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Simple Question, Simple Answer… Not

Filed under: — group @ 8 September 2008 - (Français) (Japanese) (Finnish) (Czech)

Guest commentary by Spencer R. Weart, American Institute of Physics

I often get emails from scientifically trained people who are looking for a straightforward calculation of the global warming that greenhouse gas emissions will bring. What are the physics equations and data on gases that predict just how far the temperature will rise? A natural question, when public expositions of the greenhouse effect usually present it as a matter of elementary physics. These people, typically senior engineers, get suspicious when experts seem to evade their question. Some try to work out the answer themselves (Lord Monckton for example) and complain that the experts dismiss their beautiful logic.

The engineers’ demand that the case for dangerous global warming be proved with a page or so of equations does sound reasonable, and it has a long history. The history reveals how the nature of the climate system inevitably betrays a lover of simple answers.

The simplest approach to calculating the Earth’s surface temperature would be to treat the atmosphere as a single uniform slab, like a pane of glass suspended above the surface (much as we see in elementary explanations of the “greenhouse” effect). But the equations do not yield a number for global warming that is even remotely plausible. You can’t work with an average, squashing together the way heat radiation goes through the dense, warm, humid lower atmosphere with the way it goes through the thin, cold, dry upper atmosphere. Already in the 19th century, physicists moved on to a “one-dimensional” model. That is, they pretended that the atmosphere was the same everywhere around the planet, and studied how radiation was transmitted or absorbed as it went up or down through a column of air stretching from ground level to the top of the atmosphere. This is the study of “radiative transfer,” an elegant and difficult branch of theory. You would figure how sunlight passed through each layer of the atmosphere to the surface, and how the heat energy that was radiated back up from the surface heated up each layer, and was shuttled back and forth among the layers, or escaped into space.

When students learn physics, they are taught about many simple systems that bow to the power of a few laws, yielding wonderfully precise answers: a page or so of equations and you’re done. Teachers rarely point out that these systems are plucked from a far larger set of systems that are mostly nowhere near so tractable. The one-dimensional atmospheric model can’t be solved with a page of mathematics. You have to divide the column of air into a set of levels, get out your pencil or computer, and calculate what happens at each level. Worse, carbon dioxide and water vapor (the two main greenhouse gases) absorb and scatter differently at different wavelengths. So you have to make the same long set of calculations repeatedly, once for each section of the radiation spectrum.

It was not until the 1950s that scientists had both good data on the absorption of infrared radiation, and digital computers that could speed through the multitudinous calculations. Gilbert N. Plass used the data and computers to demonstrate that adding carbon dioxide to a column of air would raise the surface temperature. But nobody believed the precise number he calculated (2.5ºC of warming if the level of CO2 doubled). Critics pointed out that he had ignored a number of crucial effects. First of all, if global temperature started to rise, the atmosphere would contain more water vapor. Its own greenhouse effect would make for more warming. On the other hand, with more water vapor wouldn’t there be more clouds? And wouldn’t those shade the planet and make for less warming? Neither Plass nor anyone before him had tried to calculate changes in cloudiness. (For details and references see this history site.)

Fritz Möller followed up with a pioneering computation that took into account the increase of absolute humidity with temperature. Oops… his results showed a monstrous feedback. As the humidity rose, the water vapor would add its greenhouse effect, and the temperature might soar. The model could give an almost arbitrarily high temperature! This weird result stimulated Syukuro Manabe to develop a more realistic one-dimensional model. He included in his column of air the way convective updrafts carry heat up from the surface, a basic process that nearly every earlier calculation had failed to take into account. It was no wonder Möller’s surface had heated up without limit: his model had not used the fact that hot air would rise. Manabe also worked up a rough calculation for the effects of clouds. By 1967, in collaboration with Richard Wetherald, he was ready to see what might result from raising the level of CO2. Their model predicted that if the amount of CO2 doubled, global temperature would rise roughly two degrees C. This was probably the first paper to convince many scientists that they needed to think seriously about greenhouse warming. The computation was, so to speak, a “proof of principle.”

But it would do little good to present a copy of the Manabe-Wetherald paper to a senior engineer who demands a proof that global warming is a problem. The paper gives only a sketch of complex and lengthy computations that take place, so to speak, offstage. And nobody at the time or since would trust the paper’s numbers as a precise prediction. There were still too many important factors that the model did not include. For example, it was only in the 1970s that scientists realized they had to take into account how smoke, dust and other aerosols from human activity interact with radiation, and how the aerosols affect cloudiness as well. And so on and so forth.

The greenhouse problem was not the first time climatologists hit this wall. Consider, for example, attempts to calculate the trade winds, a simple and important feature of the atmosphere. For generations, theorists wrote down the basic equations for fluid flow and heat transfer on the surface of a rotating sphere, aiming to produce a precise description of our planet’s structure of convective cells and winds in a few lines of equations… or a few pages… or a few dozen pages. They always failed. It was only with the advent of powerful digital computers in the 1960s that people were able to solve the problem through millions of numerical computations. If someone asks for an “explanation” of the trade winds, we can wave our hands and talk about tropical heating, the rotation of the earth and baroclinic instability. But if we are pressed for details with actual numbers, we can do no more than dump a truckload of printouts showing all the arithmetic computations.

I’m not saying we don’t understand the greenhouse effect. We understand the basic physics just fine, and can explain it in a minute to a curious non-scientist. (Like this: greenhouse gases let sunlight through to the Earth’s surface, which gets warm; the surface sends infrared radiation back up, which is absorbed by the gases at various levels and warms up the air; the air radiates some of this energy back to the surface, keeping it warmer than it would be without the gases.) For a scientist, you can give a technical explanation in a few paragraphs. But if you want to get reliable numbers – if you want to know whether raising the level of greenhouse gases will bring a trivial warming or a catastrophe – you have to figure in humidity, convection, aerosol pollution, and a pile of other features of the climate system, all fitted together in lengthy computer runs.

Physics is rich in phenomena that are simple in appearance but cannot be calculated in simple terms. Global warming is like that. People may yearn for a short, clear way to predict how much warming we are likely to face. Alas, no such simple calculation exists. The actual temperature rise is an emergent property resulting from interactions among hundreds of factors. People who refuse to acknowledge that complexity should not be surprised when their demands for an easy calculation go unanswered.

