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CO2 Climate Sensitivity

  1. Mar 28, 2009 #1


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    Came across a 2007 study concerning climate sensitivity.
    It was published by the Journal Nature, but only as a letter.
    Can't say exactly why they do that, but it probably hasn't
    been scrutinized as closely as it would be otherwise. Anyhow,
    in this study, atmospheric CO2 concentrations over the past
    420 million years were compared to computer models. The best
    fit was obtained using a climate sensitivity of 2.8C/CO2 doubling.

    There are of course other factors that influence CO2 levels:
    Global Co2 degassing
    Organic and Carbonate burial rates
    Land plant populations
    Solar Radiation

    When these other factors were adjusted within physically reasonable ranges,
    it was concluded that climate sensitivity is unlikely to be less than 1.5C/CO2 doubling.
    The only way the computer model would reasonably fit historical data with a climate
    sensitivity of less than 1.5C/CO2 doubling was by assuming that CO2 optimally fertilizes
    all land plants as if there were never any limits to nutrients, water or light.
    However, we know this is unlikely as there are typically large desert areas on earth
    and plants grow better with more light.

    Here is a link to the paper:

    http://www.gfdl.gov/~ih/jerusalem_papers/royer.pdf [Broken]

    Climate sensitivity constrained by CO2
    concentrations over the past 420 million years

    While this is an interesting study, it is IMO not particularly news worthy.
    It is however, consistent with the broad range of values found by most other studies.
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Mar 28, 2009 #2
  4. Mar 28, 2009 #3


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    You've got that badly mixed up, in several ways. The thread to which you link is also pretty bad. Lags or leads have to do with what is driving the change in equilibrium; not with whether the feedbacks are positive or negative.

    Consider the data. We know that as temperatures start to rise out of an ice age, CO2 levels start to rise. When temperature starts to fall into a new ice age, CO2 levels go into a decline. They are closely aligned, and data suggests that it is temperature that starts to move first.

    What can you conclude?

    A feedback loop between temperature and CO2

    Assume that CO2 and temperature are linked to each other somehow. We already know, from very basic physics, that an increasing CO2 level will increase thermal absorption in the atmosphere, and that this tends to raise equilibrium temperatures. But let's forget that for the moment. Suppose we know nothing about atmospheric thermodynamics, and are clueless about whether raising CO2 will tend to increase or decrease temperatures.

    Now think about the rising temperatures apparent as you come out of an ice age. Because the temperature rise starts first, it's unlikely that CO2 is triggering a shift in temperature. We already know that ice ages are strongly linked to small changes in Earth's orbit; the Milankovich cycles. Let's take as a working hypothesis that ice ages are triggered by a shift in the Earth's orbit of some kind. (This is indeed the conventional picture in science.)

    Very shortly after temperatures start to rise, CO2 levels start to climb. If is this is because of an impact of temperature on CO2, then it has to be that higher temperature tend to give a higher CO2 level. Let's take that as a working hypothesis also. (This too, is a conventional picture; mainly because changing ocean temperatures alter the solubility of CO2 in water, which impacts the balance between atmospheric and oceanic CO2. At higher temperatures, CO2 is a bit less soluble, and so you tend to get a shift in CO2 from ocean to atmosphere.)

    Now, what can you conclude about a feedback loop? For a feedback loop to exist, there has to be some impact of CO2 feeding back into temperature. Is this positive, or negative? That depends exclusively on whether raising CO2 tends to raise temperature (which would be a positive feedback loop) or whether raising CO2 levels tends to lower temperature (which would be a negative feedback).

    Consider three cases.
    • There's no effect of CO2 on temperature. This means no feedback. The CO2 levels are simply driven by temperature, and the temperature is simply driven by whatever else is involved -- shifts in the Earth's orbit, for example.
    • Raising CO2 levels have a negative effect on temperature. That would be a negative feedback. The temperature rise is caused by shifts in Earth's orbit, but the amount of change is reduced by the feedback from rising CO2 levels.
    • Raising CO2 levels has a positive effect on temperature. That would be a positive feedback. It would amplify the impact of shifts in Earth's orbit.

