will be equal to volume integral of the hemisphere’s weighting function times the blackbody I#, multiplied by a function of n (such as n^2) at the location times such a weighting function (if n varies by direction, this could get more complicated; I haven’t gone through that math).

    Such a weighting function (for a hemisphere of directions) can be approximated by an effective emitting (or absorbing) altitude or level, if the temperature at such a level is at or near the brightness temperature of the flux per unit area that is emitted.

    For a flux per unit area and spatially-constant optical properties, transmission of photons over distance from a surface (including scattering as a reduction of transmission) decreases as a sum of exponentials because the photons at some angles pass through a longer distance along their paths in order to get the same distance perpendicular from the surface.

    Now, in order to get the intensities and fluxes for all polarizations, one must integrated over polarizations. Then one must integrate over either the SW or LW portion of the spectrum to get the full fluxes of solar (SW) or terrestrial (LW) radiation. The effects of the shape of absorption spectra of gases are of great importance here. For the 15 micron band of CO2, the general tendency (over the finer scale texture of the many individual lines and some larger-scale bumpiness) is a linear decrease in log(optical thickness per unit CO2) going away from the peak of the band. Thus, when the central portion of the band is saturated (at the tropopause, meaning the net LW radiation across the tropopause is near zero, due to the upward and downard photons both being emitted from rather near the tropopause and thus by material of similar temperature, with very little transmission to space), each doubling of CO2 tends to shift the wavelengths of given opacities outward by some amount, and reducing the net LW flux at the tropopause by, roughly:

    the wavelength shift on each side of the band * net flux per unit wavelength in the absence of CO2 at the wavelengths where CO2 optical thickness is intermediate (on the order of 1) at each side of the band

    The difference between the instantaneous forcing at the top of the atmosphere (TOA) and the instantaneous tropopause level forcing is the forcing on the upper atmosphere; for greenhouse gas increases in general, the tropopause level forcing is greater than the TOA forcing, and this results in stratospheric cooling, a portion of which then affects tropopause level forcing, resulting in the tropopausel level forcing with stratospheric adjustment (or equilibration). The climate sensitivity is generally defined as the global average surface temperature increase per unit of that forcing.


    Radiative forcing depends on the temperatures and optical overlaps. But so do feedbacks. Thus, in the absence of hysteresis and allowing full equilibrium to be achieved after each step, removing all CO2 results in the same magnitude of temperature change as adding it all back, but both the forcing and the sensitivity will be different. The differences won’t be large for small changes, but would be important for very large changes.

  46. 446
    Martin Vermeer says:

    #442 and others — the easiest way to think about ‘appeal to authority’ is to consider the statement by an ‘authority’ as an observation. A proxy, if you like. If he, or folks like him, have a history of making valid statements, you have a working model for him or his peer group which ‘explains’ that body of observations — predictions by that model then have credibility. If not, then not.

    Domain expertise matters.

  47. 447
    Completely Fed Up says:

    “All I’ve said is that an argument based on an Appeal to Authority is not a =valid= argument.”

    And all Ray and I said was that an appeal to authority wasn’t a logical fallacy.

    And it isn’t if you’re basing that on more than “he’s an authority”.

    E.g. if they have previously been honest and worked hard and made breakthroughs, your assertion that in this case he’s likely right, so prove him wrong is not an appeal to authority, it’s a projection of past performance on current actions.

    It is also not a fallacy if you say “these forty others say so and I understand these bits of what they say and I agree they are correct”.

    After all, ALL of your learning is what “some authority told you”. If it was only and ever a logical fallacy, you would have to be your own giant to stand on your shoulders from.

  48. 448
    Completely Fed Up says:

    “Re John E. Pearson – the idea of an effective emmitting level is quite useful. ”

    Try this:

    Yes, it is useful.

  49. 449
    Completely Fed Up says:

    “Venus: greenhouse clearly but what wavelenghts do depart and cool Venus?”

    All of them.

    All frequencies.

    The *rate* is different for different wavelengths because it isn’t a black body radiator.

  50. 450
    Completely Fed Up says:

    “Re 398 CFU – …”which would require about 11 doublings to reach nearly 1 bar and then between another 6 to 7 to get near 90 bar, with a little extra mass to produce the same pressure with the somewhat lower gravitational acceleration of Venus.””

    Uh, we have 1 bar atmosphere.

    1 doubling: 2bar
    2 doublings 4bar
    3 doublings 8bar
    4 doublings 16bar
    5 doublings 32bar
    6 doublings 64bar

    therefore we have less than 7 doublings to get from our 1bar to Venus’ 90bar.

    The partial pressure of CO2 matters not a fig because Motl says that it is merely the pressure of the gas that is causing Venus to be so hot. And all gasses produce pressure. Even N2, O2 and other non-greenhouse gasses.

    Or is Motl’s proposition that only CO2 causes pressure in a gas?