623 Responses to “Simple Question, Simple Answer… Not”

  1. 101
    John Mashey says:

    re: #46 Wonderer

    Recall that I was *objecting* to the “senior engineers” generalization. Of course many have no problem sorting things out. My issue was to consider the different sorts of reasons why someone with some reasonable technical background doesn’t. We know about ideological and economic reasons, but I think there is this issue where:

    – Someone has a good technical background in one area
    – Over-generalizes from their specific area
    – Without understanding the differences

    Over-generalization is a common error we all have to fight against, but in particular, it tends to inhibit deeper insight, in this case, about who believes what, and why. One thing is clear: in explaining one’s own technical domain to somebody else, it *is* very beneficial to understand what they know, and then explain at the right level and ideally with examples that they can find relevant, and this is true whether the listener is technical or not. It’s also not easy, especially in cases when people simply do *not* want to learn.

    re: #58 rxc

    Again, I identified the issue that people overgeneralize from their own domains, you’ve just repeated that. The extraordinary claims is that all software has to be done the same way to be useful…

    I assume everyone knows that modern airplane design depends heavily on computers. Therefore, no one should *ever* fly until they’ve gotten complete disclosures of all source code, test cases, model runs, etc from Boeing, MacNeal-Schwendler, etc. Is that your conclusion? If so, the same applies to modern automobiles, especially given that the bulk of crash-crash tests are no longer in the real world, but in computers. So, don’t drive, either.

    re: #74 Lloyd Flack

    Thanks, I think the comment about discrete states versus continuous is especially useful.

    re: #89 TEBB

    Thanks. It isn’t just engineers looking at climate science, it’s the issue of someone with competence in one area over-generalizing what they know into another area. Interdisciplinary work is exceptionally productive, but usually, people who do a good job of it take time to learn a new domain, and then maybe bring their old expertise with them. (In the Great Wall of Science analogy I sometimes use, good interdiscplinary work means building bridges from one part to another, not rushing over to another piece with dynamite and trying to blow it up.

    Recall, that we’ve just had an example Once More Into the Bray, where the impetus seems to have come from a nuclear physicist & APS Fellow (Gerald Marsh) who’s on an anti-AGW crusade…

    So, it’s not just engineers :-)

  2. 102
    Hugh Laue says:

    Here in South Africa there’s a global warming skeptic who often makes his views known through his column for a local publication engineering news. I assumed that the scientific evidence for anthropogenic global warming was compelling and so I asked him for references that supported his view. I’ve been following the links, trying to look past the ad hominem attacks that appear to be an unfortunate characteristic of most blogs I have visited (from both “sides” of the debate) to see if there is indeed compelling support for anthropogenic global warming. I’m afraid I now find that I have done a 180 turn and now, if I have to label myself, put myself in the camp of the skeptics. The models may be (presumably are) built on good science but they are after all only models of a notoriously complex non-linear system with many assumptions not yet validated by actual experimental data. The models will only be validated by actual evidence from the future – until then they remain hypothetical. And as Douglass has shown the predictions of the models of an increase in the temperature of the upper layers of the atmosphere are not supported by the empirical evidence. i.e. the models fail to deliver. And how is the medieval warming from 1100 to 1250 rationalized? And the post-2003 ice core data that show (apparently – I have not seen the original references) no direct correlation between CO2 level changes and global temperature changes? The immediate reality of peak oil and the energy crisis is a much greater threat to our future well-being, IMHO, than the notion of extreme anthropogenic global warming purely based on unproven computer models.

    [Response: Douglass et are wrong on multiple levels and the data is starting to show what the models expect. Why do you think attribution of medieval warming is important for attribution of todays warming (equivalently why is working out why a forest burned 1000 years ago needed to work out why it burned this year, particularly when you saw the perpetrator walking away carrying a can of gas and some matches?). Your reference to ‘post 2003 ice cores’ not showing a connection is nonsense. I suggest you broaden your reading (start with the IPCC report – linked on the right). – gavin]

  3. 103
    mugwump says:


    RE gavin at #99:

    We have never claimed here that these really high sensitivities are plausible.

    If by “we” you mean realclimate, then yes, you have made such a claim. This is a direct quote::

    But the skewed nature of the distribution of possible sensitivities means that it is much more likely that 450 ppm will give us more than 4.5°C of global warming rather than less than 2°.

    I don’t see how to read that as anything other than a claim that the sensitivity distribution of Roe and Baker has objective validity.

    You are welcome to criticise people for what they say, but do not attribute statements to me that I have not made, nor opinions I do not hold.

    I did not attribute the above statement to you personally. The linked RC article was authored by “group” – if you disagree with it then fine.

    [Response: You misunderstand both me and that statement. The statement you quote does not mean that more 4.5 deg C is likely, it just says that it is more likely than less than 2 – both numbers are small. – gavin]

  4. 104
    Mark says:

    Re #95
    “I don’t see how that observation makes me a “pseudo skeptic”.”

    You remain wrong, however.

    Your insistence that you are not incorrect leads you to act appropriate to a skeptic. You can insist you aren’t but you are still acting in accordance with what such a mentality would manage.

  5. 105
    Mark says:

    “Now, GCM modelers don’t necessarily estimate the free parameters by directly inferring them from model behaviour”

    Says one thing: some of the free parameters are from microclimate modelling and other precise simulation techniques. Then you segue into

    “but they certainly adjust the parameters to get the model output to “fit” the 20th century instrumental record”

    which doesn’t allow any parameters to be what earlier was allowed to be extracted from simulation.

  6. 106

    Re: 92
    I think the problem with your self-educative approach is that you have let your skeptic dictate what questions you investigate. It’s not just “all about the models,” as one skeptic of my acquaintance proclaims. 4 things we know NOT involving models:

    1) The warming trend is clear and well-documented (see for instance the 2007 Climate Report on the National Climate Data Center site);
    2) CO2 et al. have been demonstrated to absorb IR as advertised (as discussed on this site);
    3) Isotopic study confirms that the atmospheric CO2 is of fossil (ie., human-mediated) origin;
    4) Satellite data clearly show the stratosphere to be cooling; inexplicable except as a result of the greenhouse effect. (An “Inconvenient Truth” I have never seen show up on a denialist blog yet.)