    Note carefully that whether the feedback is positive or negative is entirely independent of whether CO2 is leading or lagging temperature change.

    When the Milankovich cycles were first proposed as an explanation for the ice ages, there was a major theoretical problem, in that the orbital shifts involved are small. They do result in change to insolation that helps drive temperatures in the appropriate direction, but the change in insolation is very small; too small to account for the big temperature changes involved.

    The solution to this puzzle has been the amplifying effects of positive feedback. CO2 is not the only feature involved. Ice cover is also a positive feedback. Dropping temperature tends to increase ice cover. More ice tends to lower temperatures, because less sunlight is absorbed. That's a positive feedback. Together with a positive feedback through ice cover levels, the large temperature changes of the ice ages are explained.

    What's raising CO2 levels now?

    Physics is no different now than it was in the ice ages. But the processes involved are different. CO2 levels are rising sharply at present, and this is NOT being driven by temperature change. The rising CO2 levels are from geological carbon moving into the atmosphere, caused by the burning of fossil fuels. There are rising temperatures being measured as well; but there's a lag. CO2 increases came first.

    The fact that CO2 levels start to increase before temperature has nothing to do with positive or negative feedback. It's simply because the major driving process to shift equilibrium is at present is the increasing CO2 levels.

    Rising temperatures may cause other changes. For example, it's leading to reduced ice cover. That's a positive feedback, between temperature and albedo, just as it was in the ice ages.

    What about the feedback from temperature to CO2 levels? Well, this has to be at work as well, but it manifests a bit differently because the whole shift is being driven from CO2 to start with. Most of the CO2 we transfer into the atmosphere actually ends up being dissolved in the ocean. It's a slow process, and so it certainly can't flush CO2 out of the atmosphere as fast as we are adding it. But there is a steady transfer of CO2 into the ocean at present, which can be detected by measurable falls in the pH of seawater.

    From the ice ages data we have reason to think rising temperature tend to raise the natural equilibrium levels of atmospheric CO2. From chemistry, we can see how it works, by the impact on solubility. The implication in the present is that as temperatures rise, the rate of take up of CO2 into the ocean tends to fall somewhat, which will tend to accelerate rising atmospheric levels for a given rate of emissions. It's probably not a huge effect, as the atmospheric levels are so much higher than the natural equilibrium level. But it is one of the processes involved.

    Other feedbacks.

    I've mentioned two feedbacks so far. One is the feedback between temperature and CO2. Another is between temperature and ice cover.

    At present, the CO2 feedback with temperature is probably not all that important. CO2 levels are being driven mainly by fossil fuel burning.

    The magnitude of the response of climate to elevated CO2 levels is going to depend on the feedback between temperature and other variables.... just as the magnitude of the response of climate to Milankovitch cycles in the ice ages is affected by feedback processes.

    There are several other processes that can are involved. With changing temperature, there's likely to be changing cloud cover, which alters albedo and insolation. There's likely to be changes in humidity. Raising humidity has two effects. On the one hand, it increases IR absorption, which increases the magnitude of the greenhouse effect. On the other hand, the moist adiabat is more gradual that a dry adiabat, which means the lapse rate in the atmosphere tends to fall. That tends to decrease the magnitude of the greenhouse effect. So there's both a positive and a negative feedback involved with humidity.

    Now all of these feedbacks I have mentioned operate independently of CO2 levels. Suppose, for example, that the output from the Sun rises, or falls, for some reason. That's going to alter temperature. And as a result of temperature change, you'll alter ice cover, and humidity and clouds, and so on. CO2 doesn't impact directly on glaciation or humidity or cloud. The feedbacks get involved because they are linked to temperature. If something else impacts on the temperature (Milankovich cycles, solar cycles, too much hot air in physicsforum discussion :wink:, etc) then the feedbacks help determine the total temperature response. This is the notion of "climate sensitivity".

