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On temperature and CO2 in the past

Posted on 29 May 2010 by Riccardo

Guest post by Riccardo

One of the most famous paleoclimate graphs for "amateur climatologists" like me is the Vostok ice core reconstructions of temperature and CO2 concentration over the last 420 kyr. It shows how nicely the two follow each other and that our climate has overall "oscillated" within two relatively well defined limits. One may wish to look at this correlation a little better. So let's take the Dome C ice core data which cover 800 Kyrs and plot temperature versus CO2 concentration.


Fig. 1: Dome C temperature and CO2 concentration data (dots) with the best fit line (red line). To make the two series coherent in time, I spline-interpolated both to a common time step of one point each thousand years.

This graph shows how our climate system behaves naturally. The straight line is the fit to the data and in some way represents the correlation between the two quantities. Whatever the driver of these changes was, what we can say is the climate system finds its (quasi-) equilibrium with roughly defined values of temperatures and CO2 concentrations.

This concept is made explicit in a recent paper (Etkin 2010) where the author makes a state-space (or phase-space) analysis of ice cores and recent instrumental measurements. In the graph shown below, the data points, i.e. the (T,CO2) pairs, are connected with lines to show the temporal sequence of the various states. 
 


Fig. 2: State-space plot of the Vostok, EPICA and Law Dome ice core data and Mauna Loa direct measurements. (From Etkin 2010).

As expected, the system behaves chaotically; neverthless, T and CO2 concentration are definitely correlated with a correlation coefficient of 0.86, excluding Law Dome and Mauna Loa data. The green ellipse represents the domain inside which the climate system has naturally wandered for 420 Kyrs.
What the graph also shows is that, starting about a couple of centuries ago, the system has been suddenly pushed out of its shell and moved to a completely different domain. The slope of the curve is hugely different, indeed almost flat, which suggests that the driver of the climate is different from anything seen in half a million years.

Although we were able to come to some general qualitative conclusion from the analysis above, strictly speaking the correlation of temperature should be sought with forcing, not CO2 concentration. The extra energy trapped in our climate, more appropriately called forcing, by an increase in CO2 concentration may be approximated by the simple relation F=c*ln(C/Co) where c is a constant equal to 5.35 W/m2, C and Co are the actual and an arbitrary reference CO2 concentrations. In this way, the CO2 concentration axis may be readily converted into forcing.

Masson-Delmotte et al. 2010 did something similar (and much more!). They made a thorough analysis of the EPICA Dome C data and in their fig. 5b, reproduced below, they show a graph similar to the ones shown above. The difference is that temperature is shown vs. the sum of CO2 and CH4 forcings instead of concentration.

The straight line fit has a slope of 3.9 °C per W/m2, which represents a sort of local climate sensitivity defined as l=DT/F, i.e. the local temperature increase for each W/m2 increase in forcing.


Fig. 3: EPICA Dome C data temperature anomaly vs. CO2 and CH4 radiative forcings (points) with straight line and quadratic best fit to the data. (From Masson-Delmotte et al. 2010).

The authors also added a quadratic fit, which gives a statistically significant improvement of the fit. The slope of the curve is related to the local climate sensitivity and then a non-constant climate sensitivity between glacial and interglacial periods may be inferred. In particular, during the warm periods the climate sensitivity is higher than average. In other words, the temperature increase produced by a forcing is higher when the system is in its warm phases. It's worth noticing that Hansen et al. 2008 also found a higher climate sensitivity in warmer past periods due to slow feedbacks.

The bottom line is that paleo data gives much important information on the way our climate works. They clearly show that we are already far outside the range of natural variability during the last half a million years and heading forward. The news along this path may well not be as good as anyone would like. 

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Comments

Comments 1 to 46:

  1. My immediate impression looking at your top graph was that the residuals are not normally distributed around the regression line, especially at high values, and that a linear model might not be appropriate. Then, scrolling down, I saw the quadratic fit to similar data applied by Masson-Delmotte et al. 2010.

    I've posted previously about the potential risks of using past behavior as an analog for the present. I think it's worth noting that all the previous data points in your graph represent responses of the system interpreted to have been initiated by subtle changes in incoming solar radiation, related to Milankovitch cycles, which set off a complex sequence of feedbacks, partially involving CO2. In the present circumstance, warming is being initiated by increasing CO2, so it's not evident that the same feedback mechanism will prevail. Note that I'm not "saying", I'm asking, because I don't understand the behavior of the system sufficiently well to 'know' anything. Nevertheless, the non-linear trend of the data, together with the extreme departure from "natural" levels of CO2, and the potential for slow feedback mechanism(s) that are not yet fully understood, could pose potentially serious consequences for future warming.
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  2. I would post a similar comment as CoalGeologist: The influence of temperature on CO2 levels is quite linear: about 8 ppmv/K over the 420 kyr Vostok ice core period. The opposite is more problematic: neither in recent times (Law Dome, Mauna Loa), neither in long past times (previous interglacials) there is much influence of CO2 on temperature visible.