  7. 107
    Lawrence Brown says:

    There are, to be sure, no quick and easy answers concering future climates. One needs only to look at figure 3-26 in Ruddiman’s “Earth’s Climate Past and Future”,showing the interactions involved in a 3-D GCM, to gain a sense of the complexity, and then add a time component to track these grid boxes over time.
    Yet, we learn to crawl before we walk. Which is why a post here about a year and a half ago,
    though the assumptions do not quantitatively apply to the real world,is still a very useful introduction and will point anyone who wants to learn more about the physics behind climate modeling (including an engineer like myself)in the needed directions.

  8. 108
    Hugh Laue says:

    Dear Gavin, Kevin, thanks for your considered responses. I have not been looking at just models but also trying to get a sense of the reliability of the data upon which the models are based. Anyway it is clear that I have much more research to do (including reading the IPCC report). I’m not sure I understand the response to my comment on the warm medieval period. Can you direct me to any papers that explain this in support of the GHG warming hypothesis? In other words, do any of the current models explain/fit the proxy data of the last 2000 years or however far back it goes?

  9. 109
    bsneath says:

    What you do not state in your article is the level of inaccuracy and unreliability found in complex modeling. Very small adjustments to individual assumptions may have cascading and material effects on the outcomes. Further, it is too easy for scientists, regardless of how objective they believe they are, they are still subject to human frailties, to input biases that ultimately substantiate preconceived hypotheses. A common fallacy is to accept without question input assumptions whereby the model behaves as predicted but to thoroughly question input assumptions that provide results that contradict. The resulting is model bias.

  10. 110
    David B. Benson says:

    Hugh Laue (108) — There is now an Antarctic ice core record extending back about 800,000 years, I believe. However, the longest GCM run that I know about was done in Japan, providing a decent fit from 125,000 years ago to around 8,000 years ago; that’s from interglacial 2, the Eemian to interglacial 1, the Holocene climatic optimum.

    Regarding reading, on the side bar are listed several books (but I also include two by W.F. Ruddiman: “Earth’s Climate, Past and Future” and his popular “Plows, Plagues and Petroleum”). I’ve read several of these and I still find plowing through the IPCC AR4 though going.

  11. 111
    Lamont says:

    Gavin: so, what graduate-level textbooks are there that discuss the details of the Manabe-Wetherald paper and 1-dimensional climate models in detail? And i’ve already got a background in astronomy and physics, so i understand the modeling of stellar interiors and should be able to deal with the physics (although modeling convection may cause me to completely give up any hope of replicating Manabe-Wetherald, but i’d at least like to do the reading up until the point where I make that decision).

    [Response: David Archer’s book, or Ray Pierrehumbert’s draft are both good starts. Houghton’s Physics of Atmospheres would be the next step up. – gavin]

  12. 112

    This thread seems to have been overtaken by several trolls.

    Gavin, as a regular Realclimate reader (though rarely posting), I admire your patience in responding to the same contrarian arguments and fundamental misunderstandings over and over again. Your work on this website is very useful for public education even if sometimes you feel you are stuck in a scene from the movie Groundhog Day.

    [Response: Sometimes even Kafka. – gavin]

  13. 113
    woodentop says:

    @ #106

    “4) Satellite data clearly show the stratosphere to be cooling; inexplicable except as a result of the greenhouse effect. (An “Inconvenient Truth” I have never seen show up on a denialist blog yet.)”

    Try here:

    [Response: Pretty sure lucia would bridle at your assumption. – gavin]

  14. 114
    John Mashey says:

    re: #100 TEBB
    re: books
    I’d hardly claim to offer a definitive list of such, but you might look at that How to Learn About Science (Great Wall of Science)” post I mentioned.

    I think you are looking for Category B & C books in the bibliography included. Search for this section:

    “Critical Thinking:

    For general defense against disinformation of various sorts: BES2001, CAP1987, HUF1954, JON1995, KUR2001, MON1991, PAU1998, TUF1983.

    Scientists can believe strange things and stick with them: ARP1998, EHR2001, EHR2003

    Many people can believe really strange things FRA1986, GAR1981, GAR2000, PLA2002, RAN1986, SCH1994, some of which the originators believe, and some of which are hoaxes. Some retain belief even after the hoaxers show them how they did it.

    Starting from Scratch on Climate Science (B & C)

    If I had to pick one book to read, it would be RUD2005.

    Useful popular books are GOR2006, MAN2008, REV2006. Normally, I wouldn’t recommend a politician’s description of climate science, but in this case, it’s a well-presented, mostly-accurate equivalent of talks by many climate scientists. MAN2008 is a nice recent addition.

    One might go on to GRA1997.

    At some point, one should learn more of the history of this topic, via WEA2003, or through the first half of Naomi Oreskes’s video “The American Denial of Global Warming.” mentioned above. Many key basics of climate science are actually quite old.”

    Hope that helps.

  15. 115
    Chris Maddigan says:

    Are not many of the parameters in the models statistically estimated? If so how can there be sufficient data of sufficient quality to both estimate the models and validate them.

    An additional question. If all the models are derived from the fundamental physics and are modeling the same earth climate system, why are they all different. This would imply that they are all incompletely specified, wrongly specified or are introducing arbitrary elements not derived from the science.

    [Response: Read this – it might help. – gavin]

  16. 116

    Wonderful to see Dave Letterman deliver his Simple Statement on global warming; Who knows better than a professional entertainer how to make a snappy presentation.

    Short 3 min video:

    Here is the CBS description of words he delivered:
    ( snipped to subject of AGW )

    ACT 2:
    Dave admits to being a little late getting on the global warming/climate change band wagon. When he first heard about it, he figured it was just a bunch of tree huggers making noise. But now, Dave’s eyes are wide open. Have we ever had this many hurricanes? Something is hinky. Our weather is going all screwy. And just a half hour ago, Dave learned a big huge ice chunk the size of Rhode Island just fell off the South Pole. People are finally now trying to do their part to stop our killing of the planet, but their efforts are meager and won’t amount to a hill of beans. People proudly say things like they are reusing party toothpicks to conserve. But it’s too late. We need to get the over abundance of carbon dioxide out of the atmosphere. And why isn’t anything being done? Because since 1980 we have had no leadership, no Republican, no Democrat has stepped forward and taken the lead. JFK inspired us to get to the moon in ten years. Today, every politician is afraid to talk about climate change because they don’t want to hurt the feelings of their big oil buddies. Dave cries out, “It’s too late! We are dead meat!”
    Dave exhales, then says, “Alright, let’s try to have some fun now.” But Dave can’t let go. He says climate change is no longer part of the Republican platform. “We are so screwed!” Dave says that if everyone in the world stopped driving and started riding bicycles, EVERYONE IN THE WORLD TODAY, if everyone stopped driving, due to the carbon buildup in our atmosphere, the planet would still continue to heat for the next 60 years. We are so screwed.