    We can calculate tolerably well how changes in the concentration of various gases alter the transmission of radiation in the atmosphere, on the assumption that temperatures and insolation remain the same. That is, we can calculate how hard the climate gets pushed. What's much harder to sort out is how far temperature move in response, after all the various consequence of temperature change have their own contribution. That is the climate sensitivity.

    Study of ice ages can help put a constraint on sensitivity, and that is what the research described in the first post of this thread is about.


    This post is too long, again, so I'll try a more concise summary.

    • The fact the temperature leads CO2 change in the ice ages is evidence that temperature has an impact on CO2 levels. There's also a solid theoretical basis for this.
    • The ice ages are triggered by changes in Earth's orbit.
    • The magnitude of temperature change in the ice ages is too large to be caused by orbital changes alone.
    • We know from basic thermodynamics that infrared absorption in the atmosphere helps keep Earth warm. We know that CO2 is an important contribution to this absorption.
    • The fact that CO2 helps increase temperature, and that temperature helps increase CO2, means there's a positive feedback.
    • A positive feedback helps amplify the impact of orbital changes.
    • There are other feedbacks in the climate system as well, both positive and negative. They help determine how sensitive climate is to any stimulus, be it CO2 emissions, solar cycles, or orbital cycles.
    • Data from the ice ages helps constrain the plausible values for climate sensitivity. The sensitivity has to be high to account for the ice ages, and this also is evidence for a net positive feedback to greenhouse forcings.

    Scientists such as those who wrote the article in described at the start of this thread are not "disdaining causality" at all.

    Cheers -- Sylas
  5. Mar 28, 2009 #4


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    Thanks Sylas!

    Just because global temperatures are sensitive to changes in atmospheric
    CO2 concentration does not mean that CO2 is the only factor that can
    influence temperatures. So, it is possible for CO2 to either lead or lag
    temperature changes.
    Anyhow, the current problem isn't really causality.
    Instead it is narrowing down the range of sensitivity which is known
    to be between 2°C to 4.5°C with most studies centered around a 3°C value.


    The study presented at the start of this thread actually
    found a range slightly wider than what is currently accepted. This
    does not mean the accepted range is wrong. Instead, it shows that
    the method employed contains greater uncertainity. Still it is assuring to
    to find that independant methods tend to support each other.

    Of course there may be some studies that find ranges significantly out
    of that which is currently accepted, but so far I have not come across any.
  6. Mar 28, 2009 #5


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    Here's some food for thought from the IPCC:

    In other words, if we are under estimateing the affect of
    aerosol cooling, then it is possible that the climate CO2
    sensitivity may be as high as 6°C.

    I would add that the huge heat capacity of the oceans
    is another reason why the full impact of rising CO2
    concentrations has not been fully realized in atmospheric temperatures.
  7. Mar 28, 2009 #6
    yes your post is way too long. Let's go back to the basics Royer et al assume that CO2 is forcing temperatures with more than 1.5 C per doubling. A simple plot of the ice core data show that temps lead CO2. Cause is mostly leading the effect, unless you can prove otherwise, now be so kind and provide us with a link to the detailed model that can explain why things can be happening with positive feedback, consistent with the data/proxies/records of the Epica Dome C ice core.

    Curiously enough the same author, Dana Royer et al, found out that during the warm Paleocene, the CO2 levels appeared comparable to those in the much cooler present.

    Furthermore the proposed chain of events about ice ages disdain quite a lot of problems, like the causality problem for Milankovitch, which is not getting better with recent research as Spencer Weart wraps up:

    we are not a single step further now and everything is just supposition.

