RSS feed for comments on this post.

  1. We have to be careful here. One problem in the debate is people (engineers for example) who understand just enough math to get into trouble. Models that leave out convection, for example, can give weird, runaway results, which at one early point even cast some doubt on the whole theory. See my historical essay on simple models, in particular this incident.

    Case in point: the statement “Point 2: Radiative forcing – whether from the sun or from greenhouse gases – has pretty much the same effect regardless of how it comes about.” Maybe true for a globally average temperature, but solar forcing causes warming at all levels, whereas greenhouse gases cause warming at the surface and lower atmosphere but cooling in the stratosphere, above where the radiation is blocked. In fact that is what is happening, and this “signature” has been cited by review groups as important evidence that the current warming is due to gases and not solar activity.

    Simple models are valuable “educational toys” (as one scientist called them) for experts who understand what the models can and can’t tell, but they are toys with sharp edges.

    [Response: Your points are very well taken…. Thanks. -gavin]

    Comment by Spencer Weart — 10 Apr 2007 @ 8:36 AM

  2. I must protest! You said simple!

    Comment by __earth — 10 Apr 2007 @ 8:40 AM

  3. I’d like to see more of these posts. It’s illuminating to see how things work in a concrete model that one can plug numbers into and play with.

    Comment by NU — 10 Apr 2007 @ 9:14 AM

  4. EdGCM is another very simple model that people can learn with. It is a bit more complex than the few equations in this post, but based on them, and simpler than most other GCMs. We’ve taken the time to move what are normally hard-coded or binary inputs to simplex external text files, so people can plug and play with different numbers and examine results.

    Comment by mankoff — 10 Apr 2007 @ 9:39 AM

  5. Thanks for the math. Because of the multitude of simple explanations I can find at your site, I’m now ready for more technical explanations like this one. (There’s no need to post my comment; I’m just responding to the question.)

    Comment by JG — 10 Apr 2007 @ 9:41 AM

  6. There is nothing to be scared about equations. This type of simple and fundamental atmospheric physics is exactly what the general public needs to know in order to counteract the non-sense put out by so many climate skeptics. Bravo.

    Comment by DT — 10 Apr 2007 @ 9:48 AM

  7. I actually prefer to see some more math from you guys. It will give me more elements to “fight” those skeptics ;)

    Comment by Seba — 10 Apr 2007 @ 10:18 AM

  8. Would have been interesting to see the saturation point of the carbon radiation in the equations, as they don’t re-emit to infinity – as might be suggested here. A doubling in PPM from 200 to 400 may double temperature increase(for instance), but an increase from 400 to 800 will be less than double due to this saturation limitation.

    [Response: That is an issue at a significantly higher level than you can properly deal with this model. You could just think about the emissivity being a logarithmic function of CO2, but actually there is a limit here of 1 for lambda – in the real world there is no such limit (which is related to the vertical structure of the atmosphere, the spectral nature of the absorption and things like pressure broadening effects). Look at Venus for an example of extreme CO2 forcing…. The effect doesn’t saturate, it just slows. – gavin]

    Comment by PR — 10 Apr 2007 @ 10:23 AM

  9. Personally, I’m glad for the math. But then, I’m a mathematician.

    I suggest against doing this all the time; you’ll alienate much of your readership. But the occasional indulgence for those of us who want a quantitative rather than qualitative exposition, is a “breath of fresh air.”

    And by the way, I find the exposition very clear.

    Comment by tamino — 10 Apr 2007 @ 11:10 AM

  10. psuedo code so people could try it out for themselves…or some sensible range for numbers. nice to see variations in the articles.

    Comment by M — 10 Apr 2007 @ 11:15 AM

  11. Although I love math (and already said so), I’ve had a lot of experience discussing scientific topics with non-scientists, and it’s most assuredly true that as soon as you mention numbers, a lot of their eyes “glaze over,” and if you dare actually to write an equation, most of their stomachs turn.

    So I suggest against using math in public discussions and personal debates, unless you know that the parties involved are OK with it. Nothing will turn people off faster than equations.

    That aside, I’d love to see more posts with equations from RealClimate (but for the sake of the lay readership, not too many).

    Comment by tamino — 10 Apr 2007 @ 11:37 AM

  12. Just one complaint: while I appreciate the math, and would like to see more, I’d appreciate it even more if I could actually see the equations, instead of a sprinkling of random dots. Not really your fault, since HTML is majorly defective when it comes to displaying math, but would it be possible to add links to a pdf and/or LaTeX file?

    [Response: Which browser/platform are you using? the equations are based on Latex derived images. I can see them clearly in Firefox, but if this doesn’t work on other browsers we won’t use it again… – gavin]

    Comment by James — 10 Apr 2007 @ 11:47 AM

  13. It just occurred to me, rereading this, that you’ve got 0 emissivity for no greenhouse effect and 1 for maximum greenhouse effect. Shouldn’t it be the other way around? If nothing is emitted the greenhouse effect should be infinite. On the other hand, if it’s one, you’ve just got the Stefan-Boltzmann equation.

    Are you using emissivity in a different sense from the epsilon in the SB relation? I’m probably misunderstanding something here, so please set me straight.

    [Response: I’m talking about the atmospheric emissivity (which equals absorption). No absorption = no greenhouse effect. – gavin]

    Comment by Barton Paul Levenson — 10 Apr 2007 @ 12:13 PM

  14. From an anthropological standpoint, I am concerned that we humans are repeating the errors of our predecessors. As I understand it, at least eight civilizations have perished because they diverted too much of their resources to attempting to control the climate. Although primitive by modern standards, these resources included even human sacrifice to try to make it rain. They perished from not only crop failures, but also reduction of their populations below a critical mass.

    The issue that I have not seen explained fully enough with respect to global climate change is the effect of the heat of the core of the earth. I can’t help but notice the recent reports of increases of tsunami, earthquakes, el nino events, and volcanic eruption. If memory serves, these are products of the cooling and shrinking processes of the earth. As the inner core of the earth is hotter than the surface of the sun and heat rises, it stands to reason that the rise in ocean temperatures and chemical content of the sea and air, as well as contributions from the outer core and the earth’s mantel may be attributable to these. I would expect that these different contributions would manifest themselves differently on the earth’s surface due to tectonic plate overlap, differing depths of these contributions and depth and size of the various fissures in the earth.

    Does anyone know of scientific studies that address these potential aspects of global climate change?

    I just don’t want our civilization to mis-allocate it’s resources and go belly-up as a result.

    Thank you in advance for any and all information provided.

    Comment by Skip — 10 Apr 2007 @ 12:39 PM

  15. >equations
    Wait, check the _other_ browsers first.

    This page shows only a few errors in the validator

    Those aren’t, I don’t think, related to the equations.

    Problems viewing may not be browser/HTML either.

    Check your browser menu for something like /View/Character Encoding settings at the home end, see what fonts your computer/browser settings show it’s currently using; try Unicode (UTF-8) and Reload.

    Some people may need ASCII (is this still true for vision-impaired, using text-to-speech? Used to be true for text browsers, like Lynx).

    You could offer a picture of the equations in a JPEG file and a link, so those who can’t see them onscreen can download and print them.

    Please, please do keep this up. I always need help thinking about things mathematically.

    Comment by Hank Roberts — 10 Apr 2007 @ 1:16 PM

  16. I like the post, allthough I had to read it several times to follow the arguments.

    By defining a model, I guess you can say we will get to the point where we get to control the model and change it. This has infinite advantages, but I am afraid the model is so complex that it will be very hard to define it accurately. And this is because there are so many factors that influence the terms of the equations.

    Still, defining models is a must. And if it were that easy, we would have been able to determine weather trends.

    Comment by Adrianne — 10 Apr 2007 @ 1:37 PM

  17. I think your site is a great benefit to clarifying issues around cc and maintains a high degree of objectivity and scientific clarity,so thanks for that.Over the last couple of years I have followed the development of the cc issue but have become suspicious about a possible ingredient within the observations that may have some bearing and does not really get considered.I suspect the reason for excluding this phenomenon may be to do with a general view of the physics as they stand ,I dont know but here goes.I believe it is the case that the core of the earth itself is getting warmer.If this is the case then the consequences will be feeding into and magnifying other anthropogenic changes as well as increasing the influence of positive feedbacks in the climate system.I would appreciate your views on this, regards matt fairs

    Comment by matt — 10 Apr 2007 @ 1:58 PM

  18. Thanks for a really good site and informative debate.

    I have a query which is taxing an engineering mind.

    RC appears to be satisfied that CO2 resides in the atmosphere for about 200 years, and that CO2 concentration has not exceeded 300 ppm in the last 400 kyear. I also see references to the absence of CO2 spikes in the ice core records as evidence that large volcanoes have not been a significant source of CO2 in the past.

    I read elsewhere that samples of air in the ice cores might have been smeared by physical processes in the ice. This could be local mixing during compression, and possibly upward migration of the less dense air bubbles, a phenomenon which must result in some local mixing. Without getting too far into these details, the net effect would be akin to time-averaging . Detail will have been lost as a result.

    Let’s say the atmospheric response to a large influx of CO2 is roughly the same as the response of a first order differential equation. The 200 year CO2 residence time would then equate to a time constant of about 66 years (i.e. only 5% of CO2 will remain longer than 200 years).

    I have read that the ice core records of T and CO2 look like a 500 to 1000 year moving average. If this is reasonable, the ice core would hide actual CO2 perturbations following an event such as a large volcano. Only a small percentage of the amplitude of sudden perturbations would be evident.

    If there is a significant averaging effect in the ice core, we would need to look again at those peaks. Whenever the peaks are close to the 300 ppm level, averaging could be hiding shorter periods when the CO2 concentration exceeds 300 ppm.

    Do you have any references to literature which addresses these issues?

    My guess is that there should be no averaging effect greater than 33 years (i.e. about 20% attenuation of sudden perturbations).

    [Response: The 200 year number is already a great simplification and you can’t model it as a simple diffusion process – there are too many different physical processes and they all have different time scales. See this comment for more details: and post – gavin]

    Comment by John Ross — 10 Apr 2007 @ 2:06 PM

  19. Re seeing equations: I’m using Opera on Linux, FWIW, but the problem isn’t browser-related. It’s down to the fact that because HTML doesn’t know about math symbols, equations are commonly rendered into images. Your images are black text on a transparent background, no?

    That’s fine if the reader is using a colored background, but since more than a few minutes of looking at a colored background gives me a nasty headache, I have my browsers (and everything else I use) set to display colored text on a nice, restful black background. Which unfortunately means that the equation images show nothing more than vague outlines where grey pixels were used for antialiasing. This isn’t something an HTML validator is going to catch, since the HTML is perfectly valid but produces an unviewable result.

    One partial solution is to render the images with a colored rather than transparent background (as some sites do), in which case I’ll see a white block containing the equation. A link to pdf or LaTeX source, though, would guarantee readability – plus the latter makes it possible to copy equations at need :-)

    [Response: Hmm. We are just using a standard plugin for the LaTeX rendering (latexrender). If you know of a fix or tweak to adjust the rendered images to have a white background instead of transparent, let me know. – gavin]

    Comment by James — 10 Apr 2007 @ 2:25 PM

  20. [[The issue that I have not seen explained fully enough with respect to global climate change is the effect of the heat of the core of the earth.]]

    That’s because it’s trivial. The Earth system absorbs an average of 240 watts per square meter of sunlight. The geothermal flux averages 0.090 watts per square meter. Divide A by B.

    [[ I can’t help but notice the recent reports of increases of tsunami, earthquakes, el nino events, and volcanic eruption. If memory serves, these are products of the cooling and shrinking processes of the earth.]]

    Earthquakes are due to plate tectonics, which are driven by convection in the mantle, so to that extent you’re right. El Nino events are climate rather than geology.

    [[ As the inner core of the earth is hotter than the surface of the sun ]]

    It isn’t. The Earth’s core is at something like 3000 K, whereas the sun’s surface is 5779 K (and its core is at about 16 million K).

    [[and heat rises, it stands to reason that the rise in ocean temperatures and chemical content of the sea and air, as well as contributions from the outer core and the earth’s mantel may be attributable to these.]]

    No, the effect on temperature is trivial.

    Comment by Barton Paul Levenson — 10 Apr 2007 @ 2:33 PM

  21. Re #1: What’s with the attitude towards engineers? This is the second such comment I’ve seen on this blog in the last few weeks. Is this a bitter attitude over past encounters, or professional snobbery? With an MSEE degree, I’ve had more than just enough math to be dangerous. And having spent significant time developing and using electromagnetic simulation programs, I’m plenty sympathetic towards the plight of the climate modeler. Feedbacks are a rather pedestrian concept in my field, and in any case, I didn’t find the post terribly difficult to follow.
    Apart from the moderately contemptuous comments, I find your site fascinating and informative. For now, I’ll ignore those comments and just assume it must have been a result of unpleasant encounters with engineers from the lesser disciplines ;-)

    Comment by The Wonderer — 10 Apr 2007 @ 3:06 PM

  22. Can anyone here explain why average July temperatures at low-elevation, extremely dry areas in the Desert Southwest are 3-4 degrees C higher than temperatures at the same latitudes east of the Rocky Mountains, which have extremely high absolute humidity? Both areas have the same top-of-atmosphere solar radiation, virtually same elevation. There appears to be some type of negative feedback in the east. Is it the influence of the Gulf of Mexico? Is it a negative water vapor feedback?

    Comment by jae — 10 Apr 2007 @ 3:59 PM

  23. Great to see this math – what I’d really like to see is a clear explanation of what it is about the real Earth that makes the sensitivity number several times as large as this simple model gives you. Aside from the factors you mention, there’s also the issue of pole-to-equator and summer/winter temperature variations that this simple zero-dimensional model misses (and I guess this is related to convection issues), but from the simple analysis I’ve tried that only adds a fraction to the sensitivity number. I’ve read a lot of the history on Dr. Weart’s site, excellent history by the way, but I find it very hard to track down a good physical explanation for what bumps up the sensitivity so much in the real climate system.

    Comment by Arthur Smith — 10 Apr 2007 @ 4:05 PM

  24. I recently prepared a short set of high level slides on global warming for my Rotary Club.

    One of the concepts I drew upon was radiative forcing, using info on NOAA’s web page,

    I did two calculations that were pretty interesting. Total solar energy reaching the earth on a daily basis. Total radiative forcing on a daily basis. The results were interesting, but also unsettling.

    For the first calculation, net solar energy, I used the following. Energy per square meter – 235 watts. Diameter – 7914 miles (averaging polar and equatorial diameters). Result? Solar energy at 2,875,000 million terawatt-hours/day. An impressively big number.

    For the second calculation, CO2 radiative forcing, I began with a value of about 1.66 watts/meter squared. I extrapolated to the planet as a whole. Result? 20,300 terawatt-hours/day.

    I found the comparison unsettling. 20,300 terawatt-hours/day, sustained over a year, is a pretty big number, well over two full days worth of solar energy. Intuitively it feels like the sort of energy stream that’d heat the planet pretty darn fast, much faster than anyone is now seeing.

    This leaves me wondering if I should have taken a different approach.

    Should I have used a delta? Let’s say the Year 2007 begins at 382 PPM for CO2 and ends at 384 PPM. Using NOAA’s calculation approach, that’d give a Year 2007 delta of 0.028 watts/meter squared, or, planet-wide, a Year 2007 delta of 341 terawatt-hours/day.

    Hansen and others have said that new increments of CO2 take 20 to 30 years to get fully absorbed by the oceans, the land, the air. 341 terawatt-hours day – if absorbed over 20 years at a linear amount – would translate into 1,250,000 terawatt-hours added to the heat of the planet. Equivalent to a shade less than half a day’s solar energy.

    Intuitively, this approach feels much more reasonable. Is this how I should think about radiative forcing? As a year-by-year delta? This year’s new CO2 becomes this year’s new radiative increment, an addition to the heat of the planet that may take 20 to 30 years to be fully absorbed? Thanks for any insight you can give.

    Comment by Steven H Johnson — 10 Apr 2007 @ 4:09 PM

  25. On #22 – isn’t this a simple consequence of the high heat capacity of water relative to typical surface materials (i.e. rocks)? If there’s a lot of water around, it takes a lot more energy to raise the temperature than if it’s very dry. The low heat capacity of dry regions means they also lose heat a lot more easily, so their temperatures will tend to be lower at night and in winter. Anybody who’s lived near a coastline knows of the moderating influence on local climate.

    The water vapor feedback discussed here is more of a net effect and much smaller than local daily or annual temperature variations: averaged over the year, does more water in the air tend to make things slightly warmer or not. Water is a known greenhouse gas, and night clouds retain heat, so it seems pretty clear the feedback is positive. There are many previous discussions of this effect on realclimate.

    Comment by Arthur Smith — 10 Apr 2007 @ 4:13 PM

  26. Gavin — This is well done! I encourage more similar snippets, maybe once each six weeks or so…

    Comment by David B. Benson — 10 Apr 2007 @ 4:14 PM

  27. >deserts, hotter

    Speculating: less water vapor in the air by which actual incoming infrared from sunlight is being intercepted, so more direct heating of the ground by that band. And as noted, no significant water or water-containing organic material on the surface.

    “Stay in the shade during the day. Sit on something 12 or more inches off the ground, if possible. DO NOT SIT ON THE GROUND as it can be 30 degrees
    hotter than a foot above the ground…..” — common desert emergency info

    Comment by Hank Roberts — 10 Apr 2007 @ 4:21 PM

  28. Re #14: [I can’t help but notice the recent reports of increases of tsunami, earthquakes, el nino events, and volcanic eruption.]

    I think this one is easily explained: just rearrange “reports of increases” to “increased reports of”. These events aren’t (AFAIK, anyway) any more common than before; it’s just that, as with so much else, an omnipresent media reports on every isolated incident, and often enough inflates the reports to justify the coverage.

    Comment by James — 10 Apr 2007 @ 4:48 PM

  29. 25: Yes, the increased water vapor in the east holds more heat and lessens diurnal variability, but this extra heat is not being registered as higher temperatures. Therefore, is the water vapor exerting a negative impact on surface temperature?

    Comment by jae — 10 Apr 2007 @ 4:52 PM

  30. My math is getting a little rusty, along with my old brain. Can someone show how the three equations under the “Greenhouse Effect” section can be used to derive the equation for “surface temperature as a function of the incoming solar (radiation) and the atmospheric emissivity?”

    Comment by jae — 10 Apr 2007 @ 4:56 PM

  31. On #22 There are several effects that make desert environments hotter than an equivalent environment laden with moisture: 1.soil moisture slows the warming of the soil and therefore the subsequent conduction of thermal energy to the atmosphere in contact with it as the soil moisture evaporates, 2. Moist areas usually have more vegetation, vegetation transpires moisture, which takes energy and absorbs solar radiation, some of which is used for photosynthesis and therefore also not available to heat the atmosphere, 3. A humid atmosphere is usually more turbid than a dry atmosphere. In this case I am referring to relative humidity, not absolute humidity, with less thermal energy available in the humid environment to do the work of evaporation (or alternately to keep the vapor in the gasseous phase)other materials in the air readily absorb moisture. These materials are called hygroscopic (sea salt, nitrate fetilizer dust, etc.)and are partly responsible for the formation of the haze in the “lazy, hazy days of summer”. The haze is the subject of “global dimming” of the sun, which by the way may be responsible for an underestimate of the amount of global warming, 4. Humid atmospheres may have more cumulus cloud cover.
    This is not comprehensive but gives an idea of the many factors involved.

    As far as mathematics, explanations and the public are concerned, generally forget it, I prefer to rely on concepts, analogies and simple explanations (i.e. very general or stripped of complications). It is amazing how the public misses the beauty and elegance of simple mathematics and has a panic attack at the very mention of an equation.

    Comment by Steve Horstmeyer — 10 Apr 2007 @ 5:19 PM

  32. I like this post. It may be hard on some readers (although the above comments are encouraging), but it’s great for us sciency people who haven’t had the opportunity to take a college course in climatology.

    Comment by Marcus L. — 10 Apr 2007 @ 5:36 PM

  33. Re: #30 (jae)

    Divide equation 2 by (2*lambda), you get A = 0.5 * G

    Substitute (0.5 * G) for A in equation 1, you get S + 0.5 * lambda * G = G

    Rearrange that, you get S = (1 – 0.5 * lambda) * G

    Divide by (1 – 0.5 * lambda), you get G = S / [1 – 0.5 * lambda]


    Comment by tamino — 10 Apr 2007 @ 6:04 PM

  34. This would have saved me a lot of time and searching a few weeks ago. I’ve already managed to drag myself up to this level and need more. Could you expand this with hyperlinks to more detail/complexity?

    #31 Isn’t it actually the other way around? Ground water should speed the transfer of heat from the surface to the atmosphere which keeps the surface temperature from rising. Look at track temperatures at car races for example (or parking lots or sandy beaches). When the sun is out the (dry) track temperature is always much higher than the air temperature.

    Comment by DeWitt Payne — 10 Apr 2007 @ 6:50 PM

  35. 33: Thanks!

    Comment by jae — 10 Apr 2007 @ 6:51 PM

  36. Jae, think about nighttime in the desert. What happens then?

    Comment by Hank Roberts — 10 Apr 2007 @ 7:00 PM

  37. I liked this article. A few comments.

    A few of the assumptions in this model should have been more clearly stated. Eg.

    1. It was assumed that the atmopshere is transparent to incident solar radiation (why the S term did not appear in the Atmospheric radiative balence equation)

    2. A single layer atmosphere with no lapse rate was used.

    and the like. I thought the article was very well written, but I had to rely on my own knowledge of the subject to know what assumptions were begin made and how the model would deviate from reatlity.

    I would love to see more articles of a similar nature however. Good work!

    Comment by Chris C — 10 Apr 2007 @ 7:08 PM

  38. I second that motion, whats with the attitude for engineers? I also have a MSEE and can’t quite get the attitude as we don’t get a primer for math we get the full treatment!
    I appreciate posts such as these as well and had no trouble following it. You did well using simple math so the details don’t bog down what you are trying to say. I use IE7 and the equations looked fine. Is more stuff like this going to be forthcoming? (Since this is your day job! :) )


    Comment by Jim — 10 Apr 2007 @ 7:35 PM

  39. I liked the post and the math is fine.

    Can anyone point me to a quantitative explanation, at about the same level of detail as this post, of the relationship between emissions and atmospheric concentrations of greenhouse gases?

    Comment by Patrick Kennedy — 10 Apr 2007 @ 7:55 PM

  40. (in general, nice math, please do it some more, but consider suggestion at the end):

    #31: re math & public … it could be worse, and maybe it’s getting better…

    Amusement, then serious point.
    During the late 1990s, I had occasion to visit the US Congress’s computer people, who were proud of their efforts to get Congress to use computers & Microsoft tools. I naively asked:
    so, what do Senators really use? do they do email? use Word? Use Excel? PowerPoint?

    They laughed: “Are you kidding, they’re mostly lawyers, they like words a lot, but numbers and graphs?? forget it.” They said there were a few who could use such tools. I suspect it should be better now.

    Seriously: making math accessible to a broader audience:

    I sometimes ask:
    for numerical calculations, what “programming language” is used by the most people?
    people answer: FORTRAN? C? C++? Visual Basic? Java? Mathematica?

    but I claim the likeliest answer is: Excel (or equivalents)

    After all, people who do not think of themselves as progrmmers routinely do calculations with sometimes-nontrivial equations, that years ago would have required BASIC or FORTRAN coding. These days, Excel is often taught in middle-schools.
    Google: excel equations middle school spreadsheets : 242K hits

    For better or worse, many people who will go blank at classical math equations with lambdas and sigmas and such … could be handed the equivalent equations in an Excel spreadsheet [especially with a few embedded graphs], and would feel quite comfortable, and could easily play with the data.

    SUGGESTION: like it or not, a lot more people read/write Excel than feel good with classical mathematical and notation, and the following can be really valuable, if the goal is to communicate the math more broadly:

    a) Show Excel formulae as well as standard math notation.
    b) Better, have a repository for simple, well-commented spreadsheets that can be downloaded and played with.

    In addition, it becomes much easier to build on what’s there, given the wealth of builtin functions that one would never expect a person to use by hand, especially if examples ever want to get into simple statistical analysis.

    This is *not* to suggest that standard math notation should be abandoned, or that Excel is the end-all tool (shudder), just that if one wants to communicate math broadly, it may well be that optimal pedagogy is in a state of rapid change, and many more people now “speak” Excel fluently than standard math notation….

    Comment by John Mashey — 10 Apr 2007 @ 8:21 PM

  41. Re #39: Patrick Kennedy — I went web trawling on the search phrase carbon cycle to find many excellent sites. Is this what you wanted?

    Comment by David B. Benson — 10 Apr 2007 @ 8:29 PM

  42. Personally I think the maths is extremely welcome; it gives a fresh restatement of what I’m attempting to learn formally. But I humbly submit that some well placed diagrams would be excellent aids to understanding as well. For example, a simple illustration showing that ‘the atmosphere radiates both up and down’.

    [First ever comment, but I eagerly read everything posted here…]

    Comment by Justin Wood — 10 Apr 2007 @ 8:58 PM

  43. Nice job. It’d be great to see more posts – and more of us science bloggers writing posts – like this. Though that may tempt “some” people to argue that we are not properly framing our information.

    Comment by Simon Donner — 10 Apr 2007 @ 9:42 PM

  44. This is the Internets, home of “cheat sheets”

    What we REALLY need are cheat sheets, not on the whole global warming climate change thing but on simple subdivision.

    e.g. cheat sheet on C02. Would show net contribution of C02 by oceans, show various sinks and sources.

    Or a cheat sheet on greenhouse gases. how water vapor responds to temperature change.

    Thinking you take a FAQ of typical objections or questions and responses and a couple of stylized diagrams and just titles of objections and questions with 1 or 2 sentence summaries of the answers, mayhaps a couple of equations.

    Comment by Marion Delgado — 10 Apr 2007 @ 9:54 PM

  45. I’m not sure I picked up the distinction between atmospheric absorption and atmospheric emission (not an engineer). How do these two relate?

    Comment by Steve — 10 Apr 2007 @ 10:19 PM

  46. It’s nice to see some reasonably sophisticated discussion of climate modeling. I would just note that once the feedbacks are introduced the system becomes useless as a predictive tool. See for example for some examples of the sensitivity of a coupled, non-linear, dynamic system. Sorry, more math at that page.

    [Response: Not really. Because there are systems that are unpredictable, it doesn’t follow that all systems are. Why does the climate cool systematically whenever there is a large volcanic eruption? Why are the ice age patterns so regular and related to orbital forcings? Why are the seasons so clear? If the whole thing was completely chaotic and unpredictable none of this would be observable. – gavin]

    Comment by Tracy Platt — 10 Apr 2007 @ 10:29 PM

  47. As another engineer with plenty of math background, I too appreciated this post and would like to see more along the same lines. (A few sketches indicating the direction of the various components of the energy balance might make it even clearer, though.)

    One reference I’ve found to be accessible is Roland Stull’s “Meteorology for Scientists and Engineers”. His chapter on climate change has an analysis similar to Gavin’s, with more on water-vapor, cloud, and albedo feedbacks at a similar level of detail.

    Comment by David Warkentin — 10 Apr 2007 @ 10:36 PM

  48. I apologize in advance — I haven’t figured out how to write equations in Latex. For those who know just a smidgeon about math, it might have been nice to mention that the factor 0.25/T^3 comes from the derivative of the Stefan Boltzmann equation: dT/dQ = (4T^3)^{-1}

    [Response: I edited your equations to work with latex. You simply enclose them in [ tex ] and [ / tex ] pairs (no spaces). – gavin]

    Comment by Jeff — 10 Apr 2007 @ 11:38 PM

  49. I can read the equations OK, but they don’t copy. I could take snapshots [shift-control-3] or I could copy the article into Word5 for Mac and then re-create the equations with equation editor. But #33’s method:
    Divide equation 2 by (2*lambda), you get A = 0.5 * G
    Substitute (0.5 * G) for A in equation 1, you get S + 0.5 * lambda * G = G
    Rearrange that, you get S = (1 – 0.5 * lambda) * G
    Divide by (1 – 0.5 * lambda), you get G = S / [1 – 0.5 * lambda]

    works really well. Why not do the math that way since we can all read and copy it? I am using a 16 year old Mac with OS 9.1 and ie5. The machine cannot be upgraded further. To read Adobe Acrobat [no higher than version 4] I have to sneakernet to another ancient machine. The max sneakernet file size is 1.3 meg. I cannot translate acrobat to word. LaTeX is out of the range of possibility. Please use Tamino’s method of writing math.

    Comment by Edward Greisch — 10 Apr 2007 @ 11:55 PM

  50. This is an excellent addition to Real Climate, even if the math totally eludes me thus far. I will figure it out.

    For those of you old folks who grew up in Massachusetts, you probably remember Channel 4 meteorologist Don Kent often mentioning radiational cooling as being the cause of very low temps. on clear winter nights in places like Athol, Mass. and Keene, New Hampshire. Don Kent often took time to explain exactly what radiational cooling was, and how a clear dry winter night, without water vapor or clouds in the sky, allowed more heat to leak back into space, thus radiational cooling. I remember this from when I was 7 years old.

    Also the history material provided by Spencer Weart in Comment #1 is outstanding.

    This site is an enormously valuable resource, which is why I cite and post it as often as possible.

    Comment by Doug Watts — 11 Apr 2007 @ 2:08 AM

  51. I enjoy the challenge of obtaining a more robust understanding. Most people some to this site for more in depth analysis so I expected some math earlier. I support similar posts – but not to many. I suggest that you have a section on your site for a mathematical analysis. In addition you should have some links to “atmospheric math/science for dummies” so a lay person such as myself could get an even deeper understanding. In time there would be interest for sporadic intermediate or higher level postings that could be heavily linked for a newbie to obtain the necessary knowledge to follow the argument. Keep up the great work.

    Comment by Zane Lewis — 11 Apr 2007 @ 2:19 AM

  52. I would like to see one article in the future.

    It is clear that different factors affect the climate.

    For example, solar, C02, …

    Given the data it is possible to build a model that shows the contribution of each of the factors to global temperature in a statistical way. This shows how important in each factor was in the historical climate record.

    The factors of which I’m aware are solar, atmosphere constituents, volcanos, orbital mechanics.

    They all contribute and in somes cases with lags.

    The statistical model then shows which are significant and which aren’t.

    Now you move forward to the industrial era and you can now show what man’s contribution is, and whether or not it is statistically significant.

    You can also take the models, and see if they predict the historical record, and if they are statistically different.


