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Estimating the impact of CO2 on global mean temperature

  1. Apr 15, 2009 #1


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    In another thread (see [post=2155677]msg #17 of "Only dirty coal can save the Earth"[/post]), user Bystander suggested I lay out more carefully for critical examination the physical basis for the impact of CO2 on climate, so that the assumptions can be seen clearly. This is an excellent idea, and here is my attempt.

    This post is a calculation, cited to the literature as forum guidelines advise, quantifying the importance of CO2 to climate. It aims to be transparent, so each step in the calculation is clear and assumptions can be identified.

    There's nothing here that is scientifically original or unusual. I am not attempting to cover every factor impacting climate, nor a full account of every period of history. I show that the impact of CO2 is physically bound to be significant in the present. There are other factors, both positive and negative, known and unknown. CO2 is one of the simplest. Its impact is basic physics, and necessarily a major contributor in recent decades.

    This thread is not intended to take up every point of climate on which there is disagreement. I am specifically addressing quantification of only one of the many factors involved, to show that CO2 is necessarily significant in the present. I request that we maintain that primary focus, and leave detailed discussion of other aspects of climate science to other threads.

    Any point here can be expanded upon as needed. I will defend it vigorously as elementary physics. In my view, and in the view of nearly all scientists working on climate, popular disbelief on this specific point is poorly founded, and supported with bad science. But I will engage disagreement on that with civility and respect, and questions are certainly welcome. I will deal with objections on their own merits, and not by belittling people good enough to come and join in the thread. Be welcome, be comfortable, and for some of you -- be challenged!

    The short form

    Here's the sequence in summary form.
    \textrm{Energy balance} & \approx 239 & W/m^2 & \textrm{(energy }\text{flux to, and from, space)} \\
    \textrm{CO2 forcing} & 3.7 & W/m^2/2xCO_2 & \textrm{(change to balance per doubling)} \\
    \textrm{Current CO2 increase} & 2 & ppm/year \\
    \textrm{Current 2xCO2 per year} & \log_2(1+2/385) = 0.0075 & 2xCO_2 / year & \textrm{(using 385ppm for current levels)} \\
    \textrm{Climate sensitivity} & 3 \pm 1.5 & K/2xCO_2 & \textrm{(Temperature response for forcings, to restore balance)} \\
    \textrm{Temperature impact of CO2} & 0.022 \pm 0.011 & K/year & \textrm{Estimated contribution of CO2 to current warming trends}\end{array}

    This is a very conventional way of evaluating climate impacts in science. What follows is a brief explanation of the steps, with citations for the numbers and methods.

    (1) Energy balance

    Earth absorbs about 239 W/m2 from the Sun, accurate to within a couple of percent. This is a global annual average, corresponding to a mean for the whole planet on the time scale of a couple of years, in Watts per square meter.

    All of that energy has to go somewhere. Almost all of it is radiated back into space as IR thermal radiation. A small excess can be taken up with Earth's own finite internal stores of energy. The largest available internal store is the heat capacity of the ocean, and recent research indicates that a bit under 1 W/m2 is currently being absorbed into the ocean, as it gradually increases in temperature. This is large by comparison with what is normal for the Earth. The flux into the ocean is known with about 20% accuracy at best; a recent published estimate is 0.85 +/- 0.15 (Hansen et al 2005).

    (2) The atmosphere

    Earth's atmosphere is the reason why temperatures here are on average so much higher than on our airless moon.

    The Earth's surface is radiating something like 390 W/m2 as IR radiation from the surface, known to within a couple of percent. Most of that ends up heating up the atmosphere, which then sheds heat into space. On top of that, thermal convection and heat of evaporation transfers almost another 100 W/m2 into the atmosphere from the surface. Most of the Earth's thermal radiation into space actually comes from the atmosphere.

    The atmosphere radiates in all directions, and on average something like 330 W/m2 ends up coming back down to the surface. The net flow of energy is thus something like 60 to 70 W/m2 radiant energy leaving the surface, plus the additional 100 or so W/m2 as convection and latent heat. This is what balances with the energy absorbed at the surface, from the Sun.

    Here is a recently published diagram, summarizing how energy flows at present between space, the surface and the atmosphere (Trenberth et al, 2009).

    (3) Forcing the energy balance.

    Temperature is governed by the flow of energy. The Earth's temperature is at a level that keeps a balance between energy received from the Sun, and emitted back out to space. There can be a small imbalance while excess energy is absorbed or released into the oceans. As equilibrium is reached, the whole planet has average temperatures sufficient for energy balance between solar input and thermal emission back out to space.

    If anything occurs to upset the balance, such as a change in the Sun, or in Earth's albedo (reflection), or the atmosphere's composition (absorption), then the temperature of the Earth will respond until the balance is restored. An increase in energy flowing inwards will heat up the surface; and an increase in energy flowing outwards will cool the surface.

    A forcing is defined as a change to the energy balance at the top of the troposphere, before balance is restored by changing temperatures. This definition is useful, because the temperature response to different forcings depends mainly on the magnitude of the imbalance, and not so much on how it arises. (Ramaswamy et al 2001)

    (4) The forcing of carbon dioxide

    Many factors for climate are hard to quantify, but carbon dioxide is one of the most straightforward. The impact, as a forcing, can be calculated. The effect is approximately logarithmic, meaning that the magnitude of the forcing depends on the factor by which concentrations increase. Doubling of concentration is a wildly used benchmark.

    The method of calculation is as follows. The atmosphere is treated as a column of gas, with a longwave input at one end (the surface), and short wave input at the other (the Sun). Using the known absorption spectra of gases in the atmosphere, the calculation proceeds line by line through the spectrum to calculate how much radiation is transmitted and absorbed and emitted all along the atmospheric column. The end result is a profile of radiative heating and radiation flux, with a power spectrum of longwave emission at the top, and another for backradiation and solar transmission at the bottom. The calculation is repeated for different gas concentrations, and different conditions. With higher concentrations, the backradiation increases and the emission at the top drops. The forcing, by definition, corresponds to the change in longwave emission at the tropopause.

    A standard reference for the calculation is in Myhre et al, (1998). The forcing for any doubling of CO2 is about 3.71 W/m2, or 5.35 per natural log. This is known to high precision for well defined conditions, and to about 10% accuracy in general for the Earth. That is, doubling CO2 in the atmosphere results in 3.7 W/m2 less IR emission escaping into space… until the surface heats up sufficiently to restore the balance.