    In the previous interglacial (the Eemian), there was a huge overlap between temperature increase and CO2 increase, which makes it near impossible to know the two-way influences. But the end of the Eemian is quite interesting: the temperature (and CH4 levels) were decreasing until a new minimum, while CO2 levels remained high (for unknown reasons). After that, CO2 started to drop about 40 ppmv, but that had no measurable influence on temperature, nor ice sheet formation. Which points to a low influence of CO2 (including fast and slow feedbacks) on temperature. See here
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  3. We have given the climate the biggest kick it has had in millions of years. Is it not likely that the climate will give the biggest fastest response in millions of years? It would seem inevitable that we will go beyond the "well defined limits".

    The evidence, that the Milankovich cycles plus the movement of the earths orbital plane through the solar plane have provided the timing of the Earth's glacial cycles, is overwhelming. Tiny changes in the energy reaching Earth have produced some massive climatic changes.

    The Milankovich cycles might be the trigger, but what was the bullet. We have given that trigger a mighty yank, we will undoubtedly do much learning over the next few decades.
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  4. CoalGeologist,
    as i said at the end of the post, the study of past climate is done not to make analogies but to understand how our climate works. If we had to follow the fit in fig. 1, today's CO2 concentration would correspond to 11 °C which is way beyond any resonable estimate.
    But the problem is still there. Whatever initiated the warming or cooling in the past, whatever the feedback that kicked in, the climate system found its new state in a limited region of T and CO2. Today we're way out of that "natural" region and, at the very least, it's risky.

    FerdiEgb,
    what I showed here is not a detailed analisys of any particular event. On the contrary, I was looking at an overall picture as large as 800 Kyrs of just two variables, T and CO2. For sure it misses a lot of details.

    Tony O,
    the climate proved to be quite sensitive to small changes. Indeed geologists had hard times some decades ago before accepting that Milankovitch cycles were producing such wild swings. We already are beyond the limits, as Etkin 2010 shows, but we still have the right pedal at hand, the brakes.
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  5. FerdiEgb at 08:09 AM on 29 May, 2010

    That's problematic on a number of levels Ferdi.

    Firstly, one can't really analyze the temperature/CO2 relationships through the glacial cycles by simple inspection (other than perhaps assessing temporal lags and the relationships at points at the start and end of transitions where the system has found a new "equilibrium"). Otherwise one really needs to address these questions by modelling.

    More specifically to your point about Eamian temperature/[CO2] relationships, one needs to be careful in addressing this in relation to what we know. The temperature fell very slowly due to Milankovitch effects as we know. That's what dominated these fascinating phenomena. The [CO2] changes were purely feedbacks and relatively small (it's easy to determine that the contribution from [CO2] change of ~ 270-230 ppm, to the 4-6 oC globally averaged temperature change during the period you're describing, was around 0.7 oC within a climate sensitivity of 3 oC - it might have been somewhat more if very slow feedbacks enhanced the Charney sensitivity during these long transitions). But these feedback effects are "mixed in" with the Milankovitch-induced changes and simple inspection of graphs doesn't really allow these to be deconvoluted visually. We should also remember that once [CO2] gets into the atmosphere it can take a long time for levels to drop (e.g. Archer and Brovkin 2008).

    Your statement: "neither in recent times (Law Dome, Mauna Loa), neither in long past times (previous interglacials) there is much influence of CO2 on temperature visible.", is difficult to support in the light of the evidence. During the period (e.g. since mid 19th century) where we've got decent high resolution data from the Law Dome core, and excellent resolution from Mauna Loa, there is a very strong influence of [CO2] enhancement on temperature (around 0.8-0.9 oC's worth of temperature change!). Detailed analysis of attribution indicates that the dominant influence on surface temperature rise is the result of the massive ramping up of atmospheric [CO2] during this period.

    Likewise there is very stong evidence for a high [CO2]-temperature relationship throughout the entire Phanerozoic (see Detailed High CO2 in the past, Part 2, and papers cited in this post.
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  6. Hey, Riccardo, thanks for a really neat post. Fig 2 and Fig 3 are really thought-provoking.