    [Response: Try: -gavin]

    Comment by Nick — 11 Apr 2007 @ 5:07 AM

  53. Bring on the math. As the lucky father of a mathematically gifted 12 year old I’ll have him explain it to me.
    Seriously though, unfortunately, most people think like the infamous jornalist Richard Cohen who wrote the piece entitled “What Is the Value of Algebra?”

    Comment by Fernando Magyar — 11 Apr 2007 @ 6:12 AM

  54. I’m not good at maths but the way to get better can’t be no maths.

    Comment by Peter Hearnden — 11 Apr 2007 @ 6:34 AM

  55. Gavin,
    I know this is already a simple model, but I think it would be a great addition to post the diagram that always gets drawn with it. I can try to dig one up at work, but I believe that just sketching a couple of arrows and scanning the figure would really help to make this actually “simple.”

    [Response: You are absolutely correct. A figure has now been added. – gavin]

    Comment by FTG — 11 Apr 2007 @ 6:50 AM

  56. Re #55 It seems that this is a well known model. Does it have a name, or is there another way to cite it?

    Comment by Alastair McDonald — 11 Apr 2007 @ 8:21 AM

  57. [[I’m not sure I picked up the distinction between atmospheric absorption and atmospheric emission (not an engineer). How do these two relate? ]]

    For an object in “local thermal equilibrium,” the emissivity equals the absorptivity (Kirchhoff’s Law). In English:

    Assuming no chemical or nuclear change, light can only interact with a material object in one of three ways —

    * absorption — the object can absorb the light, usually heating up.

    * reflection — the object can bounce back or scatter the light.

    * transmission — the object can let the light go right through it.

    Expressed as decimal fractions, these three have to sum to 1:

    A + R + T = 1

    To pick an example, the Earth’s surface absorbs about 95% of incoming light in the visual range, reflects about 5%, and transmits none at all (it’s opaque).

    Now, every object not at absolute zero radiates photons. The power (energy per unit time per unit surface area) radiated by an object is:

    F = ε σ T4

    where F is the output per unit area (F for “flux”), σ is the Stefan-Boltzmann constant (5.6704 x 10-8 in the appropriate units in the SI), and T is the temperature (degrees Kelvin in the SI).

    The quantity ε is the “emissivity.” This can range from 0 to 1 for any real object. A perfect radiator with ε = 1 is a “black body” or “black body radiator.” But in practice very few objects are perfect blackbodies, most have an emissivity between 0 and 1.

    Under “local thermal equilibrium,” ε = A (Kirchhoff’s Law again).

    Comment by Barton Paul Levenson — 11 Apr 2007 @ 8:27 AM

  58. Engineer’s know just enough to get in to trouble? I think the engineer’s have a better handle on it than the scientists who never took the really hard classes. We actually have to design things that work. This article should have contained some info. on the stefan boltzmann equation forcing more cooling with increase in surface temp. but didn’t. “cooler because of adiabatic expansion (air cools as it expands under lower pressure)” Please check the def. of adiabatic. You may have meant the right thing but said it in the wrong way.

    Comment by KS — 11 Apr 2007 @ 9:12 AM

  59. Re: #58 (KS)

    The solution to engineer-bashing is not scientist-bashing. Let’s judge each argument on its merits, regardless of its origin.

    As for “cooler because of adiabatic expansion (air cools as it expands under lower pressure) Please check the def. of adiabatic,” a parcel of air does indeed cool as it expands adiabatically. Adiabatic does not mean isothermal.

    Comment by tamino — 11 Apr 2007 @ 9:36 AM

  60. One has to wonder what kind of engineer is being talked about here with “just enough math to get in trouble”. Obviously not engineers who have taken thermodynamics, and have been talking about convection on this subject for a long time. Maybe software “engineers”? “Hot air rises” is not a new concept…

    Comment by Harry Haymuss — 11 Apr 2007 @ 9:42 AM

  61. P.S. you’re letting your prejudice show:

    “Now we can make the model a little more realistic by adding in ‘feedbacks’ or amplifying factors”

    Feedbacks are also damping factors.

    [Response: Hmmm. Who is lettering their prejudices show? Who ever said that an ‘amplifying factor’ cannot be a ‘negative feedback’ (i.e., a ‘damping factor’ depending on precisely which variables you are talking about). Consider the radiation of outgoing longwave radiation (OLR) to space. As you increase the surface temperature, you tend to increase the OLR, in proportion to the 4th power of the temperature in fact. Seems like an ‘amplifying factor’ to me. Of course, its obviously a ‘negative feedback’ as well (warmer surface temperatures leading to greater heat loss from the surface), in fact the key negative feedback that prevents runaway warming of the Earth’s surface over time. In other words, it is an ‘amplifying factor’ with respect to OLR, but a ‘damping factor’ with respect to surface warmth. – mike]

    Comment by Harry Haymuss — 11 Apr 2007 @ 9:49 AM

  62. re: 60. ??? Nothing in the original statement said ‘feedbacks’ could not be damping factors. It was “‘feedbacks’ OR amplifying factors” (emphasis added). To assume otherwise is showing your prejudice.

    Comment by Dan — 11 Apr 2007 @ 10:03 AM

  63. Adding up the A1B scenario greenhouse gas forcings for 2100 taken from the IPCC TAR I get about 4.1 Watts/m^2, most of which (3.48) comes from CO2.

    The calculation above gives a temperature rise of 1C relative to 2000, but the models (in the 4th assessment report SPM) give a range of about 1.8-4.2C rise for the A1B scenario which require upto 8-9 Watts more forcing.

    So what are the other processes in the models that are causing the additional warming? Section suggests that water vapour doubles (or more) the warming. Is this it? Or are there other major effects.

    Comment by Steve Milesworthy — 11 Apr 2007 @ 10:18 AM

  64. Steve —

    Doubling CO2 increases the Earth’s temperature 1.2 K by itself (Houghton 2004) but 2-4 K with all the feedbacks (IPCC 2001, 2007).

    Comment by Barton Paul Levenson — 11 Apr 2007 @ 11:57 AM

  65. Thanks for this introduction to climate modeling.

    A quantitative model is a quantitative hypothesis. We have observed historical climate data over the last 150 years which we can test against climate models/hypotheses. A climate model which ‘simulates’ (fits) past observations better than another is more likely to be true. There are too many variables so some approximation is inevitable.

    The climate debate is about whether there is a significant human cause of current global warming.
    – Climate skeptics no longer doubt that the earth is warming, they claim the causes are purely natural eg sunspots and volcanoes.
    – The IPCC does not doubt that there are natural causes of recent global warming but they claim 90% certainty that this warming has a significant human cause.

    These competing hypotheses can be tested by quantitative models see UK Met Office Climate Change Myths.

    The two graphs next to Myth 2 show that natural causes alone cannot explain the increase in earths temperature since about 1975. But If human factors are added to natural causes we get a much better fit to the observed data.

    AFIK climate skeptics have not been able to provide a quantitative model of natural-only causes which fit the observed data so well. Please correct me if I’m wrong.

    This is the key data the climate skeptics ignore, instead they attack the straw man that ALL climate change is man-made.

    Comment by Isidore — 11 Apr 2007 @ 12:08 PM

  66. So, climate models do simply explain it all?

    (Yes, I am a denialist, an skeptical, or whatever thing you call those people who does not trust the global warming as a matter of faith)

    Comment by SebastianDell — 11 Apr 2007 @ 12:36 PM

  67. #62, The context is feedbacks (aka) amplifying factors, as RC typifies feedbacks as generally positive. This statement just entirely negates the potential for damping feedbacks – RE#64. Of course #64 discounts the fact we know next to nothing about cloud feedbacks – even the sign.

    #65, don’t confuse CO2 forcings with all anthropogenic forcings, including land use changes, black carbon and other dust on ice, etc. Re those other changes, could not we tell the magnitude of the difference in CO2 forcing compared to some of the other anthropogenic forcings by looking at the temperature trend of the Arctic vs. Antarctica?

    Comment by Harry Haymuss — 11 Apr 2007 @ 12:44 PM

  68. #63 and #64 I know that water vapour is a feedback, not a forcing, but since water vapour seems to be so important I’m really looking for an addition to the simple model that says X amount of warming results in Y increase in water vapour, and barring clouds etc. this water vapour adds an additional “radiative forcing” of Z – such that a few iterative calculations can provide an estimate of the temperature rise.

    If such a simple extension is not helpful, then why not?

    Comment by Steve Milesworthy — 11 Apr 2007 @ 1:39 PM

  69. re: the parentheses in 66. Of course it is not a matter of faith. No one shoud accept it as that. It is a matter of science. Data, experiments, hypotheses, conclusions, peer review…the scientific method. It works. And the science behind global warming is quite strong.

    Comment by Dan — 11 Apr 2007 @ 1:57 PM

  70. Feedbacks come in two very different types. 1) Negative feedbacks which, despite their name, are good and stabilise the system by damping any changes. 2) Positive feedbacks which, unlike their name, are bad and amplify changes. Once they get over 40% they cause oscillations or strange attractors. If they get over 100% they produce a runaway effect – just like what happened in the rapid climate change at the end of the Younger Dryas stadial.

    So you can have negative feedbacks and amplifying factors, or damping effects and positive feedbacks, but not feedbacks and amplifying factors. “Amplifying factors” is redundant when used that way.


    Cheers, Alastair.

    Comment by Alastair McDonald — 11 Apr 2007 @ 2:04 PM

  71. re: 67. No, not at all. RC does not typify feedbacks as generally positive. To assume so is a quite clear prejudice. As a simple example, a quick search on “negative feedback” at the top of the page yields, among other things,
    Both positive and negative feedbacks are discussed in that one specific example. Now particular feedbacks may be discussed as positive, such as CO2 or water vapor, simply because they are.

    Comment by Dan — 11 Apr 2007 @ 2:10 PM

  72. Ian Plimer is again getting some mileage here in Australia. This ran as a lead story on and has already been the subject of a couple of op-ed pieces here. Lots of tired old stuff that have been covered countless times before, yet for some reason, this fellow seems to attract more media than he deserves.,23599,21542564-2,00.html

    Comment by Joe White — 11 Apr 2007 @ 2:33 PM

  73. I just wanted to say that I’m very glad to see this sort of article on your site. RealClimate is one of the most popular climate sites on the net so I think that you do your readership a great service by bringing them up to speed on the basics of climate science. The people who honestly want to learn about climate science understand that they need to learn the basic mathematics of the science.

    I’d go even further and say that I think you should long running series of articles based on this simple model that eventually build up to as close of a model to the ones found in IPCC report as possible. Given the collective will of reasonable people to not kill life on earth, using your site to raise the cognitive models of how people view climate should help raise the level of debate due to people with good models being able to trash the arguments of people with bad models. You do that a lot here in your comment section, so I think by putting a series of articles together that can help others learn to trash similarly poor arguments they encounter in their own lives you give the truth a weapon.

    In short, kudos and I hope this is not the last of the “more technical” articles. This site is your bully pulpit and I think your readership will appreciate any help in lifting their cognitive models.

    Comment by EntropyFails — 11 Apr 2007 @ 2:47 PM

  74. Thanks…now if these types of articles were just available as PDFs (or even PS files)….quibble, guibble…More of the same would be fine with me.

    Comment by Bill — 11 Apr 2007 @ 3:11 PM

  75. re: #72:
    As I recall, belongs to Rupert Murdoch, i.e., like Fox News.
    I conjecture that’s adequate reason for this to appear there.

    I’ve been in Oz about dozen times, and unless it’s changed recently:
    a) You have a *lot* of coastline, and most Australians live near it.
    b) Most of the big cities aren’t very far above sea level. I’d be a little nervous for places like the Whitsundays, Freemantle, the Gold Coast, Cairns, even with 1-2-foot rise. Canberra seems safe.
    c) You could use more water.
    d) Like here in CA, you have trouble with forest fires, especially when it’s hot.

    At least the article was a nice checklist of bad ideas :-)

    Comment by John Mashey — 11 Apr 2007 @ 3:16 PM

  76. Re: #73 (EntropyFails)

    you should long running series of articles based on this simple model that eventually build up to as close of a model to the ones found in IPCC report as possible…

    I’d love to see such a work. But it would involve much more complicated mathematics (vector calculus), and much more complicated physics (the Clausius-Clapeyron equation is not for everybody). So I don’t think it would be appropriate as a series of blog posts.

    It would make an appropriate textbook. So if any of you RC guys have such a work, at that level, available as pdf, then … bring it on!

    Comment by tamino — 11 Apr 2007 @ 3:46 PM

  77. because I’m not sure where else to post this, is there any resource that I might use to explain climate anomalies such as the cold snap we are having in April, within the global warming debate?

    Comment by Jamie — 11 Apr 2007 @ 4:04 PM

  78. Gavin

    You made mention of being careful about cold events in relation to climate change.

    Strikes me with more energy in the system – gradients are steeper and boundary conditions between high and low pressure systems may vary from the longer term geographic norms… stronger Pacific storms might force cold continental systems further south and east at times just as a for instance.

    More energy retained I would think would produce more chaotic boundaries with higher energies, – an abnormal incursion of warm or cold air masses might push farther and run into geophysical regions ( ie Great Lakes or mountain funnels not reached in a less energetic atmosphere. )

    Seems to me that gradients might build higher before releasing as well in an energetic/chaotic climate so while cold events might occur outside the norms from time to time as air masses collide with more energy.

    I would also think the jetstreams would show increased energy levels which again might mean unusual cold intrusions.

    I’d be happy to be set straight but seems to me that “outside the norm” excursions of cold air or water could be expected in some locales in an overall more energetic system.

    Comment by MacDoc — 11 Apr 2007 @ 4:58 PM

  79. Jaime, someone (maybe you? I forget) asked that elsewhere recently. Weather isn’t climate, so this is the wrong website; have you tried NOAA?

    Comment by Hank Roberts — 11 Apr 2007 @ 5:48 PM

  80. One more for Jamie, this might be helpful (just found with a quick Google search, not something I can evaluate, you might find reading up on this a challenge worth taking on):

    Comment by Hank Roberts — 11 Apr 2007 @ 5:50 PM

  81. Could not we tell the magnitude of the difference in CO2 forcing compared to some of the other anthropogenic forcings by looking at the temperature trend of the Arctic vs. Antarctica?

    [Response: No. The impact of any forcings depends on a number of issues – local heat capacity (much higher in the Southern Hemisphere due to the greater extent of oceans), difference in dynamics and impacts of other factors (like the ozone hole). It’s therefore not as straightforward as one might hope. – gavin]

    Comment by Harry Haymuss — 11 Apr 2007 @ 6:12 PM

  82. Re #77 (Jamie): The question is whether the cold snap that we are having here in the Eastern U.S. is really that unusual. Sure, it has been colder than average for several days…maybe even a couple standard deviations colder than average for a few of them. But, I didn’t get the impression it was record-setting cold. (A few places may have broken DAILY records…that is the record for a particular day…but those are relatively easy to break.)

    The point is that in the absence of crunching through the statistics, one can’t really determine how anomalous this cold is. And, frankly, I don’t get the impression that it is that anomalous. It takes a lot of work to actually pull out a trend from a system with large fluctuations.

    Comment by Joel Shore — 11 Apr 2007 @ 9:22 PM

  83. Reference #57

    First off, thanks for responding.

    This “local thermal equilibrium” concept appears important.

    I can understand the idea of solid objects radiating at each, and having the same radiation field if they are at the same T and are made of the same material. I think I have a reasonable grasp of black body radiation coming from objects based on the temperature of the object.

    It makes sense that bodies of gases in the same state should have the same radiation properties.

    In either case, the net radiation should be zero.

    Black body to balck body, gas to gas.

    You are losing me at the gas/solid interface. Does this concept of “local thermal equilibrium” apply to the gas/solid interface? Are there other concepts that are necessary to consider in this case?

    If a gas is in contact with a black body, and they are both at the same temperature, does the concept imply that they will have similar radiation characteristics? I am not clear on this point.

    Comment by Steve — 11 Apr 2007 @ 9:26 PM

  84. These kind of posts are very valuable and much appreciated, even if they take much longer to read through. :)

    Regarding “Point 1: It’s easy to see that the G (and hence T(s) ) increases from S to 2S as the emissivity goes from 0 (no greenhouse effect) to 1 (maximum greenhouse effect) i.e. increasing the greenhouse effect warms the surface.”, I’d suggest including a graphical representation of the equation, with lambda on the x-axis and both G and T(s) on the y-axis. A picture of an equation is a lot easier for the layperson to understand than an algebraic expression and helps remove the equation fear factor (and is also easier to see).

    Also, simple terms like emissivity can be confusing, but wikipedia and other sites have good descriptions:

    As to how engineers can get into trouble with math, this is not really a dig at engineers – cross-field misunderstandings are many. Comments on positive and negative feedbacks by engineers whose experience is with electronics are a good example and have appeared on RC. Understanding feedback in an electronic circuit doesn’t mean that you understand the multi-variable and competing positive/negative feedbacks that affect climate, from albedo to water vapor to carbon cycle effects (once I spent five minutes talking to a history teacher about positive and negative feedbacks and climate before I realized he thought I was saying ‘good’ and ‘bad’ – whoops!)

    Anyway, this kind of thing is very useful. A simple box model of the carbon cycle could be treated similarly.

    Comment by Ike Solem — 11 Apr 2007 @ 9:31 PM

  85. Interesting. thanks for your responses. The type of people I am in conversation with at times use this as “evidence” of the “myth” of global warming.

    Comment by Jamie — 11 Apr 2007 @ 9:34 PM

  86. I think this post is great!

    It clearly breaks down the basic “voodoo-witchery” mystery of how climate models work for the public.

    This is something they can see, feel and manipulate…and dare I say relate to better now because of this post. Outstanding! Great topic!

    Comment by Richard Ordway — 11 Apr 2007 @ 10:01 PM

  87. As a friendly note to those who suggested Mr. Schmidt et al. should do “this” or “that” on this site. Do it yourself or give these folks a $100 or more donation.

    I do find it funny about those who demand extreme levels of scientific proof that high amounts of CO2 can heat up a planet, given … hmmm … Venus.

    It’s that neon-argon Venusian atmosphere, I guess.

    Comment by Doug Watts — 11 Apr 2007 @ 10:57 PM

  88. #77 This Southern cold snap was one month in the making in the North American Arctic (during March), studied it with great fascination before it went to your location, it simply slowly moved South since early April. I would rather look at the rest of the world, as a sure sign of the summer weather to come, In its wake, Arctic temperatures made an about face, total rebound in temperatures, from record cold to record warm in a few days. I’ll have an optical breakdown of this March cold air mass on my website at the end of April, Density weighted temperature reached 231 Kelvin at its coldest point, it was like being in the reverse eye of an hurricane, no wind, extremely low tropopause and very little heat.

    I appreciate this post, as there is not enough equations…. Examples about practical use of these equations would be greatly appreciated.

    Comment by wayne davidson — 11 Apr 2007 @ 11:40 PM

  89. RE #22:

    In addition to good points made by Steve in post #31, I would add the following.

    Some of the solar energy turns liquid water and soil moisture into water vapor instead of “heating” the surface and near-surface air. Instead of raising the temperature of the soil, it induces the phase change. The resulting water vapor is lofted upward (lower density than the “air”). The total heat in this case is the same – its just distributed differently making the effective air temperature at the surface cooler. In the desert, the heat is concentrated at the surface of the absorbing/reflecting object.

    At night, in the desert, a significant fraction of the heat absorbed is quickly radiated away. In the wet environment, the additional water vapor created during the day absorbs the long wave radiation emitted at night (greenhouse effect) and then as the night wears on and the air cools, the water vapor condenses back to the surface warming the surface and near-surface air by giving “back” the heat required to become vapor. Of course, some of the water vapor lofts high into the atmosphere and flows away from the source redistributing that heat elsewhere (stupid complexity issues…)

    The net effect being the desert is really hot during the day – but fairly cool at night. Over areas of high moisture (ocean, jungle, etc). The day is very warm (but typically under 40C) and humid, but the night is warm and humid. If the albedo effects are a “wash” and the convection doesn’t carry off too much vapor, the “average” temperature (24 hour day) is going to be higher in the wet climate than the desert climate at the same latitude. But you can die from heat stroke in both places.

    Comment by Robin Johnson — 12 Apr 2007 @ 1:42 AM

  90. I aint a scientist but id like to know what HAARP contributes to global warning if any?

    Comment by pete — 12 Apr 2007 @ 4:06 AM

  91. Being a simpleton, and not having been forced to endure mathematics for a couple of decades, it would be helpful if you better explained all math symbols (particularly the subscripts and superscripts, Kelvin scale, the tilda, etc.) used (even if that bores you and all of the engineers), to plug in real figures, and to provide more explanation of the involved factors. I followed some of the equations but eventually gave up.
    Don’t underestimate the ignorance of the lay person…

    Comment by Mark Ritzenhein — 12 Apr 2007 @ 8:21 AM

  92. Here is Gavin’s model (without feedbacks) in the Just Basic programming language. Sorry for the way it appears in HTML, e.g. the apparent lack of indents. < pre > wasn’t much of an improvement. For anyone who wants to use it, just cut and paste into your own Basic interpreter or compiler, or translate to C or Fortran or whatever.

    ‘ Gavin.bas implements a simple greenhouse model.

    sigma = 5.6704e-08 ‘ Stefan-Boltzmann constant.
    answer$ = “Y” ‘ Response from user.

    while answer$ = “Y”
    input “Solar constant? Observed is 1367.6: =>”; S
    input “Bond albedo? Observed is 0.306: =>”; A
    input “Emissivity? Observed is 0.769: =>”; lambda

    Ftop = (S / 4.0) * (1.0 – A) ‘ Find absorbed flux.
    G = Ftop / (1.0 – 0.5 * lambda) ‘ Find ground emission.
    Ts = (G / sigma) ^ 0.25 ‘ Find ground temperature.

    Print “Ftop =”, Ftop ‘ Display results.
    Print “G =”, G
    Print “Ts =”, Ts

    input “Again [Y/N]? =>”; answer$ ‘ Repeat if user wishes.
    answer$ = upper$(answer$)

    Comment by Barton Paul Levenson — 12 Apr 2007 @ 8:58 AM

  93. RE “factor 4 deals with the geometry (the ratio of the area of the disk to the area of the sphere)”

    I like to visualize things. Does this 1/4 have to do with the sun hitting a flat (if made small enough thru calculus) area on earth, as opposed to a spherical area. Or does it have to do with a flat area (if made small enough thru calculus) of the sun aimed at us, as opposed to the radiation from its entire spherical surface (i.e., we don’t get the whole of the sun’s radiation, only 1/4 — which seems a bit large, since we are so small)?

    What is the Stefan-Boltzmann constant? Is that the temp of the earth, if you go down, say, 6 feet? I know there is a some constant of about 55 degrees F (assuming there isn’t a extreme deep freeze that bursts the pipes).

    If so, I believe that’s the principle behind geothermal heating/cooling systems. If it’s 10 below zero F outside, you pump 55 degree air through the underground pipe system, then warm it a bit more to comfort level. I think it may also work as an AC as well.

    What is “emissivity”? Is that like reflection of warmth, or reflection plus existing warmth (the earth’s constant being maintained in the process)? Or infrared waves?

    Comment by Lynn Vincentnathan — 12 Apr 2007 @ 11:19 AM

  94. Hi chaps,

    How about sending this article to that Viscount Monckton? Not that I’m implying anything of course of someone who’s not afraid of sending in the lawyers…,,2053520,00.html

    Comment by Mike Donald — 12 Apr 2007 @ 11:30 AM

  95. Here are some links, some of which have to do with models underestimating the rate of world-glacier/ice shelf disintigration.

    The models don’t include yet (or weakly model) alot of the ice physics, such as positive feedbacks such as melt ponds, crevasse propagation, thermal ice diffusion, buttressing/ keystone effects, moulin, water lubrication effects ..remember Gavin’s feedback equations above!!!)…

    and some mention of Gavin’s work too. Fascinating and understandable.

    Comment by Richard Ordway — 12 Apr 2007 @ 11:39 AM

  96. Re: #94 (Lynn Vincentnathan)

    RE “factor 4 deals with the geometry (the ratio of the area of the disk to the area of the sphere)”

    I like to visualize things. Does this 1/4 have to do with the sun hitting a flat (if made small enough thru calculus) area on earth, as opposed to a spherical area. Or does it have to do with a flat area (if made small enough thru calculus) of the sun aimed at us, as opposed to the radiation from its entire spherical surface (i.e., we don’t get the whole of the sun’s radiation, only 1/4 — which seems a bit large, since we are so small)?

    It has to do with the fact that the earth intercepts sunlight proportional to its cross-sectional area (pi * R^2), but that energy gets spread over the earth’s surface area (4 * pi * R^2). So the 1366 W/m^2 for a square meter directly facing the sun, is diluted by (p * R^2) / (4 * pi * R^2) = 1/4 of that, or about 341.5 W/m^2.

    What is the Stefan-Boltzmann constant? Is that the temp of the earth, if you go down, say, 6 feet? I know there is a some constant of about 55 degrees F (assuming there isn’t a extreme deep freeze that bursts the pipes).

    No, the Stefan-Boltzmann constant relates the energy emitted by a radiating object to its temperature. Warm objects (“warm” meaning above absolute zero) radiate away some of their energy as electromagnetic waves (light). The amount they radiate depends on temperature. Since energy is measured in one set of units (Joules, ergs, watt-hours, whatever) and temperature in another (deg.K), there has to be a conversion factor: the Stefan-Boltzman constant is it.

    If so, I believe that’s the principle behind geothermal heating/cooling systems. If it’s 10 below zero F outside, you pump 55 degree air through the underground pipe system, then warm it a bit more to comfort level. I think it may also work as an AC as well.

    The Stefan-Boltzman constant is unrelated to geothermal heating. But the earth, below its surface, is indeed hotter than the surface, and we can use that temperature difference to drive a heat engine, extracting the energy for useful work. Also, the earth’s subsurface temperature doesn’t follow the same annual cycle (seasons) that surface temperature does. And, the deeper you go into the earth, the hotter it is.

    What is “emissivity”? Is that like reflection of warmth, or reflection plus existing warmth (the earth’s constant being maintained in the process)? Or infrared waves?

    No, it’s the radiation of energy. The energy is already there, as heat (or other forms), but objects naturally tend to give that energy away as electromagnetic waves (light) — that’s emissivity.

    Comment by tamino — 12 Apr 2007 @ 12:39 PM

  97. [[I like to visualize things. Does this 1/4 have to do with the sun hitting a flat (if made small enough thru calculus) area on earth, as opposed to a spherical area. Or does it have to do with a flat area (if made small enough thru calculus) of the sun aimed at us, as opposed to the radiation from its entire spherical surface (i.e., we don’t get the whole of the sun’s radiation, only 1/4 — which seems a bit large, since we are so small)?]]

    The Earth intercepts sunlight on its cross-sectional area, which is pi R^2, where R is the Earth’s radius. But its actual surface area is that of a sphere, 4 pi R^2. So the Solar constant has to be divided by four to see how much sunlight hits an average square meter of the Earth.

    [[What is the Stefan-Boltzmann constant?]]

    It’s the proportionality constant in the Stefan-Boltzmann radiation law:

    F = \epsilon\sigma T4

    F is the flux the object radiates, power per unit area (watts per square meter in the SI). \epsilon is the object’s emissivity (discussed below); \sigma is the Stefan-Boltzmann constant, T is the temperature (degrees Kelvin in the SI).

    The value of the Stefan-Boltzmann constant is about 5.6704 x 10-8 W m-2 K-4 in the SI. In the English system it would have a different value and the units would be something like BTUs per second per square foot per Rankine degree to the fourth power.

    [[What is “emissivity”?]]

    It’s µ from the above equation, and it describes an object’s efficiency as a radiator. An emissivity of 0 means the object radiates nothing at all (it’s surrounded by some kind of perfect insulator). An emissivity of 1 means the object is a perfect or “black body” radiator. Most real objects have an emissivity somewhere in between.

    Comment by Barton Paul Levenson — 12 Apr 2007 @ 12:57 PM

  98. Re 93 (Lynn’s comments)
    One way to visualize the factor of four difference due to the geometry of a disk versus a sphere is to imagine a colander, which one might use to strain spaghetti, for example. The top surface, which is open, is shaped like a disk, while the bottom screened surface is shaped like a hemisphere. The same quantity (heat, light, electric field, etc.) that passes through the curved surface must pass through the disk-like surface, as long as no heat, light, or charge is generated in the colander itself. In other words, the flux passing through the curved surface must be the same as the flux passing through the disk. This is the essence of Gauss’s Law. When you calculate a flux, you have to take into account the angle between the field line and the normal to your surface. If the sun’s rays come in at a glancing angle, your flux is smaller. The flux is zero at the edges of the sunlit side of Earth, and it is a maximum at the center of the sunlit surface. Now you could systematically integrate across the hemispherical surface of Earth, taking into account the angle of the sun’s rays, or you could remember that the flux is the same for a disk or a hemisphere. The reason for this is because the sun’s rays are perpendicular to the disk everywhere.
    As for your question about Stefan-Boltzmann’s constant, it might help to consult a reference such as Wikipedia to get a feel for what the relationship is. I have my students investigate the Stefan-Boltzmann law by using a light bulb connected to a variac, which is used to systematically change voltage. They have to connect an ammeter and a voltmeter, so that they can calculate the resistance of the tungsten filament as the bulb gets brighter and brighter. By examining published tables for resistivity of tungsten as a function of temperature, students can estimate the filament temperature at each voltage step. By plotting power (current times voltage) against temperature on a log-log plot, they get an exponent of about 3.9. My hope is that by using commonplace objects, students will realize that many objects obey Stefan-Boltzmann’s equation, not just distant stars like our Sun.

    Comment by Jeff — 12 Apr 2007 @ 1:03 PM

  99. Re #93: [If so, I believe that’s the principle behind geothermal heating/cooling systems. If it’s 10 below zero F outside, you pump 55 degree air through the underground pipe system, then warm it a bit more to comfort level. I think it may also work as an AC as well.]

    Err… Not exactly. What you’re describing is ground source heating/cooling, though it’s often miscalled geothermal in ads. A true geothermal heating system uses heat from a hot spring or similar. A ground source system uses a heat pump to take advantage of the fact that the ground below the frost line stays at a fairly constant 55F or so year round. Thus in the winter, the system can actually move heat from the relatively warm ground to the house using less energy than it would to heat the cold outside air, while in summer the reverse is true.