    It is a common convention in the literature to use 2xCO2 as the unit for forcing, rather than W/m2. There are good reasons for this, which are a bit beyond the scope of the post. Essentially, it is because the energy imbalance definition has about five different forms when you really nail it down, whereas doubling of CO2 concentrations is comparatively unambiguous, with a straightforward radiative impact.

    (5) The temperature response to forcing -- climate sensitivity

    If nothing changes other than temperature, the response is straightforward. Emissions in general are proportional to the fourth power of temperature, and on Earth, with surface temperatures of about 288K and emissions to space of about 240 W/m2, we get about 0.3C for each W/m2 forcing. You can nail that down more carefully, but it does correspond closely to what you get with a radiation transfer calculation. It's called the "Planck response" in climate science. Converting forcing units, this corresponds to about 1.1C per 2xCO2.

    In reality, when you change temperature, all kinds of other things start to change as well, someone of which then have an impact of their own on the energy balance. This is called "feedback", and it means the climate response may be amplified, or damped. Several important feedback mechanisms are known (humidity, cloud cover, lapse rate, ice-albedo) and there have been attempts to quantify them. There are both positive and negative feedbacks involved, though the positive feedbacks are stronger. That is, the climate response in reality is rather more than 1.1C per 2xCO2.

    For this post, I will use observational constraints. The question is, what is the temperature response in degrees per unit forcing? This is called climate sensitivity, and it can be estimated with data for known episodes of climate change.

    One line of research has been study of the brief episode of global cooling that follows a large volcanic eruption. Wigley et al (2005) study a number of eruptions, and three in particular where the data allows estimates of climate sensitivity. The estimates in K/2xCO2 (with 2σ confidence limits) are 2.83{1.28 .. 6.32}, 1.54 {0.3 .. 7.73} and 3.03 {1.79 .. 2.59}. Sensitivity has also been constrained by a number of other cases, most especially the last glacial maximum some 20,000 years ago. There is quite an extensive literature on this, and nearly all of it continues to estimate sensitivity in the range of about 2 to 4.5C. A useful survey and attempt to combine estimates is by Annan and Hargreaves (2006). A very few isolated papers propose lower sensitivities, but these invariably are flawed by plainly identified methodological problems.

    Sensitivity is a genuinely open research question with considerable uncertainty. It is, by far, the largest source of uncertainty for the conclusions of this post. I submit that climate sensitivity is very likely in the range 2 to 4.5 K/2xCO2, and highly unlikely to be less than 1.5.

    (6) The contribution of CO2 to modern warming

    We have quite a good idea of atmospheric CO2 levels in recent history. Pre industrial levels are about 280 ppm, and current levels are about 386 ppm. The current rate of increase is about 2ppm/yr.

    For any change in CO2 concentrations from A to B, the corresponding change in temperature is going to be S*log2(B/A), where 1.5 < S < 4.5 is the climate sensitivity. You can also use Se*Ln(B/A), where 2.2 < Se < 6.5, which will be easier for most calculators. Best estimate is S=3, or Se = 4.3.

    For example, over recent decades the rate of increase of CO2 has been around about 2ppm/year, on top of about 385ppm. The corresponding contribution of CO2 to rising temperature is about Se*Ln(387/385), which is in the range 0.011 to 0.034 C/year, with a best estimate of 0.022 C/year.

    Direct measurements indicate that globally averaged surface temperatures on Earth are increasing in recent decades, at around about 0.02 C/year. (Brohan et al, 2005)

    There are many factors that must be involved in any credible account of the causes for rising temperatures. It is certainly not driven by CO2 only. The calculations here demonstrate that CO2 is necessarily an important factor, and may help show why it figures so prominently in the scientific literature for modern global climate.


    In order to keep discussions grounded in legitimate science, the Earth forum requires sources to be peer reviewed. I have therefore given a more than usually thorough list of references for the numbers used in this post.
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 18, 2009 #2
    Hi Sylas,

    What you state above is a simplification of the physical problem.

    It is not a fact that a doubling of CO2 will increase forcing by 3.71 W/m^2. Why do you make that statement?

    The consensus is the lower atmosphere is saturated from the standpoint of direct heating effects of CO2. Adding more CO2 to the lower atmosphere will not result in higher surface temperatures.

    The CO2 warming is hypothesized to occur in the upper atmosphere, however, upper atmosphere temperatures have not increased as predicted by the models. A second indication that something is incorrect (GCM vs physical system) is that in the past CO2 levels have been high when the planet was cold and low when the planet was warm.

    It appears based on measurements that something is incorrect with the basic modeling assumptions.
  4. Apr 18, 2009 #3


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    Thanks for joining in Saul. I was getting worried that no-one would be interested! I'm going to disagree with you (as promised :wink:) but I appreciate the chance to go over some common points of popular dispute!

    Because it is a fact. I gave the reference, and you can find plenty of others that give similar figures. It's a physical inevitability, given the nature of how CO2 interacts with thermal radiation, and we can demonstrate it with some calculations of radiation transmission in the atmosphere. I'll give a pointer to a suitable calculator here, and a worked example for doubled CO2.

    That's incorrect. As far as the physics is concerned, adding CO2 inevitably leads to higher surface temperatures. The real question is how much. We know the forcing pretty well, but the sensitivity is not as well known.

    When you speak of "saturation", the proper use for this term is radiative transfer; not temperature. We say that a part of the spectrum is "saturated" if the atmosphere is opaque in that band; that is, if all the light in that band of the spectrum is completely absorbed.

    There is a consensus -- or better, it is a basic fact of life -- that CO2 interacts with some wavelengths of light and not others; and that for most of the spectrum, the atmosphere is either saturated at those wavelengths, or else it is a band where CO2 is transparent.

    If that was universally the case at every wavelength, independent of concentration, then it would be true that adding more CO2 would have little effect. The impact of additional CO2 arises because as you add CO2, the bounds of the saturated bands shift a little bit. This is a general effect not limited to CO2, or to Earth's atmosphere. There is additional absorption in the "wings" of the absorption region, and this is the major cause of the forcing.