    Please explain why that other thread is bad.
  8. Mar 28, 2009 #7


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    I'll try to make this as simple as possible so that it can be easily understood:

    CO2 is not the only thing that can cause global temperatures to change.
    Therefore, temperature changes may lead changes in CO2.

    However, just because other things can cause temperature changes does not
    logically mean that CO2 changes have no impact on temperature.
  9. Mar 28, 2009 #8
    Let me make it even a lot more simple.

    The summary of policy makess of the TAR ensured us that there was only one thing that affected climate. All other things were futile.
  10. Mar 28, 2009 #9
    you are trying to fix once source [ CO2 ] to the temp change
    problem is there are many inputs
    solar output is a big one
    we are currently cooler by less solar input do to the current no sun spots cycle
    iceages just may owe more to solar then local effects
  11. Mar 28, 2009 #10


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    A good reference for this is Martin, P., D. Archer, and D. W. Lea (2005), http://www.agu.org/pubs/crossref/2005/2003PA000914.shtml", in Paleoceanography, 20, PA2015, doi:10.1029/2003PA000914.

    This paper uses the positive feedback between temperature and CO2 to account for the temperature swings of the ice age.

    In order to follow this paper, you're going to have to shed some really fundamental misconceptions. Most important, perhaps, is recognizing that whether CO2 lags or leads temperature has nothing to do with the feedback being positive or negative.

    Your question appears to carry an implicit presumption that there's something about the fact that temperature leads CO2 that has an implication for feedbacks being positive or negative. That's just wrong. The real reason for the lead of temperature over CO2 is simply that the loop is being driven by something pushing on temperature, rather than by something pushing on CO2. That something is the Milankovich orbital cycles. As the system settles into a new equilibrium condition in response to changed insolation patterns, there's an interaction with CO2. Whether the loop is a positive feedback or a negative feedback is a consequence entirely of whether the feedback amplifies, or damps, the response of temperature to orbital cycles directly. In either case, you still get temperature leading the CO2 change, because that's the initial stimulus driving the loop.

    Now, you are not likely to just take my word for that as some kind of oracle, so here's a bit of maths that may help. If it's all too long, then just read the comments above and confirm it with the cited paper… which you will find is even longer.

    (A) An example model

    Part of the reason I write long posts is because I like to explain things in more detail. Sometimes it's too much, sometimes it can help. The real answer is above, and here's a demonstration if you want to dig into detail a bit more.

    Let's consider three variables. T for temperature, G for CO2 levels, and X for other input parameters to the combined system.
    T & = & f(G,X) \\
    G & = & g(T,X)
    The function f represents the natural equilibrium level of mean global temperature for a given level of CO2, and g represents the natural equilibrium levels of CO2 for a given mean surface temperature. For a given value of X, there's an equilibrium point where the G and T are balanced with each other. When the system is disturbed, it tends to return to this point.

    You will see graphs a bit like this in the paper I have cited.

    For a given fixed value of X, there's a feedback between T and G. Whether it is a positive or a negative feedback depends on the relative sign of the partial derivatives.
    \textrm{feedback is...} & \frac{\partial f}{\partial G} > 0 & \frac{\partial f}{\partial G} < 0 \\
    \frac{\partial g}{\partial T} > 0 & \textrm {positive} & \textrm {negative} \\
    \frac{\partial g}{\partial T} < 0 & \textrm {negative} & \textrm {positive}

    To a first order, we can use a linear approximation.
    T & = & T_e + a.(G-G_e) + c.X \\
    G & = & G_e + b.(T-T_e) + d.X
    In these equations, Te and Ge represent the equilibrium for X=0. The constants a, b, c, d represent partial derivatives evaluated near the equilibrium. Canceling out G and applying a bit of algebra, we have:
    T & = & T_e + X(ad+c)/(1-ab)

    For the case of the ice ages, X represents an input from the Milankovitch cycles. The initial effect of this is to alter temperatures by altering insolation patterns. There's no particular effect on greenhouse levels, however, except by the feedback with temperature. That is for the Milankovitch parameter X, we have d=0. The equilibrium temperature is:
    T & = & T_e + X.c/(1-ab)
    If a and b have the same sign, then the feedback is positive. If the product is greater than 1, then you have a "runaway" effect, where feedback drives the system without limit far from the equilibrium. But if [itex]0 < ab < 1[/itex], then you have a new stable equilibrium which is amplified by [itex]1/(1-ab)[/itex] over what you have without the feedback. The quantity ab is called the gain.