    If this seems like magic to you, well, it does to me too :-)

    Comment by James — 12 Apr 2007 @ 1:34 PM

  100. Re:

    The basic case is set up like so: Solar radiation coming in is S=(1-a) mbox{TSI}/4, where a is the albedo, TSI the solar ‘constant’ and the factor 4 deals with the geometry (the ratio of the area of the disk to the area of the sphere). The surface emission is G=sigma T_{s}^{4} where sigma is the Stefan-Boltzmann constant, and T_s is the surface temperature and the atmospheric radiative flux is written lambda A=lambda sigma T_{a}^{4}, where lambda is the emissivity – effectively the strength of the greenhouse effect. Note that this is just going to be a qualitative description and can’t be used to quantitatively estimate the real world value

    It isn’t the math that gets me, when I was taught pi=C/D I was also told what circumference and a diameter was.

    What is albedo, what is the disk(area of sunlight?) (is the sphere is earth?) , and Stefan-Boltzmann constant, and surface temperature and the atmospheric radiative flux

    Comment by Larry Risch — 12 Apr 2007 @ 2:30 PM

  101. Lynn-

    The geometry of the sphere works like this. If we draw a circle around the Earth where light transitions to dark and then project an imaginary cylinder back to the Sun, we can measure the solar output striking the Earth. Even though the Earth is a bulge at the bottom of that cylinder – the amount of solar light hitting the Earth (at whatever angles) is just the cross section of the cylinder – which is exactly the area of that circle we drew – which is, of course, given by Ï� * r2.

    It turns out that the surface area of a sphere is given by the formula 4 * � * r2. Even though the light is only striking half the Earth, we really want to know the total energy distributed across the entire surface area of the Earth since the acquired heat is not instantaneously radiated back into space. Given that, we divide the area of the sphere by the circle, we get really simple ratio of 4 to 1. So, we have to divide the solar output per meter squared by 4 to get the actual solar output per square meter over the Earth.

    Comment by Robin Johnson — 12 Apr 2007 @ 2:38 PM

  102. [what is emissivity]

    An emissivity of zero means the object in question is either a perfect reflector or is perfectly transparent and as a result does not absorb and hence cannot emit radiant energy and has nothing to do with being surrounded by insulation. Gold metallized plastic film is a near perfect reflector and is used on spacecraft to prevent radiant heating from sunlight. A planet with an atmosphere of a noble gas like argon would have no greenhouse effect because argon is transparent in both the visible and infra-red wavelength region. If you have an infra-red kitchen thermometer and don’t use the emissivity correction, a stainless steel pot full of boiling water will apear to be at a much lower temperature than a black anodized aluminum pot full of boiling water. Stainless steel is a good reflector and thus has a lower emissivity than black anodized aluminum.

    Comment by DeWitt Payne — 12 Apr 2007 @ 5:31 PM

  103. If lambda can’t be greater than one, then isn’t the maximum surface temperature 303 K with this model, given a constant solar irradiance of 240 W/sq.m.? Yes, that’s fifteen degrees warmer than now, but it’s also an upper limit. I second the motion for something between this oversimplified model and a full bore planetary GCM. How about creating a multi-layer spreadsheet model or program of a one-dimensional, clear air, Earth normal nitrogen, oxygen and argon atmosphere containing only water vapor and carbon dioxide as ghg’s with graphs and charts of temperature and pressure with altitude. Of course, the more user adjustable parameters, the better. Including sensible and latent heat transfer from the surface and how they change with surface temperature and humidity would be nice too.

    Comment by DeWitt Payne — 12 Apr 2007 @ 7:17 PM

  104. Re: #84: Ike,

    I agree cross-field misunderstandings may be many and Iâ??m certainly not suggesting that engineers are all-knowledgeable or infallible, by any means. Climate science is certainly rich in underlying complexity, and I do not pretend to be an expert (unlike the engineer to whom you refer). Iâ??m just saying the misunderstandings are probably not due to the math itself. Linear algebra as used in this example should be in the basic toolkit of any engineer, and while climate feedbacks are multi-variable and non-linear, they are conceptually the same if not analogous to those found in other disciplines. Someone who believes that engineers â??know just enough math to get into troubleâ??, lives in the modern world, and is otherwise rational, should be very afraid to get out of bed in the morning. As far as history professors, wellâ?¦. theyâ??re interesting too.

    Comment by The Wonderer — 12 Apr 2007 @ 7:24 PM

  105. Here’s how I might try to qualitatively introduce radiation transfer in a more complete manner:

    (LW = longwave = terrestrial = the kind of radiation emitted at typical atmospheric (except thermosphere, which, in terms of amount of energy, has a very small role to play in the totality of atmospheric radiation) and near-surface temperatures of the Earth – as opposed to SW = shortwave = solar (radiation))

    (optical depth, optical thickness, optical length, optical distance* = a measure of path length relative to the rate of absorption+scattering along that path – an opaque object has infinite optical depth, a transparent object has zero optical depth; the proportion of light starting at a point and moving along a path of optical thickness t which is neither scattered nor absorbed is exp(-t)
    * PS I’m assuming all these terms can be used, correct me if I’m wrong)

    (To the degree that objects are exchanging LW radiation, the net heat transfer via radiation will be from hot to cold)

    At any given level in the atmosphere (and at any given wavelength), radiation coming from any direction is originating from a distributed source along the pathlength, the distribution declining exponentially with optical distance; as the optical thickness increases along a given geometric distance, photons travel shorter paths, so the radiative energy exchange increases along shorter distances while decreasing along longer distances; hence, for LW radiation:

    increasing LW opacity (from increasing greenhouse gas concentration, or from clouds)
    => increased cooling to space from those parts of the atmosphere optically closest to space, decreased cooling from the surface and, if the starting opacity is high enough, lower atmosphere, to space, and if the starting LW opacity is high enough, decreased cooling from the lowest parts of the atmosphere to the colder upper parts, although – depending on the temperture profile and other details (wavelength dependencies) – increased cooling from the very top of the troposphere and the upper stratosphere to the base of the stratopshere, etc.

    Temperature rises or falls until, at any given level, emitted radiant power per unit atmosphere = absorbed radiant power per unit atmosphere + convergence of sensible heat transport by convection + net latent heat release per unit atmosphere

    net latent heat release = ((condensation + freezing) – (evaporation + melting))

    Comment by Pat — 12 Apr 2007 @ 9:55 PM

  106. Re the response to #81, that sounds good until one remembers that Antarctica is over 13 million square km. Surely you’re not suggesting ghg warming of that much area is all damped by an ocean sometimes thousands of km away? Just doesn’t hold water…

    Comment by Harry Haymuss — 12 Apr 2007 @ 10:09 PM

  107. Re #71, your example of water vapor being a positive feedback is unrealistic. Clouds are a product of water vapor, and it is not known if that feedback is positive or negative. To say “water vapor is a positive feedback” is academic – and I thought we were trying to address reality here.

    You didn’t address #64, which states feedbacks *double or triple* the effect of CO2.

    Comment by Harry Haymuss — 12 Apr 2007 @ 10:16 PM

  108. Concerning G: Am I right that the given expression assumes that the emissivity of the ground is 1? There was a presentation at Santa Fe (2006) by Hartwig Volz from RWE showing that neglecting the emissivity of the large ocean surfaces (which is lower than 1) leads to climate sensitivities that are too high, and that this correction is absent from all (?) climate models used by the IPCC. What does Gavin think about this?
    BTW: I really appreciate some more theoretical contributions like this one. Please go on! Just a recommendation from someone who has taught physics since nearly 40 years: please don’t jump over intermediate calculating steps (like the derivative of G), short-cuts are a challenge for the reader but may put off someone used to more extended developments.

    [Response: This derivation assumed an emissivity of 1 at the surface. In the real world it’s slightly less (0.95 or so depending on various conditions), but that just divides through to the sensitivity and actually makes it slghtly larger (since dG/dTs is smaller => dTs/dFtop increases). This is important in various remote sensing applications, but a minor effect on the climate. And since it doesn’t change appreciably as a function of climate, it can’t be a dominant force in climate variability. -gavin]

    Comment by Francis Massen — 13 Apr 2007 @ 2:52 AM

  109. re: 71. Goodness. You obviously did not read the link I provided:
    More specifically, the link contained in that link to Soden’s paper.

    Case closed. It is really not all that difficult to research it yourself and actually learn something instead of trolling with no basis in fact. Talk about reality. Sheesh.

    Comment by Dan — 13 Apr 2007 @ 4:59 AM

  110. re: 71. Lots more on water vapor being a positive feedback:

    Again, that took 10 seconds to research.

    Comment by Dan — 13 Apr 2007 @ 5:57 AM

  111. Re 109 and 110:
    I’m not arguing that water vapor itself, with everything else remaining constant, is not a positive feedback.

    You are confusing that simple concept with the reality that increasing water vapor (including increasing the rate of convection) increases cloud cover, and we don’t know the overall effect of that.

    Look at the Pliocene. Much warmer, but indications are that the tropics were not much warmer than today and that may have been due to cloud cover.

    Comment by Harry Haymuss — 13 Apr 2007 @ 7:39 AM

  112. Appropos to tropical clouds and feedbacks: Lin, Wielicki, et al., 2002, “The Iris Hypothesis: A Negative or Positive Cloud Feedback?” which found a weak positive feedback from tropical upper-tropospheric anvils. From

    Comment by Dan — 13 Apr 2007 @ 8:48 AM

  113. [[There was a presentation at Santa Fe (2006) by Hartwig Volz from RWE showing that neglecting the emissivity of the large ocean surfaces (which is lower than 1) leads to climate sensitivities that are too high, and that this correction is absent from all (?) climate models used by the IPCC.]]

    I think you’re right that most (not all) GCMs set surface emissivity to one. I looked up emissivity figures for water and found these:

    0.93 — Transcat News,

    0.92-0.97 — Oke, T. R., (1987) Boundary layer climates. 2nd ed., Methuen, N.Y.

    0.95 — Jin Menglin and Liang Shunlin 2006. “An Improved Land Surface Emissivity Parameter for Land Surface Models Using Global Remote Sensing Observations.” J. Climate 19, 2867-2881.

    0.9637 at 3.7 microns, 0.9775 at 10.8 microns, 0.9431 at 12.0 microns, and 0.9967 at 8.5 microns — Surface Spectral Emissivity Derived from MODIS Data, Yan Chen, Sunny Sun-Mack, Patrick Minnis, David F. Young, William L. Smith, Jr. 2002. Extended Abstract for SPIE 3rd International Asia-Pacific Environmental Remote Sensing Symposium 2002: Remote Sensing of the Atmosphere, Ocean, Environment, and Space, Hangzhou, China, October 23-27, 2002

    [Response: I checked with our radiation people, and find that indeed, we do include longwave emissivity/albedo effects (which depend on spectral frequency and wind speed). It is a minor effect though. – gavin]

    Comment by Barton Paul Levenson — 13 Apr 2007 @ 9:13 AM

  114. Got cut off from that last one when my keyboard failed. Had to do a hard reboot to get it back again.

    The mean of the eight emissivities I found for water is 0.96, the standard deviation is 0.047. This is a significant difference; if applied over the whole Earth, it would mean we’re radiating at 374 watts per square meter instead of 390, a difference of 16 watts per square meter. Can any professionals comment? It looks like the skeptics might actually have a point here.

    Comment by Barton Paul Levenson — 13 Apr 2007 @ 9:57 AM

  115. My modest contribution to the discussion.

    I’d appreciate any feedback you think relevant, thx:-)

    Comment by Brian Coughlan — 13 Apr 2007 @ 11:12 AM

  116. [[I’m not arguing that water vapor itself, with everything else remaining constant, is not a positive feedback.
    You are confusing that simple concept with the reality that increasing water vapor (including increasing the rate of convection) increases cloud cover, and we don’t know the overall effect of that.

    I don’t think it’s clear that increased water vapor does increase cloud cover. I know Hart (1978, 1979) used such a relation in his model, but I think that was one of the parameterizations Schneider and Thompson (1981) said might not be valid. I’m not sure what the state of the question is these days. Does anyone know what determines cloud fraction, or it still an open question?

    Comment by Barton Paul Levenson — 13 Apr 2007 @ 11:20 AM

  117. RE the water vapor issue, see Robust Responses of the Hydrologic Cycle, Held&Soden 2006 for a discussion of the robust increase in lower tropospheric water vapor. The key number is the relationship of the saturation vapor pressure to temperature; for a 1K increase in temp there is a 7% increase in saturation vapor pressure. For a 3K equilibrium climate sensitivity, that’s about 20% increase in the amount of water that exists as vapor in the air (that’s derived from Clausius-Clapeyron). One of the robust responses is horizontal moisture transport from the equator to the poles (which also means latent heat transport). This means that warming at the poles should continue to accelerate, and a moister atmosphere should also encourage hurricane formation, as should warmer sea surface temps.

    What is less certain is the upper tropospheric water vapor, but the EOS MLS program is now measuring that. The greatest uncertianty wrt clouds seems to be the radiative effect of tropical clouds in the marine boundary layer… but is there any indication that cloudiness is increasing as the planet warms? In fact, the glocal record produced by the International Satellite Cloud Climatology Project shows a decreasing trend in global cloudiness, but the suitability of the data for trend analysis has been questioned (Evan et al 2007)… but it doesn’t seem that there is any evidence of increasing cloudiness.

    Incidentally, Lindzen has been given yet another media platform to promote his viewpoints: Newsweek ran “Why So Gloomy” in which Lindzen now claims that “A warmer climate could prove to be more beneficial than the one we have now.” and he also claims that “There is no evidence, for instance, that extreme weather events are increasing in any systematic way” (what does he mean by ‘systematic’? Is he ignoring the hurricane trend? The heat waves?) He also states that “Sea levels, for example, have been increasing since the end of the last ice age” while attributing the vastly accelerating rate of sea level rise to ‘short-term fluctuations’.

    Amazingly, he trots out this statement: “Many of the most alarming studies rely on long-range predictions using inherently untrustworthy climate models, similar to those that cannot accurately forecast the weather a week from now.” This is just nonsense.. see the real climate post Short and Simple Arguments . (this is why realclimate is such a valuable site!)

    He then goes on to make an economic argument, something he knows nothing about: “Moreover, actions taken thus far to reduce emissions have already had negative consequences without improving our ability to adapt to climate change”. This is even more nonsense, since renewable energy technology will result in economic expansion, new jobs, global energy security in an era of tight oil supplies – solar photovoltaics and wind technology coupled to innovative energy storage systems (hydrogen production, for example) are topics that Lindzen also ignores, while instead claiming that ethanol production will result in global starvation (and he also claims, like Sherwood Idso’s CO2science, that agricultural productivity will increase in a warmer world – ignoring the effects of temp extremes and drought…)

    What Lindzen also completely ignores is the well documented changes occuring in polar regions, and he makes no mention of the potential instability of the West Antarctic and Greenland Ice Sheets. The article reads like a list of fossil fuel lobby talking points, and has already been reposted all over the web. You can email Newsweek at and let them know what you think of this.

    Comment by Ike Solem — 13 Apr 2007 @ 1:11 PM

  118. Re 17:
    Aren’t you putting the cart before the horse when you say: “For a 3K equilibrium climate sensitivity, that’s about 20% increase in the amount of water that exists as vapor in the air ”

    Also, aren’t you being dogmatic when you deny even the *possibility* that warming may be good for us?

    Plus, I know I’m being a heretic here, but what exactly did you find wrong with Lindzen’s statement? Certainly not all of it…

    Comment by Harry Haymuss — 13 Apr 2007 @ 1:34 PM

  119. Similar to comment #103, I checked the ratio of the temperature with full greenhouse effect (lambda=1) to no greenhouse effect (lambda=0). It is 2^0.25 = 1.189, so that going from no atmosphere to a fully absorbing atmosphere in this simple model only increases the surface temperature by 19% ! It seems to me that by definition no physical object can have emissivity greater than one, so that this simple model cannot explain the runaway greenhouse effect like on Venus. Could you elaborate on some of the other physical effects that can increase the temperature even more beyond this simple model for much higher concentrations of CO2 than exist on Earth now, like on Venus?

    [Response: You can make the strength of the effect as large as you like by adding layers. Each additional layer adds a factor of 1.189 to the temperature difference between the blackbody and the surface. However, in the real world the percentage difference between having a greenhouse effect and not (measured in Kelvin of course), is around 11 to 12% (i.e. 33 deg K out of 288 K). You are correct though, this model as is couldn’t cope with Venus… – gavin]

    Comment by Eric — 13 Apr 2007 @ 1:37 PM

  120. Is not the solar constant even more divided, at high latitudes? Is their not an obliquity factor related to the latitude of the location? 288 Kelvin may be a number for the equator? It gets interesting at the Poles especially when there is no Solar constants during the long night, when S/(1-0.5*lambda) is equal to 0.

    Comment by wayne davidson — 13 Apr 2007 @ 1:57 PM

  121. Wayne. See post #96.

    Comment by Robin Johnson — 13 Apr 2007 @ 3:12 PM

  122. [[Aren’t you putting the cart before the horse when you say: “For a 3K equilibrium climate sensitivity, that’s about 20% increase in the amount of water that exists as vapor in the air “]]

    If you plug a 3 K increase in temperature, from 288 K to 291 K, into the Clausius-Clapeyron equation for saturation water vapor pressure, you get a 19% increase.

    [[Also, aren’t you being dogmatic when you deny even the *possibility* that warming may be good for us?]]

    It’s not really an open question at this point. We’re looking at narrowing of growing belts, increased drought in continental interiors, more violent weather on continental margins, and unpredictable changes at the local level. Bad seems more likely, on the whole.

    One doesn’t want to be dogmatic about it. No doubt some areas will benefit. But on average, it seems to be a bad prospect.

    Comment by Barton Paul Levenson — 13 Apr 2007 @ 3:24 PM

  123. There is a critical flaw in the basic model.

    In the radiation field of a blackbody, a gas will obtain the Boltzmann distribution of states. This equilibrium is maintained by collision.

    I am aware of the LTE hypothesis.

    It is true that two black bodies radiating at each other will have the same radiation field at the same temperature, and thus absorption will equal emission.

    It is also true that two gas samples in the same state (composition, pressure, temperature, etc.) will have identical radiation properties and when in thermal equilibrium there will be no net transfer of radiation, absorption = emission.

    It is not true that a gas in the cavity of a black body will take on the radiation characteristics of the black body at thermal equilibrium of the entire system.

    Thermal equilibrium simply means that the average kinetic energy of the two systems is the same. A particle in a gas has considerably more translational freedom than a particle in a solid. Because of the large amount of continual random translational motion in a gas, it should be expected that its radiative power, when at the same temperature as a solid, will be considerably less than that of the solid.

    A solid at a given T will radiate as a function of T^4. A gas will not. A gas will radiate as a function of the T, which collisionally provides the Boltzmann distribution between excited and ground states,and the pressure, which must be used to account for the excited state lifetime. This provides for a considerably smaller radiation field associated with a gas than that of a solid.

    The basic assumption in the very first atmospheric layer that all of the energy the gas absorbs from the planet must be emitted is false. This assumption is then propogated up through the atmosphere layers. The net effect is that the model claims a T^4 power dependence for gas emission, because the surface (which is solid) has this power dependence.

    A much better model is to use the Boltzmann distribution for the gas excited state population in the radiation field of a black body – Atkins is a PChem book that provides a reasonable basic treatment.

    Using a basic two level system for the 15 micron absorption band provides an estimate that 4% of the CO2 molecules will be in the excited bending mode at any given time, when in the field of a black body at about 300K. This takes into account stimulated absorption and emission.

    Spontaneous emission is trivial at 1 atm pressure. It is present however, and a small radiation field will be maintained, and passed from atmospheric layer to atmospheric layer.

    It is simply incorrect to assume that all of the radiation CO2 absorbs from the planet’s surface will be subsequently reemitted, and it is this incorrect assumption that drives this theory.

    Consider however if it were true. In this model, only the CO2 is actually being heated, not the molecules around it. All excited states survive to emit, and the radiation field is maintained. Such a model actually does not lead to warming of the atmosphere, just the CO2 component.

    Gasses are not solid, and should not be treated as such. The Boltzmann distribution is well known, and should be used.

    It is not an accident that much of the basic theory used for global warming was devised before the introduction of quantum mechanics in 1900. The T^4 power dependence in these models is continuously scaled throughout a calculation because of the attempt to stuff a gas phase problem into a solution devised for solids. (Need we explain the band theory of solids and how it provides for continuum radiation whereas gas phases do not?)

    Well, I suppose that should rile a few folks and provide quite a bit of clucking. Sometimes it is fun to stir the hornets nest.

    [Response: No hornets here. I produced this to demonstrate pedagogically how the greenhouse effect works, not as a model for the real atmosphere (as I think I made clear). If you think that your explanation serves that purpose better, I would beg to disagree. Serious models (i.e. line-by-line codes or the radiative transfer models in GCMs) do this properly and certainly do not assume that all radiation absorbed is re-emitted. – gavin]

    Comment by James — 13 Apr 2007 @ 3:36 PM

  124. 89 and related responses to #22: I understand that more energy is “used” to form water vapor support photosynthesis in more humid/lush areas, compared to deserts. But this use of energy appears to lower the temperature, compared to a desert situation. My question was: does this not show that water vapor feedback exerts a NEGATIVE feedback to surface temperature?

    Comment by jae — 13 Apr 2007 @ 4:07 PM

  125. re. 118 Troll. Please read this site before asking your question:

    [[Also, aren’t you being dogmatic when you deny even the *possibility* that warming may be good for us?]]

    If you did read this site, you would find that the negative effects far outweigh the good effects of warming.

    Warming can and does have some beneficial short-term effects by benefiting longer growing seasons in some areas, reducing heating bills, reducing freezing deaths, increasing some crop growth rates and opening up new navigation areas (already done)…but this is most likely minor compared to:

    The possible negative effects of ending/changing monsoons, water shortages, increasing storm damage, crop failures, flooding, sudden rising sea levels, abrupt climate change, wars, unrest, increased allergies, lung deaths (low-level ozone), mass human migration, species extermination (most likely already happened), coral destruction (oops, now many second and third world countries would lose alot of their fishing), increased diseases, ocean acidification (if you dump in co2) and possible wholesale evacuations of cities, islands and coastlines…

    and dare I say it…a threat to the integrity of our whole civilization itself through suddenly straining our federal system past its limits to adapt, fund and control too many combinations of sudden immigration pressures (tens of millions of “starving people ain’t goin to stay ‘down there’ when we ‘rich folks’ got food up here”), food shortages, mass evacuations, world economic collapse, civil unrest, and multiple simultaneous wide-spread disaster relief efforts…

    While suddenly trying to fight a rapidly increasing terrorist movement derived from a billion+ possible candidates from the second and third worlds who suddenly might not have food, a government or hope and lots of free A-bombs.

    Science always tries to be open to “possiblities”, so you do hear some of the possible good short term effects of warming.

    However, if you read the literature and talk to real scientists who do sustained peer-review research (that holds up under long-term scientific scrutiny), they will almost invaribly tell you that this current rapid average rate of warming is not good overall, is potentially very dangerous and far outweighs the possible good effects.

    …and by the way, Lindzen does not currently do peer-reviewed global warming research that stands up under scientific scrutiny…

    Comment by Richard Ordway — 13 Apr 2007 @ 4:12 PM

  126. Question: Why isn’t the equation for surface flux: S + 1/2*lambda*A = G, since half the atmospheric flux goes up and half goes down?

    Comment by jae — 13 Apr 2007 @ 4:14 PM

  127. re: #125

    There may be short-term benefits of warming (like Richard Selley’s amusing comments about the great future for wineries in Scotland after 2100), but there are plenty of concrete, specific issues that matter-of-fact state economic planners worry about … and this shows up rather strongly in which states are pushing for policies to deal with climate change. These people are not dealing with global theoretical concepts, they are trying to quantify direct effects in specific geographic areas they understand.

    Here in California:

    a) The state planners take the issues *very* seriously, because we already have serious water problems, and lower Sierra snowpacks don’t help one bit.

    b) 50% of the USA’s fruit and vegetables are grown here, sometimes in very limited areas where the soil & climate are “just right”, and a significant change of temperature in either direction will be disruptive.

    c) Good wineries won’t be helped either.

    d) We have a lot of coastline, and we have some farmlands that are already below sea level [Sacramento Delta].

    e) We have noticable travel industry, including ski resorts … and lower snowpack doesn’t help there either.

    f) Peak power usage is summer afternoons, i.e., air conditioning.

    f) In fact, for CA, it’s hard to identify economic benefits of warming, and easy to identify large downsides.

    g) All of this has something to do with CA’s persistence in pushing on energy efficiency, gas mileage improvements, clean air acts, etc.

    For others, there may be some mixed blessings: it’s probably milder in State College, PA, than when I was going to school there, but it’s not even an unmixed blessing for Northern states:

    – New Hampshire and Vermont worry about their ski resorts as well, for the same reason as California, but with less altitude. At least in NH, many southern resorts have closed for good, and tourism taxes are very important (to keep other taxes down).
    – They worry about the future of maple sugar … [sugar maples need cold]
    – They worry about the brilliant Fall Foliage (tourism) migrating 100-300 miles North.
    – Maine, Massachusetts, Rhode Island, Connecticut, New York, New Jersey have substantial low-lying seacoast. Most have at least some dense cities right on the coast, and have had experience with storm surges there.

    Southwest states worry about drought and cost of more air-conditioning; Pacific Northwest states worry about snowpack.
    Southeast has lots of coastline, water issues, and will want more air-conditioning.

    Anyway, I’ve long been curious about Lindzen’s current worldview, but I certainly trust state planners more to know whether warming benefits them or not.

    Comment by John Mashey — 13 Apr 2007 @ 6:47 PM

  128. #121 Robin thanks double that Tamino! I was referring to what the equation speaks out loud, which is solar radiation spread out evenly on Earth as a sphere despite instantaneous solar radiation reaching only one side at any given time, half a sphere. There may be some deeper meaning to this; why is the radiation condidered spread out evenly when in reality it does not? The very reason for Climate/Weather is a differential in temperature , pressure driven by diurnal effects and the strength of solar radiation at every given location. A philosophical question so to speak, just exploring the meaning of this ‘spread the energy evenly about idea.’.. I would rather enjoy equations dealing with the dark side of the Earth and one with only the bright side. Applying 1/2 a sphere with T^4=S/(SBconstant *(1-0.5*lambda))gives interesting results,applying it to the dark side does not give any result. I really like simple models /equations as concepts explaining things, if well written they have great impact on spreading out knowledge of climate science. …..This is another great post!

    Comment by wayne davidson — 13 Apr 2007 @ 9:15 PM

  129. Regarding no. 126.
    In the model, the 1/2 lambda going down to hit the earth will be re-radiated by the earth, giving an additional 1/4 lambda to space, 1/4 lambda back down to earth. That 1/4 lambda will be re radiated, of that, 1/8 will go up, 1/8 down.
    You wind up with a series 1/2 + 1/4 + 1/8 + 1/16…. that sums to 1.

    Comment by Alan D. McIntire — 13 Apr 2007 @ 9:48 PM

  130. Re #124 (jae)

    Well. Its tricky actually. And do you mean globally or locally?

    Locally, comparing a dry area [desert] with a wet area [ocean/forest] the main observable effect is that the daytime air temperature is lower but night time temperature is higher in the wet area. Since water vapor is a strong GHG, there is more heat rentention overnight plus the condensation effect – so more heat is retained by a wet atmosphere than a dry. But water vapor forms clouds which increases albedo reduces solar heating – a negative feedback. Also, water vapor is not as dense as “regular” oxygen-nitrogen air so it undergoes strong convection and lofts high in the atmosphere creating wind which transfers heat towards the polar regions [local negative feedback – but negative and positive global feedbacks]. The presence of plenty of non-frozen water means lower albedo – either its open water (very dark) or heavily covered in vegetation – so that’s a positive feedback assuming the desert is lighter in coloration (there are exceptions but that’s fairly true). Oceans however convect heat into the deep, convert heat into mechanical energy [currents] and plants consume energy to grow, retain water and sequester carbon. So those are negative feedbacks.

    Globally, warming the polar regions creates, you guessed it, more water vapor increasing the GHG effect – so that’s another set of positive and negative feedbacks. However, this convection process has taken the water vapor higher up where its longwave radiation leaves the atmosphere more easily (less absorption) creating a negative feedback. Also, heat escapes more readily from the polar regions – its drier and less hours of sun – also a negative feedback. Rain and snow have both negative and positive feedbacks.

    YET the global negative and positive feedbacks reach equilibrium at some point for a given solar input and other factors (atmosphere thickness, planet albedo, geography, other GHG).

    Locally, I as claimed earlier, the average temperature (total heat?) is probably going to be higher in the wet environment. But the day time high is going to be much higher in the dry desert than the wet forest. But that’s okay – its a DRY heat…

    Comment by Robin Johnson — 13 Apr 2007 @ 11:40 PM

  131. Interesting gas vs. solid discussion. When does a gas become dense enough to act like a liquid/solid? What is the surface of the Sun, e.g?

    Comment by Rod B. — 14 Apr 2007 @ 12:48 AM

  132. You may not want to answer this quesion, since it is politically tainted, but Laurie David and Sheryl Crow are currently touring the country lecturing to college students about global warming. One of their major points is that the current and recent unusually cold and snowy national weather is a sign of anthropogenic global warming, she is quoted here: “The things you mention like worse snowstorms and a chaotic start to baseball season are all symptoms of global warming. Global warming causes extreme weather in BOTH directions. For example, the reason the blizzards are getting worse in the Northeast is because the Great Lakes are no longer freezing over thus fueling the stronger snow storms that are topping the headlines and disrupting the start of the baseball season”. Many of my students know better and challenge this as unsceintific, but it seems this is becoming urban legend. I know this blog is usually politically sympathtic to the likes of Ms. David, but is there any science to back up her pronouncements? Thanks.

    Comment by Dr. M. Jorgensen-Petersen — 14 Apr 2007 @ 10:31 AM

  133. #132, The last bit of cold in USA and Southern Canada now, was caused by the lack of mixing, a stable body of cold air in the North American Arctic in March. It is a small part of the world which is cooler than Normal, the big picture, planet Earth: is on the whole warmer at the same time. The two, cooler in North America and warmer rest of the world are linked by weather systems which exacerbate cooling by creating relatively small windows of clear air especially at locations in darkness or with low sun elevations which are surrounded by much larger above warmer than normal areas. The reverse can happen as well, when clouds and advection warm up the Polar regions, this translates into much warmer weather at lower latitudes, the latter has been happenning more often over the last few years. Being just a meteorological observer, I am recently seeing stranger and stranger weather, having very unfamiliar patterns. There is definitely Climate system Change going on on a world wide scale all of it linked by overall warming. So I do care about what the singers and poets are thinking, especially when they are right.

    Comment by wayne davidson — 14 Apr 2007 @ 3:09 PM

  134. I’m hoping you’ll notice this comment, because I found a seriously demented article that you all might be inclined toward responding to

    Is Climatology a Science?

    by the wonks at Real Clear Politics. If anyone ought to answer this question, I thought it would be this group. Robert Tracinksi amusingly cites Richard Lindzen, a man known to be in the employ of various petroleum interests.