    ACT 3:
    Dave continues about climate change and how the polar bear will soon disappear. Dave exclaims, “In 6 years there will be no ice left on the peaks of the Rocky Mountains!”
    Paul, bewildered, asks, “Dave, what this ‘Polar Bear.’?” A crushed Dave mentions, “Ladies and gentlemen, this is sad. Paul Shaffer doesn’t remember polar bears.” And now due to the global warming and 68 degree Februarys, organisms are coming up from the earth and eating and destroying things. The fly beetle worm comes up from the ground and are eating pine trees. They are not supposed to do that. They are supposed to frozen to death in the deep freeze of winter, but there are no longer deep freezes. We are all screwed.

    ACT 6:
    THOMAS L. FRIEDMAN: the 3-time Pulitzer Prize winner has a new book, “Hot, Flat, and Crowded,” all about climate change, the earth, and what we are doing about it.
    Dave wants to know, “So, how are we doing?” Thomas says we are falling behind the curve. The weather is going to get weird; the hot will get hotter, the cold colder, the wet wetter, and the droughts longer. Worst case scenarios that were predicted for the year 2050 have now been accelerated to be here in 2012! The question is why isn’t someone in political power doing something about it? Where is this person? Friedman says the chant at the Republican Convention of “Drill, baby, drill” certainly isn’t the answer. Friedman says we are on the eve of an energy revolution and our Republican leaders are crying “Drill, baby, drill.” It would be like being on the edge of the internet revolution 20 years ago and chanting, “IBM Selectric Typewriters! IBM Selectric Typewriters!” We need to move beyond our 20th Century thinking. What we should be chanting is “Invent, baby, invent.” Friedman is not against new drilling, but we need to invest in renewables. His book, “Hot, Flat, and Crowded”:
    “Hot” refers to global warming.
    “Flat” refers to the rise of the middle class all over the world.
    “Crowded” refers to the rapid population growth. The earth will be home to another billion people in 12 years.
    Energy Technology (ET) is the next great revolution. Whatever country owns that industry will be the richest and most powerful. Energy Technology will create new renewable energy and nation building. The United States has to get involved all the way to lead the world in this. I think I mentioned this last time Friedman was here, or maybe it was Robert F. Kennedy Jr . . . . . to make energy technology really appealing, we have to stress the money that can be made from this. It’s the financial interests that will get the ball rolling. People pretend they are interested in saving the Earth, but what they really want is money and a second home on the beach. Once it is realized how much money is to be made in new energy and how it will make all Americans richer, then we will get behind it.
    Thomas Friedman – always interesting, and speaks a language we can all understand.M
    “Hot, Flat, and Crowded” – it’s in stores now, and if you turn on your TV right now, you’ll probably see him. He’s all over the place this week.
    “Invent, baby, invent!”

    And that was our show for Monday September 8, 2008.

  17. 117
    mugwump says:

    RE #103:

    [… The statement you quote does not mean that more 4.5 deg C is likely, it just says that it is more likely than less than 2 – both numbers are small. – gavin]

    Actually, the statement by RC says 4.5C is “much more likely” than 2C (not just more likely), and it also says “…the skewed nature of the distribution of possible sensitivities…”, which would imply that RC endorses the functional form of Roe and Baker’s distribution (the skewed sensitivity distribution is, after all, the whole point of the paper).

    In fact, according to Roe and Baker, the expected sensitivity is infinite, so the probability that it is greater than 4.5C is 1.

    [Response: Well, since that is obviously nonsense perhaps you should go and read the paper again. – gavin]

  18. 118
    mugwump says:

    Actually, the probability that the sensitivity is greater than 4.5C is not unity under Roe and Baker (my mistake), but the expected sensitivity is infinite, and the greater than 4.5C probability is around 10 times the less than 2C probability.

  19. 119
    Al Tekhasski says:

    Gavin, I have a question:
    According to Figure 4.12 from Ray’s book,
    Eye-balling the general slope of the absorption function, doubling of CO2 leads to a shift in optical thickness boundary of the main CO2 absorption band by about 7 cm-1 (the other edge is covered by water vapor, so I neglect it), correct? The OLR flux at the edge is about 0.3 W/m2/cm-1, according to upper picture. Therefore, the CO2 doubling reduces the flux through atmospheric window by 0.3*7= 2 W/m2. Would it be a fair order-of-magnitude estimation of 2xCO2 “radiative forcing”?

    [Response: No. The forcing is about 4 W/m2 calculated much more accurately. -gavin]

  20. 120
    Hudibras says:

    I’ve been following the AGW debate for a few years and have concluded there is a great deal of reasonable doubt about the suggestion that increasing/decreasing CO2 concentration by humans has a high impact on climate.

    As a result I would not support expensive actions to manage CO2. I believe my view is shared by an ever growing number of people world wide.

    [Response: Believe what you want. Doesn’t make it true. – gavin]

  21. 121
    Chris Colose says:


    Where in Roe and Baker did you get the impression that they say a sensitivity is greater than 4.5 C?? At best, you can argue that a sensitivity greater than 4.5 C is unlikely but the possibility is not zero.

  22. 122
    Chris Colose says:

    Please delete last post (got cut off from symbol use)


    your interpretation is still incorrect. The temperature response is the product of the sensitivity and the forcing (neglecting efficacy), so if one of those terms goes to infinity, then the temperature goes to infinity.

    What you may mean is that you can model the climate response as an infinite power series (e.g., 1 + f + f^2 + f^3…f^n) where f is the feedback factor and is between zero and one. Thus, a small change in ‘f’ produces a a larger change in the overall response, which is why we may not see a singificant reduction in the 2 to 4.5 C range.