    There are a number of tools available for looking at absorption spectra. I'll use an http://geosci.uchicago.edu/~archer/cgimodels/radiation.html [Broken], made available at the University of Chicago, which uses much the same techniques as in the paper I cited above, (Myhre 1998). It is not as accurate as fully up to date calculations, but it is able to run quickly for an on-line server, and thus makes a useful pedagogical tool. You can try this yourself as well.

    First of all, here is a spectrum for a 1976 US-standard atmosphere profile. CO2 levels are set to 375 ppm, no rain is considered, a surface temperature is set to 288.20K (about 15C) and the result is the spectrum you see coming up from the surface with a detector at an altitude of 20km (roughly the tropopause).
    I've labeled three parts of the spectrum in this diagram, to illustrate how it works.
    • A saturated band. The spectrum here follows close to a 220K blackbody, which corresponds to radiation from the top of the atmosphere. The atmosphere is opaque at these wavelengths.
    • A transparent band. The spectrum here follows a bit above the 280K blackbody, which corresponds to radiation from the surface. The atmosphere is transparent at these wavelengths.
    • A partial absorption band. The absorption here is nearly all H2O; CO2 is transparent in this part of the spectrum. H2O is not evenly distributed in the atmospheric column, which is part of the reason the spectrum fits neither surface temperatures nor top of the atmosphere temperatures. CO2 is much easier to handle in the calculation.
    In this spectrum, the total outgoing energy flow is 258.893 W/m2.

    Now here is the spectrum calculated for the same atmosphere, but with 750ppm CO2. It looks almost the same; so I've done an overlay of the 375 spectrum on the right, to help compare. You can see that the 750 CO2 spectrum absorbs a little bit more radiation along the wings of the main saturated band; enough to reduce the outgoing energy by a little over 1%. Outgoing radiation this time is 255.470 W/m2. The difference is 3.423 W/m2; close to what is obtained by the more precise calculations used in the literature. You should get similar differences when you try other atmospheric profiles or conditions, and double the CO2.
    Since I am not an expert in my own right, you are well advised to check up further from more authoritative sources, such as any undergraduate level text on atmospheric radiation. They should all deal with the concept of absorption in the wings of a saturated band. The spectra I have provided here are calculations, based on solidly established physics. The details of line broadening and absorption in the wings of a saturated bands can be seen directly in experiments. The current spectrum of the Earth can be observed from space, and it conforms to the theoretical calculation for prevailing conditions.

    The real situation is a lot more complex than that. In fact, the major difference between greenhouse warming and other potential factors is that the greenhouse effect leads to strong cooling in the upper atmosphere, above the tropopause.

    I think you may mean that there is expected to be strong warming in the middle troposphere, which is quite true. But that's not a greenhouse effect; we expect that for just about any cause of warming.

    (1) Stratospheric cooling

    The upper atmosphere is mainly warmed from the Sun. It is far from the surface, and above the tropopause which marks the limit of convection. The thermal radiation which is absorbed by greenhouse gases is already absorbed lower down, and the only thermal radiation received in the stratosphere is either at wavelengths where there's no absorption anyway to let heating occur (the transparent bands), or else at wavelengths being emitted the top of the troposphere, which is actually colder than the stratosphere (the saturated bands). Hence greenhouse gases don't help for heating the atmosphere at high altitudes. On the other hand, greenhouse gases still can emit thermal radiation very effectively. So the stratosphere is warmed by solar input absorbed by ozone in particular, and then sheds its heat by thermal radiation from greenhouse gases. The more greenhouse gases, the more efficiently the upper atmosphere is cooled.

    (2) Mid troposphere warming

    The troposphere is heated mainly from the Earth's surface. Heat is transported into the troposphere by convection, by latent heat, and by thermal radiation. Any source of increased heat at the surface is going to increase the energy flowing up into the troposphere, whether it be from extra greenhouse gas concentrations, more solar absorption, or more solar input.

    Any surface warming is expected to be magnified in the mid-troposphere. This is nothing particularly to do with greenhouse effects; it is mainly a consequence of a changing lapse rate. With additional surface warming, for any reason, the lapse rate (the rate at which temperatures falls with altitude) is expected to drop. The "dry adiabat" shows a much sharper fall in temperatures than the "moist adiabat", and a warmer surface means more moisture and a reduced lapse rate – especially around the tropics.

    The dry adiabat is about 9.8C degrees per kilometer. The moist adiabat can be half that. Now imagine that the surface warms, for any reason at all, by 5 degrees. At the same time, due to additional specific humidity, the lapse rate drops from, say, 6 to 5 degrees per kilometer. Then one kilometer above the surface will have warmed by 6 degrees, and two kilometers above the surface by 7 degrees, and so on; up until the atmosphere dries out a bit and the lapse rate comes back to normal. Hence the strongest warming is expected in the middle and high troposphere, in the tropics, but below the tropopause.

    (3) Comparison with observations

    It's a lot harder to measure temperature trends in the atmosphere than at the surface. There are many sources of error in measurements, and a sure sign of second rate information is when there's no quantification of these uncertainities.

    Up until a few years ago, there was a genuine puzzle about tropospheric temperature measurements. The expected rise in temperature was not apparent, and it should have been, even given the measurement difficulties. Although this has often been presented as a problem for greenhouse warming theory, in fact it is nothing to do with greenhouse; but is a problem with the expected physics of temperature and heat transport in general.

    More recently, these problems have been somewhat resolved. There are still large uncertainties in the numbers, and there's still lots of room for more careful measurements and testing of our models for lapse rate and atmospheric heat transport. But some sources of error have been clearly identified which obscured the tropospheric warming, which does seem to be there as expected. There's quite a lot of literature on this now; although it remains an active focus of research. Mainly it is a problem of trying to narrow down measurements. The big take home message, however, is that the question is entirely distinct from greenhouse warming. It's about how the atmosphere responds to any warming at all.

    A major recent paper on this is:
    This remains unfinished business, but as matters stand today there is no major inconsistency between theory and observation.

    The stratosphere, on the other hand, has been cooling nicely just as expected. There are multiple causes of this; a reduced ozone concentration and reduced solar absorption has a major role alongside increase greenhouse concentration and enhanced thermal emission. But basically the measurements of the stratosphere give a strong confirmation that it is an enhanced greenhouse effect that is the major cause of global temperature trends over recent decades.