    Comment by theBhc — 14 Apr 2007 @ 3:12 PM

  135. Re #132: Dr. M. Jorgensen-Petersen — Your question is about weather, not climate. Nonetheless, in an amateur way, I’ll attempt to answer part of it.

    It is my understanding that a frozen lake can produce no so-called lake effect.

    But some web trawling on your part can probably locate a more definitive and reliable answer to your question.

    Comment by David B. Benson — 14 Apr 2007 @ 3:23 PM

  136. #132, from a scientific perspective, you cannot pin a single weather event on GW.

    However, from an environmentalist or victim’s perspective (or the perspective of those concerned about the world) of avoiding false negatives, you cannot prove beyond a shadow of a doubt that the weird weather we are experiencing is NOT caused or enhanced in some way or another by GW.

    At least one of my predictions (I’m a social scientist) is coming true — we are shifting from a period of underattribution of GW effects to overattribution (I even mentioned that on RC some years back), though it’s happening sooner than I had thought. So, if Cheshire Wogburton in Miami bumps his head on April 29th, it’s gotta be due to GW :)

    And I further predict that this trend in overattribution will continue and strengthen (not based on any good study, but just my general knowledge of humanity).

    Only problem is there is a serious lag between knowledge of and desire to solve environmental problems, and actual action to solve them (it’s like a disconnect) — and that IS based on a study.

    Comment by Lynn Vincentnathan — 14 Apr 2007 @ 4:18 PM

  137. Re # 134: The cited article asks thes question at the end: Does climatology have a well-developed, thoroughly proven theoretical framework, derived from decades of observations and earlier discoveries? Does it have a proven set of laws to explain what factors drive the global climate on a scale of centuries? Does climatology have an established track record of being able to predict next week’s weather, much less the next century’s weather?

    Simple answers are Yes, Yes and No – but only because climatology is not concerned with predicting next weeks weather. More detailed answers are easy to find.

    Comment by Doug Lowthian — 14 Apr 2007 @ 5:25 PM

  138. Greenhouse effect ??? Sorry, that only occurs in greenhouses – this specific effect does NOT occur on a global scale – this fact was proven around the turn of the previous century (1900s) by a German scientist; of course, there is global warming but greenhouses do not get warm because of heating due to absorption/re-radiation of longer wavelength photons- it is simple insulation effects by the glass only – the German built a greenhouse out of NaCl and it was the SAME temperature as the greenhouse made of glass – QED.

    Comment by Dennis Brown — 14 Apr 2007 @ 5:38 PM

  139. In Comment 138, 14 Apr 2007 @ 5:38 pm, Dennis Brown says: “Greenhouse effect ??? Sorry, that only occurs in greenhouses – this specific effect does NOT occur on a global scale – this fact was proven around the turn of the previous century (1900s) by a German scientist; […]”

    Specifically who was the “German scientist”? Would you cite a particular report for further study?

    Comment by Burgess Laughlin — 14 Apr 2007 @ 7:00 PM

  140. Re #132 Dr. Jorgensen-Petersen,
    Regardless of whether the two singers have their facts straight on that specific point, or not, your students would be well advised to focus on the ladies’ music, and learn science from scientists.

    For what it is worth, the only Great Lake that reliably freezes over completely is Lake Erie, and there have always been years when it hasn’t froze completely, or when the ice lasts only a month or two (as opposed to 3-4, or even 5, months of ice in a cold winter). You can see the historical records of Great Lakes ice cover for yourself at:

    Comment by Chuck Booth — 14 Apr 2007 @ 7:37 PM

  141. I would like to recommend that Buffalo Bill be posthumously recognized as a top-notch environmentalist. He killed thousands of methane spewing critters that were about to cause global destruction. His quick actions saved the planet. By the way, shouldn’t folks get some kind of carbon credit or something for being descended from people who wiped out countless herds of greenhouse gas producing monsters, like buffalo, elephants, maybe even whales. Whales are big, do they flatulate alot? Everyone get your guns. It’s time to wipe out more species and save the planet from extinction!

    Comment by Harry Robertson — 14 Apr 2007 @ 7:53 PM

  142. Ummm… I didn’t seriously believe you would post that…

    Comment by Harry Robertson — 14 Apr 2007 @ 8:47 PM

  143. Re 139 greenhouse effect

    I don’t think a greenhouse, whether made of glass or NaCl (?) provides much insulation; glass (or plastic) has a low insulation value. The glass (or plastic) does greatly reduce convective heat loss, and this can play a significan role in keeping the interior warm, depending on the wind velocity, amount of solar heating, and other factors.

    Comment by Chuck Booth — 14 Apr 2007 @ 10:02 PM

  144. Re 141 – funny.

    Re 126, 129

    The equations in this model are set up to be solved without need of iteration. The atmosphere in this model is a ‘graybody’. A graybody emits as epsilon times blackbody emission. This emission is a flux – power per unit area – and is emitted from any surface; in the case of the atmosphere, the bottom surface and the top surface. The surface of the Earth can not radiate downward because it’s opaque; the radiation upward is unaffected by that.

    More technically, the emissivity is determined by the effect of optical depth or optical path length integrated over solid angle; for an isothermal atmosphere with top and bottom emitting surfaces, emission from either side will be the same; but for a complex shape, even if isothermal and homogeneous in other ways, emission from within the shape emerging from a given surface can be geometrically dependent (and refraction can play a role, too). You can visualize this by … well its simple and yet hard to explain clearly…

    Re 123,130 – The interaction of electron energy levels within solids generally gives rise to broader absorption/emission bands (over wavelength). Gasses tend to have more isolated absorption or emission peaks in their spectra, as far as I know. A single molecule would have a line spectrum. However, collisions of molecules and the range of velocities of molecules of a gas can spread the absorption/emission out from the lines due to the Doppler effect and what is called pressure broadenning. Higher up in the atmosphere the pressure broadenning is weaker.

    Emmissivity and absorptivity vary with wavelength in general. The black body radiation formula given for this model assumes emissivity and absorptivity are constant over wavelength (a ‘graybody’ approximation) and gives the total radiant power emitted over all wavelengths; this is fine for a simple model being used to illustrate the greenhouse effect as a general principle. In such a case, while a given mass path length (ie distance times density – is mass path length the right term?) through a gas may yield considerably lower emissivity than through a solid At a given wavelength, if the emissivity is independent of temperature, emitted radiant power per unit area will be proportional to the fourth power of temperature, even for a gas.

    To actually calculate the greenhouse effect of the Earth and it’s dependence on atmospheric composition, one must take wavelength into account. At a given wavelength, Thermal radiant emission can be expressed as a wavelength-dependent emissivity multiplied by the monochromatic blackbody radiation, which can be given as power per unit area per unit wavelength, and is a precise function of temperature and wavelength. Because of varying conditions with height, there will be differences in radiation intensity at different angles, so it is actually better to start with emissivity * spectral blackbody intensity, which is radiant power per unit area per unit wavelength per unit solid angle (this might also be called spectral radiance, whereas integration over a hemisphere solid angle weighted by the cosine of the angle from perpendicular to a plane gives the spectral (monochromatic) irradiance which is the spectral flux … sorry for all the jargon – and I may have been imprecise myself in some of the terms – someone correct me if my terms are mixed up.))

    Comment by Pat — 14 Apr 2007 @ 10:04 PM

  145. RE #128


    Well… The reason it makes sense to spread it across the whole surface is due to the latency and diffusion of the heat transfer mechanisms.

    For example, heat absorbed in the tropics is converted to mechanical energy in the form of winds, water vapor and currents that release the heat many days later mostly in the higher latitudes. The longwave radiation absorbed and re-radiated (in all directions) by the atmosphere sends a significant fraction of that re-radiated heat into the higher angle and dark parts of the planet in minutes. Also, obviously, the heat absorbed by objects during the day is radiated throughout the night while the Earth rotates around.

    So, for a “total average” energy budget it makes reasonable sense.

    In a more precise, complex model, you actually model the heat transfer mechanisms in blocks (100km across I believe is the current working standard in the GCMs) and account for the high angle effects, heat transfers in all their mathematical glory, etc. And use swags for cloud cover. The GCMs are currently fast enough to be used by the weather guys to give a global picture to inform their forecasts and more regional computer simulations.

    The ocean current guys have more trouble – water is much harder to model than air plus accurate initialization data is meager by comparison.

    Comment by Robin Johnson — 14 Apr 2007 @ 10:23 PM

  146. Has anybody calculated how much each mode of vibration of the CO2 molecule is responsible for the retention of the heat (radiation)?
    The CO2 is a linear molecule that has many modes of vibrations,is one mode more responsible than the others?

    Another question is that these heat excitation are like photoexcitation, what is their quantum yields?

    Comment by Marcel Labonte — 14 Apr 2007 @ 11:01 PM

  147. Search Google Scholar for “greenhouse effect” +misnomer

    The first hit will suffice:

    Clarification of Selected Misconceptions in Physical Geography
    by Burton D. Nelson, Robert H. Aron, and Mark A. Francek

    “… In this paper, a number of misconceptions relating to location, and to the earth’s hydrosphere, atmosphere; and lithosphere are discussed with appropriate correction and explanation…. it is intended principally for elementary and secondary level teachers who may have limited training and background in geography.”

    Comment by Hank Roberts — 15 Apr 2007 @ 1:44 AM

  148. Re 138

    A Greenhouse (made of glass) retains a hotter atmosphere within than the surrounding environment not because of any radiative insulating properties. A greenhose traps heat because it prevents convective heat transfer with the outside environment.

    Incident solar radiation penetrates the glass, causes the surface to warm, and re-radiate back some of this energy into the air contained within the greenhouse, which causes its temperature to rise. This air cannot mix with the air in the environment around it. Hence, it is unable to transfer heat, and becomes hotter than the surrounding environment.


    This is why a salt greenhouse should act similarly to a glass greenhouse. Provided it is transparent to solar radiation and inhibits convective mixing, the results shoulod be very similar.

    The term “greenhouse effect” is somewhat of a misnomer, as it is the absorption of thermal (infra-red) radiation by atmospheric constituents rather than mixing inhibition that results in the warming experienced on Earth.

    Comment by ChrisC — 15 Apr 2007 @ 2:29 AM

  149. Wonderer (#21)

    First, no one’s saying there’s anything wrong with the average engineer.

    But frankly, engineers have given the world more than their share of cranks, including a small population that does know exactly enough math to get in trouble, i.e., they know that general relativity is a hoax (or global warming, or any number of other things).

    Take a look at this, for instance, by science fiction and alleged nonficion author James Hogan: | . Note in particular this bon mot: “Science really doesn’t exist. Scientific beliefs are either proved wrong, or else they quickly become engineering. Everything else is untested speculation.”

    I blame the Heinlein mystique partly. If you’ve ever read Ed Regis’ Great Mambo Chicken and the Transhuman Condition, look at the culture around Keith Henson (whom I know through Scientology critic circles) as an example.

    Also probably something to the EE/ME etc. divide. Advanced study in ME makes you an awesome seat of the pants calculator, but you don’t learn a very broad spectrum of math. In that sense, “rocket science” is a kind of misleading expression.

    Comment by Marion Delgado — 15 Apr 2007 @ 4:03 AM

  150. Hi Marcel,

    In reply to your comment 146, the following is a link to Jack Barrett’s paper “Greenhouse molecules their spectra and function in the atmosphere.”

    See figure 9 for data from the Nimbus satellite that shows the reflected spectra from three climatic regions of the earth: Mediterranean, Sahara, and the Antarctic.

    Comment by William Astley — 15 Apr 2007 @ 5:12 AM

  151. #109 I’m getting to grips with feedbacks, but in the Soden and Held paper it talks about “Planck” feedback of about 3.2W/m^2/K calculated from models. Where exactly is this measured, given that it is different (and lower) from the expected increase in G of about 5.5W/m^2/K.

    [Response: That the longwave increase as temperature increases – i.e. what you would get just from the Stefan-Boltzmann \sigma T^4. It’s slightly different in each model because the temperature distribution is slightly different, but those differences are not very significant. -gavin]

    Comment by Steve Milesworthy — 15 Apr 2007 @ 6:54 AM

  152. {I would like to recommend that Buffalo Bill be posthumously recognized as a top-notch environmentalist. … Whales are big, do they flatulate alot? Everyone get your guns. It’s time to wipe out more species and save the planet from extinction! } – Comment by Harry Robertson

    Partner, this town ain’t big enough for both of us.

    The problem with your theory is very similar to the problem with the veggie lover theory of eating less beef – incompletely thought out.

    On the whole, countries that don’t eat much meat tend to have more cattle, not less. To control a cattle population you need to kill them on a fairly regular basis.

    The Buffalo Bills were dead enders. They worked their way to the unemployment line. My ancestors, along with other stockmen like them, brought in fine purebred bulls from England – Herefords and Shorthorns, etc. – and before long our bulls had knocked up enough cows to refill the vast prairies, from Texas to the Dakota territories, with tens of millions of tasty methane belching bovines. We quickly nullified your ancestors’ work.

    I doubt elephants and whales produce much methane. It’s not the animal’s size that does it. I would bet a little goat produces a whole bunch more methane than an elephant or a whale.

    If you think cow methane is a joke, you would be belching a mistake.

    Comment by J.C.H — 15 Apr 2007 @ 8:21 AM

  153. Sorry for the naive question, but wouldn’t a salt greenhouse dissolve when it rains?

    Comment by Figen Mekik — 15 Apr 2007 @ 8:31 AM

  154. I would like to thank the commentator above (currently 138) who has shared with us proof that the greenhouse effect does not exist, thus saving many of us from unneeded worry and misdirected study. And I doubt anyone here is in a position to question the authority of someone who has the depth of knowledge to combine the shorthand notation of a chemist with that of a mathematician in a single post. Dennis, I would like to alert you to another important proof from 1934 ( here ), highlighting the impossibility of bee flight (reportedly originating from an engineer, no less). I desperately need someone who is willing to invest the time to alert everyone on the beekeeping blogs to this result, and I think you are just the right person for the job.

    Comment by The Wonderer — 15 Apr 2007 @ 8:56 AM

  155. Marion (#149)

    I am not making an argument as to whether engineers have more cranks in the ranks, but that when we have those crank engineers, it is not a result of insufficient math in school. Therefore, it is not any more dangerous for Gavin to put math in his posts. I now apologize to everyone for stoking this thread, and second Tamino’s request above to judge on the issues alone.

    Comment by The Wonderer — 15 Apr 2007 @ 9:14 AM

  156. Sorry that this is a bit off topic:

    Re #132 Dr. Jorgensen-Petersen
    As it turns out, the comments from Laurie David and Sheryl Crow about lake effect snow are supported by research from Colgate University:

    …at least in the short term. With further warming, lake effect snowfall may diminish:

    Comment by Chuck Booth — 15 Apr 2007 @ 11:00 AM

  157. Re 149.

    I will stoke it some. I am one of those pesky MS EE guys. So I guess calculus, multivariable cacl, ODE,PDE, Linear algrebra, complex variables, probability theory, numerical analysis, discrete mathematics thermodynamics, electromag field dynamics, static/fluid dynamics are not a broad spectrum of math eh? Don’t forget that CE/ME/EEs have to take organic chem, at least one quantum physics course, computer programming languages.(In my case ADA95, C, Fortan77/90, and micro assembly) We have to take all of this stuff before we can even take classes that deal with the major such as core EE and electives.

    What you said is perposterous, and it is not like phsyics majors have to take any more math.

    In any case every scientfic field has it share of cranks. To assume that one has more than any other is simply snobbery and is not true.

    Comment by Jim — 15 Apr 2007 @ 1:19 PM

  158. Question. I am somewhat confused by the Venus comparison. I thought that the CO2 warming was rather small, but amplified by a large water vapor feedback. If Venus had water to cause this enhanced greenhouse effect, but now does not have water, why didn’t the planet cool at least a little after all of the water was gone?

    Comment by steve — 15 Apr 2007 @ 1:47 PM

  159. [[In this model, only the CO2 is actually being heated, not the molecules around it]]

    CO2 is part of the atmosphere. If it increases its energy, and heats up, it will radiate. Some of the radiation will go back to the ground. Some of it will be absorbed at other levels. But it’s silly to say only the CO2 will heat. Try heating just one color in a boiling pot full of oil paints.

    Another way the CO2 can lose the new energy is by bumping into another nearby molecule — “collisional de-excitation.” That then speeds up the neighboring molecule. Since temperature is a function of molecular motion, this happening on a large scale means the whole local atmosphere heats up.

    James, your model violates conservation of energy.

    Comment by Barton Paul Levenson — 15 Apr 2007 @ 2:00 PM

  160. [[Question: Why isn’t the equation for surface flux: S + 1/2*lambda*A = G, since half the atmospheric flux goes up and half goes down? ]]

    Because the total energy radiated by the atmosphere (in this model) is 2 lambda A, not lambda A.

    Comment by Barton Paul Levenson — 15 Apr 2007 @ 2:02 PM

  161. [[#121 …why is the radiation condidered spread out evenly when in reality it does not? The very reason for Climate/Weather is a differential in temperature , pressure driven by diurnal effects and the strength of solar radiation at every given location. A philosophical question so to speak, just exploring the meaning of this ‘spread the energy evenly about idea.’.. I would rather enjoy equations dealing with the dark side of the Earth and one with only the bright side. Applying 1/2 a sphere with T^4=S/(SBconstant *(1-0.5*lambda))gives interesting results,applying it to the dark side does not give any result. I really like simple models /equations as concepts explaining things, if well written they have great impact on spreading out knowledge of climate science. …..This is another great post! ]]

    The model is averaged over time. You can consider a lit day side and a dark night side, but it doesn’t apply entirely because there’s a little bit of thermal inertia. Long-term averaging seems to work better.

    Comment by Barton Paul Levenson — 15 Apr 2007 @ 2:04 PM

  162. [[Interesting gas vs. solid discussion. When does a gas become dense enough to act like a liquid/solid? What is the surface of the Sun, e.g? ]]

    Gas starts acting like liquid when, either due to low temperature or high pressure, or both, the non-zero size of the atoms or molecules affects their motion. The ideal gas law assumes atoms/molecules which are mathematical points.

    Liquids become solids when the individual particles can’t easily move around or through one another any more.

    I think the surface of the sun is a gas. (Jumpin’ Jack Flash, it’s a gas gas gas!)

    Comment by Barton Paul Levenson — 15 Apr 2007 @ 2:07 PM

  163. re: engineers
    “But frankly, engineers have given the world more than their share of cranks”

    This is a mathematical statement: of the population of cranks, a higher percentage are engineers than the percentage of engineers in the overall population. The cited evidence seems insufficient to support this … assuming that one can define a crank.

    From a 2001 poll, 28 percent of respondents believed in astrology, 52 percent didn’t, and 18 percent weren’t sure…
    I’m not sure where the line is crossed from “Read the horoscopes” into astrology crankhood, but it would nor surprise me if there were more of the latter than there are engineers in the US :-).

    While anecdotes are not good statistics, I’d observe that few disciplines are immune from crankhood, including physicists & chemists:

    – William Shockley, physicist (Nobel for transistor) … then race, eugenics

    – Linus Pauling, quantum chemist (Nobel for chemical bond research, plus Nobel Peace prize) … then off into Vitamin C (I have no strong opinion about potential efficacies of Vitamin C, but it is clear that Pauling’s strength of belief in it got way ahead of any evidence).

    – John Mack (Harvard MD/psychiatrist) – UFO abductions

    – Frederick Seitz, Fred Singer, William Nierenberg, Robert Jastrow [all physicists] … then George C. Marshall Institute, SEPP, etc…

    In any case, at least based on the sampling from various blogs, it’s not clear to me that either scientists or engineers have more than their share of cranks compared to people with minimal technical background, but when they are, they tend to be more visible and get quoted as authorities. If you read CSICOP’s “The Skeptical Inquirer”, many of the crank ideas come from people neither engineers nor scientists.

    re: James Hogan (whose SF stories I’ve often enjoyed): I once took him over to Silicon Graphics to see the current state of immersive visualization, and then went out to dinner. He of course has not worked as an engineer for a long time, but has a positive fascination with offbeat theories … which of course, can be a good source for story ideas.

    Comment by John Mashey — 15 Apr 2007 @ 2:38 PM

  164. Re #s 134/7: Just to clarify, Real Clear Politics is a wingnut site and the author has long-time associations with the Ayn Rand “Objectivist” school of libertarianism, which latter seems to have decided that Lysenko knew something when it comes to the science (in that any science that has implications conflicting with their ideology must perforce be wrong). Snark aside, I don’t think these right-wing echo machine pieces by non-scientists are worth responding to.

    Comment by Steve Bloom — 15 Apr 2007 @ 4:22 PM

  165. Barton,

    That is the point. In the model where CO2 radiates the same energy as it receives, only the CO2 heats up. This is because CO2 will absorb and radiate in precisely the frequencies that it can absorb and radiate, and no others.

    I didn’t actually propose a model. I said that the Boltzmann distribution needs to be used for a gas. The Boltzman distribution is based on a collisional distribution of states. If the gas radiates all of the energy it receives, thermodynamics is violated.

    This assumption was built into Gavin’s model, which, as he stated, is only a very rough model, so I’ll give him no further grief about it.

    If, as I said, a considerable amount of the energy is distributed into gas motion, which is unavailable to the solid, then the gas will radiate less energy than it receives. Try out the absorption and radiation model, but scale the reemited energy by a factor on the order of 10^-7. This provides a more realistic idea of the background radiaiton contribution of CO2.

    This does not consider additional absorption by the rotational wings of the bands, nor absorption by the numerous CO2 combination bands which are not saturated.

    The energy remaining in the spectrum that can be absorbed by CO2 dwarfs any warming effect of reradiation.

    And yes, only if CO2 discards the vibrational energy it receives by collisional deactivation can it heat its surroundings. It does indeed do this quite effectively. The surroundings are warmed, and the radiaiton from CO2 is reduced dramatically. Remember that energy from the excited bending mode can either be reemitted, or it can be collisionally distributed to warm the atmosphere. Doing both is a violation of conservation of energy.

    [Response: But what is your point? More complicated models (i.e. GCMs) conserve energy – the radiation absorption by GHGs adds to the layer temperature, just as the radiation from the layer is a cooling term. The net radiation budget is not closed (since temperature changes can occur due to multiple effects – latent heat release, advection, convection etc.) but the net effect of atmospheric absorption has impacts very similar to that shown above. Your point would only be a fundamental flaw if the resulting behaviour once you include these effects was completely different. It’s not. – gavin]

    Comment by James — 15 Apr 2007 @ 5:09 PM

  166. #145 Robin, Thanks again, I did see much longer string equations from a GCM model or two, the standard simplifcation given by Gavin helps describe the entire climate system relatively well, but It is solar centric, much rather see an equation recognizing the atmosphere itself as a heat source, independent of solar input, the atmosphere is warming the dark polar regions, there is a great misunderstanding of it, I give you one example: 2005 , At about the time when NASA, Hansen and NOAA declared 2005 as going to be the warmest year in history, NOAA seasonal forecast came out with a very cold winter 05-06 projection, prompting amongst other things a spike in fuel costs, history showed the winter of 05-06 quite warm except for Central Russia (and some parts of Europe), on what basis does the warmest year in history cools down faster in darkness? Heat radiation in darkness needs simplifications. Even in near isolation, somehow Isolated from weather systems which were warmer, as with March 2007 for North American Arctic, with little or no advection from the South, the atmosphere maintained a warm surface temperature at about -46 C (High Arctic) at the coldest peak of the coldest North American Arctic air mass in years. I somehow doubt that the High Arctic got a great piece of that heat transfer process from locations having direct solar radiation, at least not on the surface.

    Comment by wayne davidson — 15 Apr 2007 @ 5:24 PM

  167. The point is that we can put a limit on the total warming by CO2.

    Once radiant energy is absorbed by CO2, fractionally a very small part is reemited. That reemited portion will be slowed in its escape to space if CO2 concentrations increase, similar to putting more rungs in a ladder. If the reemitted portion is large enough, than it will be a controlling factor in temperature, and will continue to increase temperature regardless of band saturation. My point is that the reradiated portion is very small relative to the absorbed and not reradiated energy. This provides a limit for total CO2 warming.

    The larger portion of the absorbed energy will not be emitted to space by CO2. It’s residence time in the atmosphere will be roughly determined by the speed with which it can travel through the atmosphere mechanically, something on the order of the speed of sound in a particular layer of atmosphere. Increases in this component lead to much larger T effects, but fortunately can be bounded by the absorption spectrum.

    Basically, looking at the current absorption spectrum, and subtracting it from a fully saturated absorption spectrum, should provide an amount of energy roughly equal to what is left for CO2 to absorb and dissipate as heat.

    [Response: This doesn’t follow at all. There are multiple emitters/absorbers in the atmosphere and radiative cooling (by clouds, water vapour and CO2) occurs whatever the temperature the air is. This cooling is a very large part of the emission to space and that is certainly not a minor effect. The only limit you could conceivably get would be if all of the CO2 absorption bands and their fringes were saturated. But they aren’t, and Venus demonstrates quite adequately that any effective limit on CO2 forcing is significantly warmer than anything we’d really like to deal with (not that that is likely on Earth). -gavin]

    Comment by James — 15 Apr 2007 @ 5:37 PM

  168. Re 123 – (echoing 159) – I attempted to calculate a likely ratio of collision frequency to photon absorption/emission frequency, and found it quite high, at least below 100 km (where almost all of the atmosphere is). This suggests that molecular collisions are frequent enough that CO2 will be at essentially the same temperature as the air containing it.

    (If 300 ppm CO2 in air were able to absorb or emit 0.05 W/m2 along a path length of 1 kg air/m2 (that would be 1 meter path through air at a density of 1 kg/m3, or a 10 meter path through air at a density of 0.1 kg/m3, etc.) (in the band centered at 15 microns), this would mean that for every absorption or every emission of a photon by CO2, there would be around 16 trillion collisions with another molecule at the surface (around 100 million collisions per second), or around 1.6 million at 100 km height (around 1000 collisions per second).

    Even if at 300 ppm CO2 the entire blackbody radiation at 300 K (just under 460 W/m2) in a path of 1 kg air/m3 (I’m pretty sure that’s far more opaque than CO2 actually is), the ratio of molecular collisions to photon absorptions by a CO2 molecule would be 1.6 billion at the surface and 160 at 100 km.

    Comment by Pat — 15 Apr 2007 @ 6:15 PM

  169. Basic difference between the absorption and dissipation vs. absorption and reemission.

    Increasing absorption and dissipation provides primarily a decrease in the escape of radiation from the planet’s surface to space. This effect is acting on the lambda G component of the model.

    Increasing absorption and reemission increases the residence time of the radiation absorbed. The excited state lifetime of the CO2 molecule is rather long compared to how long the photon remains unabsorbed once emitted. Multiple absorptions and reemissions lead to increased residence time of the energy in the atmosphere. Emitting in all directions also slows escape to space. This is acting on the Lambda A component of the model.

    If the lambda A component of the model is on the same order of magnitude as the lamda G, it can quickly dominate. The excited state population for a particular gaseous state can be described as a percentage of the total gas molecules in the sample. Doubling the sample (or the CO2 concentration in this case) will double the number of excited molecules. The excited molecules are candidates for emission or collisional deactivation. Based on the state of the sample, the number of excited molecules that survive to emission is also a percentage of the total number of excited molecules. What happens here is that because both the number of excited molecules and the number of emitting molecules are based on a percentage of the whole, if you double the number of molecules, you will double the emission.

    Obviously, both effects happen simultaneously, but considered separately, a doubling of the CO2 concentration doubles the emission, the lambda A effect, while doubling the CO2 concentration does not double the lambda G effect, which follows a log relation.

    If the lambda A effect is on the order of the lambda G effect, then it becomes very large and is controlling. If the lambda A effect is orders of magnitude smaller than the lambda G effect, then it will not be significant.

    Comment by James — 15 Apr 2007 @ 6:45 PM

  170. Re 165,167

    You seem to be focusing on the immediate aftermath of a photon absorption. True, most of the radiant energy absorbed by greenhouse gasses will be redistributed by collision before it can be reradiated – after one time step wherein a population of photons are absorbed by a population of molecules.

    But that just heats the air. By collision, the temperature of CO2 will tend to be the same as that of the air, and it will emit photons thermally. The lack of heat resulting from this emission is again redistributed by collision, cooling the nongreenhouse gas molecules.

    The same goes for greenhouse agents in general – clouds, etc. – and also for SW radiation (solar radiation) absorption in the air. The transparent component of the air just adds heat capacity – you could think of it as attaching a pool to a lake. water can be flow into the pool and out of the pool by hoses (absorption and emission); flow between the pool and the lake causes the water level to move more slowly in response to an imbalance in inflow and outflow in the hoses than it otherwise would (heat capacity).

    Yes a gas will have different radiative properties than a solid or liquid, but this just changes the emissivity and absorptivity – you can still multiply emissivity by the blackbody radiation to find the emitted radiation (do this as a function of wavelength to reduce emissivity’s dependence on temperature), assuming local thermodynamic equilibrium, which is accurate in the vast majority of the atmosphere for the vast majority of the energy involved.

    (visualization – each molecule in a population of like molecules can be assigned a (wavelength-dependent) cross section – an absorption cross section (equal to the emission cross section if the population of molecules is in LTE), and if necessary a scattering cross section. What this means is that, averaged over time, each molecule acts as a sphere with a cross sectional area (through the great circle of the sphere) which can absorb radiation from any direction proportional to the intensity of the radiation * the (absorption) cross sectional area, emit as a blackbody from the surface of this sphere (emission cross section), and scatter light intercepted by the sphere defined by the scattering cross section. (PS scattering cross section + absorption cross section = extinction cross section.)

    Over a short enough distance that the path is nearly transparent, cross sections of each kind add linearly, but when emission and extinction become significant, there will be significant overlap as molecules block each other (from the viewer); over longer and longer distances the cross sections fill in the holes and emissivity approaches 1; absorptivity + scattering (as in a kind of diffuse reflection) approaches 1, transmission (from the other end) approaches 0.)

    Comment by Pat — 15 Apr 2007 @ 6:57 PM

  171. I’ll try this again.

    1 atm
    15 micron bending mode
    Boltzmann distribution, roughly 4% excited

    400 ppm CO2
    16 ppm excited bend of CO2

    Only excited CO2 can emit.
    1 atm pressure
    about 10^5 collisions of CO2 in the spontaneous emission excited state lifetime

    Of the excited CO2 molecules, roughly 1 in 10^5 actually emit a photon, the rest collisionally deactivate.