  23. 123
    Joe Triscari says:

    @101 Your response to rxc is nonsense. He certainly was not claiming that he requires the code from Boeing. I find it hard to believe you don’t know this. I expect that all the models used to make an airplane to be rigorously documented and I trust that they are. I don’t need to see that documentation because the FAA has experts to examine them and Boeing has lawyers that understand liability laws. I don’t expect to be supplied those documents because when Boeing is asked by authorities, they don’t don’t do any of the following:

    1) Averaging models. If Boeing said that we used two models to make this airplane: one predicted a crash by a hard turn to the left and the other predicted a crash by a hard turn to the right so on average it flies straight, I wouldn’t get on the plane. I’ve never heard of the notion that averaging models gives an answer close to the truth is “confirmation.” It generally means one or both models are wrong.

    [Response: BS. Every weather or hurricane forecast is from an ensemble. Any conclusion from a complex turbulent flow is drawn from an ensemble. – gavin]

    2) The general tone of the AGW people is exceedingly shrill. The world will end and the science is settled. There’s consensus, etc… Shrill is something many senior engineers have seen coming out of the mouths of people who were obviously – and later proven to be – wrong. Quite often.

    [Response: The tone of people like you misrepresenting the science is extremely arrogant. That’s definitely a sign that’s something wrong and that their opinions are rooted in politics. Quite often. – gavin]

    3) I haven’t seen it recently but I have seen plenty of jibberish about how it can only be understood by climate scientists. This is a red flag. If you expect me to put resources against your problem, you had better be able to say why. Saying that the risk is too big if we don’t is not enough. Saying that it is encoded in a model that should determine public policy but is not available to the public is not enough.

    [Response: Let me get this straight. You come to website that has working climate scientists trying to explain climate science to the public and you think are only point is to tell people they can’t understand? Please go back and think about it for more than a microsecond. – gavin]

    4) Psychoanalysis. I can’t imagine why you guys think this is convincing to anyone. This may shock you but senior engineers have seen people replace technical arguments with an analysis of the motives of their opponents many, many times. It isn’t the sign of a serious scientist. It’s the sure sign of a politician.

    5) “It’s basic physics – until it isn’t.” To listen to some parties, AGW is as fundamental as Newtonian physics, basic thermodynamics, the Copernican solar system and evolution. “But if you want to get reliable numbers – if you want to know whether raising the level of greenhouse gases will bring a trivial warming or a catastrophe – you have to figure in humidity, convection, aerosol pollution, and a pile of other features of the climate system, all fitted together in lengthy computer runs.” If the quote is true stop comparing people who don’t believe AGW to people who don’t believe in some basic science. Basic science can be taught to teenagers. AGW apparently involves computer runs not available to everyone.

    [Response: The greenhouse effect is basic science. The increases in GHGs due to human activities is basic science. The observed warming is basic science. The attribution of warming to increasing GHGs is slightly more sophisticated science. The long term impacts of further increases is sometimes clear, sometimes uncertain. People discussing the latter two are in a completely different category than people disputing the first three. – gavin]

    When Boeing and MD starts doing any of the above in response to FAA requests, I’ll start buying bus tickets. When AGW people stop all of the above, I’ll begin to consider the possibility that the science is settled or that there’s any science at all.

    [Response: Settled/not settled is false binary distinction much beloved of certain think-tanks. Nothing is ever completely settled, and yet much is understood. – gavin]

  24. 124
    mugwump says:

    RE #117:
    I said:

    “In fact, according to Roe and Baker, the expected sensitivity is infinite”

    Response: Well, since that is obviously nonsense perhaps you should go and read the paper again. – gavin]

    Ok, derivation:

    Roe and Baker (RB) model the “total feedback factor” f as a gaussian. Climate sensitivity is proportional to 1 / (1-f). Obviously, we should bound f to be between 0 and 1, which a gaussian doesn’t do, but we can just truncate and rescale to get a valid probability density function for f, which will still have the functional form of a gaussian for f between 0 and 1.

    So, the expected climate sensitivity is proportional to the integral from 0 to 1 of 1 / (1-f) * N(f), where N(f) is proportional to the normal density function.

    Now, since f is bounded between 0 and 1, N(f) is bounded below by some number greater than zero, call it K. Hence the expected climate sensitivity is greater than some (positive) constant times the integral from 0 to 1 of 1 / (1-f).

    But the integral of 1 / (1-f) is -log(1-f). So the integral from 0 to 1 of 1 / (1-f) is -log (1-1) + log (1-0) = -log(0) = infinity.

    Thus, the expected climate sensitivity under the RB model is infinite.

    [Response: The mean of a Cauchy distribution is undefined, but the probability of lying between any two values is bounded (and less than 1) – it is therefore your corollary that is nonsense. -gavin ]

  25. 125
    Dan O\'Donnell says:

    DOE has announced that it will provide 10 million hours of time on three of its most powerful computers (ANL, ORNL, LBNL) to NOAA for further exploration of advanced climate change models. This should help improve the models as well as help the scientists understand both the models and the climate change effect.

  26. 126

    rwx writes:

    I am not a climate scientist, but if the climate scientists cannot produce documentation like this, then their claims cannot be believed.

    I agree. And if physicists can’t produce that kind of documentation for computer models of gravitons, I think we can forget about that silly “gravity” business.

  27. 127
    pete best says:

    Re #120, Well now that you have found real climate you should read some of the articles and then form a more objective opinion. Maybe you can start by mentioning the things that stop you from supporting action on CO2 emissions?

  28. 128

    mugwump writes:

    Now, GCM modelers don’t necessarily estimate the free parameters by directly inferring them from model behaviour, but they certainly adjust the parameters to get the model output to “fit” the 20th century instrumental record (it could be argued that the fit between models and the 20th century instrumental record is the sine qua non of progress in the field).

    GCMs are not statistical models fit to climate time series. When a GCM is revised, it’s because a better way has been found to represent some part of the physics.

    You were told this, in some detail, on Deltoid a couple of months ago. Yet you keep repeating the same false idea. Why is that?

  29. 129

    Yoron writes, quoting a math site:

    Non-linear equations can be extremely difficult, and are often insoluble.

    You can’t conclude from that that you can’t use those equations. Equations which can’t be solved can often be made to give highly accurate answers by means of numerical successive approximations or integrations. An example would be the Planck law for radiation — it’s an integral that can’t be solved. Nonetheless, it’s easy to write a numerical integration that can give you answers accurate to as many decimal places as you want. Even I’ve done it.