    As a minor point, you have the situation with the past backwards. Throughout the past, high CO2 is found with high temperatures, and low CO2 with low temperatures. There's a kind of two way effect involved here, which is the more usual source of popular confusion. Rising temperatures can raise CO2 levels, and rising CO2 can raise temperatures. They tend to feed on each other, so it's not always clear which one is in the driver's seat! But the relationship is a very clear positive correlation throughout Earth's history.

    Cheers -- Sylas
    Last edited by a moderator: May 4, 2017
  5. Apr 18, 2009 #4
    Sylas, do you agree with my comment that increased CO2 does not cause direct warming of the troposphere? i.e. The troposphere is "CO2 saturated". I believe there is direct observations that supports that assertion.

  6. Apr 18, 2009 #5
    This is the paper I was referring to that shows that atmospheric CO2 levels have been high when the planet was cool and low when the planet was warm.

    Atmospheric carbon dioxide levels for the last 500 million years by Daniel H. Rothman


  7. Apr 18, 2009 #6


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    I don't understand what you mean; and I think this is because you are a bit confused. You are using technical terms in ways that don't really make sense.

    I explained what "saturated" means for you before. You usage here is distinctly odd.

    Adding more CO2 will increase the amount of absorbed radiation. That's a fact. If you mean by "saturated" anything different, then you're just wrong. Check any text on the physics of radiation in the atmosphere. There are many available, and they will all explain about saturation, and absorption, and about how increased absorption in a saturated mixture will occur at the wings. The same physics is used for Sun's photosphere, for the Earth's atmosphere, for a laboratory gas cell.

    What you mean by "direct" is also unclear. On the one hand, the greenhouse effect only works because the atmosphere is warmed indirectly, from the surface rather than directly from the Sun. So in that sense the greenhouse effect works by indirect heating of the atmosphere with solar energy that has been first absorbed at Earth's surface.

    As for how heat is actually transferred into the atmosphere from the surface, there are three major mechanisms. From least to greatest importance of total magnitude, they are convection, latent heat and radiant transfer. The radiant transfer is by far the largest flux of energy into the atmosphere, and it works by direct absorption of thermal radiation, captured by gases opaque to those wavelengths. In this sense, the greenhouse warming of the lower troposphere is as direct as all get out.

    If you mean something else you'll have to spell what you mean by direct and indirect heating. It might help if you could cite some kind of source. It's a requirement of this forum that you use peer reviewed sources; and this restriction has been imposed, I think, mainly because of the climate discussions, where there is one heck of a lot of bad information out there.

    Now personally, I don't mind all that much. But it's still worth checking. If you are getting your information from a blog or a newspaper or private web pages, you should be able to see what sources they are using. If you can't, that's a bit of a red flag. But in any case, feel free to indicate what you mean with a citation to these observations you speak of.

    Cheers -- Sylas

    PS. Aha. Our posts crossed, and I see you have added a reference. Thanks -- that will help. I'll have a look and get back to you.
    Last edited: Apr 18, 2009
  8. Apr 18, 2009 #7
    The total theoretical increase in planetary temperature due to a doubling of CO2, is less than 1C. The 3C warming that is often quoted comes about due to positive feedback rather than negative feedback.

    As observations do not match AWG (CO2) theory (long term)/General Climatic Models (short term), something must be incorrect with the base assumptions or there must be other processes that have not been modeled correctly.

    Regards -- Saul
  9. Apr 18, 2009 #8


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    About the earths climate over the last 500 Million years.

    Rothman's figure 4 highlights periods when earths climate was relatively cooler and warmer. That does not mean any were absolutely cooler than the present climate

    For example, he list a cool period some where between the Jurassic and Cretaceous periods.

    While the Cretaceous was cooler than the Jurassic, it'd be a huge mistake to conclude that either of these periods or their boundry was cooler than our current climate. They were both significantly warmer on an absolute measure.
  10. Apr 18, 2009 #9
    If you look at figure 4 there are 4 ice epochs on the planet. We are living during the fourth. For the other ice epochs CO2 was above 2000 ppm which seems to indicate that the effect of CO2 on the planet's temperature, saturates at some level.


    I have another paper that notes there is a lack of correlation of planetary temperature and CO2 levels during this ice epoch.

  11. Apr 18, 2009 #10


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    OK; I've had a look. Saul cites:

    Rothman, D.H. (2002) Atmospheric carbon dioxide levels for the last 500 million years, in PNAS, April 2, 2002 Vol. 99 No. 7, pp 4167-4171

    There are several important points. First, and by far the most important:

    (A) This is a complete non-sequitur

    The existence or otherwise of other factors that may be driving climate cycles apparent over long times spans, of 10 million years or more, is completely irrelevant to deciding whether or not CO2 has a significant impact over the scale of recent decades.

    The scale difference here is enormous. What is short term for Rothman is anything less than 10 million years. That is enough to encompass the entire Quaternary period several times over, with all its many the cycles of ices ages and interglacials!

    This cannot be emphasized sufficiently strongly. There are many different factors impacting in climate, and in principle there is nothing implausible at all about long term climate change, on the scale of 10 million years or more, being driven primarily by factors other than CO2. This is in no conflict whatsoever with the immediate physical impact of changing CO2 levels, which is about solid as anything ever gets in science. It is truly elementary thermodynamics.

    If people get nothing else from the thread, they should at least get this. A long term climate trend driven by something other than CO2 is no conflict at all with CO2 being a factor to drive climate above and below this other putative larger and slower trend.

    It's as if you were using the theory of continental drift, which moves whole ecosystems vast distances over the scale of millions of years, to refute the idea of biological factors being important for the short term shifts in the boundary of a rainforest.

    (B) Rothman himself explicitly denies the application being attempted in this thread

    This should kill the argument dead. Looking at the extract from Rothman's paper, which Saul provides, Saul appears to have missed the implication as far as this thread goes. Rotham states:
    Superficially, this observation would seem to imply that pCO2 does not exert dominant control on Earth's climate at time scales greater than about 10 My. A wealth of evidence, however, suggests that pCO2 exerts at least some control [see Crowley and Berner (30) for a recent review]. Fig. 4 cannot by itself refute this assumption. Instead, it simply shows that the “null hypothesis” that pCO2 and climate are unrelated cannot be rejected on the basis of this evidence alone.
    The last sentence there is a triple negative, which can be confusing! But the rest of the paragraph is better. Rothman suggests, on the basis of his reconstruction, that CO2 is not dominant on long time scales. As I have noted, this is completely consistent with the obvious immediate physical impact of CO2 on shorter time spans.