    400 ppm CO2
    16 ppm excited bending mode
    16 x 10^-5 ppm emitting

    In the field of a blackbody at 300K and 1 atm pressure of air, the emission from CO2 is several orders of magnitude smaller than the absorption. The difference is made up collisionally. CO2 will not emit radiation at the same rate as the solid, because it has many more modes of kinetic energy available to it then the solid has.

    In the above example, 800 ppm CO2 will have twice as many photons generated, but the absorption of planetary radiation will not double because it is governed by a log dependence.

    [Response: This is irrelevant. Any additional absorption will increase the mean temperature of the layer, which will cause an increase in emission from all radiating components (clouds, water vapour, and yes, CO2). -gavin]

    Comment by James — 15 Apr 2007 @ 7:20 PM

  172. Re 168 (last paragraph)- I rounded the blackbody radiation at 300 K up to 500 W/m2 to get a factor of 10,000, I forgot to note that.

    (For the following – did I already post this – I had left my computer for a while after typing something similar and then it was gone and I don’t remember what I did with it – sorry if this is redundant:)

    Re 166,167:

    You seem to only be looking at the immediate effect of a population of photons being absorbed by a population of molecules. Yes, molecular collisions redistribute energy from absorbed photons from the absorbing molecules to the entire local population of gas molecules. But as the emitting molecules as a population have the same temperature as the other molecules because of those collisions, they can thermally emit radiation as they would at that temperature. And the loss of energy by emission is also redistributed among the other molecules.

    The transparent component just adds its heat capacity to the process; the radiation emitters and absorbers allow energy to be gained or lost until the temperature approaches equilibrium, while the redistribution of energy among the other components means that the process happens with the heat capacity (energy per unit change in temperature) of all components present (generally including even nongaseous components, some of which may be absorbers, emitters, and/or scatterers).

    PS for those of you with a few hours of free time on your hands – with the essentially accurate assumption of LTE (local thermodynamic equilibrium), I attemped an in depth description of the greenhouse effect and atmospheric radiation (among some other things) here:
    (starting at November 25; you can stop when you get to “January 19, 2007 @ 22:59” – or you can stop earlier, of course)

    Comment by Pat — 15 Apr 2007 @ 9:13 PM

  173. I do not see how the simple model disproof’s, Warwick Hughes’ methodology to estimate the earth’s sensitivity to a change incoming radiation & back radiation. (See link attached below for Hughes’ data and thoughts. Also note that Hughes does not differentiate whether the back radiation is from GHG, or other molecules in the atmosphere. Also note Hughes includes incoming solar radiation.) Can the planet be treated as a black box where the variable is X (solar incoming radiation plus back radiation) vs Y planetary temperature? (See next comment and paper for details concerning the Global Mean Energy Budget.)

    There is a significant amount of energy that is transferred from the earth’s surface to higher regions of the atmosphere by thermals and latent heat. See my next question.

    Also, I do not understand why the simple model does not include the estimated 24 W/m2 for thermals and 78 W/m2 for the latent heat of water that is evaporated at the earth’s surface and then is condensated higher in the atmosphere (See the link to Kiehl’s paper “Earth’s Annual Global Mean Energy Budget”, below, page 206 of his paper.) As oceans cover roughly 70% of the earth’s surface would there be an expected increase in evaporation that would partially offset an increase in back radiation due to a GHG increase or an increase incoming radiation due to a decrease in cloud cover?

    [Response: Idso’s experiments all involve random temperatures divided by random fluxes – all at the surface and none related to global long term feedbacks – they have absolutely no relevance to climate sensitivity as normally defined. There were whole journal issues devoted to pointing out the flaws in Idso’s arguments (Climatic Change for instance). -gavin]

    Comment by William Astley — 15 Apr 2007 @ 10:11 PM

  174. Regarding #152 which doesn’t belong in this thread, but I
    suppose two wrong postings cancel out ;) J.C.H states — “On the whole, countries that don’t eat much meat tend to have more cattle, not less. To control a cattle population you need to kill them on a fairly regular basis.”

    If by “on the whole” you mean India, then this is probably true, but the
    top 5 countries with the biggest cattle populations are (in order):

    Brazil, India, China, US, and Argentina.

    The top 5 cattle meat producers are (in order):

    US, Brazil, China, Argentina, Australia.

    India is the 10th biggest producer of cattle meat.
    Partly this is because its animals are small — average carcase weight
    103kg. The average US carcase weight is 347kg. All
    this data is from the FAO database.

    When the wool price crashed in the 90’s Australia reduced its sheep flock from
    160 million to about 110 million — this lead to a large regrowth of what
    we call ‘scrub’. Australia will meet it Kyoto targets, and the only sector which
    has made significant emissions saving is “land use change” and all that
    regrown scrub is a big part of that — I’m currently trying to work out
    exactly how big. The bottom line here is that livestock reduction can
    be an effective source of emission reductions. It involves no new technology,
    and has an immediate impact on forcings. Livestock reduction works on
    many levels, reduced methane, increased (re)afforestation, and reduced fossil
    fuel emissions.

    Comment by Geoff Russell — 15 Apr 2007 @ 10:53 PM

  175. Hello,
    I know this is slightly off topic, but I was wondering if someone could point me to some articles (this site or others) which you feel best describe the consequences of global warming. Obviously, the most important thing to consider with regards this issue is the EFFECT of global warming on mankind, and not the warming per se.
    Ideally, I would like to see verifiable/verified predictions of how GW will impact our lives — i.e. what crops will be harmed and when/where, how high will sea levels rise, which species of plants/animals may be threatened and which species may be HELPED (I’m assuming it can’t be bad for everyone/everything), etc.
    Fred Mann

    Comment by Fred Mann — 15 Apr 2007 @ 11:50 PM

  176. Re: 118 “Plus, I know I’m being a heretic here, but what exactly did you find wrong with Lindzen’s statement? Certainly not all of it…”

    How about most of it? The main premise is that things won’t be so bad due to global warming, but this is in the face of overwelming evidence to the contrary in the most recent IPCC report

    and in a report by a group of generals and admirals who cite serious national security concerns.

    For instance,

    * Projected climate change poses a serious threat to America’s national security.

    * Climate change acts as a threat multiplier for instability in some of the most volatile regions of the world.

    * Projected climate change will add to tensions even in stable regions of the world.

    * Climate change, national security and energy dependence are a related set of global challenges.

    In particular, with regard to the potential negative effect on the economy that Lindzen basicly cites as a reason to do nothing,

    Gen. Anthony “Tony” Zinni, Bush’s former Middle East envoy, one of the authors of the report, said,

    “We will pay for this one way or another,” wrote Zinni, former commander of U.S. Central Command. “We will pay to reduce greenhouse gas emissions today, and we’ll have to take an economic hit of some kind. Or we will pay the price later in military terms. And that will involve human lives. There will be a human toll.”

    Finally, this may be nit picking, but for Lindzen to cite the late Roger Revelle as saying that,

    “the evidence for global warming thus far doesn’t warrant any action unless it is justifiable on grounds that have nothing to do with climate.”

    seems rather disingenous to me since the good professor passed away in 1991. I would submit that the evidence “thus far” has changed just a bit since then.

    Comment by Tavita — 16 Apr 2007 @ 5:35 AM

  177. [[In any case every scientfic field has it share of cranks. To assume that one has more than any other is simply snobbery and is not true. ]]

    Engineering is a professional field, but it’s not a “scientific field.”

    Comment by Barton Paul Levenson — 16 Apr 2007 @ 9:30 AM

  178. Re #138, well, it’s been over 40 years since I took college intro to physics & my memory is quite fuzzy, but if I recall (I think in the optics chapter), that when light goes through glass (or water) at an angle it sorta breaks up into different bands (like a rainbow), and something about the infrared section of light not being able to reflect back out through the glass (or water) as well, due to its wavelength being longer. And that’s the band of light that causes the (most) warming.

    So what I understand, the GHGs sorta act like that glass & don’t let the infrared bands out as much, but reflect or deflect them back down to earth.

    I’m probably totally totally off on this. My memory is extremely fuzzy.

    Comment by Lynn Vincentnathan — 16 Apr 2007 @ 11:16 AM

  179. Re #177,

    BPL, you’re correct when you say that engineering is a professional field, not a scientific one. All I would add is that it is important to understand the dependency/synergy between engineering and science.

    Engineering needs to be grounded in sound science to produce the amazing developments, such as PCs and air travel, that we take for granted. Poor engineering can usually be traced back to flawed understanding of the underlying science.

    Science needs engineering to create the tools, such as satellites and particle accelerators, they use to advance our knowledge.

    Without good engineers, scientists would not have journals to publish their papers in (no printing technology), or the internet we’re using for this dialog. Any scientists who feel engineers aren’t their peers are welcome to try to carry out their studies using only pencil and paper. Oops, both pencils and paper are products of engineering. They should try carrying out their studies by writing on animal hides with a burnt stick.

    As you may have discerned, I’m an engineer.


    Comment by Phillip Shaw — 16 Apr 2007 @ 11:56 AM

  180. RE #178: The light that comes from the sun has many wavelengths. Most of those wavelengths come through our atmosphere and bounce off of the surface of the plant. Green house gases don’t absorb all wavelengths, they only absorb very specific wavelengths, most of those being in what is called the infrared band. Carbon dioxide responds to a few bands, which are very narrow. Water vapor responds to quite a few bands. You can pretty much tell how much of the infrared gets absorbed in the atmosphere, by how much infrared leaks back out into space. Currently, our satellites pick up almost no infrared going out, so the carbon dioxide and water vapor is already absorbing all of the infrared that is hitting the earth. According to the FTIR spectroscopists, all of the infrared is being absorbed within about 100 feet of the surface of the planet.

    Comment by Carol — 16 Apr 2007 @ 12:03 PM

  181. [[Without good engineers, scientists would not have journals to publish their papers in (no printing technology), or the internet we’re using for this dialog. Any scientists who feel engineers aren’t their peers are welcome to try to carry out their studies using only pencil and paper. Oops, both pencils and paper are products of engineering. They should try carrying out their studies by writing on animal hides with a burnt stick.]]

    And let engineers try to get along for a month without the food raised by farmers.

    The point stands — engineers are not scientists, and scientists are rightly pissed off when engineers call themselves scientists, especially when they go on to babble about how the scientists are all wrong about some well-established theory (evolution, global warming, relativity, quantum mechanics, etc.).

    Comment by Barton Paul Levenson — 16 Apr 2007 @ 12:21 PM

  182. Re #64: Warning here, I am an engineer, so I may not see things the same way as some of the pure scientists do . . .

    Just out of curiousity: I hear that doubling the carbon dioxide will increase the temperature by a certain amount. If the carbon dioxide in the atmosphere is already saturated, then where will the extra infrared come from that will cause the temperature to increase? That is, if you compare carbon dioxide to being a very large sponge, and you are sopping up a tablespoon of water that was spilled, then what does it matter if you have a larger sponge? The amount of infrared that is coming into the atmosphere is a constant. Carbon dioxide already absorbs everything that it can from the wavelengths that it can absorb from. Why would the temperature increase?

    [Response: Because it is not saturated. -gavin]

    Comment by Carol — 16 Apr 2007 @ 12:32 PM

  183. RE #181 [engineers are not scientists, and scientists are rightly pissed off when engineers call themselves scientists]

    You have it slightly wrong. Engineers are rightly pissed off when anyone calls them a scientist. And if the scientists are not doing their job (scientific method) of questioning everything, especially those well-established theories that everyone knows are right, then it falls to the engineers to enter into heated debate about these issues.

    Arguing with an engineer is like wrestling in the mud with a pig. After a few hours, you realize the pig likes it.

    Comment by Carol — 16 Apr 2007 @ 12:38 PM

  184. Wait!
    Carol, re 180/178, you wrote:
    “… Currently, our satellites pick up almost no infrared going out, so the carbon dioxide and water vapor is already absorbing all of the infrared that is hitting the earth. According to the FTIR spectroscopists, all of the infrared is being absorbed within about 100 feet of the surface of the planet.”

    What’s this then? Infrared photographs from satellites are routine.

    Where did you read that “our satellites pick up almost no infrared going out, so the carbon dioxide and water vapor is already absorbing all of the infrared” and who are the “FTIR spectroscopists” you rely on?

    Have you read this previous thread?

    Comment by Hank Roberts — 16 Apr 2007 @ 12:45 PM

  185. Re #181,

    I am not disagreeing with you. Anybody, no matter how accomplished they may be in their area of specialization, is essentially a layman in matters outside their specialty. Perhaps a well-informed layman, but still a layman, and the professionals in any field are justified when they get irritated by pushy laymen. As Clint Eastwood said “A man’s got to know his limitations.”. Words to live by.

    I have never called myself a scientist, nor am I aware of any of the hundreds of engineers I’ve worked with during my career calling themselves scientists. So I feel that’s a bit of a strawman.

    My only point is that scientists and engineers are, in reality, a team. It is counterproductive for one element of a team to deride another. The reason I get irritated with comments such as #1 and #149 above are the explicit put-downs of engineers and the implicit elitism that scientists are superior and somehow removed from petty human foibles. There are as many cranks and egotists among scientists as there are in any cross-section of our population.

    Engineeringly Yours,

    Comment by Phillip Shaw — 16 Apr 2007 @ 1:09 PM

  186. Note — trying to be thorough in replying, for the subsequent readers who may come along and need more help sorting out who claims what to be true.

    These are the top two links from a Google search
    “Carbon dioxide” +infrared +saturated +bands

    The first is to the American Institute of Physics page, Spencer Weart’s comprehensive history (also linked in the sidebar).

    The second is to the PR/advocacy site JunkScience.

    AIP first — documented, you can read the footnotes and check this yourself:
    The Carbon Dioxide Greenhouse Effect

    “… The early studies … were measuring bands of the spectrum at sea-level pressure and temperature. Fundamental physics theory, and a few measurements made at low pressure in the 1930s, showed that in the frigid and rarified upper atmosphere, the nature of the absorption would change. The bands seen at sea level were actually made up of overlapping spectral lines, all smeared together. Improved physics theory, developed by Walter Elsasser during the Second World War, and laboratory studies during the war and after confirmed the point. At low pressure each band resolved into a cluster of sharply defined lines, like a picket fence, with gaps between the lines where radiation would get through.(24)
    … theoretical physicist Lewis D. Kaplan …. In 1952, he showed that in the upper atmosphere the saturation of CO2 lines should be weak. [Bands are not saturated–hr] Thus adding more of the gas would make a difference in the high layers, changing the overall balance of the atmosphere. Meanwhile, precise laboratory measurements found that the most important CO2 absorption lines did not lie exactly on top of water vapor lines. Instead of two overlapping bands, there were two sets of narrow lines with spaces for radiation to slip through.(25)
    (snipped from the AIP History page, link above).

    Second Google hit with that search is to the PR/advocacy site,

    I don’t provide links to junk PR sites myself, I don’t see any reason to increase their Google page rank when I’m pointing them out only to note that they’re bogus, not good info. Google doesn’t make that distinction when ranking number of links counted.

    I’d imagine you know how to find them; I wonder if they’re your source for what you believe? If so, be skeptical of people who claim they’re on your side in politics.

    Compare what they say there to the AIP history page. JunkScience is telling you — if it were the current truth —what the physicists knew a century ago.

    Who ya gonna believe, the people who pretend they’re on your side, and feed you lies and spin? “Just because you’re on their side doesn’t mean they’re on your side.” — Teresa Nielsen Hayden.

    Comment by Hank Roberts — 16 Apr 2007 @ 1:18 PM

  187. Gavin,

    In fact it is quite relevant.

    The starting point of some climatological models appears to be the “local thermodynamic equilibrium” argument, as understood by climate scientists.

    This provides the postulate that to maintain thermal equilibrium, radiation absorption and emission between substances must be the same, the radiation cancels, and the substances remain in thermal equilibrium.

    This model is incorrect, and not just by a little bit.

    In fact, substances emit radiation characteristic of the state of the system.

    The concept of requiring equal radiation for equal temperatures is based on Kirchoff’s laws from 1887. There is also Arrhenius’ writing in 1896.

    Boltzman published his theory of the distribution of states in 1896, and committed suicide in 1906 because his theories were widely rejected by his peers.

    S=klogW is written on his tombstone.

    Max Planck published quantum theory in 1900.

    Kirchoff’s laws work quite well for substances that are similar to each other, solids fall into this category due to the restriction of particle movement within them. Kirchoff, however, did not have the benefit of knowing the Boltzman distribution, neither did Arrhenius. Both brilliant men, but science progresses past the best of us eventually. Many folks thought physics was finished with Newton.

    Two substances in thermal equilibrium will have the same average kinetic energy of the particles that compose them. If these samples are composed of the same substance, in the same state, then the radiation fields will also be the same. Otherwise, the radiation fields will not be the same.

    It would be difficult perhaps to have two substances more different than solid and gas, particularly with respect to the distribution of energy within the phases.

    Because gasses have orders of magnitude more mechanical motion available to them than do solids, the radiation field of a gas at the same temperature as a solid (thermal equilibrium) will in fact be orders of magnitude less than the radiation field of the solid.

    It doesn’t really matter whether the gas receives its energy by radiation, or by collision. The Boltzmann distribution will prevail.

    Moving up out of the atmosphere, the next layer of gas adjacent to the first one will be in largely the same state, and will therefore emit radiation just as its predecessor.

    The big conceptual error occurs with the starting point of the model.

    When the gas is in thermal equilibrium with the planet, it most emphatically does not have a radiation field anything like that of the planet. Hence my rough guess of decreasing lambda A by about seven orders of magnitude.

    In fact, the emission from a gas is not dependent on same scaled function of T^4.

    To calculate the emission from a gas requires knowledge of the state parameters of the gas. Any statement that a gas must emit what it has absorbed from the planet blackbody like radiation field is simply incorrect. Scaling the T^4 dependence is similarly incorrect. Such a model probably requires dynamic correction of the T^4 coefficient as the model falls outside of measured temperature values while tracking the radiation upward to higher altitudes.

    Remember, you can model any data set an infinite number of ways, but most of these ways will be incorrect and will not lead to useful predictions. We can use an epicycle on epicycle model of planetary orbit, or we can declare the solar system center of mass to be somewhere in the sun instead of at the earth.

    As several folks have pointed out, the CO2 excited by earth’s radiation field very effectively dumps its energy into the atmosphere, causing a warming effect.

    For CO2 to then emit this same energy requires a reaccumulation of the energy in the CO2 excited mode. Clearly CO2 cannot emit from the ground state. The reaccumulation of any fraction of that original energy on the same order as that absorbed from the planet’s radiation field is entropically unlikely.

    The gas will obtain the Boltzmann distribution at its T, which can be measured, and will emit based on that value and the collisional frequency.

    You can try this at home. Go to your local gym. Drop a basketball on the floor. The ball will bounce successively lower, and then stop bouncing. Wait for the ball to spontaneously begin bouncing by gathering energy dissipated into the floor as heat. WHen the ball begins to bounce on its own by gathering heat from the floor, come back to your computer and post that absorption = emission because the ball and the floor are in thermal equilibrium.

    [Response: With all due respect, LTE does not imply that “radiation absorption and emission between substances must be the same”, only that the energy of the all the molecules in the air mass is distributed evenly – something which is easily true up until the mesosphere and is related precisely to the much faster collisional losses vs. radiative losses. Looking at any GCM you would see clearly that net LW radiation is not zero in the atmosphere. The emission by GHGs in any layer is governed by the temperature of that layer, not by what the absorbed radiation is. You continue to confuse a pedagogical tool (which in any case could be easily adapted to include this effect), and GCMs which do this as correctly as possible. -gavin]

    Comment by James — 16 Apr 2007 @ 1:45 PM

  188. #180 (re #178 & 138), you’ve said it better than I did, but the question raised in #138 was about whether GHGs are like real greenhouses, with similar principles involved. I sort of thought this might be the case, based on what I learned 40 years ago, but I may be wrong.

    At any rate, the effect of GHGs is at least like a real greenhouse in that the world warms, as do greenhouses. But I’m unclear whether the actual mechanism of absorption and reflection of light is similar between the 2 (GHGs & glass).

    Even if not, I still think “greenhouse effect” is a good metaphor, since it is easy to understand. We’ve all had the experience of a car with closed windows sitting in the sun being hotter than the outside temp.

    And I also think “Venus effect” & “runaway warming” are okay metaphors for a hysteresis or limited runaway situation of positive feedbacks becoming predominant over negative feedbacks for some time (as happened on earth 55 & 251 mya & could happen again), even if earth cannot go into a permanent runaway condition (until the sun becomes much hotter billions of years from now). And I understand that even in the worst-of-the-worst-case scenarios, our current warming period would not extend beyond 100,000 years, maybe 200,000 years max, before cooling back down, and that this is very unlikely, though possible.

    Metaphors are not perfect or exact, only suggestive, and are used as a short-hand for something that is difficult or complicated to explain.

    Comment by Lynn Vincentnathan — 16 Apr 2007 @ 3:11 PM

  189. In a greenhouse, the gas keeps hot air from rising (i.e. it “inhibits convection”). That’s the main thing that keeps a greenhouse hot. In the atmosphere “greenhouse effect,” certain gases trap infrared radiation, heat up, and radiate their own increased heat back to the ground (as well as in all other directions). So it’s a misnomer. But at this point, the usage is too well-established to correct. I think some astronomers tried to get everybody to call it “the atmosphere effect” for a while, but they didn’t get anywhere.

    [Response: If you keep the metaphor at the level of ‘the greenhouse/greenhouse gas reduces heat losses and keeps the surface warmer than it would otherwise be’, it works fine. As does the ‘blanket’ metaphor. All metaphors break down at some point and this one is as useful as can be expected. Nit-picking on whether the relevant heat loss is radiative or convective is really beside the point. – gavin]

    Comment by Barton Paul Levenson — 16 Apr 2007 @ 3:34 PM

  190. Is there a good place to read about quantitative questions on absorption
    of infrared by CO2 and water vapour?

    The kind of questions I have in mind are:

    How close are we to saturation for the frequencies absorbed by CO2
    (respectively, water vapour)?

    What is the overlap?

    As I understand it (correct me if I’m wrong!) it’s believed that on Venus
    there was a runaway greenhouse effect involving temperatures rising to
    the boiling point of water and all the water evaporating. But now the
    atmosphere of Venus is almost all CO2 (??), so currently the Venusian
    greenhouse effect is all due to CO2, and the temperature is something
    like 735 K. I’m a bit confused about how that’s consistent with us
    (Earth) being anywhere close to saturation of CO2 absorption and only
    being around 300 K. I think Venus is less than 10% closer to the Sun
    than we are: does that make such a big difference, or is there another

    [Response: See here for a discussion about the overlaps on Earth: – gavin]

    Comment by Jeremy — 16 Apr 2007 @ 3:36 PM

  191. Re #175: Fred Mann — See the IPCC report linked on the side-bar…

    Comment by David B. Benson — 16 Apr 2007 @ 3:46 PM

  192. Re 190: see also
    Kiehl and Trenberth, 1997 –

    Comment by Pat — 16 Apr 2007 @ 6:32 PM

  193. Hello, from the Nit-picker:
    First, this site has an outstanding degree of solid facts and very knowledgeable people writing in and I enjoy reading the posts as well as the articles.
    Global Warming is a misnomer – pure and simple. Like all such misnomers, it is irritating – like the term Big Bang for the “start” of the universe – it was neither big nor a bang (as quoted from others) so I guess we can or have to live with another one.
    The article I read the original discussion on salt and glass green houses and the explanation about how these structures really stay warm was in the Science weekly magazine (published some time in the late 1980’s??? Sorry for the lack of a date.)

    P.S. a calculation of the thrust/lift issue of a bee’s flight dynamic by using standard (non-critical) aerodynamic theory fails to capture the correct method that these amazing creatures exploit to achieve flight; yet I fail to see the relevancy of that keen observation has with my discussion of a valid point on the relevancy of “Green House” term but I guess, using the writer’s logic, I must conclude that they just don’t like bee’s.

    Comment by Dennis Brown — 16 Apr 2007 @ 7:05 PM

  194. I found this posting of great help in figuring out the whole climate change and the short lesson that Gavin gave is great and there should be more like it and allow people to work through and think about the debate and know for themselves what is total bull and not. I believe that people should discover things and idea. If more people would try to do just that the debate would be easier. thanks also the EDGCM people and staff it is a great program and look forward to using it with the youung adults I work with and mentor on science.

    Comment by greg — 16 Apr 2007 @ 7:11 PM

  195. I would appreciate comments about how effective Nitrogen is as a greenhouse gas. Thanks.

    [Response: N2 is not a greenhouse gas at all. N2O (laughing gas) is, and human related increases mean it has a ‘radiative forcing’ of about 0.15 W/m2 (compared to about 1.6 and 0.6 W/m2 for CO2 and CH4 respectively). -gavin]

    Comment by Ken Coffman — 16 Apr 2007 @ 7:38 PM

  196. Actually Barton, I think you are a little wrong with your line of reasoning, and it sounds alot like snobbery.

    Someone here posted (I think it was you as a matter of fact.) that the difference between scientists and engineers was that scientists developed new ideas and engineers made products. That is a fallacy. I have known “scientists” that did engineering and engineers that did what you call “science”. I have worked with lots of each at LANL NHMFL so I have a good data sample to use. Also I worked with an engineer that worked on the Apollo spacecrafts at LANL. To say he did not do that for the love of science because he is an “engineer” is totally insane!

    The educations of both are very very similar. You are implying that scientists by education are more savy than engineers. Sorry that does not compute as again the education and math/science backgrounds are almost the same.
    In any case scientists are also “professionals” as they get paid for their work, just like engineers. I have never heard of physicists getting food stamps!

    You don’t hear of biologists being good at physics and physcists being good at geology. Same as engineers. To say that a “scientists” can grasp concepts that are outside of their competency than engineers is wishful thinking considering the similarity of say physics and engineering.

    This pig doesn’t like it when the cows say that he doesn’t know the color of corn!

    Comment by Jim — 16 Apr 2007 @ 8:16 PM

  197. Oh boy! I have been catching up on this thread and I am astounded to find the engineer versus scientist posts. Just cool it folks. I was trained as an engineer in the 50s (whoa, yeah, that long ago) and remember those silly debates at that time. For basic science, I depend on the scientists who are specialists in the field under consideration. If they have an engineering problem, I assume they will check with an engineer. Gee, we got more important problems just now…

    [Response: Well said. No more of these comments, ok folks. – mike]

    Comment by Ron Taylor — 16 Apr 2007 @ 8:28 PM

  198. Re: Discussion of the greenhouse effect – I have written up my understanding of how it works (mainly learned here, though any errors are my own) on this page.

    I hope this is helpful. Any comments or corrections would be appreciated.

    Comment by Blair Dowden — 16 Apr 2007 @ 9:01 PM

  199. James,

    I think you may have missed the point of this post. It is a simple model that is used to explain the basics of the greenhouse effect to the lay-person.

    It is not a skelatal structure for a Atmosphere-Ocean Global Circulation Model. It is not even a structure for an advanced energy balence model. The Quantum mechanical effects are included in theses models, as well as full radiative transfer models, dynamic effects from atmopsheric/oceanic motion, pressure and doppler line broadening etc…

    They do not assume LTE. They do not assume Kirchoff’s law is valid and they most certainly do not assume that the atmosphere is solid.

    The model presented in this article is to illustrate the concepts. Too attempt to explain a GCM with the effects you have mentioned would be well and truley beyond the grasp of a layman, ad they’d get lost in the detail.

    Comment by Chris C — 16 Apr 2007 @ 10:34 PM

  200. Fine with me. I just don’t like being patronized.

    Comment by Jim — 16 Apr 2007 @ 10:52 PM

  201. Re 196 You don’t hear of biologists being good at physics

    Actually, you do, if you try…Andrew Biewener at Harvard(, and Steve Vogel ( and Steve Wainright at Duke ( are three that come to mind. Biology and physics are well integrated in the fields of biophysics and biomechanics.

    Comment by Chuck Booth — 16 Apr 2007 @ 11:18 PM

  202. If you used the GSMs from the “Big Five”, made logical assumptions, applied those assumptions to the models, at about what period in the future would we reach the Point of No Return? This exercise appears to be worthwhile because it is doubtful that man will do much to address warming for many years.

    Comment by Jon C — 16 Apr 2007 @ 11:39 PM

  203. the Wonderer:

    That’s very well put and I agree its easy to lose focus. I have to add that the rigour we need to discuss climate science is at first frustrating, because some of the people “bucking” the consensus aren’t honest, and the others seem a little odd in what they’re willing to believe or not, but when a scientific topic comes up on other forums, it’s interesting how often I think, man, that level of vagueness, lack of sources, double standards, whatever, would never fly discussing climate change. Although we compare it with things like the evolution debate, I’d say the “opponents” are more formidable in climate science than in most controversies.

    Comment by Marion Delgado — 17 Apr 2007 @ 12:58 AM

  204. also to clarify and definitely not to stoke anything i was speculating that there might be community differences between Mechanical Engineering culture and Electrical Engineering culture, with the latter taking a broader spectrum of math. Hence, an MS in EE would be, by what I was saying, taking a broader spectrum of math, not a narrower one, so that reinforces the question I was musing over, not contradicts its premises.

    I literally took only one grad engineering class, and it happened to be in ME. I noticed that as a big difference with my undergrad and grad physics classes, but that’s obviously too small a sample for me to have learned anything definitive. It just seemed to me at the time that Mechanics and Mechanical Engineering have lengthy calculations where things can go wrong and having a sense of what you’re doing is important, whereas my E&M stuff and Thermal and Statistical were more wide-ranging idea classes. It seemed to me E&M was definitely more arcane in the math involved.

    Also, I sometimes see parallels in science between things like engineering and things like physics to US military interservice rivalries. Some of it is tradition.

    Comment by Marion Delgado — 17 Apr 2007 @ 1:14 AM

  205. Re 195:

    Gavin, won’t virtually any IC engine produce N02?

    Comment by Marion Delgado — 17 Apr 2007 @ 1:18 AM

  206. Re: 199: Minor hiccup on the link there – this one should work

    Does anyone know of a good comparative summary of the various models currently in use or in development? And for that matter information about what we can expect in future. How much better will they get and at what rate? Are we going to approach some limit any time soon in prediction capacity that is inherent in the chaotic nature of the atmosphere? What are the key areas for improvement? What are the key hurdles to be overcome. Etc.