  30. 130

    TEBB posts:

    a list of your favorite science books for non-science (i.e. liberal arts majors who don’t work in science but find it interesting) would be wonderful to have. I have a lot of good evolution and biology books, but none on global warming because I’m afraid of accidentally getting something outside the climatologists’ consensus.

    Some good popular discussions with very little math are:

    Philander, George S. 1998. “Is the Temperature Rising?”

    Weart, Spencer 2003. “The Discovery of Global Warming.”

    Both are thoroughly within the scientific consensus.

  31. 131
    rutger says:

    well 100 years of warming, doesnt mean it has been cooling over the last 3 million years either

    .. for instance why did the lenght of the glacials increase from 40 kyears tot 100 kyears
    in the last million years..

    we actually need this warming.. nobody likes glacials

  32. 132
    Mystified says:

    What if you had overlooked something really important.
    I don’t really expect an answer but i found this paper more than appropriate to raise serious doubts about the validity of the explanations you usually give.
    Best regards.

    [Response: Curious. You’d rather believe that an obscure website has found a trivial algebraic flaw that thousands of other scientists had missed. A flaw so fundamental that all radiative transfer calculations – including those for all the satellite imagery people are using to track sea ice and hurricanes – must be wrong. Hmm…. or Miskolczi made a mistake in his derivation. Which is more likely? – gavin]

  33. 133
    andy says:

    Isn’t there any step between a simple equation, and the global climate model? Like, is there modelled something simplier, like how is the air column cooling on a windless night in spring time vs autumn time when the CO2 concentrations are slightly different? Or compare what are the results now, and what they will be in 5 years with higher CO2 levels?

    [Response: There are intermediate steps – like radiative-convective models used by Manabe, but simple weather or seasonal analogs? no. – gavin]

  34. 134
    Mark says:

    Hubris, #120. What makes you reach that conclusion? What poll did you make concerning the worldwide opinion? Why would the world think the same as you?

  35. 135
    Mark says:

    re: Gavin’s response to 109.

    Actually, 2 is well within an order of magnitude of 4.

    So is 10.

    The difference Al gets is because he’s not *accurately* accounting for the change, but it is about right. What may also be a problem for his calculation is igoring the water-bound side of the equation. With both CO2 and H2O obstructing IR radiation, the height above sea level of one optical depth at that wavelength is a lot higher. Higher = cooler. Cooler = less re-radiation and so more entrapment of that energy within the system.

    This is why “IR bands are completely absorbed already so more CO2 can’t affect the warming” is wrong.

    ‘course this breaks down in ways stellar physics doesn’t bother with when the optical depth passes beyond the tropopause.

  36. 136
    Dan Hughes says:

    re: # 84

    rxc was referring to computer programs developed for analyses of physical phenomena and processes occurring within the reactor; not to the equipment components themselves. The models must predict the response of the entire nuclear steam supply system under both steady operating conditions and off-normal upset conditions.

    By the same token, the design of the equipment components must take into account the responses of the system. The components must be designed to accommodate the most extreme conditions anticipated to occur during the life of the system. And this is true for almost all engineered systems in general. The result being that in fact this statement is not correct:

    Each piece put into a nuclear power plant is specified in advance and you know what it’s made of.

    And the statement is a mischaracterization of the design process for almost all engineered systems; passenger aircraft, space shuttles, bridges, elevators, etc. being additional important examples.

    Also re: #101

    Therefore, no one should *ever* fly until they’ve gotten complete disclosures of all source code, test cases, model runs, etc from Boeing, MacNeal-Schwendler, etc.

    Complete disclosures of all the information listed has occurred and been subjected to Independent Verification and Validation and other Software Quality Assurance procedures and processes. These activities are required by federal law, and equally important, are simple good sense for all calculations that have potential impact on the health and safety of the public.

    Do you seriously think that any aircraft or automobile company would not follow the most strict requirements necessary to ensure the reliability of all calculations?

    The problem, and it’s a critically significant problem, is that we continue to read that Climate Science seems to be the only community that cannot preform these fundamental tasks. While at the same time the calculations performed by the community have the potential to impact the health and safety of almost everyone on the planet.

    [Response: Dan, repeating the same thing a hundred times does not make it true. If you want to campaign to double the climate modeling budget so that we can employ an extra thousand code checkers, great. But funders have made it absolutely clear that they prefer that we focus on science (we are scientists after all) and that no doubling of funding is on the horizon. The priorities are reversed in the nuclear industry and so they do things differently. If you want to check though our code, go ahead – nightly snapshots of our repository are on our website. All bug fixes will be greatly welcomed! In the meantime, feel free to ignore all modelling and instead base your projections on the tea leaves in your cup. – gavin]

  37. 137
    Mark says:

    mugwump, #124.

    If ANY point in that distribution has a probability of 1, then EVERYWHERE ELSE MUST be zero.

    Hence your mathematics is incorrect.

    Either there’s no “1” and your log(0) isn’t there, or there IS a 1 and the average is the same as the value in the range that has a probability of 1. Which still isn’t infinity.

    Hell, I’ve only got an A level in maths and I know what you did was wrong!

  38. 138
    Jess says:

    You know, with the skeptics the debate reminds me a lot of the one surrounding smoking.

    You can’t prove smoking causes cancer. After all, people got lung cancer before cigarettes became widespread. And the correlation between smoking and lung cancer is just that, a correlation.

    I could even point to the fact that lung cancer rates in France weren’t much higher than those in areas of the U.S. where smoking was much more restricted.

    As late as the 1980s cigarette companies were saying that smoking wasn’t a problem. They could even trot out a few experts to say so.

    But I don’t think any serious person thinks smoking is not unhealthy and a major cause of many diseases.

    The real issue, I think, is that there’s a segment of the population that is very., very unhappy with certain changes in their lifestyles that are just going to have to happen. Sorry, you just won’t be able to drive a Hummer that gets 2 gallons to the mile. What is interesting to me is that it is just so important to have consumer “choice” that all else takes a back seat. Mugwump’s comment about environmentalists’ political goals was revealing. What are those goals exactly?