    Rothman is explicit that there is a wealth of evidence for CO2 having at least some impact, and that his diagram does NOT refute this.

    The clumsy final sentence in Rothman's paragraph claims that the other evidence – which he does not actually discuss! – can't reject the null hypothsis of no impact. That is an odd remark. Of course the evidence goes powerfully against the null hypothesis. The implication of Rothman's reconstruction as shown in his figure 4 is rather that the relationship with CO2 may be over ridden on longer time spans by other unidentified factors. In principle there is nothing wrong with that notion, and it is in no conflict at all with the plainly demonstrated physical impact of CO2 in recent decades.

    Rothman says this explicitly when he notes that his reconstruction "cannot by itself refute this assumption". Quite so. So let's stop pretending that it does.

    But Rothman's work on the longer term scales ALSO has problems of its own. This is the next point:

    (C) Rothman's reconstruction is at variance with related work before and since.

    A summary of different attempts by a number of authors to estimate CO2 levels over this period is available in Bergman, et al (2004).

    I've taken the figure 4 from that paper, which compares a range of published work using proxies or other others, and superimposed upon it the figure 4 from Rothman (2002) in green, rescaled so that the diagrams align. I have also included the icehouse periods identified in Rothman's diagram. Rothman's work diverges sharply from all other reconstructions past about 300 Mya BP.
    paleoco2-rothman.GIF COPSE.intercompare%2Brothman.GIF
    This is a much less important point than recognizing that putative unidentified long term climate drivers is completely consistent with the physical importance of CO2 on short time spans. But I think it is worth noting for the record that Rothman's reconstruction has problems of its own with other lines of evidence. It's all open research, of course; and none of it is any problem whatever for the simple physics of CO2 and radiative transfers.

    (D)Saul actually confirms the approximate magnitude of CO2 forcing

    Above, Saul speaks of the theoretical CO2 impact:
    Of course. This is precisely what my original post explains. What you here call "theoretical" is the "Planck response" that I describe at point #5 of my first post. Repeating what I said originally: If nothing changes other than temperature, the response is straightforward. […] It's called the "Planck response" in climate science. Converting forcing units, this corresponds to about 1.1C per 2xCO2.

    There's a minor flaw in Saul's numbers if he gets less than 1C, but more importantly, this is not a "theoretical" impact for Earth at all. It's the impact for some other place where nothing changes as temperatures alter. The real theoretical work for Earth suggests an impact of about 3C per doubling; but I didn't cite theory for that. I went straight to observational constraints.

    That climate feedbacks are positive is a real observation. The evidence I cited in my original post is empirical, and there's a lot more than my chosen example. Observations of the real world indicate that climate response is somewhere from 1.5C to 4.5C.

    More amusingly still – by acknowledging the no-feedback "Plank response", Saul is actually using the very 3.7 W/m2 that he started out by denying, or something very close to it! He acknowledges that there really IS a theoretical basis for non-feedback response of about 1C. Great. That means a forcing of about 3.3 W/m2; which is how much extra emission you get from Earth with a 1C rise as the base Planck response. Snap.

    (E) A few loose ends

    On tropospheric warming:
    This bland assertion comes with no reference. Santer et al is pointing out errors in an incorrect analysis of older data. The truth of the matter is that data from 1999 to 2008 all shows that the troposphere is warming more rapidly than the surface. The real disputes are over how much; but the claims that troposphere amplification is absent are flatly false.

    The major sources of information for recent years are satellite data from Remote Sensing Systems (RSS) and University of Alabama, Huntsville (UAH). This is an interesting case, because for a long time the whole issue was confused by UAH claims for a lack of warming. This was shown in 2005 to be an algebraic error in their analysis. It was as basic as doing a subtraction when they should have added. The UAH team acknowledged the problem promptly, and now everyone agrees that measurements show tropospheric amplification. The remaining differences are over how much; but frankly the UAH team has something of a credibility problem now.

    Bottom line. Expectations are that the troposphere should warm more than the surface. This is what is measured. There remain large uncertainties in the measurement, so that it is hard to give a strong constraint on theory, but as matters stand observations are consistent with theory. The theory involved is entirely independent of greenhouse effects, and deals with lapse rates and any source of temperature change.

    Since your premise is false, the rest doesn't follow. Observations do most definitely match the physically expected impact of CO2, especially on the time scale being addressed in this thread.

    There are of course other processes that are not yet being modeled well, and which apply over time spans of hundreds of millions of years. We even know some of them, and the modeling is very difficult. (Continental drift; changes in land cover, both with new species and different biogeographic distributions.) What's the albedo of a Cambrian swamp, for example? Be that as it may, pretty much all work in very long term climate trends recognizes the impact of greenhouse gases along with whatever else is going on.

    There's no basis in any of this for disputing the elementary physics that means CO2 is necessarily significant for trends over recent decades.

    No, you don't. It's the exact same paper: Rothman (2002). This is a rather revealing screw up. You even quoted the text from the paper, which confirms its source, but if you are speaking of it as "another paper", it suggests aren't really working direct from papers you have to hand at all, but that you are picking up extracts found in some secondary source.

    Secondary sources can often be useful – but take care, because in this particular subject area many of them are utterly atrocious. For really basic stuff like saturation and absorption you are best to simply go with established text books. The forcing from carbon dioxide is not some open research question, but elementary undergraduate physics.

    Cheers -- Sylas
    Last edited: Apr 19, 2009
  12. Apr 19, 2009 #11
    It should be noted the lack of correlation of CO2 level and planetary climate is supported by other data. The problem with the CO2 driver hypothesis is the there is no mechanism to reduce CO2 and detailed analysis indicates CO2 levels were high when the planet was cooling, in the Cenozoic.