    Comment by Craig Allen — 17 Apr 2007 @ 6:19 AM

  207. [[As I understand it (correct me if I’m wrong!) it’s believed that on Venus there was a runaway greenhouse effect involving temperatures rising to the boiling point of water and all the water evaporating. But now the atmosphere of Venus is almost all CO2 (??), so currently the Venusian greenhouse effect is all due to CO2, and the temperature is something like 735 K. I’m a bit confused about how that’s consistent with us (Earth) being anywhere close to saturation of CO2 absorption and only being around 300 K. I think Venus is less than 10% closer to the Sun than we are: does that make such a big difference, or is there another reason?]]

    Venus has a semimajor axis (distance from the Sun in Earth-Sun units) of 0.723. When it formed and the primordial nebula cleared away, it was too hot to keep its oceans liquid — there was CO2 and H2O in the air, that heated the atmosphere, H2O evaporated from the oceans, that heated the atmosphere more, and so on in a cycle that “ran away” until there was no ocean left. Then sunlight dissociated the water vapor in the upper atmosphere. The hydrogen escaped, the oxygen combined with Venus’s surface rocks.

    Most analyses of planet climate histories (Rasool and deBergh 1970, Hart 1978, 1979, Kasting et al. 1993) conclude that any planet that formed closer than about 0.95 AUs to the sun would have undergone such a runaway greenhouse effect. Earth was just far enough out that the process never ran away.

    The Venus greenhouse is maintained mostly by carbon dioxide, but also by the 75% sulfuric acid droplet clouds that cover the whole planet, and by minor gases such as water vapor, sulfur dioxide, hydrocholoric acid and hydrofluoric acid.

    The idea that CO2 absorption is “saturated” in Earth’s atmosphere is wrong. It was developed in the early 20th century in response to Arrhenius’s 1896 global warming paper, and was standard doctrine until more careful spectra of CO2 and H2O were developed in the 1940s, and the process of radiative transfer at many levels in the atmosphere was better understood.

    Comment by Barton Paul Levenson — 17 Apr 2007 @ 6:33 AM

  208. [[The educations of both are very very similar. You are implying that scientists by education are more savy than engineers.]]

    No, that’s not what I said at all. I said that what engineers do and what scientists do are two different things, and that some engineers don’t seem to understand the difference, and claim to be scientists (and in many cases, better scientists than the real scientists). No matter how much engineers like science, love science, or admire science, what they do in their jobs is not science. It is not empirical research and does not get published in peer-reviewed science journals. Engineers are engineers. Scientists are scientists. They’re both admirable professions, but they are not the same profession. That’s all I’m saying, and I’m saying it not out of “snobbery,” but because we’ve had engineers come in here claiming to be scientists, and telling the climatologists here that they were wrong about this, that and the other thing (the models, how the greenhouse effect works, etc.).

    Comment by Barton Paul Levenson — 17 Apr 2007 @ 6:39 AM

  209. Mike,

    Sorry, I saw that response after I posted my last message. Withdraw that one if it’s out of line.


    Comment by Barton Paul Levenson — 17 Apr 2007 @ 6:41 AM

  210. Barton, what is a scientiest and what is an engineer? Is a professor doing research in a subject like structural dynamics or control theory a scientist according to you? I am interested because I want to know if I am a scientist or not.

    Why this bs about scientist and engineers anyway? Engineers do mistakes, scientists do mistakes and both belives and write incorrect things as can be seen on this very website.

    Comment by Fredrik — 17 Apr 2007 @ 8:03 AM

  211. The difficulty I have in following this piece is not the mathematical operations, but understanding and retaining the concepts that are expressed as a single letter. If you put up a sidebar with 1-2 sentence definitions of each letter variable, that might help. Also, it would help to include the English pronunciation of the Greek letters. I retain this stuff by vocalizing it, and never actually studied Greek. (I Googled the Greek alphabet, and that helped.)

    Comment by Steve Funk — 17 Apr 2007 @ 8:41 AM

  212. Question for the mods (or anybody, off the topic of this thread).

    Something’s been nagging at the back of my head. A while ago, a post was made about CO2 change leading temperature change during deglaciations. It was stated that “something” starts warming, which then increases CO2. In discussion (here and elsewhere), much was made of the uncertainty in the “something starts warming” statement. What starts warming?

    Isn’t it obvious? Milankovitch cycles start melting, and the albedo change induced by melting starts the warming.

    So … what am I missing?

    Comment by tamino — 17 Apr 2007 @ 8:49 AM

  213. Regarding N2 as greenhouse gas.

    Thank you, Gavin, for your comment. To be sure, you’re saying N2 has zero effectiveness as a greenhouse gas, compared to CO2? It has no capability to absorb or reflect radiant energy? Zero sounds like a troublesome number. 5%? 1%? 0.1%?

    [Response: The ability to absorb in the infrared is a function of various vibrational modes. Symmetric two atom molecules do not possess the requisite degrees of freedom that tri-atomic (and higher) molecules have (think of all the different ways that O-C-O can oscillate compared to N-N). Thus for all intents and purposes N2 is not a greenhouse gas. Nothing is ever truly zero, and it’s conceivable that isotopic variations/higher energy bands make a difference – the HITRAN database would be the place to look for them – but I would be astounded if they were even a thousandth as important as CO2. If someone knows the exact number, let me know. – gavin]

    Comment by Ken Coffman — 17 Apr 2007 @ 10:29 AM

  214. #212, Tamino, you not missing much ! As an example, In modern times, Arctic Ocean ice use to be more spread out:

    now a days it is much less expansive particularly around Novaya Zemlya

    This has tremendous impact on not only temperatures, Polar wildlife and sea transportation, but on the very time when the sunrises from the long night:

    When the sun was seen while it was -5.7 degrees below the horizon, an historical record established in 1597, not broken since.

    Comment by wayne davidson — 17 Apr 2007 @ 10:42 AM

  215. The sun’s photochemical action on carbon dioxide. Ultraviolet photons of wavelengths less than 169 nm can photodissociate carbon dioxide into carbon monoxide and atomic oxygen.

    Will the sun save us?

    [Response: This sink is tiny and only occurs in the mesosphere, and so the answer is no. -gavin]

    Comment by lars — 17 Apr 2007 @ 12:25 PM

  216. RE#212, The problem with basing the initiation strictly on the milankovitch cycles seems to be that over the past 900,000 years the main signal has been the 100,000 year cycle, while in the 2 million years prior to that the main glacial was 41,000 years, which was ascribed to the Milankovitch obliquity (the onset of N. Hemisphere glaciation was 2.75 million years ago). So, there seems to be no agreement on what sets the timing for the more recent 100,000 year glacial cycle. There is a paper that discusses the problem (and proposes their solution) at :

    Paleoclimatic evidence from ice cores, ocean sediments and other sources reveal oscillations in climate and atmospheric CO2 over the last million years, with major signals in 20, 41 and 100 ky (thousands of years) frequency bands (Hays et al., 1976; Petit et al., 1999; EPICA, 2004). While changes in solar radiation caused by perturbations to Earth’s orbit appear to be directly responsible for the 20 ky and 41 ky cycles, the explanation of the dominant 100 ky cycles remains elusive (Imbrie et al., 1993; Roe and Allen, 1999; Wunsch, 2004).

    It is increasingly clear that internal feedbacks in the Earth’s climate system play a major role in the 100 ky cycles, whether it is pacemaked by orbital forcing or not. Atmospheric model simulations show that the 80-100 ppmv lower CO2 is the dominant factor in producing about 5C cooler glacial climate, with additional contribution from ice-albedo and other effects 5 (Broccoli and Manabe, 1987; Lorius et al., 1990; Weaver et al., 1998). It is very difficult, if not impossible, to simulate the observed glacial cooling in comprehensive models without changing CO2. Thus carbon-climate interaction may provide key internal feedbacks that have rarely been included in comprehensive models interactively.

    CO2, CH4 and N2O levels were all well lower during the glacial-interglacial period, (by 100-200 ppm relative to current values for CO2) CO2 and other gas levels changed much slower during the transitions than they are today (by a factor of 30 or so). Thus, it’s difficult to related such changes to current circumstances – multiple factors appear to control the glacial/interglacial cycle, but they produced a semi-stable periodic response. However, it’s doesn’t seem that current warming will be a repeat of a glacial-to-interglacial transition, of which there is only one well-recorded example, that of the Holocene.

    In the Pliocene period that preceded the onset of glacial cycles, temps were ~3C higher and sea levels were 10-20 meters higher, and CO2 levels were some 30% higher than present values. Some people say that this is the best model of what future climate will be like. The main real issue still is the speed of the climate response to the accelerating greenhouse forcing… for which there is no good ‘recent’ historical analogue.

    Comment by Ike Solem — 17 Apr 2007 @ 1:09 PM

  217. The sun’s photochemical action on carbon dioxide. Ultraviolet photons of wavelengths less than 169 nm can photodissociate carbon dioxide into carbon monoxide and atomic oxygen.

    Will the sun save us?

    [Response: This sink is tiny and only occurs in the mesosphere, and so the answer is no. -gavin]

    So all we need is a ultraviolet photon generator…..

    [Response: Sorry, but no again. CO in the lower atmosphere oxidises to CO2 very quickly (due to the OH formed from photolytic reactions involving water). -gavin]

    Comment by lars — 17 Apr 2007 @ 2:49 PM

  218. [Isn’t it obvious? Milankovitch cycles start melting, and the albedo change induced by melting starts the warming.

    So … what am I missing?]

    Add in the air cooling that takes place from the heat of fusion melting the ice. The calories required to melt ice can only come from the air. Need to have something happen that raises temperatures (and then the carbon dioxide levels), and keeps pumping calories into the air to make up for the calories absorbed by the ice to make it turn to liquid. The likely candidates could include massive geothermal events or variations of the sun. Solar variations probably account for most of the climate variations that have occurred.

    [Response: Milankovitch forcings makes differences of ten’s of W/m2 on these timescales – plenty enough energy to melt the ice. -gavin]

    Comment by Carol — 17 Apr 2007 @ 4:22 PM

  219. I’m glad nitrogen was brought up. So N20 is a GHG. Now don’t laugh, I’m not a chemist, but what about N02 or NOx (whatever they are)? It seems I’ve read something somewhere about them being GHGs. Also that car & power plants emit them, and that synthetic fertilizers emit them.

    And also one of these guys is a ozone depletor, as well.

    So much for a little knowledge…(well, you know the rest).

    Comment by Lynn Vincentnathan — 17 Apr 2007 @ 4:43 PM

  220. One more comment and then I will leave it alone.

    Barton, alot of engineering is purely empirical, that is the part that you are missing. (I am taking that you mean empirical is the for the furthering of knowledge not so much to create a product for the market.) Engineering is not just about making products, it is also about researching new ideas, processes or things. (Yes they do get published in peer reviewed journals too!) Which, to me, is what science is all about and no one discpline of science (Whether you like it or not engineering is an applied science) has exclusive abilities to further science and to learn new science outside of their fields. You said that becuase engineers can plug numbers into some math eqs that they think they know science. I am sure there are some which mostly comes from the emphasis in our later classes in practicality and about the requirement to produce timely results. (This tends to make a lot of engineers confident and pragmatic and very cynical about “blue sky” ideas.) Whereas empirical research does not obey deadlines and often does not yield the desired results. (It is research after all.) In any case, overconfidence and cyninism are not unique to engineers, it is present in any science profession and you were making a broad generalization of one displine of it. What you were saying was exactly snobbery and you knew that when you said it.

    I have participated in many empirical research activities such as building 33Tesla, 54 Tesla and 900Mhz DC continous (not pulsed) magnets. (BTW what have you done?) We designed and built most of those beasts from scratch.

    New methods in Controls,Neural Nets, Digital Signal Proccessing, materials synthesis new transistors, and random process research, also count as empirical. (Along with lots of other things.)

    If all you are basing your opinions of engineers on is how some guys post on a blog, well then you are definitly using flawed judgement. In any case a quick set of google searches reveals that it is not just engineers that challenge AGW or say silly things about it, but some physicists/geologists/biologists etc.etc don’t preach from the AGW bible either. Does that make all phycists idiots too just becuase of a few bad apples? If I used your line of reasoning it would.

    Re 201.

    You will have a couple of outstanding folks in any field. That is what the Nobel Prize is for after all!

    Take your average biology grad and ask them to work out some ODEs or a couple fourier series, Laplace Transforms, or to show a time domain function in the frequency domain. (The eyes will glaze over.) See if they can do it. Then go ask a physics/math/engineer grad if they can.
    Post the results. Of course, ask those some physics/math/engineer about the details of cellular mitosis and you will also some eyes glaze over! The point being is what I said ealier no one discpline in science is any better at grasping the other disciplines that are outside of their core competencies. What is required of anyone is an open, agile, and thoughtful mind.

    Comment by Jim — 17 Apr 2007 @ 7:03 PM

  221. Great article – the maths is always welcome. Certainly more welcome than politics – I know this is an important issue and we need people to understand…

    Through pure coincidence, I imagine, Kerry Emanuel talked about this model a few weeks back (the basics, not the feedbacks) in his Tropical Meteorology Course at MIT. It is always amazing to me how well simple models can do. Take this model, add a few more levels and some sort of tropospheric lapse rates and we can get very close to reality!

    Comment by Joseph Andersen — 18 Apr 2007 @ 12:35 AM

  222. More like this please.

    Consider these threads in a forum I am a regular reader of and contributor to.

    I could not find anything online that was simple enough to support my views and at the same time objective.

    For me, there is still a paucity of publicly available data from simple, basic science experiments that demonstrate the fundamentls of greenhouse warming, etc. I did find some of the raw data used in the IPCC models, but it was not clear to me what the data were. It seems this information may be locked away in science journals whose publications are not publically available.

    I am an ex scientist, whose field was not in cliamte science. When I apply my scientists’ skepticism to the climate change debate I find the available data to be wanting. Which means I cannot be in support of the case for climate change as much as perhaps I should. And this is from someone who wants to believe in the reality of climate change.

    Comment by Adam Nealis — 18 Apr 2007 @ 4:34 PM

  223. Re #222: Adam Nealis — Once a scientist, always a scientist. :-)

    Seriously now, have you read the AIP history of climatology linked in a sidebar? How about any of a number of textbooks, beginning perhaps with W.F. Ruddiman’s Earth’s Climate: Past and Future?

    But for AGW, the issue is very simple. Cardon dioxide is a so-called greenhouse gas. Humans have been producing a huge slug of it by burning fossil carbon, especially in the last 50 years. Therefore it will become even hotter, globally…

    Comment by David B. Benson — 18 Apr 2007 @ 4:56 PM

  224. Re 223.

    That made it soooo clear!
    He is wanting more raw data, not polished answers. He wants to try to figure it out for himself. You telling him “we say we did so you can believe us” is not what I thought he was asking.

    Comment by Jim — 18 Apr 2007 @ 8:32 PM

  225. “Who ya gonna believe, the people who pretend they’re on your side, and feed you lies and spin? “Just because you’re on their side doesn’t mean they’re on your side.” — Teresa Nielsen Hayden.”

    Where does this come from Hank? The author and I aren’t on speaking terms because she said I wasn’t a real Democrat. In fact, I wasn’t one at all according to St. Teresa. She disemvoweled me and there’s been hard feelings ever since. Public blog comment humiliation isn’t much fun. I thought her tactics resembled the Puritan stock treatment. I’m a Democrat, and have been since McGovern. I’m also a biologist. She’s a vehement partisan. I wouldn’t expect anything resembling objectivity from her anymore than the wingnuts. I do assume a sci-fi editor respects science itself, unlike these co-opted shills. If not those of us who do science for a living.

    Comment by Mark A. York — 18 Apr 2007 @ 10:34 PM

  226. It might amuse to consider this simplified model at the point where there are no greenhouse gases in the atmosphere. By which I mean that the atmosphere is totally transparent at all frequencies.

    Such an atmosphere can neither absorb nor emit radiation.

    Its only source of heat exchange is with the surface. What sort of atmosphere would this produce? What would be its equilibrium state?

    Unlike the original model I will be assuming that the greenhouse affect is distributed in a vertical gas column capable of convection, and conduction but not much else.

    At equilibrium there would be no net heat exchange at the surface as the atmosphere can not dissipate heat to space. This atmosphere would have no net source nor sink for heat, it would be thermodynamically dead.

    On course to equilibrium it may manifest many of the aspects of our atmosphere, it may pass through adiabatic equilibrium with a lapse rate but that lapse rate would necessitate a net upward flow due to conduction which, as the top of the atmosphere can not dissipate heat, does not represent an equilibrium condition.

    Equilibrium would be reached when the atmosphere was evenly heated throughout with no macroscopic temperature gradients. Its temperature thoughout would be the same as the earth’s surface.

    Given that all of that is true (comments welcomed) what would be the effects of adding greenhouse gases to this dead atmosphere.

    Well a major impact would be that the top of the atmosphere could now dissipate heat into space. The atmosphere would be alive again. Now do not think for a minute that I am going to hint that this indicates cooling.

    As space above the top of the atmosphere is now a net sink the only other location for net heat exchange, the surface, must represent a net source. This could be in the form of warming there resulting in a conductive flow, as well as the absorption of infrared radiation by the atmosphere. The effect of both would be to create a temperature gradient with the surface hotter than the atmosphere. With increasing greenhouse gasses added the atmosphere would reach adiabatic equilibrium and convection would increasingly become a significant transport mechanism. With increasing greenhouse effect, convective flows would increase and radiative flows would decrease as proportions of the total flow. It might help to consider the limiting state at which the atmosphere is totally opaque, a dark gas at all infrared frequencies yet still transparent to shorter wavelengths. The only significant means for transport would then be convection, ignoring any increase shorter wavelength radiation from the surface due to excessive temperatures.

    An important point of this model is that the temperature gradient needs only to be sufficient to maintain the flow necessary to match the radiative loss at the top of the atmosphere by either radiative of convective means.

    I realise that this is a different way of looking at things but hopefully, perhaps with some corrections, it might be useful.

    In this view it is the ability of the greenhouse atmosphere to dissipate heat into space that is the significant driver. The flows of heat in the atmosphere are the result of a need to supply that loss in a sustainable fashion.

    A key question is: what temperature does this indicate for the top of the atmosphere?

    Well in the totally IR transparent regime it will be the same as the surface temperature. In the totally IR opaque regime it will be the same temperature. In that state, for IR emission purposes the top of the atmosphere is the IR surface so it must have the same temperature as the surface of the earth in the totally transparent case as the same amount of heat needs to be dissipated. So at each extreme the temperature of the top of the atmosphere is the same. I can only speculate that it is the same at all greenhouse gas densities (comments welcomed).

    So if the temperature of the effective IR top of the atmosphere is basically unchanged, greenhouse gases must give rise to a net warming of the earth surface.

    Just how hot the surface gets in this model depends on the likely contributions of convective and radiative flows.

    Both depend on the temperature gradient. This may not be obvious.

    As IR passes through the gas column it is constantly absorbed and emitted. This applies to both upward and downward flows. The net upward flow is only sustained by the temperature gradient causing the upward flow from each lower level to the next higher level to be greater then the downward from the upper level to the lower one.

    I have no figures, but I would not think that convection is a particularly good heat transport system considering the large amounts of heat that need to be transported to fuel the IR being emitted at the top of the atmosphere. I think that the world would be a very nasty place before the primary transport mechanism was convection. (Comments welcomed.)

    So in the simplified model all we really need to know is the amount of heat being dissipated into space by the top of the IR atmosphere which given that the temperature up there would be relatively constant under increasing GH effects will reach a maximum at the point where all IR in the range of the GH gas is being absorbed and emitted close to the top of the atmosphere. So the increase in temperature necessary to feed this loss is a function of the opacity, which gives us the temperature gradient, which in turn must be integrated over the effective depth of the atmosphere to give the surface warming.

    Hopefully, given the restraints of the model I have not strayed too far away from the physically possible. And further that some points like the relationship between temperature gradients and net IR flows may be useful.

    All comments welcomed.

    Alexander Harvey

    Comment by Alexander Harvey — 21 Apr 2007 @ 10:12 AM

  227. Mark, I don’t recommend arguing about other bloggers’ policies here, if anywhere.

    Berkeley advice:
    “Don’t argue with crazy people on the streeet — passers-by can’t tell which of you is crazy.”

    Any writer’s name (however many people use it) is easy to find with Google. I can search for
    “some name” +banned
    and find a lot of hits, but it’s impossible to tell who’s behind each instance of the name.

    — When when a host says a tone is not acceptable and uses disemvowelling, it’s their call — it’s their blog.
    It happens. Some hosts stir up shit; some don’t care.

    — When a host says several names are sock puppets all coming from one IP, it’s their call — it’s their blog.
    It happens. Some hosts let it to stir up shit; some don’t care; most consider it a reason to block the IP.

    — Trolls pick up names and post stupid stuff under them as recreation. Only the host can see the IP; we bystanders can’t tell who’s using the name. It happens.

    Posting to someone else’s blog is like sending them unsolicited email—-if they like it well enough to keep it and show it to their friends, that’s great; if they don’t, learn not to take offense. No point arguing.

    “Ever tried. Ever failed. No matter. Try again. Fail again. Fail better.” —-Samuel Beckett

    I recommend calling attention to your good work, not your troubles, when using other people’s forums.

    Comment by Hank Roberts — 21 Apr 2007 @ 11:54 AM

  228. [[At equilibrium there would be no net heat exchange at the surface as the atmosphere can not dissipate heat to space.]]

    It can’t do so by conduction or convection, but it can dissipate heat by radiation, and does. Even worlds without atmospheres (or without significant atmospheres) — Mercury, the Moon, asteroids — can lose heat that way. Otherwise they’d steadily heat up in the sun until they melted and then vaporized.

    Comment by Barton Paul Levenson — 21 Apr 2007 @ 4:54 PM

  229. Re 226 – That’s one good way to approach the matter. There are some complexities, of course, but we’re starting with the idea of a simple model here.

    (PS I prefer to use SW and LW rather than IR –
    SW = short wave, the kind of radiation mainly from the sun;
    LW = long wave, the kind of radiation that can be emitted at typical terrestrial (Planet surface and atmospheric) temperatures.
    This differentiation is more convenient because SW includes UV, visible, and some IR (out to around ~ 4 microns – of course the sun emits some radiation even in the LW band and the Earth emits a tiny amount of radiation even in the SW band but the great majority of the energy in each case can be seperated into non-overlapping bands. (Are you familiar with black body radiation as a function of wavelength?)

    There is an idea of an effective emitting level in the atmosphere that radiates to space; this level must then have the temperature that corresponds to the temperature of the surface with an atmosphere transparent to LW, assuming same overall albedo. This would be at the top of the atmosphere if the atmosphere were perfectly opaque in LW.

    It does become a bit more complicated when the atmosphere has a varying degree of opacity. The source of emission to space is distributed over the vertical thickness of the atmosphere; along a vertical coordinate corresponding to optical depth, the source would be concentrated at the top. But if the optical depth of the atmosphere is low, some still comes from the surface of the Earth. Then, all of this varies over wavelength, even within the LW band (in the absence of clouds and tropical humid air, the atmosphere is somewhat transparent between 8 and 12 microns.) There is also some atmospheric absorption in parts of the SW band, mainly from water vapor in the troposphere and ozone in the stratosphere, and there is some absorption, I think by molecular and atomic oxygen, at the very top of the atmosphere. The air’s absorption/emission spectrum varies with height in part because H2O and O3 concentrations vary, and also because at higher pressure and temperature near the surface, discrete molecular absorption lines are spread out into bands, while higher up in the atmosphere they are less spread out.

    Typically a planetary atmosphere has a troposphere, in which temperature falls with height, and a thermosphere, in which temperature rises with height; because of the Earth’s ozone layer, the Earth’s atmosphere also has a stratosphere and mesosphere in between.

    I think generally convection tends to maintain a representative lapse rate in the troposphere close to a moist adiabat (the rate that air cools at while it rises if condensation is occuring). This actually decreases at increasing temperature because at a given x % relative humidity, the concentration of water vapor increases with temperature so moist updrafts starting at a higher temperature cool off less quickly with height.

    I’m leaving some loose ends here, …

    But see my comment 105 above.

    For a simple one dimensional radiative-convective equilibrium model, one can set a maximum allowable lapse rate – a constant or a moist adiabat, for example – then the resulting temperature profile requires in places which are at such a lapse rate (the troposphere) that the total radiative heating or cooling rate is nonzero. The surface will also typically have a net radiative heating rate. This must equal the convection rate from the surface, and the variation in convection with height can be infered by the radiative cooling rate (which at equilibrium equals the convective heating rate, which is the convergence of the convective heat flux, or the negative rate of change with height of upward convective heat flux).

    I would guess that you’re right that convective heat transport should generally increase as the greenhouse effect increases. Some effects which would reduce that increase are that radiative transfer across a difference in temperature increases with an acroos the board temperature increase, especially at the shorter end of the LW band (not as much at longer wavelengths). Also, there is the SW absorption by water vapor. On the other hand, an increase in temperature would reduce the moist adiabatic lapse rate, which would slow radiative transfer within the lower atmosphere.

    While increasing the LW opacity decreases radiative energy transfer at longer distances (with the temperature profile held steady), it can increase radiative energy transfer across shorter distances (the cut off between longer and shorter is itself reduced by increasing opacity – across a fixed distance, with a fixed temperature distribution, increasing opacity from zero at first results in increasing radiative energy transfer, which reaches a peak, and then declines). What happens with increasing opacity is that radiation is exchanged across shorter distances, which tend to involve smaller differences in temperature, and so there is less of an imbalance in radiation – that is, the net radiative energy transfer decreases…

    Comment by Pat — 21 Apr 2007 @ 5:47 PM

  230. I’m relatively new to Realclimate (been following for about a month), and like the site a lot. I think this type of post describing the modelling is well worthwhile and very interesting.

    A few comments on detail.

    I’m not surprised some people found the geometric factor of 4 hard to understand. I don’t think it’s immediately obvious. I think the way I’d express it as something like “the solar constant gives the energy when the sun is due overhead, but for this model we are interested in the average over the whole globe, day and night as well as all latitudes.”

    It took me a little while to get my head round “atmospheric radiative flux is written lambda A = lambda sigma Ta to the fourth” because my natural reaction was to cancel the lambdas. I’d be tempted to leave the temperature part out altogether until after the basic formula has been derived, and then have a separate little bit as part of the ‘Climate Sensitivity’ section to point out that these changes in energy are expressed through temperature.

    I can’t decide whether the equation of emissivity with absorptivity (Kirchoff’s Law) is so obvious that it’s not worth mentioning, or so profound that it merits a whole exposition in itself. I think it probably does need to be explained that lambda is variously representing emission and absorption at different places in the three energy balance equations.

    But those are bagatelles. The part that really confused me (and to an extent still does) is the ‘Radiative Forcing’ section. To me, the second (Delta G) equation is almost obvious because all you are doing is differentiating your first (G) equation (it’s a fine-balanced decision whether the equations should be numbered as nothing screams ‘impenetrable techy geekiness’ to the typical reader like numbered equations, IMO), whereas the FTop equation to me comes out of nowhere. Where are you going with it and why are you introducing this concept?

    In the end I had to look up ‘radiative forcing’ on Wikipedia (not a bad thing in itself, but I suspect you are losing readers right there). I’m still not sure I’ve understood why radiative forcing is a useful concept – it seems to me it’s being used like a sort of convertible currency for any external stimulus to the climate: “we can (in the model) treat any externally (including human) generated change, such as an increase in the amount of carbon dioxide in the atmosphere, just as if it were a change to the amount of energy coming in at the top of the atmosphere. The magnitude of this energy is known as the radiative forcing. This feature carries over to more complicated models as well as the real atmosphere [I assume that’s true]. This is useful because…” I think this is really what you are getting at with your Point 2.

    I think some of my confusion arose from the use of the phrase “instantaneous change” in this section. The trouble is that by this time I was thinking in terms of the model, where time is not represented (the ground and atmosphere have undefined heat capacity), so my reaction was “how can there be a change in the energy balance? It’s always zero by definition” and it took me a little while to sort myself out.

    Finally, there’s a cultural trap here. If I’d read the substance of this post in a textbook, or heard it in a lecture, I would have expected to get a pen and paper and do some sums before I was sure I’d got it all. Because I read it on a blog, I expected to read it through once and understand it first time and was mightily affronted for a while that that didn’t work.

    I hope this hasn’t come off as an ‘it’s really all about me’ comment, but I’m starting out from the assumption that the post is not really about climate, but about effective popular communication of science, and I wanted to record some of the false starts and blind alleys as likely being relevant to other readers and other attempts to do this sort of thing.

    Finally, I have to say I love the argument that, because greenhouses don’t use the greenhouse effect to keep warm, the earth can’t be using it either, and so it can’t be warming.


    Comment by David — 22 Apr 2007 @ 3:43 PM

  231. # 228

    I think that you misunderstand me.

    You wrote:

    “It can’t do so by conduction or convection, but it can dissipate heat by radiation, and does.”

    Actually I think that you will find that a non-greenhuose gas can’t!

    If a gas can not absorb SW radiation it can not emit SW radiation and vice versa.

    The planetary surface would be the only source of SW radiation. If a gas can not radiate heat into space then that sink is not present.

    #229 Many thanks for your comments. I think I am aware of some of the complications. In particular the detailed way that real greenhouse gases must absorb and emit radiation and the factors that determine its emissivity at each frequency. Unfortunately this seems horrible complex and intractable and I presume certain rule of thumb parameterizations are used instead.

    I must read your postings again before commenting further.

    For know thanks.

    Comment by Alexander Harvey — 23 Apr 2007 @ 7:26 AM

  232. [[“It can’t do so by conduction or convection, but it can dissipate heat by radiation, and does.”
    Actually I think that you will find that a non-greenhuose gas can’t!
    If a gas can not absorb SW radiation it can not emit SW radiation and vice versa.
    The planetary surface would be the only source of SW radiation. If a gas can not radiate heat into space then that sink is not present.

    Any body at a temperature above absolute zero is constantly emitting photons, non-greenhouse gases as well as greenhouse gases. Nitrogen at 288 K emits radiation just like carbon dioxide does, though there may be a different emissivity in the equation. But the idea that an atmosphere — any atmosphere — can’t radiate heat into space is just wrong.

    Comment by Barton Paul Levenson — 23 Apr 2007 @ 10:01 AM

  233. #232

    I suggest you go looking for the LW absorption spectra for the monatomic gases. I doubt you will find one.

    I have found something quotable from

    “Homo-nuclear diatomic molecules such as O2, N2, H2 and Cl2 and monatomic gases such as helium, and radon do not have infrared bands and therefore must be measured by non-infrared means.”


    There is a significant difference between the ways that different gases absorb and emit EM radiation. The monatomic gases simply lack the rotation and vibration modes that produce LW emissivity in greenhouse gases.

    If you are saying that all gases emit some radtiation at atmospheric temperatures no matter how small and no matter which part of the spectrum then you are right but risk pedantry.