    The fact is there are plenty of economic controls we accept because we (as a society) decided that not doing so would be really, really bad. We control the labor market by not allowing slavery, for instance, because even though it might be terribly efficient for certain industries (it actually worked pretty well for agriculture) the human cost is just too high. Similarly, we don’t allow cigarettes to be sold via vending machines in grade schools. Nor do we allow factories to simply poison their workers with the idea that if the products are cheaper, then it’s ok.

    Maybe it’s because I live in New York, and haven’t owned a car for some time. I do not see the need to have an SUV. I’m quite confident in my manhood, thanks. (I used to drive a 1986 Toyota Corolla, which gave me fantastic gas mileage for more than a decade — a tank got me all the way from Boston to Rochester, NY on a regular basis).

    Or maybe I’m too cautious. I figure if there’s a nonzero chance, say 30%, that sea levels will rise enough to put a chunk of Florida real estate underwater, than it is far better to take steps that are sort-of-pricey-but-manageable now than to wait until things get even more expensive. I’m weird, perhaps, or maybe it’s a tree-hugger thing.

    Many “skeptics” don’t seem to think CO2 can have that big an effect. Let me remind some of them that it was the work done studying the atmospheres of other planets as well as the Earth that helped get the science going. Want to see how big an effect CO2 has? Go to Mars. The blackbody temperature of the planet should be something around 228 K (I haven’t done the math in a while, if someone has a better answer let me know, I used the minimum solar distance for Mars). It bottoms out at about 180 K when the planet is farther from the sun.

    But the actual average temperature on Mars gets as high as 273 K. It averages just above the 228 K figure, usually in the 230s.

    That’s because Mars has an atmosphere, made up almost entirely of CO2. It’s really, really thin — on the order of 1% of Earth’s.

    Yet the CO2 provides measurable forcing to Mars’ climate.

    Now, if such a small amount of CO2 provides that much heating over there, then it’s reasonable to assume that it does so here as well. Even in small concentrations CO2 packs a bit of a punch. Mars has much more CO2 in its atmosphere than Earth does (pound for pound as it were), of course, but it’s notable that with an atmosphere that’s near nonexistent you get 2 degrees K or thereabouts. That’s a lot.

    To compare, the Earth’s temperature “should” be 255 K, or -18 C on average. The water vapor, oxygen, CO2, methane, and nitrogen all make it much balmier than that. And calculating the effects of each of these is complicated, but not that hard (assuming a static atmosphere). Space scientists have done this for years to make sure the models for other planets were in the ballpark and to get an idea what to look for.

    Dump gigatons of CO2 into the atmosphere faster than it can cycle out and it seems elementary you’d get a huge effect in short order (on geologic timescales). The simplest thing to do is stop doing so much of it. After all, we don’t use rivers as open sewers in most places anymore, even we could always find another river, and some rivers are so big that we could never pollute them to the point where they do things like catch fire, right?

  39. 139
    Dan Hughes says:

    Thanks for the very reasoned response, gavin.

    The use of “an extra thousand code checkers” totally validates my characterization of the Climate Change Community to these issues.

    To begin the task that you suggest that I do, I need the documentation for the model equations and the coding. Can you point me to the peer-reviewed publication that contains the final form of the continuous equation for the momentum balance in the vertical (radial) direction and the as-coded form of the discrete approximation to that equation? I’ll need additional documentation for the actual coding.


    Thanks again.

    [Response: Sure. Send me enough money so that I can employ a programmer and documentation expert to make it easy for you. Or you could actually try looking up references. If that isn’t possible check out NCAR’s code instead. They have about 4 times the staff we do and a very nice online manual. – gavin]

  40. 140
    Ray Ladbury says:

    Dan Hughes, so where is the code used to discover the Top quark archived? How about the code used to analyze the seismic waves and come up the Earth Reference Models? How many people pored over that code looking for errors outside of the groups that did the work?
    Science works by different rules. Analyses are conducted independently, and it is critical to the methodology that the analysis methods–including code–remain independent as much as possible.
    The problem in my opinion is that we don’t have a discipline of “climate engineering,” that is people whose job it is to figure out how bad things COULD become and figure out if we can engineer against them or if the consequences are so severe that the threat must be avoided. This is the case in part because the potential impacts of climate change are so wide-ranging that such an engineering effort is daunting indeed. More to the point, we don’t have such an effort in place because many continue to deny very cogent scientific evidence that climate poses a credible threat. Maybe if you and your buddies accept the science, we can get your wish of reliable engineering code to mitigates climate change.

  41. 141
    mugwump says:

    [Response: The mean of a Cauchy distribution is undefined, but the probability of lying between any two values is bounded (and less than 1) – it is therefore your corollary that is nonsense. -gavin ]

    Oh come on, I corrected the corollary immediately at #118. Both #117 and #118 were in the moderation queue simultaneously, so you knew I had corrected it when you made your “nonsense” claim.

    And it is worse than “the mean of a cauchy is undefined”. A cauchy distribution is symmetric. It has no mean because the mean is essentially “infinity – infinity” which is undefined. Roe and Baker’s model is not a cauchy. It is not symmetric (that’s the point). In fact the probability of sensitivities less than 1.2C is zero under their model (assuming feedback is positive). The expected climate sensitivity under their model is simply infinity (not “infinity – infinity” = undefined).

    Back to your comment on the realclimate article on Roe and Baker:

    [… The [realclimate] statement you quote does not mean that more 4.5 deg C is likely, it just says that it is more likely than less than 2 – both numbers are small. – gavin]

    RB estimate the parameters of their distribution from a bunch of published GCM studies. They come up with a number of different values, but they are all clustered around a mean f of 0.7 and a standard deviation of 0.14.

    Plugging those numbers into their distribution, I get a 40.5% probability of climate sensitivity greater than 4.5C, and a 0.27% probability of climate sensitivity less than 2C. That makes 4.5C 150 times more likely than 2C under their model, and certainly not “small” as you claim. [plugging in other values for mean and standard deviation from their paper yields similar results]

  42. 142
    Dan Hughes says:

    Ray Ladbury, where are the applications of the results of the code used to discover the Top quark that have the potential to impact the health and safety of the public?

    Lacking any such applications, I don’t need to know anything about that code. Or any other codes the results from which do not have the potential to impact the health and safety of the public.