    Chris, your comments are as always very informative.
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  7. Hm, I sometimes have problems with the definition of a "Wild Swing" in temperature. Having looked at the Vostok Ice Cores extensively, we're seeing a delta T of 10 to 12 degrees C-which is very large-but over a space of 25 to 50 kyrs. To put that into a modern-day perspective, its an average rise of about +0.005 degrees per decade. The modern day warming has been at a rate of +0.1 degrees per decade!
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  8. Ned,
    you made my feelings explicit, thanks.

    Marcus,
    I was talking about geologists and, you know, they use a very slow clocks and would call instantaneous something that happens in a few thousand years. :)
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  9. Figure 2 is a pretty stunning visualization. "Thought provoking", as Ned understates.

    Thank you, Riccardo.
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  10. Riccardo,
    Very interesting. The top two graphs are quite telling. The first suggesting CO2 increases with warming, while the second clearly indicates a deviation from this natural locus due to man's excessive fossil fuel combustion.
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  11. "what I showed here is not a detailed analisys of any particular event"

    It seems to me this isn't exactly true because the past 100 years is given very particular analysis by the presence of the Law Dome and Mauna Loa data. So the data that stands outside the green ellipse is generated in a very different way to the rest.

    I thought it's worth posting the Vostok record. Hopefully this version is accurate.

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  12. Very interesting pictures. As Riccardo points out in a comment, the first thing you think when you see figure 2 is that this means that no matter what we do from now on, we will eventually get a temperature increase of at least 11 degrees. That's not good.

    But the situation is very complex, and a first look might be deceptive. There are many variables involved, and we are only keeping track of two - local temperature T and CO2 level C. Lets simplify and assume that local temperature is a good proxy for global temperature. There will be some the temperature forcings T' around (the one due to Mr. Milankovic and others). Then we have a suggested relationship between T and C. That is, we have a an equation f(C)=T, where f is an unknown function, which expresses approximately what temperature we would expect at a certain concentration of CO2. At the same time, we expect C and T to be largely determined by the forcing T', so that we actually have two functions T=t(T') and C=c(T'), related by the condition fc(T')=t(T').

    Actually there are positive feedbacks between T and C. If one rises, so does the other. C can rise because there is a reservoir somewhere (in the oceans, in living stuff etc.) which contributes more CO2 to the atmosphere as the temperature goes up. Historically, the amount of carbon available in the atmosphere plus the carbon in the reservoir is a constant C', because at that time presumably no carbon was added to the system.

    Today we are changing C' by burning fossile coal. This means that at the same level of C, there will be more carbon left in the reservoir than before. It seems to me that this change of C' will change the feedbacks between T and C. But I don't know this for sure, correct me if I'm wrong! Maybe there is some sneaky way of constraining how these feedbacks depend on C'?

    So we would assume that today T and C depend on both T' and C'. We actually have T=t(C',T') and C=c(C',T'). If C' changes, we assume a new relation T=f(C',C), but I can't see how we can reconstruct the way T depends on C' from the paleo data, since C' didn't change before. There are no old data for varying levels of C'.

    The upshot seems to be that we don't really know if we will get the 11 degrees. From these pictures alone it could be 3 degrees or maybe 20. It depends on how the feedbacks between CO2 level and temperature react to an increase in the total amount of available carbon, and paleo data from the last half million years can't help us there.
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  13. Marcel Bökstedt at 20:57 PM on 29 May, 2010

    "As Riccardo points out in a comment, the first thing you think when you see figure 2 is that this means that no matter what we do from now on, we will eventually get a temperature increase of at least 11 degrees."

    Actually Marcel, Riccardo pointed out that todays levels of [CO2] would (in the context of the ice core data), require temperatures of around 11 oC in Antarctica in order to arise naturally by temperature-induced recruitment of CO2 from ocean and terrestrial stores.

    The real point of the data and its presentation is that we are way outside the regime where [CO2] levels are a result of natural phenomenon (the balance between CO2 release and sequestration, and temperature). The data say's little about the Earth surface temperature that will result when the Earth comes to equilibrium with the forcing resulting from 392 ppm (current [CO2]). That requires an understanding of climate sensitivity. The likely values are still centred around 3 oC of surface warming per doubling of [CO2] (with the possibility of a little bit higher sensitivity if very long term feedbacks are included).