    According to this definition all gases are greenhouse gases.

    For the purposes of what I have written the monatomic noble gases do not radiate at room temperature. Get them hot enough (thousands of degrees) and they will radiate via electon state transitions but this I think largely confined to the UV, and visible bands. The same is true, or perhaps nearly true of the symmetric diatomic molecules. (I am not sure that the quote above is strictly true of N2.)

    There is something special about the greenhouse gases. Which is that they are “significant” radiators at room temperatures. This is what makes them greenhouse gases.

    If you are saying that a Helium atmosphere at Earth atmospheric temperatures and pressures must radiate miniscule amounts of UV and visible radiation then I suppose you are right and I am wrong.

    If you are going to protest that planets do not have pure monatomic atmoshperes then all I can say is that I never suggested they did. I was merely considering how this simplified model might perform if ours did.

    If I am wrong give details, not bald statements, and I will fall on my sword like a gent. As it stands I know of no mechanism by which the noble gases can emit significant radiation at standard atmospheric temperatures and pressures.

    Comment by Alexander Harvey — 23 Apr 2007 @ 11:55 AM

  234. [[I suggest you go looking for the LW absorption spectra for the monatomic gases. I doubt you will find one.
    I have found something quotable from
    “Homo-nuclear diatomic molecules such as O2, N2, H2 and Cl2 and monatomic gases such as helium, and radon do not have infrared bands and therefore must be measured by non-infrared means.”
    There is a significant difference between the ways that different gases absorb and emit EM radiation. The monatomic gases simply lack the rotation and vibration modes that produce LW emissivity in greenhouse gases.
    If you are saying that all gases emit some radtiation at atmospheric temperatures no matter how small and no matter which part of the spectrum then you are right but risk pedantry.
    According to this definition all gases are greenhouse gases.

    I know the difference, thank you, between a greenhouse gas and a non-greenhouse gas. I think part of your problem seems to be that you think if something doesn’t emit at IR wavelengths, it doesn’t emit at all, leading to your idea that an atmosphere without greenhouse gases wouldn’t emit any radiation.

    How does such an atmosphere work? I can only think of a few possible mechanisms:

    1. It is at absolute zero temperature.

    2. It is a perfect insulator (the emissivity term in the Stefan-Boltzmann equation is identically zero). The planet beneath it absorbs sunlight, but nothing gets out, which means the planet will heat steadily until it melts and then vaporizes.

    Which explanation do you favor?

    Comment by Barton Paul Levenson — 23 Apr 2007 @ 2:41 PM

  235. #234

    At Earth like temperatures and pressures blackbodies only emit any significant amount of radiation in the Infrared. You can check this, go outside on a dark night.

    If a gas has no significant spectra in the infrared than it does not radiate any significant amount of energy at earth like termperatures and pressures.

    I have never said that the surface does not radiate, quite the contrary.

    I have said that an atmosphere that can not radiate LW radiation, does not radiate LW radiation and at earth like conditions and does not emit any signifcant amounts of SW radiation

    Please explain the mechanism by which you say that it must. Other than that you say so. Or is your augument that the emission is not precisely zero and as miniscule is not precisely zero, you are right and I am wrong, which I have alredy accepted.

    Which state transitions correspond to LW transmissions in noble gases?

    A substance does not radiate simply because it is warm. It does so because it is warm and a mechanism exists. If there is no mechanism by which it can radiate LW radiation then it can not do so. If it is not hot enough to radiate any significant amount of SW then for all intents and purposes (except it seems yours) it is dark. I have accepted that small amounts of SW will be emitted but as the night sky is not aglow with light generated by the atmosphere I do not accept that it makes any material difference to what was a model suitable to aid thinking about generalized atmospheres.

    As I have said; show me some evidence that noble gases emit significant amounts of energy at Earth like temperatures and pressures and I will retract.

    Comment by Alexander Harvey — 23 Apr 2007 @ 3:39 PM

  236. [[I have never said that the surface does not radiate, quite the contrary.]]

    Ah! Now we’re getting somewhere.

    Your original discussion seemed to be saying that without greenhouse gases, heat would be transmitted to the atmosphere by conduction and convection but would have no way to dissipate the energy to space. If it doesn’t dissipate the energy, where does the energy go?

    If your reply is that such an atmosphere would heat up without limit — well, we’re back to Olbers’s paradox. A sufficiently hot atmosphere, whatever its composition, will radiate. It will not have zero emissivity. That’s why dust veils in the way of the starlight can’t explain the dark night sky. With a uniformly bright sky, the dust would heat up until it glowed.

    So would the greenhouse-gas-less atmosphere you describe.

    Comment by Barton Paul Levenson — 23 Apr 2007 @ 3:47 PM

  237. I am afraid that you do not seem to have understood the original posting. Or that I did not make it completely clear.

    The satement: “At equilibrium there would be no net heat exchange at the surface as the atmosphere can not dissipate heat to space.”

    meant no net heat exchange between the surface and the atmosphere. I thought that the obvious heat exchange between the surface and deep space would be understood.

    That said I am still waiting to hear from you a statement about which mechanism noble gases can use to emit significant radiation into space at Earth like temperatures and pressures. I think that this is the crux of your augument.

    Please advise.

    Comment by Alexander Harvey — 23 Apr 2007 @ 5:23 PM

  238. This type of post with some simple math that demonstrates some of the relevant points behind the most important topics is very useful. I welcome this as an easier alternative to reading a textbook on atmospheric science.

    Instead of these types of posts maybe Gavin could go on the Daily Show again! ;)

    [Response: [grin] – gavin]

    Comment by Joseph O'Sullivan — 23 Apr 2007 @ 10:41 PM

  239. [[meant no net heat exchange between the surface and the atmosphere.]]

    What would stop conduction and convection from happening?

    Comment by Barton Paul Levenson — 24 Apr 2007 @ 6:45 AM

  240. Alexander, Actually, your model, as phrased is not physical. All matter radiates at finite temperature–it doesn’t require an atmosphere at all. Moreover, all matter has absorption bands–and that is why the true black body does not exist in nature. So, in the absence of greehnouse gases, the effect would be that light is incident on the surface. The surface absorbs the light and warms. It then re-radiates back into space with a spectrum appropriate to its temperature. This heats the atmosphere, and heat is transported by convection (very effective, by the way) and radiation through the atmosphere and out into space. At equilibrium, input equals output–same as always. Adding greenhouse gases simply changes the spectrum of the light incident on the surface and leaving the atmosphere–it has gaps in the absorption bands. The reason there is a net greenhouse effect is because sunlight peaks in the green, while, the peak of thermal emission from the surface is in the IR. Voila, an extra 30 degrees to make life possible

    Comment by Ray Ladbury — 24 Apr 2007 @ 8:45 AM

  241. Re 239,240

    Well, I understood’s Alexander’s post to be a look at what happens if a dimension of the atmosphere is varied from one extreme to the other (LW opacity), and so will necessarily have unphysical aspects at the extrema but be instructive nonetheless.

    With the (unphysical) simplification that there is no SW absorption within the atmosphere, it seems quite clear that in a perfectly LW opaque atmosphere, essentially all heat flow starts as SW absorption at the surface, flows only by conduction to the air and then convection through the atmosphere, and then is emitted to space only at the top of the atmosphere (which is all troposphere, no stratosphere, mesosphere, or thermosphere). This is assuming of course that the surface and lower atmosphere do not get so hot as to emit in SW – of course, with the simplification of no SW absorption in the atmosphere, it would only be SW emission from the surface, and so all significant heat transfer from the surface to the atmosphere and within the atmosphere would still be conduction and convection. In the opposite extreme, a completely transparent (at both SW and LW) atmosphere, the surface would be (at equilibrium) in radiative equilibrium with SW absorption and LW emission to space. Given that, at equilibrium there could be (in a 1 dimensional atmospheric column, at least) no heat transfer to or from the atmosphere, suggesting the atmosphere would approach by conduction an isothermal equilibrium state. If some atmospheric SW absorption were thrown in, then heat would be conducted downward from an entirely thermospheric atmosphere to the surface, etc…

    This could be expanded in three dimensions – in terms of cross section per unit mass, for example, LW emission/absorption cross section, SW absorption cross section, and SW scattering cross section (for any given surface characteristics – SW albedo and LW emissivity). This would be a simple scenario where the atmosphere is chemically homogeneous, the effects of clouds (if counted) being smeared out, etc…

    Comment by Pat — 24 Apr 2007 @ 10:01 PM

  242. Hi All,

    I do not have a lot of time right now.

    Can I separate things out and deal with just one bit at a time.

    The statement that all matter radiates at finite temperature seems blindingly obvious. But how true is this statement. Can it be used as a maxim?

    To answer this it is necessary to be very careful about what we mean by matter and temperatures.

    At one extreme it is “believed”, not known, that most of the mass of the universe is both warm (estimates of a few degrees to thousands of degrees) yet does not emit any detectable radiation.

    This is highly exotic stuff but is this sufficient to challenge the statement that if it has a finite temperature it “must” radiate.

    Less exotically Helium gas, lacks the normal mechanisms by which gases radiate at room temperature. So does it radiate at this temperature, I do not know for certain. What I know is that “I do not know how it can”.

    I know not the mechanism by which it can.

    Helium detectors use the atoms internal excited states to produce a spectra because of the lack of other excitations (rotation-vibration).

    The energy required to produce a spectra is around 19.8eV (first excitation state). At 300K the energy distribution is centred around ~0.07 eV, less than 1/250th of the required energy.

    Rememering that the energy distribution is dependent on the exponent of this ratio, I think that the chance of a random 19.8eV collision event is very small, possible but very, very small. Even then I do not know if such a collision could be inelastic, I do not know if it corresponds to a permitted transition.

    You see there is a lot that I do not know, but I do know that in order to agree with you and say it must radiate I need to know that it does (a spectra, or a measured emissivity at 300K). Or in the absence of that evidence, sound reasons why, in this particular case, it must. For that I need to know how it can radiate and why it must do so.

    If anyone here can elucidate the mechanism by which Helium gas can, by itself, from only its Helium – Helium interactions, radiate at 300K I would be very much obliged to you.

    I have pointed out what I see to be the difficulties and what makes the noble gases and particularly Helium a special case. Gases do not just radiate, they radiate via mechanisms, permitted pathways.

    I am not saying I am right or that you are wrong.

    If you know that you know that you are right just explain the mechanism or point to the evidence. If you only think that you know then perhaps the matter can not be decided either way.

    Comment by Alexander Harvey — 25 Apr 2007 @ 6:31 AM

  243. Well, that’s all very interesting, Alexander, but we weren’t talking about dark matter or anything exotic; nor were we talking about pure helium (and you’re wrong here, also)–we were talking about a planetary atmosphere. The radiation we are talking about here is blackbody radiation–nothing to do with molecular levels, except as those levels absorb wavelengths out of the blackbody spectrum. As a matter of fact, matter is not necessary at all–space itself radiates as a black body at 3.2 Kelvin. And most black body radiation experiments actually look at emissions from an evacuated cavity. You can read about it here:

    but basically blackbody radiation is a result of scattering between the atoms and the incident radiation.

    Comment by Ray Ladbury — 25 Apr 2007 @ 7:38 AM

  244. Ray, take away all green house gases in the earth atmosphere.

    Would some radiation from the earth be absorbed by the atmosphere? If yes, how many procents? Would the atmosphere radiate something out in the space? If yes, how much?

    I belive that the answers to the above questions it for all practical considerations no. Isn’t that the difference between C_2 and H_2 0 for example? One is transparent for the radiotion from the earth and one isn’t.

    Comment by Fredrik — 25 Apr 2007 @ 7:52 AM

  245. All matter absorbs radiation. Whether there is a significant effect depends on what spectral range the matter has its absorption bands in and whether the radiation source radiates in that range. Earth, being roughly 300 K radiates in the IR predominantly, so the relevant greenhouse gases are H2O, CO2, CH4 etc. On the other hand, if Earth radiated significantly in the UV, Ozone would be a “greenhouse” gas (not to mention that it would be bloody hot!). So, basically, if you take away all the gasses that absorb where Earth radiates, yes, there’d be no absorption of radiation from Earth into space, and aside from effects of albedo (which would be considerable on a frozen Earth), the planet would radiate like a black body.

    Comment by Ray Ladbury — 25 Apr 2007 @ 8:21 AM

  246. Ray,

    Regarding the emission of radiation from a gas: I think that the quantum transitions are critical in determining how a gas absorbs and radiates energy.

    A gas is not a blackbody. Its absorption and emission are in origin discrete. Check HITRANS. I think that this is very important.

    One of the initial puzzles is how a line spectra can result in any significant absorption or radiation. This is allowed for by the broadening of the lines due to natural broadening (Uncertainty Principle), doppler effects and collisions. This results in a continous spectrum in the vicinity of the lines in the unbroadened spectrum.

    Without the line spectra there can be no broadening to produce the characteristic spectra of gases like CO2. My understanding is that in the 300K range the spectral lines are due to a combination of vibrational and rotational quantum state transitions. Which I further believe are absent in Helium gas at atmospheric like conditions.

    How do you think that the absorption/emission spectra are produced?

    You say that I am wrong concerning Helium. If you know how I am wrong, please say so. E.G. characterize the type of radiation and the mechanism.

    I am not the sort of person to be happy with a “it does”.

    Comment by Alexander Harvey — 25 Apr 2007 @ 11:27 AM

  247. Re: #242 (Alexander Harvey)

    My net searches indicate that collision processes can lead to both emission and absorbption or radiation by helium gas.

    Comment by tamino — 25 Apr 2007 @ 12:07 PM

  248. Alexander, you’re aware that helium does emit a characteristic set of spectral lines, right? You’re basically asking why it happens?

    So were these people:

    This might help, if your librarian can borrow a copy for you:

    “A closer look at the spectrum of heliumâ��[The Physics Teacher 36 …
    When observing the spectrum of helium in an introductory physics laboratory, a complete and satisfactory laboratory experience that provides insight into …”

    Comment by Hank Roberts — 25 Apr 2007 @ 12:27 PM

  249. Alexander, you are complicating things far more than they need to be. We’re not talking about atomic transistions at all when we talk blackbody radiation. Rather, we are talking about scattering of light by material. The thermal spectrum of energies of the material gives rise to a characteristic spectral shape determined by the temperature. Yes, the process is quantized, but it has nothing to do with atomic transitions. Read the primer on blackbody radiation. To a first approximation, when it comes to thermal radiation (e.g. blackbody radiation) the material is not important–you still get a spectrum characterized by Plank’s distribution.
    CO2 absorption on the other hand has to do with atomic transitions–specifically vibrational excitations of the CO2 molecule cause by IR radiation.

    Comment by Ray Ladbury — 25 Apr 2007 @ 2:08 PM

  250. Not being encumbered with a plethora of detail knowledge, I’ll try my hand at the sandbox-1 level (with a couple of minor excursions). So-called “blackbody” radiation, covered by the Stephan-Boltzman (you’ll find differing spellings) law is a different physical process (predominately) from the spectra absorption/radiation of say greenhouse gasses. It basically stems from the orbital and vibrational acceleration of electrons and some molecules/ions. Accelerating charges radiate EM waves proportional to their acceleration, which is proportional to their kinetic energy — proportional to their temperature. All matter does this, unless it’s at absolute zero, which none is. (btw, true space doesn’t, but the universe debris floating in near vacuum does, which is the “background” radiation in the microwave bandwidths.)

    Also, the body doesn’t have to be a true “blackbody” to radiate. Anything above a perfect reflector will radiate something. (It’s called “blackbody radiation” because it’s shorter and simpler.) Radiation emission and absorption capabilities are identical, and both are opposite of reflective capabilities for any specific body. Which leads to the complicating exception to the above: perfect reflecting bodies (matter) won’t radiate anything at any temperature.

    The spectra absorption/radiation process is different. Too complicated to explain simply but it has mainly to do with the atomic bonds within molecules and/or differing energy levels of the molecule or its electrons. I’m pretty sure all chemicals/elements are capable here, though some more and some less. Helium certainly does — it’s how we get He spectral lines from the spectroscope.

    Comment by Rod B. — 25 Apr 2007 @ 6:26 PM

  251. TO CLARIFY:

    radiance (or intensity) = irradiance per unit solid angle
    irradiance = power per unit area

    Blackbody radiation as a function of temperature and wavelength is an idealized variation of radiance with wavelength (or wavenumber or frequency) and temperature. The thermally emitted radiation from an actual material in local thermodynamic equilibrium can be measured relative to blackbody radiation – at a given wavelength, or over some band of wavelengths, the emissivity is the emitted radiance as a fraction of blackbody radiance at the same temperature and wavelength. Emissivity can never be greater than 1 when in local thermodynamic equilibrium, or else it would be possible to build a perpetual motion machine and decrease the entropy of a closed system; this is because absorptivity – the fraction of radiance (or irradiance) absorbed – cannot be greater than 1, and emissivity must equal absorptivity when in local thermodynamic equilibrium, or else, again, it would be possible to reduce the entropy of a closed system.

    (Interesting aside – because of total internal reflection, blackbody radiance is also proportional to the square of the real component of index of refraction. That is, a blackbody surface imbedded in glass with an index of refraction of 1.5 would emit into the glass 2.25 times the radiance that it could emit into a vacuum or into air (index of refraction is only slightly above 1). But looking at the blackbody from outside the glass, even with perfect antireflection coating, the radiance seen within the solid angle of visual field covered by the blackbody would be that of a blackbody in a vaccuum or into air, as one is typically more familiar with. The reason – again, if this were not the case, it would be possible with a system of lenses, etc, to break the second law of thermodynamics and decrease the entropy of a closed system.)

    At a given wavelength, any substance which has a nonzero emissivity can be used to construct a nearly ideal blackbody (provided there is no limit of substance available and the amount used is isothermal). This is because:

    Within a substance, if along pathlength of 1 mm, the radiance emitted is 0.001 times blackbody radiance, then along the next 1 mm, the same amount is emitted again, but also the same proportion of radiance from behind is absorbed (or otherwise blocked, if the microstructure has little surfaces mirrored on just one side, for example, with all mirrored sides facing the other way – but you get the idea). Thus after 2 mm, the emissivity along that direction is 0.001 + 0.001 * (1-0.001). Continued to infinity, the emissivity approaches 1; for radiation going in the reverse direction along the path of the same length, absorptivity will be the same as the emissivity.

    Within a cavity, if the walls have an emissivity of 0.001 and thus a reflectivity of 0.999, then following a path from one wall, the radiance is 0.001 times that of a blackbody, but after reflection off another wall, there is an additional emission of 0.001, with an absorption of 0.001 times the radiance previously emitted, so the emissivity after this reflection is 0.001 + 0.001 * (1-0.001). Continued to infinity, the emissivity approaches 1, and going in the opposite direction, absorptivity also approaches 1. Thus the cavity will become filled with blackbody radiation. If a small hole is cut into a wall of the cavity, assuming it is quite small compared to the surface of the cavity, most paths going into the hole will rebound off the inner surfaces of the cavity walls many times before coming back out, so the hole will be like a blackbody.

    Comment by Pat — 26 Apr 2007 @ 4:58 PM


    So, ideal blackbody radiation (which is isotropic, which means the radiance at any angle is indepent of angle, so integrating over solid angle and factoring in the spreading out of radiation accross a surface at higher angles to the normal of the surface,
    blackbody irradiance from a surface = pi steradians * blackbody radiance

    A steradian is a unit of solid angle; there are 2 pi steradians in a hemisphere.


    So, blackbody radiance or irradiance is a function of temperature and wavelength is not a property of any specific material but it sets a limit on what is possible for a material to thermally emit. As temperature rises, the size of energy transitions which may be involved in thermal emission increases; at a high enough temperature, the emission in visible and UV lines of a gas would become significant in thermal emission.


    Ozone is a greenhouse gas; it has an absorption band somewhere around 9 or 10 microns.

    Comment by Pat — 26 Apr 2007 @ 5:10 PM

  253. Ray (240), great post… until you got to “The reason there is a net greenhouse effect is because sunlight peaks in the green, while, the peak of thermal emission from the surface is in the IR. Voila, an extra 30 degrees to make life possible.”

    That made no sense to me. What difference does it make if insolation peaks in the green, yellow, blue or orange, or where in the IR band or even low visible band the earth’s radiation peaks?

    Comment by Rod B. — 26 Apr 2007 @ 8:54 PM

  254. Fredrik (244), gasses are “greenhouse” gasses by definition if they absorb radiation from the earth. No greenhouse gasses = zero absorption. Both CO2 and H2O are greenhouse gasses.

    Comment by Rod B. — 26 Apr 2007 @ 9:08 PM

  255. [[Ray (240), great post… until you got to “The reason there is a net greenhouse effect is because sunlight peaks in the green, while, the peak of thermal emission from the surface is in the IR. Voila, an extra 30 degrees to make life possible.”
    That made no sense to me. What difference does it make if insolation peaks in the green, yellow, blue or orange, or where in the IR band or even low visible band the earth’s radiation peaks?

    Because sunlight, peaking at 0.5 microns, largely gets through the atmosphere to the ground, while terrestrial radiation, peaking at 10.6 microns, is largely absorbed by greenhouse gases. That’s how the greenhouse effect works, and it depends on the fact that carbon dioxide (for example) absorbs very little visual radiation but a great deal of infrared radiation.

    Comment by Barton Paul Levenson — 27 Apr 2007 @ 6:18 AM

  256. Re 253. Sorry for the lack of clarity, Rod. It’s not really the peak of the distribution that matters, but the distribution itself. The point is that there is a lot less energy in the IR in radiation coming in from the Sun (BB temperature ~6000 K) than there is in radiation heading back out to space from Earth (BB temperature ~300 K). I was pointing out that this is responsible for the net positive energy from the greenhouse effect.

    Comment by Ray Ladbury — 27 Apr 2007 @ 7:04 AM

  257. I do not have a lot of time right now, but enough for one last go on gases.

    Bascally, the simpler the structure of a gas molecule the more transparent it is in the 300K region.

    The most transparent are the noble gases (He, Ne, Ar, Xe) next up are the symmetric diatoms (N2, O2, H2, etc.). More complicated molecules like CO2, H20, with their additional modes of vibration are far from transparent.

    Now the noble gases are so transparent that they are used in spectroscopy as filler to increase the pressure in samples without colouring them. They are that transparent. I believe that Xenon is commonly used for this.

    The reason they are transparent is because they lack a mechanism for absorbing or emitting radiation in that region. With out the vibrational-rotational modes of the more complex molecules they simply can not get excited by radiation in 300K region.

    This is, I believe, the essence of why some gases are LW transparent (non-greenhouse) and some are opaque in some parts of the LW (greenhouse gas).

    Now if a gas is transparent to radiation from a 300K source it neither absorbs nor radiates at those frequencies. One implication of this is that a body of that gas can not cool itself by radiating away its energy in comparison to CO2 H2O etc. which can and do.

    If you look at the simplified model that commenced this thread you will see that much of the radiation that leaves earth is radiated into space by the atmospheric greenhouse gases.

    Just to make this clear. I mean radiation produced by those gas molecules due to their temperature, not scattered radiation from the earth’s surface. A cloud of CO2 at 300K in empty space would quickly radiate heat away whereas a cloud of noble gas at 300K simply lacks the vibrational-rotational modes necessary to radiate in that fashion.

    Precisely how low the emissivity of He or Xe is at 300K, I do not know but I suspect it is very, very low indeed. Mention of them is usually confined to a simple “they are transparent in the IR”. There are no 300K spectra for these gases that I can find which as they are used as transparent fillers when measuring other gases is hardly surprising.

    I am not overly complicating things, I believe that it is detail at this sort of level and beyond that allows one to reason about behaviour of gases in a way that assuming they emit radiation by some unspecified mechanism does not. We are not talking blackbodies here, In gases radiation is confined to a small number of specific modes, the energy distribution (translational, rotational, etc.) follows the same laws but the spectrum is in origin a set of discrete lines, limited to the what is permitted by the mechanisms involved.

    Given the importance of the lack of LW transparency of CO2 one might think that the mechanisms involved would be familiar to all. Sadly it seems that the science is widely considered as all too difficult.

    Now you may feel that all of the above is nonsense or unnecessary, I do not. I brought it up precisely because it is counter-intuitive and has important consequences. The one I originally illustrated is that a non-greenhouse gas (one transparent to radiation produced by a 300K source) can neither be warmed by the upwelling radiation nor can it cool itself by turning its internal energy (kinetic) into LW radiation.

    That alone I consider to be sufficiently important to have gotten myself into this wrangle. Hopefully we will all live and learn.

    Comment by Alexander Harvey — 27 Apr 2007 @ 7:18 AM

  258. Harvey, If what you are saying is that an atmosphere of noble gasses will not absorb in the IR, I agree. In that case, the planet would look from the outside like a blackbody except for some weak absorption in the UV, where there isn’t much radiation anyway. In fact, since the solar spectrum is richer in these wavelengths than the planetary spectrum, an “inert” gas atmosphere would a net (though slight) cooling effect.
    Even the simplest model ain’t that simple.

    Comment by Ray Ladbury — 27 Apr 2007 @ 8:46 AM

  259. Mr Ladbury,

    To recap:

    I speculated on the dynamics of a simplified model at each extreme of atmospheric emissivity to radiation from a 300K earth.

    Zero emissivity leads to a very peculiar atmosphere indeed. Being totally transparent to a 300K raditaion source (by definition) it will lack the ability to either gain or lose heat through radiative processes at temperatures around 300K.

    This implies that its only sink for heat will be its contact with the earth’s surface. Once in equillibrium there it would effective be dead thermodynamically and would have no apparent method of sustaining a temperature gradient.

    This was met with some bald “all matter with a finite temperature radiates” statements. I merely pointed out that in order to radiate it must have internal energy and a mechanism. I.E. that matter does not “just radiate”, it radiates if it has internal energy and available transitions. I should perhaps have included that exceptions have to be made for ionised gases but I suspect that this really is not relevant for a noble gas at 300K.

    Now in the 300K region the noble gases are considered to be transparent i.e. they have zero emissivity at the relevant frequencies. So the criticism that such an atmosphere is “unphysical” needed a little challenging. I requested anyone who knew that these gases radiated at 300K to state the relevant mechanism, produce the spectrum, or give the emissivity. I would have certainly have learned something new.

    You alone seem to agree that the noble gases are “for all intents and purposes” transparent to 300K radiation. This requires that they have in effect zero emissivity (in the 300K band). So the model was not all that unphysical after all.

    I only pursued that is point as I consider it important in itself to understand how and why some gases have high emissivities (greenhouse gases) and some low or zero emissivities (at 300K).

    That a volume of noble gas (or a true non-greenhouse atmoshpere) can not cool itself effectively by radiating away its internal energy, seems counter-intuitive but it is I believe the case.

    So a true non-greenhouse atmosphere (zero emissivity) in the original model could lead to some interesting thermodynamics, or should that be lack of them.

    I was only pointing out that atmospheric emissivity is a two way street. It warms the earth surface but also allows the upper atmosphere to radiate into space thereby creating a sink for energy in the upper atmosphere that is a thermodynamic driver for the atmosphere.

    Comment by Alexander Harvey — 27 Apr 2007 @ 10:54 AM

  260. Alexander, I agree that blackbody radiation depends on the ability of the body to absorb radiation. To the degree that it is transparent or reflective, it is not a black body. I think where you got off on the wrong foot was that it was not clear whether you were talking about the entire planet + atmosphere system–which does radiate as a blackbody or just the atmosphere. I think I understand the point you were trying to make now is that the entire atmosphere would be an isotherm–unable to radiate away energy and insulated by the effective vacuum of space. It would not be an isobar, though, so if I’m not wrong it would be stratified and you wouldn’t have convection either. The only activity you would have would be at the boundary between day and night–midnight and noon would be still as death, but dawn and dusk quite active.
    I think where I disagree with you is that you seem to be saying that the only way there’s a sink to space is via radiation of the atmosphere, and in a completely transparent atmosphere, that’s no the case. The radiation goes from surface to space unimpeded, so there’s still a sink, and the surface is in equilibrium with whatever radiation is incident on it. Would you not agree? Or am I misinterpreting what you had to say again?

    Comment by Ray Ladbury — 27 Apr 2007 @ 3:41 PM

  261. Re 260

    I think that’s what Mr. Harvey was saying.

    Re 258

    Atmospheric SW absorption without any LW emission would tend to lead to a thermospheric atmosphere; the absorbed UV heat would still be transmitted by conduction to the surface (when in an equilibrium state).

    Comment by Pat — 27 Apr 2007 @ 4:19 PM

  262. Barton (255), Ray (256) re my 253: O.K.

    Comment by Rod B. — 27 Apr 2007 @ 8:23 PM

  263. If that’s all that Harvey was saying, then I agree, but it seemed to me — maybe I read him wrong — that he was portraying the atmosphere accumulating heat from conduction and convection and then being unable to radiate it, which would imply that it was heating up indefinitely. I also think there was some confusion between the atmosphere by itself and the planet-atmosphere system — even if the atmosphere doesn’t radiate, the planet must, or again, it will heat up indefinitely.

    Comment by Barton Paul Levenson — 28 Apr 2007 @ 4:14 PM

  264. “Once in equillibrium there it would effective be dead thermodynamically and would have no apparent method of sustaining a temperature gradient.”

    I belive this is incorrect. The atmosphere is never in equillibrium due to night and day. The air close to the earth get colder due to conduction with the earth at night, creating on inversions. The sun then warms the air, creating thermals (convection), trying to get the atmospheric adiabatic.

    I see no real difference if the greenhouse gases exist or not except in the radiation energy transfer with the earth. No more reason for a constant temperature atmosphere or an atmosphere without convection.

    Comment by Fredrik — 3 May 2007 @ 4:45 AM

  265. A short question.

    Does the greenhouse gases warm the atmosphere directly from radiation from the earth or sun, i.e. warming/coling not due to convection?

    I belive the answer is no but I might be wrong.