    The Late Cenozoic uplift – climate change paradox by William Hay , Emanuel Soeding, Robert DeConto, and Christopher N. Wold


    Regards -- Saul
  13. Apr 19, 2009 #12
    The troposphere does based on Radiosonde measurements (weather balloons) show cooling rather than warming. This paper asserts that weather balloon measurements in the 1980's had a warm basis. Even with that warm bias removed, however, there does appear to cooling of the upper troposphere/lower stratosphere.

    Cooling of the upper troposphere/lower stratosphere would as I noted be consistent with the twentieth century warming being due to reduction in cloud cover rather than the GWG (CO2) warming of the stratosphere. There are published papers that show there is reduction in planetary cloud cover during this period.

    http://homepage.univie.ac.at/leopold.haimberger/i1520-0442-21-18-4587.pdf [Broken]

    Toward Elimination of the Warm Bias in Historic Radiosonde Temperature Records—Some New Results from a Comprehensive Intercomparison of Upper-Air Data

    Refer to the figure 7 in the paper even with the removal of the warm bias the upper troposphere/lower stratosphere cools rather than warms.

    This is the paper I said that has been submitted that disputes Santer et al's conclusion that troposphere is warming. The paper uses the same data source as Santer et al and Santer et al's analysis methodology to determine the upper troposphere is not warming.


    There was also a paper that asserted troposphere wind speed indicates that the troposphere was warming which if correct would imply that the past weather balloon data was not correct.

    This new paper that has been submitted shows, however, that recent stratospheric wind data indicates that the troposphere temperatures are basically unchanged.


    Because there is evidence that shows that there are periods of millions of years when there is not correlation of planetary temperature and planetary CO2 levels (i.e. The planet is cooling when CO2 levels are high and the planet is warming when CO2 levels are low) I believe, the current evidence that shows the stratosphere is not warming deserves consideration. (i.e. One observation and analysis supports the other.)

    There are recent papers that have been published that try to explain why (Assuming the stratosphere did not warm and increases in CO2 do not warm the planet.) there is this discrepancy.
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  14. Apr 19, 2009 #13


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    An aside… When you quote extracts from my post, you should not add your own comments nested inside the quote tags. If you have a comment on my text, then give a quoted extract, and nothing else, inside the quote tags. Then add your own comment afterwards, outside the tags. Repeat as necessary. It's very easy to miss stuff improperly added within what is quoted; it just looks like part of what you are quoting. It's important to get this right, out of fairness to the person you are quoting and also for proper emphasis and clarity of your contributions.

    You also don't need to quote every part of my posts in your reply. If you do the quoting correctly, you also don't need to add your own name to indicate what you are writing.

    (For other readers, as useful background: the Cenozoic is the last 65 million years up to the present. The Quaternary is the tail end of the Cenozoic, or the last 1.8 million years.)

    You have started another thread: [thread=308288]CO2 Variance in the Atmosphere[/thread], in which you talk about mechanisms for CO2 variation. It's an interesting topic, and a useful initial post. That's the right place to talk about mechanisms. Not here.

    For the record, however, it is flatly false to say there are "no mechanisms" for reducing atmospheric CO2. Your own sources discuss some known mechanisms.

    Over the only periods when we have direct data on atmospheric CO2 levels, using ice core data, there is an unambiguous record of cycles of rising and falling CO2 levels aligned with the ice ages of the Quaternary period. The mechanisms involved are not all understood, but the correlation with temperature is positive and unambiguous. If you calculate forcings using numbers from my first post, it's fairly easy to see that CO2 change is not sufficient to explain ice age temperatures. There are other factors involved here, and the trigger is probably orbital changes. The observed fall in CO2 is important part of quantifying causes for falling temperature; but it's only a part, and it's not the trigger.

    That's going to remain true even if the correlation doesn't hold over longer time spans. There's nothing whatsoever wrong in principle with the idea that there are other factors working over long time spans that drive major swings in climate, so that the correlation is lost or even reversed on longer scales.

    This is all irrelevant to the thread. There's no claim being made that CO2 is the only factor to impact climate, and I have no problem in principle with other factors than CO2 being a major factor in the Cenozoic. We already know for sure that other factors are important in the Quaternary – and that is a period where there is definitely a secondary greenhouse impact involved, of a magnitude that is calculated using the kinds of physics set out in my very first post!

    You also quote a paper by Hay et al (2002).
    There's nothing at all in that paper to deny or contradict the basic thermodynamics of the greenhouse effect, including the role of carbon dioxide, for driving temperature change. Indeed, it seems to be taken for granted – as it should! The real argument is that some other factor must have been involved in the late Cenozoic, because the CO2 levels are not changing enough or in the right direction to be the major cause at that time.

    I've got no comment on the merits of the paper. It presents what it identifies as "an outrageous hypothesis", so I guess it is a bit of an exercise of thinking outside the box, and that's a good thing for science. You quote Hay et al as follows:
    This is specifically saying that CO2 levels can't do the job because they were too low. If he's right, this does indeed call into the question currently accepted trends on CO2 levels at this time; and that would be surprising. But in principle, it's a perfectly credible notion to be considered on its own merits. It means, in context, that there's something else that is more important for climate over this period.

    For some solid good sense on this whole issue, go one step further and read Kump (2000) directly. I've put it aside for reference in case you decide to take up the issue of climate and deep time in a more appropriate thread.

    None of this, by any stretch of the imagination, is in the slightest conflict with the simple physics of how carbon dioxide impacts temperature! You are quoting papers proposing other factors at work in deep time. It's an irrelevant distraction for this thread – and it is also not fair to the scientists being quoted, who are not denying at all the physics of greenhouse and carbon dioxide.

    The topic for this thread: estimating CO2 impact NOW

    My original post on this was crystal clear. I am talking about RIGHT NOW, where any notions of different factors driving climate can be tested with data right under our noses.

    I'm not opposed to illuminating this question with data from prehistory, as long as there is some credible basis for linking observations to the specific thread topic. Just saying that CO2 is not always the major factor is a distraction. Take it to another thread if you are interested in deep time. It could be a great topic in its own right.

    Your next post does look at the present, with atmospheric trends; I'll respond to that next.

    Cheers -- Sylas
  15. Apr 20, 2009 #14


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    Actually, the word "ice" does not appear anywhere in Rothman's paper.