    A more general point. The temperatures/temperature anomalies in the Figures (including HR's figure in post 11) are temperatures from proxies within the Antarctic cores. Due to polar amplification, the globally averaged temperature anomalies during these periods were smaller. So the full ~ 8 oC of temperature variation (glacial-interglacial-glacial) of around 8 oC corresponds to a globally averaged temperature change of 5-6 oC...
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  14. chris> I absolutely agree with you on the antarctic amplification, thats why I stressed that T is the local temperature. By unreasonable simplification one could assume that the global temperature was determined by T in some simple way.

    I suppose that what I'm really worrying about is if this type of data give any real information about long term sensitivity. It seems to me that they sample data that are subject to a certain condition - no added carbon to the entire system - that simply isn't satified today.
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  15. Thank you chris for anticipating me, you correctly got my point and explained it probably better than i could do.

    Marcel Bökstedt,
    adding to what chris said, the mechanism you described is in all respect the feedback operating between T and CO2 which there's no reason to think it's not operating now. But this alone can not reasonably tell you what the future temperature will be, and infact i did not quote any in my post. But just to try the impossible, i'll do some rather crude speculations now. (Remember, I'm not a climatologist so I can try weird things).
    If the local sensitivity in Antarctica is about 4 °C/(Wm-2) when considering just CO2 and CH4, you may want to add the ice albedo feedback which amounts roughly to the same forcing as CO2 and CH4 combined. The local sensitivity would then be 2 °C/Wm-2. To make it global we can use a polar amplification factor of about 2 (Masson-Delmotte et al. 2010). So my impossible estimate of the global climate sensitivity would have been 1 °C/Wm-2.

    HumanityRules,
    I'm not sure of what you mean by particular analisys. The Mauna Loa and Law Dome data are shown just to point out that today we are out of the natural regime in place for the last 800 Kyrs. The outcome definitely requires more knowledge than just the T and CO2 paleo data.
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  16. Congratulations Riccardo! I read your guest post several times but could not find any declaration that the CO2 concentration was driving the temperature changes over the Vostok timescales.

    Then I checked the comments and most of them referred to correlation rather than causation. Nothing for me to disagree with here.
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  17. Thank you gallopingcamel. The understanding of current climate is like a puzzle, this post addresses just one piece, better, a tiny part of a piece. Although I may know what the final image will be I cannot tell from the tiny piece. I've been careful to avoid this trap which would cause the discussion to derail.
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  18. Riccardo, the T anomaly for Figure 1 is the T anomaly for Lake Vostok, right? If that is correct, and if the temperature changes are amplified at high latitudes, might that not explain why the temperature changes globally are smaller? Present evidence suggests that the Arctic is warming ~3 times faster than global average, if that holds for the past data and for Antarctica then rather than 11C, the present CO2 might be predicted to raise global temps by 3-4C.

    Or am I wrong ahout the temp record used?
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  19. Marcel Bökstedt at 20:57 PM regarding your comments on C reservoirs, particularly "Historically, the amount of carbon available in the atmosphere plus the carbon in the reservoir is a constant C', because at that time presumably no carbon was added to the system"
    Given that the amount of C that is released into the atmosphere through combustion of fossil fuels is relatively small compared to what is in constant exchange between the atmosphere and (1) the plants and soil and (2) the oceans, then very minor changes in the ratio of the exchange could be a significant factor in what is sequestered or released from the reservoirs being referred to.
    For the soil reservoir, plant growth is the key factor that apart from the obvious inputs, relies on C as the most basic foundation of them all, it being the energy source for soil biology and thus the most basic driver of all plant growth.
    Over the time spans examined in this discussion, CO2 levels have changed from plant starvation levels to still less than desirable levels of today.
    If the 6.5Gt of carbon being released annually by burning fossil fuels today is an important factor, than anything that has, or can vary the estimated 200Gt of C in constant exchange between the plants, soil and atmosphere today has to be allowed for.
    Are there any studies out there that estimate just how much C was being exchanged through biological means when CO2 levels were about 200ppm, because it is not enough just to measure what amounts of CO2 were present in the past, but to allow for the what all other changes it was causing when trying to make the connection with any of the other indicators also measured in order to close the loop.
    A very small change in any of the natural processes could have yielded greater changes than the simple combustion of fossil fuels today.
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  20. Jeff
    the data are from the Dome C but it does not change much. Definitely to compare those data with the global average there is an amplification factor to take into account. In a comment above I quoted the value of 2 from Masson-Delmotte 2010. It would translate to about 5-6 °C, not unthinkable but on the high end side of the accepted range.
    Anyway, I think that a quantitative prediction of the expected temperature rise from just these GHG data is a bit implausible. Masson-Delmotte and co-workers expanded the analysis beyond just GHG and found a climate sensitivity varying between 0.76 °C/Wm-2 for the period 400-800 Kyrs and 0.86 °C/Wm-2 for 0 400 Kyrs, both near the central IPCC estimate. What may be a cause of concern is its increase over time and over forcing (the parabola in fig. 3 here).
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  21. Great presentation. I see there's a more thinly dotted area in the domain occupied for 420000 years, at about a quarter down from the oval top. Would this be the transitional times between glacials and interglacials?
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  22. jyyh,
    this is a good point, the distribution of the density of points is not uniform. It's higher at the two extremes, expecially in the cold phase region. This means that the climate system "prefers" to stay in the cold phase and sometimes switched to the warm phase, the two more stable phases. They are called stable attractors.
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  23. In #16, Mr. Camel states:
    "could not find any declaration that the CO2 concentration was driving the temperature changes"