    Comment by Fredrik — 3 May 2007 @ 4:52 AM

  266. [[Does the greenhouse gases warm the atmosphere directly from radiation from the earth or sun, i.e. warming/coling not due to convection? ]]

    Greenhouse gases work by allowing sunlight through to hit the ground, but absorbing infrared coming up from the ground (and from other locations in the atmosphere, e.g. if you model it as a number of horizontal layers). For an overview with a little math — nothing harder than algebra — try

    Comment by Barton Paul Levenson — 3 May 2007 @ 5:43 AM

  267. Thank you for this introductory model. It’s good to know what some of the constants and variables are involved in climate studies. It’s especially gratifying to some of us amateurs who like to tool around with numbers.For example I’ve solved a few of your equations assuming that the Earth had no greenhouse gases in its atmosphere with what( to me,anyway) is an interesting result.
    If lamda(L)( I have no greek letters on my keyboard)=0, also the^ sign stands for an exponent then:
    (1-alpha)TSI/4= (1-L)G =sigmaTa^4 and
    T=( TSI(1-alpha)/sigma)^1/4
    From google: TSI= 1370 watts/m2 (the site shows a statue of James Watt standing on a square meter): alpha=.30 and sigma=5.67×10^-8.
    Solving for T gives 254 kelvins or about -19 degrees C, which is about 0 Fahrenheit!! Cold yes but not too cold for life, such as polar bears or penguins, and perhaps many other species! Please do more of these, Gavin. Regards, Larry

    Comment by Lawrence Brown — 3 May 2007 @ 6:07 PM

  268. Barton I dont think your site answer my question. My question is about convection and how the atmosphere is warming. My understanding from reading meteorology and some thinking (I might be completely wrong though) is that the atmosphere is only warmed by conduction from the ground. The green house gases radiate some energy back to earth and thus change the earth temperature but the radiation from the earth doesn’t change the temperatur of the atmosphere directly much. If that explaination make sense.

    In other worlds. Look at a world with green house gases. Measure the earth temperatur over some time. Take away the greenhouse gases but install some warming of the eart surface such that the earth temperature is identical to before. My question is, do this result in the same atmosphere as before? I belive it does. This is related to Alexander’s thought experiment above.

    Comment by fredrik — 4 May 2007 @ 2:34 AM

  269. [[The green house gases radiate some energy back to earth and thus change the earth temperature but the radiation from the earth doesn’t change the temperatur of the atmosphere directly much. If that explaination make sense. ]]

    It makes sense but it’s wrong. When greenhouse gases absorb energy from the ground, they heat up, and the atmosphere they’re mixed with heats up. If there were no greenhouse gases in the atmosphere, the atmosphere would be colder than it is.

    Comment by Barton Paul Levenson — 4 May 2007 @ 7:00 AM

  270. yes, the atmosphere would be colder. No problem with that. I am interested in where the actual energy transfer happens.

    “When greenhouse gases absorb energy from the ground, they heat up, and the atmosphere they’re mixed with heats up.”

    The green house gases are less than 1% of the atmosphere. The green house gases warms by the radiation but the other >99% of the atmosphere must also be warmed. It needs quite a lot of energy to do that. My quess is that the warming due to the radiation is much much less compared to the warming (energy transfer) due to convection. How much difference in temperature would my thought experiment above result in?
    Does the difference be significant? Measurable?

    Comment by fredrik — 4 May 2007 @ 8:02 AM

  271. Re 268 etc. Fredrik, think of it this way: IR from the surface excites vibrational energy in the CO2 molecule, raising its ehergy, and therefore its temperature. The vibration of the CO2 molecule is weakly dissipated by the surrounding molecules–that is, the rest of the atmosphere damps the vibrational motion, taking up the kinetic energy. You can kind of see this via the equipartition theorem–the energy that goes into any one degree of freedom–kinetic, vibrational, etc. eventually gets shared via all the degrees of freedom. So, whether CO2 is 0.0001% or 100%, you get warming of the entire atmosphere any time one component heats up. Does that help?

    Comment by Ray Ladbury — 4 May 2007 @ 9:38 AM

  272. [[The green house gases are less than 1% of the atmosphere. The green house gases warms by the radiation but the other >99% of the atmosphere must also be warmed. It needs quite a lot of energy to do that. My quess is that the warming due to the radiation is much much less compared to the warming (energy transfer) due to convection. How much difference in temperature would my thought experiment above result in?
    Does the difference be significant? Measurable?

    Sensible heat (conduction and pure convection) heats the atmosphere at the expense of the surface at about 24 watts per square meter over the whole globe. Evaporation contributes another 78 W/m2. But the atmosphere picks up about 350 W/m2 in infrared radiation from the ground, so radiative effects beat other mechanisms by three to one.

    Comment by Barton Paul Levenson — 5 May 2007 @ 7:12 AM

  273. Ray, the time it would take to warm the air should depend on the amount of the green house gases. My quess is that that the time is much longer compared to convection and other air motions. Definitely in the boundary layer, it might be a difference above the boundary layer. Do you have any numbers of the warming?

    Barton, I fly paragliders and have thus a pretty good understanding of air movements in the boundary layer, night time inversions, thermals etc. Your numbers seems to suggest that the heat transfer from green house gases is much more compared to convection. I just dont belive that. I dont remember anything in the meteorology books that suggests that the air warms directly from the radiation. The energy comes from the the contact with the ground and evaporation.

    I might be incorrect because I have limited knoweledge about the subject but your answers just doesn’t convience me.

    Comment by fredrik — 6 May 2007 @ 3:24 PM

  274. Re 273:

    Lapse rate – the rate of temperature decline with height. Generally positive in the troposphere (with some exceptions – inversions near the surface in polar winters and calm clear nights, etc.), zero to negative in the stratosphere, generally positive in the mesosphere and negative in the lower thermosphere.

    Air is gains (or loses in some cases) sensible heat by conduction at the surface; it can also gain by evaporation (or lose – dew and frost) latent heat, which is converted to sensible heat elsewhere by water phase changes, ultimately leading to precipitation.

    Air rising cools adiabatically due to the drop in pressure and resulting expansion (it follows a dry adiabat). Latent heat release during condensation (and freezing) slows the cooling rate, so during such moist convection air follows a moist adiabat. If I understand correctly, the troposphere in general tends to follow a typical moist adiabat
    (with much variation in time and space, but never exceeding a dry adiabatic lapse rate on a sizable scale (there often is such a higher lapse rate only in the immediate vicinity of the ground when the surface is being heated by solar radiation – convection is limited at the ground as it interupts vertical motion, but convection to and from the thin surface layer of air is important) that would lead to instant overturning until the lapse rate is reduced to dry adiabatic)
    because moist convective processes tend to maintain such a lapse rate; an increase in the lapse rate will be more favorable for vertical motion, etc.

    But radiation exchange among the sun, the surface, space, and multiple levels of atmosphere, is quite important. The atmosphere and surface both reflect some solar (SW) radiation back to space; the rest is ultimately absorbed, some in the atmosphere, but a majority at the surface (or within some distance below the surface in bodies of water). There is temperature and wavelength dependent emission of radiation, of the LW kind, by the surface and atmosphere; the limiting value is that of a blackbody at a given temperature – I think the surface is nearly (but not completely) like a blackbody for the wavelengths in the LW band; the atmosphere’s opacity in the LW band varies over wavelength and with the concentration of water vapor, clouds, and ozone (other important greenhouse gasses are much less spatially-temporally variable (in the short term)). For example, there is an atmospheric window between wavelengths of 8 and 12 microns (interupted by ozone around 9 or 10 microns) where a sizable fraction of radiation from the surface can escape directly to space, except where the water vapor concentration is very high.

    Generally, the LW opacity (from absorption and emission – scattering may be a small factor but I think it’s much less important in LW radiation than in SW radiation, and for introductory purposes can be ignored in the LW) of the atmosphere blocks some fraction of radiation from the surface going to space – it absorbs it, and replaces it with it’s own space-bound emission – which is dimmer because the atmosphere is generally colder than the surface; hence less radiation is emitted to space then is emitted by the surface, enabling the surface to be at a higher temperature than otherwise.

    More precisely, some radiation is absorbed and replaced with emitted radiation at each level in the atmosphere, going upward and downward. A higher opacity better enables the colder upper troposphere to block emission not just from the surface but the warmer lower troposphere from going to space – increasing the opacity makes the radiation emitted to space ‘colder’, allowing heat to build up until a new equilibrium is established. (At the same time, the radiation from the atmosphere that reaches the surface will be coming more from the lowest layers of atmosphere, which are warmer).

    But in pure radiative equilibrium, the lapse rate of the lower atmosphere would be very high – convection does not allow such a situation to occur. Instead the climate tends to approach a radiative-convective equilibrium. Convection tends to keep the lapse rate of the troposphere near a moist adiabat; increasing the opacity of the atmosphere causes more of the radiation to space to come from higher up in the troposphere, where it is colder, so the surface and troposphere warm up together to compensate.

    Of course, meanwhile the stratosphere tends to cool because it recieves even less radiation from below while emitting more strongly to space…

    And as the radiation from the atmosphere to the surface is coming from closer to the surface, where it is typically warmer, the net radiative exchange is reduced…at least at first – this effect is couteracted by the nonlinear relationship between temperature and radiation, but is greatly strengthened by water vapor feedback … (See previous comments for more).

    Increasing the greenhouse effect tends to reduce the diurnal temperature range by increasing the radiation from the atmosphere to the surface, which is much less variable over the course of a day than solar heating is.

    Comment by Pat — 6 May 2007 @ 6:21 PM

  275. From
    (Kiehl and Trenberth)
    radiation from atmosphere to surface 324 W/m2
    radiation from surface which heats the atmosphere 350 W/m2
    NET: surface to atmosphere = 350 – 324 = 26 W/m2.

    So getting back to the original point of contention:
    the net heating of the atmosphere by the surface through radiation is smaller then that by convection, and I would expect it to be reduced in response to increased greenhouse forcing (while convective heating of the atmosphere from the surface would tend to increase); but it is not unimportant and is the difference between an upward and a downward radiative flux, each of which is quite large.

    Comment by Pat — 6 May 2007 @ 6:33 PM

  276. Looked through the article and especially figure 7.

    Net radiation from earth to the atmosphere is 26 W/m2 as above but the total radiation to the atmosphere seems to be -102 W/m2. Thus the atmosphere is cooling if only radiation is included. Thus the warming of the atmosphere is only due to convection and latent heat. Ofcourse some of the heat due to convection is going to radiate out into space also.

    Looking at the atmosphere without including the radiation transfer from the atmosphere in all directions much be wrong (or have I missunderstood something) and the numbers given by Pat and especially Barton is missleading.

    “But in pure radiative equilibrium, the lapse rate of the lower atmosphere would be very high – convection does not allow such a situation to occur. Instead the climate tends to approach a radiative-convective equilibrium. ”

    This and the numbers in the article seems to suggest that the atmosphere is actually to warm for radiation equilibrium. A green house atom actually emit more energy than it absorbs. It should be colder but convection/latent heat makes it warmer. Is this correct?

    Comment by fredrik — 7 May 2007 @ 3:29 AM

  277. [[Barton, I fly paragliders and have thus a pretty good understanding of air movements in the boundary layer, night time inversions, thermals etc. Your numbers seems to suggest that the heat transfer from green house gases is much more compared to convection. I just dont belive that. ]]

    Every energy budget for the climate system gets numbers close to what I quoted. For a good review, and another set of estimates (the ones I used above), try:

    You will note that the 12 other studies from 1975 to 1997 that K&T compare to their own all get similar numbers.

    Comment by Barton Paul Levenson — 7 May 2007 @ 6:17 AM

  278. [[A green house atom actually emit more energy than it absorbs]]

    No. Energy is conserved.

    Comment by Barton Paul Levenson — 7 May 2007 @ 6:21 AM

  279. [[radiation from atmosphere to surface 324 W/m2
    radiation from surface which heats the atmosphere 350 W/m2
    NET: surface to atmosphere = 350 – 324 = 26 W/m2.

    And the latent and sensible heat fluxes don’t also get cooled? Let me clue you in on something, Pat — a parcel of atmosphere doesn’t know where its heat came from, and there’s no qualitative difference between heat from convection, heat from conduction, and heat from radiation. Heat is heat. Of the mechanisms which HEAT the atmosphere, radiation dominates. Which is what I said in the first place, and which Fredrik and now you seem to want to deny.

    Comment by Barton Paul Levenson — 7 May 2007 @ 6:24 AM

  280. Fredrik, The atmosphere has to emit more radiation than it absorbs, because that is the only way for the atmosphere to exchange radiation with the vacuum of space, and space is colder than the atmosphere. What greenhouse gases do is absorb radiation near the peak of Earth’s thermal emission spectrum, keeping the atmosphere warmer than it would be if it were a perfect black body. That absorbed radiation is largely why the atmosphere is warmer than a radiative equilibrium would make it. Within the atmosphere, heat is exchanged by conduction, convection and radiation. It is only at the boundary of space that radiation becomes dominant.

    Comment by Ray Ladbury — 7 May 2007 @ 6:39 AM

  281. First I have to admitt that I dont really understand the whole system right now.

    Some comments anyhow.

    Most analysis and comments here assume that the atmosphere is in equlibrium, i.e. the net energy transfer for for example the ground is zero. This is almost never the case. The ground temperature almost always change. The same is true for most of the troposphere.

    It is true that you cant just talk about radiation by itself as I did. That was a misstake. The atmosphere is going to radiate depending on it’s temperature independent on why the temperature is at that value.

    My question could probably be posed better by noting that I am interested in the change around a mean value of tempereature in the atmosphere. The greenhouse gases make the atmosphere much warmer compared to an atmosphere without greenhouse gases but I was interested in the diurnal variations.

    “[[A green house atom actually emit more energy than it absorbs]]

    No. Energy is conserved.”

    The energy is conserved but my statement is true if the atom isn’t at equlibrium and I should say that the atmosphere almost never is at equlibrium.

    It is also true if the atom get some energy from some other source than from radiation, for example due to convection.

    My question is something like this. Does the air outside the boundary layer (i.e. no convection) change temperature as a function of change in radiation from the earth (or sun) for a clear high pressure day and night?. If that is the case how much? The radiaten should be different for the day and night but I dont think I have seen anything about a change in temperature at for example 5000 meters altitude.

    Comment by fredrik — 7 May 2007 @ 8:28 AM

  282. Fredrik, Ever spend the night at 5000 meters altitude. If so, you would have your answer–it gets bloody cold. Even during the day, the air is chilly. I remember hiking to Everest base camp, being sick as a dog and curling up on a rock to warm up. During the day, sunlight radiates through the atmosphere and is absorbed by Earth. Earth warms and radiates in the IR, and both incoming and outgoing radaition pass through the atmosphere. Moreover, air in contact with the warm rock heats up and convects, taking that heat with it. Thus, despite being transparent to most of the radiation, the air is near equilibrium with the ground. At night, most of the radiation comes from the warmed Earth itself, and some of this is absorbed by ghg molecules. If you are talking about the atmosphere far from Earth, where convection is negligible, it is mostly transparent to radaition, except in certain bands–e.g. absorption bands for CO2, H2O, etc. Thus, at these altitudes, the atmosphere won’t be in thermal equilibrium with the radiation.

    Comment by Ray Ladbury — 7 May 2007 @ 8:59 AM

  283. ” If you are talking about the atmosphere far from Earth, where convection is negligible,”

    Yes, outside the boundary layer.

    “it is mostly transparent to radaition, except in certain bands–e.g. absorption bands for CO2, H2O, etc. Thus, at these altitudes, the atmosphere won’t be in thermal equilibrium with the radiation.”

    Why want it be in thermal equilibrium? Thought you tried to explain to me in post 271 that the energy actually should be shared by all air molecules and equlibrium should thus be achived?

    ” The atmosphere has to emit more radiation than it absorbs, because that is the only way for the atmosphere to exchange radiation with the vacuum of space, and space is colder than the atmosphere.”

    Guess we are talking mean values here.
    Wouldn’t the atmosphere actually get warmer if this was true (if the convection/latent heat is included)? Why should the temperature of space matter?

    Comment by fredrik — 7 May 2007 @ 9:26 AM

  284. Fredrik, In order for it to be in thermal equilibrium, it would have to absorb the radiation (i.e. a black body), but it is transparent to most of the radiation. So, it can’t be in thermal equilibrium.

    OK, think of the atmosphere as this thin layer of gas between a warm sphere of rock that is heated by the sun (on one side) and the inky blackness of space on the other. On the sun-facing side, we have a lot of radiation, but the atmosphere is mostly transparent to it. Likewise for the longwave radiation from Earth. The atmosphere only absorbs where it has absorption lines–due to vibration (e.g. CO2 in the IR), rotation, and electronic levels. The rotational and vibrational levels can exchange energy mechanically during collisions with other molecules. Even the absorption and emission of radiation involve a change in momentum, so to some extent there is exchange between the different atoms, but there is a lot of radiation the gas molecules just don’t see. Make sense?

    Comment by Ray Ladbury — 7 May 2007 @ 9:48 AM

  285. Re 279 – Barton Paul Levenson – I think you misunderstood my intent; I agree that radiation exchange between the atmosphere and surface is quite important. Perhaps I wasn’t clear, but I did my best to explain a lot in a small space.

    Re – recent discusion:

    True, at any given location and time, equilibrium may not been achieved. Much of this discussion has pertained to the behavior of a 1-dimensional column model under time-averaged solar forcing, which nonetheless is a good place to start.

    Locally, any atmospheric column will often be out of equilibrium as cold air is advected here and warm air is advected there and the optical properties are altered as clouds and humidity and aerosols and ozone come and go and vary. But the resulting imbalances tend to drive the system toward equilibrium – a warmer layer of air will tend to cool by radiation to cooler layers of air above and below (and to the degree that the air above or below is not perfectly opaque, a warmer layer of air will cool more rapidly to the space, and to the surface if it is warmer then the surface, otherwise if it is still cooler than the surface, it will have a net radiative heat gain from the surface but it will not be warmed by the surface as rapidly as it would if it were cooler); in some conditions convection will adjust the temperature profile. It will be a dynamic equilibrium if ever achieved, and an equilibrium which is a diurnal oscillation (ie four dimensional equilibrium – if that is a valid concept (the idea being that the temperature distribution could settle into a daily cycle) – a climatic equilibrium surely must be considered this way over the course of a year…)

    ‘Locally’ above is distinctly different from ‘local’ in the context of local thermodynamic equilibrium. Local thermodynamic equilibrium is usually applied on a much smaller scale and describes a state in which the distribution of energy among states in populations of particles is in dynamic equilibrium – and consequently, for example, any subgroup of molecules of sufficient size will have the same temperature as any other such subgroup. The vast majority of the atmosphere (at least by mass) is quite close to local thermodynamic equilibrium.

    The amount of radiant energy absorbed by a parcel or layer of air can certainly be different then the amount emitted – this occurs when radiative equilibrium is not achieved. But the absorptivity and emissivity – fractions of properties with respect to an ideal blackbody – are the same in local thermodynamic equilibrium.

    The troposphere generally on average is in radiative-convective equilibrium – radiative transfer by itself is not in equilibrium even on average – more radiant energy is emitted then absorbed by radiation. In a single column model the stratosphere and above would tend to reach radiative equilibrium as convection would not penetrate to or through those levels.

    Radiative solar heating per unit mass is generally greatest at the surface (on land, anyway) because radiation is absorbed over a small distance, and in the upper atmosphere because of the ozone layer and because the greatest amount of solar radiation available is at the top of the atmosphere, before any is absorbed (scattering complicates things but the distribution of solar heating is still generally as described). In the troposphere, water vapor and clouds absorb some solar radiation. As solar radiation varies between day and night, the most rapid temperature responses occur at the surface (and consequently near the surface) on land and in the upper atmosphere. A larger diurnal temperature range does not occur away from the surface in the troposphere, but a larger diurnal range can be expected in higher surface elevations because there is less atmosphere above and thus there will be less downward radiation from the atmosphere (which itself has a smaller diurnal temperature range) because it is colder because there is less of a greenhouse effect and also directly from the smaller greenhouse effect perhaps because of less pressure broadenning of the absorption/emission bands, etc… and depending on aerosols, humidity, and cloud cover, less solar radiation may be absorbed before reaching the surface in regions of high elevation, thus making the diurnal cycle of solar heating greater…

    In pure radiative equilibrium the lowermost troposphere and surface would be warmer but the upper troposphere would be cooler than it is with convection.

    Comment by Pat — 7 May 2007 @ 6:22 PM

  286. A Spreadsheet for the Simple Model

    To get a clearer idea of the principles behind the simple model, I created a spreadsheet which calculates the positive feedback as radiation is absorbed by the surface, emitted by the surface and either reaches space or is absorbed by the atmosphere, then emitted by the atmosphere either back to the surface or to space. The positive feedback is between radiation absorbed by the surface and emitted then absorbed by the atmosphere then emitted and absorbed by the surface. At each step in the process, the temperatures of both the surface and the atmosphere are calculated, and likewise the difference between radiation entering the system and radiation leaving the system are calculated. The positive feedback effectively comes to an end when this difference is reduced to zero.

    Because this is a spreadsheet, the user can examine the formula, and assuming they export a copy as an Excel file(File->Export->Excel), modify the values within the input region.

    One of the benefits of expressing the model in this manner is that the user can view this as steps, recognizing the positive feedback which lies at the foundation of the equality between radiation entering and leaving the system. Likewise, once the user recognizes the positive feedback, they will necessarily realize that such feedback does not necessarily lead to any form of runaway effect.

    Let me know what you think…

    Comment by Timothy Chase — 7 May 2007 @ 9:28 PM

  287. PS

    Here are the equations for the feedback…

    1. In: Si = TSI*(1-a)/4

    For each generation, Si=Si-1, that is, the same amount of thermal flux is entering the surface-atmosphere system from the sun. All other indexed variables are zero when the index is equal to 1.

    2. Surface: Gi = Si-1+Ai-1
    3. [Surface to Space]i: (1-λ)Gi-1
    4. [Surface to Atmos.]i: λGi-1
    5. [Atmos. to Surface]i: Ai = (1/2)[Surface to Atmos.]i-1
    6. [Atmos. to Space]i: Ai = (1/2)[Surface to Atmos.]i-1
    7. [Out to Space]i = [Surface to Space]i+[Atmos. to Space]i

    Feedback effectively stops when [Out to Space]i = Si

    … that is, there is no additional feedback once thermal flux entering the surface-atmosphere system is equal to thermal flux leaving the surface-atmosphere system.

    Comment by Timothy Chase — 8 May 2007 @ 12:26 AM

  288. Pat, good posts, thanks.

    “Radiative solar heating per unit mass is generally greatest at the surface (on land, anyway) because radiation is absorbed over a small distance”

    Isn’t the main warming close to the ground due to conduction with the ground and micro convection and not from radiation?

    Comment by fredrik — 8 May 2007 @ 2:14 AM

  289. Re 288 – “Isn’t the main warming close to the ground due to conduction with the ground and micro convection and not from radiation?”

    Well, first, when I wrote “Radiative solar heating per unit mass is generally greatest at the surface (on land, anyway) because radiation is absorbed over a small distance”, I meant the radiative heating of the surface itself. On an asphalt surface, radiation is absorbed within a very short distance. Less so in a forest, where absorbtion is distributed from the canopy to the forest floor, but generally, for SW (solar) radiation absorption at least (and generally for LW too I think), absorption (and emission) at the surface is concentrated over a smaller mass than absorption and emission within most of the atmosphere (except for deep water surfaces in part of the SW spectrum), so radiative variation tends to cause greater temperature variation at the surface then elsewhere outside of the thermosphere (very very small mass of air that absorbs some of the shortest wavelengths of solar radiation). (Cloud boundaries would also be regions of relatively concentrated absorbtion or emission, at least relative to the surrounding air.) Air near the surface, via conduction and convection within the boundary layer, effectively adds some thermal mass to the surface but not enough to completely cancel the effect.

    At any given level in the atmosphere, there is SW (solar) radiation going down and up (from backscattering/reflection), LW (emitted by the surface or atmosphere) radiation going down and up, and sensible and latent heat fluxes up and down. Subtracting upward and downward fluxes yields (on average) a positive net downward solar flux, positive net upward LW flux, and positive net upward sensible and latent heat fluxes. The rate of change with height of the flux represents either a flux convergence or divergence – meaning some net gain or loss. In the troposphere, on average there is a net gain from the convective fluxes (sensible and latent heat) which on average balances the net loss from radiant fluxes.

    Upward and downward radiant fluxes may largely pass through a thin enough layer of atmosphere, so either absorption or emission from a thin enough layer may be quite small. In contrast, the sensible and latent heat is contained within the air and in a sense is entirely gained and lost simultaneously by a layer through which a a sensible and latent heat flux passes.

    So in a thin layer near the surface, atmospheric heat gain from the surface is dominated by conduction and convection, not radiation, but most of that gain is lost to layers above by convective fluxes… and the net gain of sensible and latent heat will be, on average, equal to a net loss by emission of radiant energy, which itself will be the difference in absorption and emission, etc…

    To make a long story short, both convection and radiation are important in the troposphere.

    Comment by Pat — 8 May 2007 @ 9:32 PM

  290. [[Isn’t the main warming close to the ground due to conduction with the ground and micro convection and not from radiation? ]]

    No matter how many ways you phrase this question, the correct answer will continue to be “no.”

    Comment by Barton Paul Levenson — 9 May 2007 @ 5:48 AM

  291. It seems to be a difference between climatologists and meteorologists. The climatologist talk alot about radiation and meteorologist more or less “ignore” the influence of radiation in the atmosphere except the absorbation at the ground. I am not completely sure about this though and I am going to go to the library and look trough some meteorology books but that is atleast what I remember from reading before. I dont know if the difference is the time scale involved.

    “So in a thin layer near the surface, atmospheric heat gain from the surface is dominated by conduction and convection, not radiation, but most of that gain is lost to layers above by convective fluxes…”

    Yes, this is the mixing of the atmospehere. The air close to the ground heats by conduction and micro convection. Making a layer with a nice name that I dont remember. This layer became super adiabatic and thus unstable and give rise to thermals. This phenomenon continues during the day making the convection go higher as the earth warms. This makes the boundary layer dry adiabatic and moist adiabatic above the cloud base. Thus the air in the whole boundary layer warms by conduction by this mechanism. Some might also be warmed by radiation but the effect seems to be so small as meteorologist with expertise in the boundary layer ignore it (atleast in their explainations. The boundary layer called be several thousand meters thick so it is a lot of the atmosphere that is warmed.

    The air close to the ground is cooled at night making a night inversion. I have never seen anyone claim that this is due to radiation but that it is due to conduction with the ground.

    The temperature close to the ground change a lot between day and night. The temperature above the night inversion warms sligtly during the day due to convection. The air above the boundary layer is pretty constant.

    I dont think this can be explained by radiation.

    My scenario was for fair weather blue weather days or with small cumulus clouds.

    “and the net gain of sensible and latent heat will be, on average, equal to a net loss by emission of radiant energy, which itself will be the difference in absorption and emission, etc…”

    The energy transfer in the boundary layer seems to be dominant by convection so I am not sure this is the case.

    Comment by fredrik — 9 May 2007 @ 6:48 AM

  292. “No matter how many ways you phrase this question, the correct answer will continue to be “no.” ”

    I am not going to trust your no without any explaination anytime soon. I looked at your homepage and nothing on it seems to suggest that you are any authority on climate science or science in general. So why should I trust you?

    “[[Isn’t the main warming close to the ground due to conduction with the ground and micro convection and not from radiation? ]]

    Take a look in any meteorolgy book and this how they explain the warming of the air close to the ground. The ground is clearly warmed by raditation if that wasn’t clear but the air close to the ground isn’t mainly warmed by radiation. To be clear, I talk about the diurnal warming. Why is it much warmer 15.00 compared to 07.00. Not the mean value.

    Comment by fredrik — 9 May 2007 @ 8:00 AM

  293. Fredrik,
    Conduction is not that effective for heat transfer without convection to cause circulation–likewise radiation. All three processes are important. Air in contact with the ground warms by conduction, but then rises due to its lower density, transporting its energy to the cool air above and cool air takes its place. Likewise, over the ocean, evaporation of water transports lots of energy upwards as latent heat. All these processes are necessary.
    Conduction warms by contact. Without convection, it would not be effective. And radiation does transport energy to all levels of the atmosphere. It does not make sense to look at any of these mechanisms in isolation.

    Comment by Ray Ladbury — 9 May 2007 @ 8:39 AM

  294. Frederik wrote (#291):

    It seems to be a difference between climatologists and meteorologists. The climatologist talk alot about radiation and meteorologist more or less “ignore” the influence of radiation in the atmosphere except the absorbation at the ground. I am not completely sure about this though and I am going to go to the library and look trough some meteorology books but that is atleast what I remember from reading before. I dont know if the difference is the time scale involved.

    This isn’t a matter of disagreement, but a matter of context.

    Meteorologists are concerned with what specifically happens in the next few days, weeks or months on the outside. They can take the total amount of thermal energy in the earth-atmosphere system more or less for granted, given the timescale of their concerns. Climatologists are concerned with the average behavior and variability of the system over years or decades rather than the specific behavior over the next few days. For climatologists, it matters whether or not the amount of thermal energy within the system is increasing over time. The more thermal energy, the higher the temperatures tend to be, and in terms of the trends for average behavior and variability, this has fairly predictable consequences.

    When will a given iceshelf collapse? How soon will the next major outgassing of a methane hydrate take place? These are specifics at a lower scale of resolution than climatologists are generally capable of. It wasn’t that long ago that climate models reached the resolution at which they could handle hurricanes, and tornadoes are still at too small a scale. But climate models have improved a great deal within the past few decades, particularly since the NEC Earth Simulator, and they will continue to do so in the next few years. We are getting a much clearer picture of where this is headed.

    Comment by Timothy Chase — 9 May 2007 @ 11:09 AM

  295. People keep coming in with this same question over and over.
    I keep asking them where they’re getting their information and why they rely on it.
    I haven’t ever gotten a clear answer to how this idea keeps being promoted, where they find it.
    But it’s been such a steady flow of new names with the same, simple, wrong idea coming in here, saying how radiation can’t be important, so the whole theory about CO2 is wrong, it has to be conduction and convection.

    I’m convinced it’s a talking point on one of the PR sites for Western Fuels, or one of the political sites.

    Please, someone, where are you getting it? Who’s being so successful at fooling new readers that they come to RC believing this stuff and then spend large amounts of time insisting the science is missing their ‘fact’?

    Comment by Hank Roberts — 9 May 2007 @ 11:10 AM

  296. [[“No matter how many ways you phrase this question, the correct answer will continue to be “no.” ”
    I am not going to trust your no without any explaination anytime soon. I looked at your homepage and nothing on it seems to suggest that you are any authority on climate science or science in general. So why should I trust you?

    Don’t trust me. Do some basic reading in the field. Read the article at the link I provided, which is where I got my figures. Read John Houghton’s “The Physics of Atmospheres” (3rd edition 2002), or Grant W. Petty’s “A First Course in Atmospheric Radiation” (2006). I’m not saying anything that isn’t said by every climatologist I’ve ever come across in the literature. Your a priori commitment to convection being more important than radiation in heating the atmosphere is just making you into a crackpot. Educate yourself!

    Comment by Barton Paul Levenson — 9 May 2007 @ 4:25 PM

Sorry, the comment form is closed at this time.

Close this window.

0.522 Powered by WordPress