    [Response: Ah, but someone has claimed the LHC will destory the world. The consensus of scientists says it’s bollocks. But have you examined their code? checked their calculations? examined their assumptions? Why not? Surely the whole world is at stake! – gavin]

    Implementation of mitigation and adaptation policies is truly ‘above my pay grade’ for all my buddies and me. That power resides in Washington DC for the USA.

  43. 143
    Nick Gotts says:

    “Actually, the probability that the sensitivity is greater than 4.5C is not unity under Roe and Baker (my mistake), but the expected sensitivity is infinite, and the greater than 4.5C probability is around 10 times the less than 2C probability.” – mugwump@118. This is of course entirely compatible with what Gavin has been saying: the >4.5C probability can be as small as you like, as long as it is positive, and the statement you make still be true. That’s the thing about highly skewed distributions: the mean doesn’t tell you much, and can be infinite.

  44. 144
    mugwump says:

    RE #137 Mark,

    If ANY point in that distribution has a probability of 1, then EVERYWHERE ELSE MUST be zero.

    Nowhere in the distribution has a probability of 1. The expectation is the integral of the climate sensitivity multiplied by the probability density function (pdf). The pdf stays well defined, but the climate sensitivity diverges as 1 / (1-f) as f approaches 1. It’s what those in the theoretical physics world call a “logarithmic divergence”.

    Hell, I’ve only got an A level in maths and I know what you did was wrong!

    I’ll see your A level and raise you a PhD plus a bunch of publications :-)

  45. 145
    Greg says:

    Well count me as another Senior Engineer and skeptic. And involved in modelling as well (LS-DYNA). What really makes me laugh is the assumption that, what with being unable to provide a direct physical exposition or any empirical proof, the burden falls on skeptics to show why we shouldn’t act.

    Here’s a little tip for those of you lounging in comfort in the ivory towers of academia – abundant fossil fuels underpin our entire civilisation and your entire way of life. You eat well, live well and have the life expectancy and health that you do entirely because of free and available energy. The burden is on you to provide the proof. And if I hear one more fool hand-wave the issue away with some comment about ‘solar and wind’, I will lose it. To answer Ray Ladbury’s “Doctor, Doctor, it hurts when I raise CO2 levels.”, I say it doesn’t hurt one whit. He can go back to the 1700s and then we’ll see how much it ‘hurts’. Unless he defines ‘hurt’ as ‘comfort, wealth and prosperity’.

    Am I worried about global warming? A little, if at all. One hundred and fifty years ago, no cars, no planes, and oil was a black ooze that came out of the ground, not an energy source. Sixty years ago, uranium was a funny rock that glowed in the dark. A hundred years from now, who knows? And who cares? Do you think that if some genius modelled the greenhouse effect in 1750, then advised everyone not to bother with the industrial revolution in order to ‘save their children’, we’d be better off now?

    Personally, I advise you all to grow a pair, and have some faith in the human race. Full steam ahead. Let us grow wealthier, stronger, and smarter, and *if* this turns out to be a problem we’ll solve it.

  46. 146
    mugwump says:

    RE #28:

    GCMs are not statistical models fit to climate time series.
    When a GCM is revised, it’s because a better way has been found to represent some part of the physics.

    Why do they revise the models? Because they don’t explain all the data (including climate time series, but also all other kinds of data).

    Do you really think when the scientists are revising the models they do so only on the basis of some abstract physical first principles? Of course they don’t. And nor should they. They look at the data, construct physical models to explain the data, test the models, make modifications, etc etc. That’s the way it works and that’s the way it should work.

    Outside of pure thought exercises like Einstein’s general relativity, there is very little science that is not data driven.

    You were told this, in some detail, on Deltoid a couple of months ago. Yet you keep repeating the same false idea. Why is that?

    Gee, I don’t know BPL, maybe because it’s not false.

    [Response: No. It is. The data and ideas that come in to drive changes in code are generally based on single processes – the scattering of aerosols, the thermodynamics of ice, the rheology of ice sheets, the impact of eddies in the ocean, and observations over a very small number of years or campaigns. The idea is that by improving the physics at the level of the single process, the emergent properties improve also. So far, and for most processes this turns out to be a correct assumption. It is not the same as twiddling with processes in order to improve the fidelity to the 20th century trend. Read Schmidt et al (2006) (and I know it’s dull), but point to me the code changes and development that are discussed that have anything to do with trends. You won’t be able to, because that isn’t how it works. – gavin]

  47. 147
    Ray Ladbury says:

    Greg says: “Well count me as another Senior Engineer and skeptic. And involved in modelling as well (LS-DYNA).”

    OK, I’ve incremented my ignorant-food-tube tally by one.

    As to his suggestion: “Personally, I advise you all to grow a pair,…”

    Personally, I’ve never seen much advantage in growing man-teats, Greg, but I hope you’re happy with yours.

  48. 148
    Nick Gotts says:

    “Personally, I advise you all to grow a pair, and have some faith in the human race.” Greg@144

    Greg, when making important decisions about the future of humanity, I consider reason a better guide than faith, and brains more useful than testes.

  49. 149
    walter pearce says:


    There’s a rather large amount of empirical proof of AGW. You could start with

    It’s odd to demand proof from the scientists on warming and offer only faith in the human race in return.

  50. 150
    SecularAnimist says:

    Greg wrote: “What really makes me laugh is the assumption that, what with being unable to provide a direct physical exposition or any empirical proof, the burden falls on skeptics to show why we shouldn’t act.”

    There is both a “direct physical exposition” and abundant empirical evidence for anthropogenic global warming. You are merely proclaiming your ignorance of these facts, which is not particularly interesting.

    Greg wrote: “abundant fossil fuels underpin our entire civilisation and your entire way of life. You eat well, live well and have the life expectancy and health that you do entirely because of free and available energy”

    In what reality are fossil fuels “free”? Have you noticed that you have to pay for gasoline at the pump, they don’t give it away?

    On the other hand, wind and solar energy are actually free, far more abundant than fossil fuels, and won’t run out on any time scale that is important to human civilization.

    Greg wrote: “And if I hear one more fool hand-wave the issue away with some comment about ’solar and wind’, I will lose it.”

    You are evidently as ignorant about energy as you are about climate science. The USA has vast commercially exploitable wind and solar energy resources, more than enough to produce several times as much electricity as the entire country uses, with today’s technology.