    However, Riccardo stated this: "... starting about a couple of centuries ago, the system has been suddenly pushed out of its shell and moved to a completely different domain. The slope of the [temp-CO2] curve is hugely different, indeed almost flat, which suggests that the driver of the climate is different from anything seen in half a million years." (Italics added).

    Perhaps if one drops back a bit and asks "What has driven this hugely different behavior of the temp-CO2 system?" See the following graph:



    Notes: 1. De-seasoned atmospheric CO2 from 3 widely-spaced sample stations (Mauna Loa, Barrow and Palmer, Antarctica)
    2. Composite Law Dome Ice Core (3 sample locations) Ice core air age used as time axis.
    3. Carbon emission data Trailing 5 years (residence time?) summed and expressed in gigatons.

    Looks like a trend to me (pardon the shameless extrapolation into the future). So let's turn the question back on the reader: What explains the relationship between increased burning of fossil fuels and increased atmospheric CO2? And what else do you offer for Riccardo's hugely different driver?
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  24. "In particular, during the warm periods the climate sensitivity is higher than average. In other words, the temperature increase produced by a forcing is higher when the system is in its warm phases."

    This assertion seems to be contrary to the basics of Eco-cybernetics. If we treat the Earth as a global Ekosfera complex system - with specific boundary conditions, the addition of energy to stabilize it. It is "richer" in energy - "can afford" to run, to strengthen the equivalent feedback - the more stable equilibrium.
    Yes because of the slowness of action of some feedback, greater stability of the system warm can be seen only over longer periods of time.

    For example, biocenosis "warm" are more biodiversity, which stabilizes ecosystems (generalizing - The diversity-stability debate, McCann, 2000). In this way, they (the biocenosis - ecosystems), one of the elements stabilizing the climate.

    "In the previous interglacial (the Eemian), there was a huge overlap between temperature increase and CO2 increase, which makes it near impossible to know the two-way influences. ..."

    "... professor Jianli Chen of the University of Texas also found that in a previous inter-glacial period called the Eemian, global temperatures were 6C higher than today, with CO2 levels roughly the same."

    ... the same - why?
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  25. How can we be wrong about the valuation feedback, I again recommend: Interglacials, milankovitch cycles, and carbon dioxide, (Marsh, 2010)
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  26. Gallopingcamel, are you saying that CO2 doesn't cause warming? You may want to check out a few of the other pieces of the puzzle, for example some recent posts here.

    Over these timescales, warming increases CO2 which causes more warming: The significance of the CO2 lag

    Has the greenhouse effect been falsified?
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  27. Arkadiusz Semczyszak at 23:20 PM on 31 May, 2010

    Which study by "Jianli Chen" are you talking about Arkadiusz? You keep saying stuff that deeper investigation shows to be untrue. Can you not be more specific in your reference to papers rather than making all these unspecified quotations? I doubt the Eemian was 6 oC warmer than now, but unless we know what you're referring to how can we explore this???
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  28. I'm trying to understand what is said. It turns out Fig. 1 in the post has nothing to do with climate sensitivity, much less with climate sensitivity increasing with temperature. The true message of Dome C is something entirely different.

    To see this, let's look at it the other way around.



    That is, CO2 concentration is considered as a function of temperature anomaly (relative to current global average). There is obviously some noise added to the function, but long term equilibrium values can be estimated by a trend line using least square fit.

    The temperature-CO2 distribution can be approximated by the quadratic

    C = 266.6 + 5.89×Δt - 0.333×Δt2 (ppmv CO2)

    It can be translated to atmospheric partial pressure of carbon dioxide as a function of temperature anomaly.