    This is not to suggest that no glaciers existed on earth between 600 to 25 Ma. It is generally understood that 500ppm CO2 will not exert enough of a warming to melt all glaciers at higher elevations in the polar regions. This is one reason why East Antarctica is not expected to melt; it is simply at too high of an elevation. On the other hand, CO2 levels impact the elevation/latitude necessary to support ice sheets and this is why there has been such a retreat in the amount of ice at both poles.


    Thanks for pointing out the inconsistencies in Rothmans reconstruction.
  16. Apr 20, 2009 #15
    You are not understanding what you are reading here.

    The older radiosondes were not well shielded and were warmed by direct radiative flux from the Sun. This resulted in a warm bias in the radiosonde data especially during the 1980s. What Hamburg et al have done in their reanalysis is correct for the bias.

    From the abstract:
    By correcting for the warm bias in the 80's the radiosonde data is more in agreement with the satellites, models, and theory.

    This paper has not been published in a science journal. It is against the forum rules to discuss it.

    The stratosphere is expected to cool as CO2 increases.

    The atmosphere cools from the surface outward until it meets the inversion layer known as the tropopause. Then it warms as you move outward. The reason is that below the tropopause the atmosphere is primarily heated by the Earth and above it is heated by the Sun. There is little mixing between the layers so very little convective heat transfer. Most of the heat loss from the stratosphere is in the form of electromagnetic radiation.

    Now enter the world of quantum mechanics. CO2 is a linear molecule with a zero dipole. O-C-O Each atom has a magnetic field and the center of the fields are equidistant from one another. When excited the molecule vibrates and has 3 primary quantum vibrational modes. http://chemmac1.usc.edu/bruno/java/Vibrate.html" [Broken] is an animation of the quantum vibrational modes of the CO2 molecule. The bending mode is the one that is significant for stratospheric cooling.

    As the molecule vibrates the magnetic fields of the molecule are in motion and interacting with one another. This creates a rapidly shifting dipole moment causing the molecule to emit a photon in a random direction. When this happens in the stratosphere there is little probability that the photon will be reabsorbed in the stratosphere. Stratospheric cooling is the expected result of increased concentrations of carbon dioxide.
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  17. Apr 21, 2009 #16


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    Even with your repeatedly raising this point, you fail to even once acknowledge the fundamental objection raised by Sylas, that you are implicitly assuming an infinite bandwidth for all feedbacks. The timescales of various mass and energy flow processes gives good reason to expect the gain from any feedback mechanism to be frequency dependent, to the extent that it seems reckless (at least to me) to assume/assert that the gain over timescales > 10MY should hold at timescales < 0.1MY

    The dipole moment of a molecule (in the context of scattering, as is the case here) refers to the electric dipole moment and has nothing to do with magnetic fields (nor is there even such a thing in general, as the center of a magnetic field). You should probably have left out the QM part of this discussion as it is partly erroneous, serves little or no explanatory purpose (at least to me), and if at all, only raises more questions.
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  18. Apr 21, 2009 #17
    I am not a physicist, and was relying on my inadequate memory and understanding of something I read a few years ago. Although my explanation and terminology may be lacking, CO2's quantum vibrations are the primary reason for stratospheric cooling since the bending vibration causes the molecule to radiate.
  19. Apr 21, 2009 #18


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    Actually, all three vibrational modes make the molecule radiate. The bending and asymmetric stretch are IR active modes (they involve a change in the molecule's dipole moment) while the symmetric stretch is a Raman active mode (it involves a change in the polarizability of the molecule). I think (this is, at best a semi-educated guess) what's special about the bending mode is that it falls plumb in the middle of the black body spectrum for temperatures around 270K.
  20. Apr 21, 2009 #19
    The symmetric stretch does not radiate and the asymmetric stretch is at to high a frequency to be excited by atmospheric temperature collisions.
    Last edited by a moderator: Apr 21, 2009
  21. Apr 21, 2009 #20


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    Not true. This is a Raman active mode, so the radiation need not be in the IR band (look up Stokes and anti-Stokes lines in the Raman spectrum of a molecule).

    But anyway, this is an unnecessary digression from the point of this thread, so I shall not pursue it any further. Besides, I have a long post to make in another thread...and too little time.
  22. Apr 22, 2009 #21
    I have heard multiple explanations for the cooling of the stratosphere.

    This is a new explanation. Are you suggesting the sun or the planet does not emit the frequencies that the CO2 molecule absorbs and emits?

    My explanation for stratosphere cooling is that there has a reduction in low level clouds over the oceans, during the last part of the 20th century. Clouds reflect sunlight back into space. Sunlight that passes through O2 and O3 twice causes a greater increase in temperature than sunlight that only passes through it once. If there is less reflected sunlight, the stratosphere cools and the planet will warm.

    There is published data that shows there was a reduction in planetary cloud cover in the 20th century.
    Last edited: Apr 22, 2009
  23. Apr 22, 2009 #22

    If I understand the 1.5C to 4.5C hypothesis. A doubling of CO2 will cause the planet to increase in temperature by 1.1C and "observations of the real world" shows the doubling of CO2 will cause a total net warming of the planet of somewhere of 1.5C to 4.5C.

    The 1.1C temperature increase is per the equation logarithmic. What is the current expected warming for the increase from 280 ppm to 390 ppm?


    We both agree an increase in CO2 from 280 ppm to 560 ppm without feedback will cause some increase in planetary temperature. The difference in our position is the magnitude of the change. I am saying based on an analysis of the paleoclimatic data (planet's response to past CO2 changes) the rise in planetary temperature to a doubling of CO2 would be around 0.7C including feedbacks.

    As you note and others note, CO2 can only absorb specific frequencies. The other frequencies pass out through the atmosphere. Is there anything that could possibly be incorrect with the 1.1C to 4.5C hypothesis?

    Based on current temperature changes is it possible to falsify the 1.1C to 4.5C hypothesis?

    If the planet were to suddenly cool would that disprove the 1.5C to 4.5C hypothesis? Or asking the same question another way, what is the maximum the planet can cool within the limits of the 1.1C to 4.5C hypothesis?

    Regards --- Saul
  24. Apr 23, 2009 #23


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    Picking up two replies in one here:

    There are two major reasons for stratospheric cooling. Reduced solar absorption, from declines in ozone concentration, and increased thermal emission, from increases in greenhouse gas concentrations.

    Each of these has multiple secondary explanations, but because there is so little convection, it all comes down changing the interaction with radiation.