    From the Epica data, we know that rising temperature tends to drive rising CO2 values. From basic thermodynamics, we know that CO2 increases longwave absorption in the atmosphere, which raises equilibrium temperatures. Thus both a and b are positive, and there is a positive feedback between CO2 and temperature. QED.

    Epica data and concrete values

    Consider the rise out of the last age as seen in the Epica core. This corresponds to a change in X that shifts the equilibrium temperature upwards. The data shows a change in CO2 levels from about 180 ppm to about 275 ppm, and a surface temperature increase of about 9 degrees over the same period. You can get the Epica data here: http://wdc.cricyt.edu.ar/paleo/icecore/antarctica/domec/domec_epica_data.html; except that it doesn't seem to be downloading at present. But I've been using this data myself as an interested amateur, and have it all to hand in my own spreadsheets. Temperature data can be given either as Deuterium ratios (from which temperature is inferred) or it can be given as a temperature directly. Some datasets give temperature above the inversion (up in the atmosphere where precipitation occurs) and some datasets give temperature at the surface. The 9 I have quoted here is the surface, I think, which is what we want.

    The CO2 change from 180 to 275 is a factor of 1.53, which is about 20.6. That is, we have 0.6 of a doubling of CO2. The letter quoted in the first post of the thread suggests a sensitivity to doubling of about 2.8. This sensitivity corresponds to the value of "a" in the simple model, when G is taken as log base 2 of CO2 levels. Assuming that all the CO2 arises from the temperature increase of 9C, and using 0.6 for G-Ge, we get "b" as 0.6/9, or about 0.067. The product ab is thus about 0.2. This is the gain of the positive feedback loop.

    Other feedbacks

    Climate discussions are frequently confused by mixing up even very simple physical concepts. For example, the "warming" due to greenhouse gases is not a continuous heating effect, but a new equilibrium. With a greenhouse effect at work, you get an atmosphere that is being heated from the surface. With a stronger greenhouse effect, you get a higher equilibrium temperature at the surface; but the actual flows of temperature are always from the surface up into the atmosphere. By mixing up the notion of the direction of energy flow at equilibrium with the direction in which an equilibrium shifts when perturbed with additional greenhouse gases, some readers incorrectly think there's some second law violation involved.

    Another problem in feedback discussions is that there are many variables and many feedbacks involved. The sensitivity of climate to greenhouse gas levels is itself determined by all kinds of other feedbacks. Hence in these discussions there is often mention of the water vapour feedback, and lapse rate feedback, and albedo feedback, and so on. These things contribute to the sensitivity "a". The sensitivity of climate to Milankovitch cycles, on the other hand, is amplified by a positive feedback between CO2 and temperature.

    You can get badly tied up in knots if you are not careful to identify which feedbacks and which control variables are being considered in a given analysis. That's a major error made in the other thread.

    Data from the ice ages, including Epica core data, is a very important source of constraining data for the sensitivity of climate to CO2. The evidence suggests sensitivity of around 2.8 degrees per doubling, with wide uncertainty margins. The value of this sensitivity in turn relates to other feedbacks, which contribute to the net warming effect that results from changes in CO2 levels. A value of 2.8 corresponds to some fairly strong positive feedbacks. But you can only know that by comparison with a base level sensitivity to CO2 in the absence of those other feedbacks.