    As density of CO2 is about 1.52 times greater than that of air, at standard atmospheric pressure of 1 atm (101.325 kPa) with CO2 concentration of 266.6 ppmv, partial pressure of carbon dioxide is 405 μatm (41 Pa).

    p = 405.1 + 8.95×Δt - 0.506×Δt2 (μatm CO2)

    The trend line above represents the equilibrium pressure. This is a long term equilibrium value for each temperature after taking into account the temperature dependent transfer between different reservoirs and all the possible CO2 (short & long term) feedbacks to temperature, because the time interval covered is extremely long (several hundred thousand years), much longer than relaxation time of any feedback.

    The largest reservoir of carbon dioxide by far is seawater. It contains about 1.215×1017 kg of dissolved CO2. All the other reservoirs (soil, vegetation, atmosphere) taken together contain only several percent of this amount, so they are negligible on this timescale. Ocean turnaround time (including deep waters) is several thousand years, much shorter than the timescale considered, therefore atmospheric CO2 partial pressure fluctuates around the equilibrium value determined by average temperature of seawater.

    Solubility of carbon dioxide in seawater decreases with increasing temperature. It means increasing partial pressure, for realistic temperatures a doubling for an increase of about 16 K.

    If temperatures recovered from Dome C core would mirror average ocean temperature, one would expect an exponential increase of CO2 partial pressure, that is, a convex function, not a concave one as seen in the figure.

    The only way out of this mess is to suppose average ocean temperature anomaly is a nonlinear function of Dome C anomaly. From the data above even the form of this dependence can be guessed:

    ΔT = 23.1×log(p/p0)

    where p0 is the equilibrium pressure of 405 μatm at 0 K anomaly and ΔT is ocean temperature.



    What we see here is just the opposite of the claim expressed in the article above. Global climate is clearly driven by ocean temperature, not by polar one. And rate of change in ocean temperature anomaly, as it is shown by history, is not magnified, but diminished by increasing polar temperature.
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  29. Berényi Péter,
    allowing for your assumption that the ocean temperature reflects global average temperature, what you derived is the Antarctic amplification. Massson-Delmotte, in their much more detailed study quoted above, found it equal to about 2. Your variable amplification at high ΔT converges nicely with this value while it's lower for lower ΔT.
    Does this make sense? Yes. Indeed, an increased polar amplification is the same thing as an increased local sensitivity, which is exactly what Masson-Delmotte claimed.
    You misinterpreted their claim. Maybe quoting Hansen who found that the global sensitivity too may be higher at higher temperatures misled you.
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  30. #29 Riccardo at 18:45 PM on 4 June, 2010
    the ocean temperature reflects global average temperature

    No, it does not. It reflects global average temperature of seawater. It is very far from average surface temperature, mostly determined by sea surface temperature close to the ice edge where downwelling can occur. This temperature is pretty constant as long as there is an ice edge somewhere. Current temperatures below the thermocline (75% of ocean volume) are close to 3°C everywhere.

    what you derived is the Antarctic amplification

    Yes, you can look at it that way. But it is the Antarctic amplification relative to average ocean temperature.

    an increased polar amplification is the same thing as an increased local sensitivity

    From the trendline alone no climate sensitivity can be derived. It represents equilibrium between temperature and CO2 partial pressure. At equilibrium there is no forcing by definition and the system's response to no forcing is only random fluctuation at best.
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  31. Berényi Péter,
    sorry if I misunderstood what you said, this sentence:
    "Global climate is clearly driven by ocean temperature"
    made me think that you believe that the global temperature is, one way or another, linked to the ocean temperature.

    As for sensitivity, you probably give a different definition than commonly accepted. Equilibrium climate sensitivity is usually defined with respect to an (arbitrary) state after the system reached the new equilibrium, i.e. λ=F/ΔT where ΔT is the equilibrium temperature difference between the two states. Using this definition, you can derive it from paleo data exactly because you can safely assume that the system reached equilibrium.
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  32. #31 Riccardo at 22:58 PM on 4 June, 2010
    made me think that you believe that the global temperature is, one way or another, linked to the ocean temperature

    I do. If that's what you mean by "reflect", I am sorry. However, it is important that "polar amplification" relative to average ocean temperature or average surface temperature are two very different beasts.