    Think about this one for a minute: it's key. The frequencies that CO2 can absorb and emit will not get from the surface to the stratosphere. They'll be absorbed, and emitted, all the way up the atmospheric column.

    What eventually gets into the stratosphere, at these wavelengths, is emission from somewhere around the tropopause, which is the very coldest part of the atmosphere. You can see this in the calculated spectra I gave back in [post=2165483]msg #3[/post], and the same thing is seen in direct satellite measurements.

    Increased interaction with thermal radiation, therefore, works up here as a cooling effect. You can think of greenhouse gases a bit like a large radiating surface, which can be used for passive heating or passive cooling, depending on whether you are hotter, or colder, than the background radiation around the radiator. This is not a new explanation at all.

    That's an interesting notion, but I don't think it can work. Reflection from cloud is important in the troposphere, but is not likely to make much difference in the stratosphere. The UV radiation that is most effective for stratospheric heating is largely used up before it gets into the troposphere, and so the spectrum of reflected radiation is strongly depleted in precisely the wavelengths that would otherwise give stratospheric heating.

    It's a neat idea, but in this forum you'll have to show that it has been seriously argued in the peer reviewed literature to take it any further.

    Most of the literature indicates a trend of decreasing cover and a net cooling effect. As best I can determine, the following reference corresponds to what most scientists working on this subject see in the available data.

    (Added in edit. Norris identifies a trend of decreasing cover, and associates it with a negative forcing. The impact of cloud is not limited to albedo. Cloud also interacts strongly with long wave radiation. More detail in the paper for anyone interested.)​

    Sorting out the cloud effects is important for improving estimates of total forcing, as this is one of the largest uncertainties. (IPCC 4AR gives the range of possible forcings for cloud albedo over the 20th c. as -1.8 to -0.3 W/m2, with a low level of understanding. The negative means it is a cooling effect.)

    Resolving this uncertainty does nothing to alter the physical contribution from carbon dioxide or other well mixed greenhouse gases, which is known to a much greater accuracy.

    A doubling of CO2 would give an equilibrium response of around 1.5C to 4.5C. That's what you get both with theory and with observation. Your "1.1C" figure there is the Planck response, which is what you would use for a planet with no atmosphere, given an equivalent forcing of 3.7 W/m2. It's not a number you can use sensibly for the Earth.

    Equilibrium response is log2(390/280)*3 (+/- 50%). That is about 1.4C, plus or minus 0.7.

    This is not a prediction, because it does not include any other forcings, either positive or negative; neither does it consider the equilibrium response lag, of at least a couple of decades. It's not a climate model. It's the estimate, from well established physics, for the CO2 impact all by itself. My aim not to explain climate, but simply to demonstrate that this CO2 impact is necessarily a significant aspect of changing climates in the present;

    Um, not trying to be rude here, but that makes no sense. You've just been arguing that paleoclimate is actually driven by some other forcing, which is plausible. But with that assumption, we've got no basis at all for estimating a CO2 response from the data.

    Unless you've got some way to estimate total forcings -- all of them, not just CO2 -- you can't possibly estimate response or sensitivity. The large uncertainty in the carbon cycle beyond the Quaternary period, and the lack of data on albedo, makes it pretty much useless as a way of estimating sensitivity. Within the Quaternary we do have more of a handle on forcings, sufficient to get into the ball park for an estimate of sensitivity during the last glacial maximum.

    Not really.

    Of course, no discovery in science is ever completely beyond question, there is always the possibility of something wrong with given estimates. What science actually does is keep trying to constrain the estimates and narrow the uncertainity.

    These estimates ARE being narrowed. The 1.5C lower bound (not 1.1) is looking increasingly unlikely, and in the light of ongoing work, a more realistic lower bound is about 2C. The upper bound turns out to be harder to constrain, and this is a mathematical consequence of the non-linear nature of feedback response. (Ref: Roe and Baker, 2007)

    So a good summary for the current state of knowledge is that climate sensitivity is from 2 to 4.5 K/2xCO2. Future developments may narrow that down, but as Roe and Baker point out, a substantial level of uncertainty is probably inevitable. Furthermore, sensitivity is not really a single precise number available to be discovered. It will vary somewhat with time and circumstance, and with the nature of forcings applied.

    The range of 2 to 4.5 K/2xCO2 for sensitivity is well supported, and there's little prospect of response being outside that range. There's also not likely to be a whole lot of narrowing of that range in the future, either. Climate is never going to simple to predict.

    That depends entirely on the forcings. A planet can only cool with a negative forcing, no matter what sensitivity you are using. If we were to see a sustained cooling effect, that would indicate a sustained negative forcing was at work – and so it would have to be something other than carbon dioxide.

    I think I can see where this is going; so I'll just note for the record. The planet has lots of natural short term variability. From year to year there are changes going on that can give unpredictable differences, and this is effectively noise in the temperature records. The last 35 years has seen a strong trend of increasing global temperature, but for a randomly chosen sequence of ten consecutive years somewhere along that 35 year period, you might have anything from twice the trend to no trend at all, within about 2σ bounds of variation.

    Such natural variations don't falsify anything, unless you know the specific forcings involved; and usually, we don't. But with a big volcano, you can estimate forcings and hence use information on the cooling response to constrain sensitivity. (Described with references in msg #1.)

    The available data has already falsified the idea that sensitivity is less than 1.5, with 3σ confidence. If a new line of evidence is inconsistent with that, then we have one of the fun times in science when you know someone has to be wrong, but can't be sure who.

    At present, however, the 2 to 4.5 estimate basically represents the range of what is credible, given all the data we can possibly throw at it.

    Cheers -- Sylas
    Last edited: Apr 23, 2009
  25. Apr 23, 2009 #24
    Here is a chart of atmospheric transmission

    The stratosphere has been cooling since the 1950's consistent with the theory.

    http://www.atmosphere.mpg.de/enid/2__Ozone/-_Cooling_nd.html"is a good site that explains it.

    No there is not. At least nothing conclusive.
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  26. Apr 23, 2009 #25


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    Sylas - could you clarify: by 'equilibrium response' do you mean to include all the additional feedback mechanisms brought on by CO2 warming? I had thought that CO2 alone, without feedbacks would have a response of 1-2C at most..
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