    Cheers -- Sylas
    Last edited by a moderator: Apr 24, 2017
  12. Mar 29, 2009 #11

    You introduced the concept of lapse rate feedback to me in the above discussion. Interesting that it is thought to impose a negative radiative forcing on average. The forcing seems to be positive in the mid to high latitudes while negative in the tropics, with the negative winning out overall.

    Here is another online climate oriented textbook you may find of interest.

    http://stratus.astr.ucl.ac.be/textbook/index.html" [Broken]

    This section covers lapse rate feedback:

    http://stratus.astr.ucl.ac.be/textbook/chapter4_node7.html" [Broken]
    Last edited by a moderator: May 4, 2017
  13. Mar 29, 2009 #12


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    Thank you very much. That looks like an excellent resource. I had not seen it before. The explanations are clear and nicely illustrated, and yet also at a reasonably high level of technical physical detail. It's designed to be used online.

    The comments on lapse rate feedback look very good.

    I've been learning much of the technical details for the relevant physics from "Principles of Planetary Climate", by R.T. Pierrehumbert at the Uni of Chicago, which I mentioned also in the other thread. It deals with physical basics that can be applied to any planet, and covers derivation of lapse rate, radiative transfers, circulation, condensation, etc at very high levels of formal detail. It's not designed for on-line use; merely made available as a large pdf file you can download from the book's website. It's not yet published, and the download (13.6 Mbytes) is a working draft, but nearly complete.

    The major difference is that Pierrehumbert's book focuses on deeper physical principles of thermodynamics, radiation and chemistry that can be applied for any planet. This also makes it very hard reading, and I get a bit lost in some of it. Your reference is going to be a much better introduction.

    Your reference also has more about feedbacks. Feedbacks are basically a diagnostic abstraction of mutually interacting causes and effects. The real physical basis are the functions which give quantities like temperature, humidity, absorption, pressure, and so on in relation to each other. Ultimately, this becomes a large set of simultaneous differential equations; though you can get a number of useful approximations. You can infer feedbacks from the equations, using principles a bit like I have given above with the partial derivatives, but that's basically a way of abstracting out aspects of the underlying equations. It's the equations themselves that are the ultimate description.

    Your reference seems to be at a higher level of abstraction, which is going to be more useful for most readers here -- me included.

    I'd started to write some more comments on feedback generally; but I'll leave it aside for the moment and just post this to back up your recommendation with thanks.

    Cheers -- Sylas
    Last edited by a moderator: May 4, 2017
  14. Mar 29, 2009 #13

    I don't think your posts are too long. I think they are concise, informative, and clearly written.

    Thank you for your contribution.
  15. Mar 29, 2009 #14


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    That is not even true from an anthropogenic point of view!

    Aerosols, Land use as well as NOx and HFC emissions are other factors.

    From your link:

    Last edited: Mar 29, 2009
  16. Mar 29, 2009 #15


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    Excellent Post and greatly appreciated!
    Actually verified that the math was correct.

    Taking it a step further, ice age data shows global temperatures
    varyed 9°C, with CO2 varying from 180 to 275 ppm; a 0.6 doubling.

    Accepted range of CO2 climate sensitivity is between 2 to 4.5°C.
    This implies CO2 contributed to between 15 to 30% of the temperature rise.
    Significant, but not even the majority of the change.

    IPCC has hedged and stated that values above 4.5°C can’t be ruled out.
    However, even 6°C of sensitivity would be only 40%.

    A misconception may be attributing the entire temperature rise to changes in CO2.
  17. Mar 29, 2009 #16
    It is not so much a misconception as it is a convenient strawman argument.

    A common claim by climate skeptics is that AGW is based exclusively on CO2 and ignores any other possible climate forcing. This accusation gets made even when the discussion turns to the glacial/interglacial epochs, where the rise in CO2 is clearly a feedback temperature as the climate responds to distribution changes of insolation and albedo flip.
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