    Using this definition, you can derive it [climate sensitivity] from paleo data exactly

    No, you can not. F in your equation is not preserved. There is no fossil record of TOA net radiation balance. You can assume one, but as we know this kind of reasoning has its own problems.
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  33. You are walking on very thin ice with your last sentence, Berényi Péter. If nothing can be calculated using known physical laws we can have no CO2 nor temperature reconstructions; nothing, i'd say. Science would not exist at all.
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  34. #33 Riccardo at 16:55 PM on 5 June, 2010
    If nothing can be calculated using known physical laws we can have no CO2 nor temperature reconstructions

    Who said nothing? It is paleo TOA net radiation budget that can't be calculated using either known physical laws or otherwise. Fossil cloud cover data are nowhere to be found, for example.
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  35. Berényi Péter,
    read again the post and look at the graphs, it's about CO2 and fig 3 adds methane. That's all it's said.
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  36. #35 Riccardo at 04:41 AM on 7 June, 2010
    That's all it's said.

    Nope. It says "The slope of the curve is related to the local climate sensitivity and then a non-constant climate sensitivity between glacial and interglacial periods may be inferred. In particular, during the warm periods the climate sensitivity is higher than average. In other words, the temperature increase produced by a forcing is higher when the system is in its warm phases."

    But the slope of the curve is not related to climate sensitivity, local or otherwise. It is determined by CO2 solubility in seawater as a function of water temperature and by the relation between ocean and East Antarctic plateau temperatures.

    Climate sensitivity comes nowhere into the equation.

    You also claim in the article "They clearly show that we are already far outside the range of natural variability during the last half a million years and heading forward."

    Now, that's true. Except it is neither "we", nor temperature, but carbon dioxide partial pressure in the atmosphere.

    This is the only tiny part of the half million years long dataset, that actually tells us something about climate sensitivity to CO2 variations. Because this is the only time when there is a well documented change in carbon dioxide independent of ocean outgassing.

    And the story it tells is rather interesting. During the fifty years between 1958 and 2007 atmospheric CO2 has increased from 314.82 ppmv to 380.42 ppmv above Antarctica.

    If the linear CO2-temperature relation derived from Dome C ice core is mindlessly applied to this 65.6 ppmv increase, it would imply a corresponding temperature jump of 8.12 K in fifty years, which is observed not to occur. On the other hand with the quadratic fit it is plainly impossible, because with that formula carbon dioxide concentration could never even increase beyond 293 ppmv. Therefore in this respect we are on unknown ground for sure.

    However, as it happens, we also have an almost complete temperature record for the Vostok site since 1958. No surface temperature trend is measured in fifty years (0.0159 ± 0.0177 K/yr).

    The null hypothesis, that local climate sensitivity to CO2 is zero there, cannot be rejected.
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  37. Berényi Péter,
    it looks like you're just trying to engage a controversy not about the science but just for the pleasure to say something.
    The sentence you quote from the post is not referred to CO2 concentration but to forcing. Please try to do science, otherwise is just a waste of time.
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  38. BP writes: This is the only tiny part of the half million years long dataset, that actually tells us something about climate sensitivity to CO2 variations. Because this is the only time when there is a well documented change in carbon dioxide independent of ocean outgassing.

    Sorry, but this comment of yours is a real mess. First, there's never a change in atmospheric CO2 independent of the ocean/atmosphere CO2 exchange. Right now we're adding CO2 to the atmosphere, and about half of it is ending up in the oceans. At the end of a glacial stade, when temperature begins to rise rapidly, the CO2 that moves from the ocean to the atmosphere amplifies the warming. The relationship between CO2 and temperature is not that T influences pCO2 via solubility in seawater; it's also CO2 influences T via radiation. Both of these were true at the last glacial maximum and both are true today!

    The magnitude of that feedback does in fact tell us something about climate sensitivity -- a low sensitivity implies a low feedback. See, e.g., Annan and Hargreaves 2006.

    I don't know why you think that we can't draw any conclusions about climate sensitivity from paleoclimate data ... or that we can only draw conclusions about climate sensitivity when CO2 is a feedback rather than a forcing.
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  39. Sorry, when I wrote "The relationship between CO2 and temperature is not that T influences ..." there is obviously a "just" missing there. It should be

    The relationship between CO2 and temperature is not just that T influences pCO2 via solubility in seawater; it's also CO2 influences T via radiation. Both of these were true at the last glacial maximum and both are true today!
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  40. And again, when I wrote "I don't know why you think [...] that we can only draw conclusions about climate sensitivity when CO2 is a feedback rather than a forcing"

    I actually meant exactly the opposite.

    Argh. This is karmic justice for my referring to BP's comment as "a mess".

    Next time I write a comment here I will read it at least three times before clicking Submit. In the mean time, apologies to everyone reading this thread.
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  41. I'm with Bérenyi Péter on this one. I think that he is asking a hard question, one that worries me too. I also believe that what he writes is related to my too complicated and too vague comment earlier in this thread.

    The problem as I see it is that in a technical, mathematical sense there seem to be too many unknowns in the equations to say something definite about climate sensitivity by paleographic studies. Maybe I'm just missing a point. The problem enters when you interprete figure 1, but it seems to me that it also enters into other attempts to estimate sensibility using historical investigations of climate.

    There are two variables that should determine the system: The temperature forcing T' (from the sun) and the total amount of carbon in the atmosphere and in seawater C'. I assume that C' did not vary in the time frame we are considering. If it did, this would only make things more complicated. On the other hand, T' has definitely changed (Milankovich etc). So we do have a lot of data on the variation of temperature T at the dome and the carbon concentration in atmosphere C as long as C' is constant.

    There are four variables T,T',C,C', and it seems that figure 1 can only give one approximate relation. But for two of the quantities to determine the two others, we need two independent relations between the four quantities.

    We don't have any historical record of what happens when the total amount C' goes up - in the time frame we are considering it never happend before, but this is what we are doing today. What we want to do is to compute the derivative dT/dC' which would tell us how much the temperature (at least at the dome) goes up if we add some more CO2 to the system.

    To get an estimate for the sensibility, we need an independent constraint on the variables involved. This cannot come from the historical data, but maybe we can derive it in another way. It could for instance come from an analysis of how the temperature T at the dome is related to the temperature of the sea at different levels. This could possibly determine how much of the CO2 goes into the atmosphere, and how much goes into the sea. But now the physics is getting too complicated for me.
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  42. Marcel Bökstedt,
    no doubt the problem is complicated and be sure no one will ever make any claim on the global climate sensitivity just from CO2 and T from an ice core. I didn't, indeed.
    But having said this, you can still have good informations on climate sensitivity as crudely shown before. For an undoubtely better and more detailed explanation I'd suggest a carefull read of both section 2 in Hansen et al. 2008 and section 4 in Masson-Delmotte et al. 2010 quoted in the post.
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  43. Riccardo> I can't see that Hansen et. al. discuss this problem in section 2, if they do maybe you can give a more precise refrence? They do consider the "Vostok ice core" and plot forcing and GHG forcing against time. They claim that this determines long term sensibility of about 6 degrees for doubling of atmospheric CO2.

    But what they don't say anything about is the following: Suppose that you add a certain quantity CO2 to the system. How much of this will eventually stay in the atmosphere and contribute to the warming, and how much will eventually stay in the ocean? One point is that "eventually" is a long time, so any quick answers are suspect. And Hansen does not discuss this point in that particular paper as far as I can see.

    My place does not have an electronic subscription to get Masson Delmotte. Maybe you could just tell if it approaches this question?
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  44. Marcel Bökstedt,
    not sure i understand what you mean by "add a certain quantity CO2 to the system". As far as climate sensitivity and climate are concerned what matters is how much is in the atmosphere contributing to the forcing. The latter is measured directly from the ice cores, whatever happens to the other CO2 reservoirs is irrelevant for the determination of climate sensitivity.
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  45. Riccardo> Yes, I agree with your analysis. Only the CO2 in the atmosphere should contribute to warming.

    But it is not true that the other CO2 is irrelevant to climate sensibility, because it will interact with the rest of the system. If we warm the planet and the sea, some of the dissolved CO2 will go into the atmosphere.

    What is happening today is that we are producing CO2, which is initially added to the atmosphere. This will initially add to the amount of CO2 in the atmosphere, but as we know, some of it will go into the sea and do bad things there.

    But the CO2 will not stop moving. We are talking about long term effects here, not short time climate sensitivity, so we will have to wait and see what happens to our added CO2. Some of it will go into the deep sea beacause of slow overturning. Some of it will go back to the atmosphere as the sea warms.

    The CO2 we initially produced will probably eventually contribute an increase in the CO2 in the atmosphere, and probably also an increase in the CO2 in the sea etc. But as you say, only the amount that goes into the atmosphere will contribute to warming.

    The eventual warming produced by the amount of CO2 we added, will only depend on the amount of CO2 which ends up in the atmosphere. On the other hand, it does not seem so easy to compute how big this proportion is. And if we don't know this, we can't say how big the long time climate sensitivity is for burning a certain amount of coal.
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  46. Marcel Bökstedt,
    i'm not denying the existence of the carbon cycle. But whatever it is, in the end only the concentration in the atmosphere is relevant to the forcing. If I can measure it, that's it, the full and actual carbon cycle is there. Only if we do not have access to it or if we want to make projections, we need to consider the full carbon cycle as you say.
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