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Climate Hustle

Understanding the CO2 lag in past climate change

Posted on 5 January 2011 by Anne-Marie Blackburn

Earth’s climate has varied widely over its history, from ice ages characterised by large ice sheets covering many land areas, to warm periods with no ice at the poles. Several factors have affected past climate change, including solar variability, volcanic activity and changes in the composition of the atmosphere. Data from Antarctic ice cores reveals an interesting story for the past 400,000 years. During this period, CO2 and temperatures are closely correlated, which means they rise and fall together. However, changes in CO2 follow changes in temperatures by about 600 to 1000 years, as illustrated in figure 1 below. This has led some to conclude that CO2 simply cannot be responsible for current global warming.

Figure 1: Vostok ice core records for carbon dioxide concentration and temperature change.

This statement does not tell the whole story. The initial changes in temperature during this period are explained by changes in the Earth’s orbit around the sun, which affects the amount of seasonal sunlight reaching the Earth’s surface. In the case of warming, the lag between temperature and CO2 is explained as follows: as ocean temperatures rise, oceans release CO2 into the atmosphere. In turn, this release amplifies the warming trend, leading to yet more CO2 being released. In other words, increasing CO2 levels become both the cause and effect of further warming. This positive feedback is necessary to trigger the shifts between glacials and interglacials as the effect of orbital changes is too weak to cause such variation. Additional positive feedbacks which play an important role in this process include other greenhouse gases, and changes in ice sheet cover and vegetation patterns.

The only conclusion that can be reached from the observed lag between CO2 and temperatures in the past 400,000 years is that CO2 did not initiate the shifts towards interglacials. To understand current climate change, scientists have looked at many factors, such as volcanic activity and solar variability, and concluded that CO2 and other greenhouse gases are the most likely factor driving current climate change. This conclusion is not based on the analysis of past climate change, though this provides key insights into the way climate responds to different forcings and adds weight to the several lines of evidence that strongly support the role of greenhouse gases in recent warming.

This post is the Basic version (written by Anne-Marie Blackburn) of the skeptic argument "CO2 lags temperature". This argument actually peeped its way into the top ten during December but then "We're heading into an ice age" shouldered its way back to the #10 spot (so there's a real dog fight between those two to climb over each other in the rankings).

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Comments 201 to 246 out of 246:

  1. gallopingcamel:

    As "apiratelooksat50" and others including myself have pointed out many times, the uncertainties are great.

    Your own rhetoric in this thread strongly suggests that you don't actually believe this. What you seem to believe — with an amazing degree of certainty - is that any potential negative consequences of AGW are negligible, or less dangerous than taking action.

    In the real world, "uncertainty" means that things could be worse than the best available science predicts. Using the things we don't know as an argument in favor of complacency would make no logical sense even if competent, peer-reviewed science supported doing so, which it certainly doesn't.
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    Moderator Response: ... and discussion of that topic belongs on the Argument thread "The science isn’t settled."
  2. Using the things we don't know as an argument in favor of complacency would make no logical sense even if competent, peer-reviewed science supported doing so, which it certainly doesn't.

    Garbled that, sorry. I mean that it would make no logical sense even if the science were far more uncertain than it actually is.
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  3. From Roles of Volcanic Eruptions, Aerosols and Clouds in Global Carbon Cycle

    Gu, L., et al, University of California - Berkeley Department of Environmental Science, Policy and Management, "Roles of Volcanic Eruptions, Aerosols and Clouds in Global Carbon Cycle", 2001

    After Mt. Pinatubo erupted in June, 1991 several observations were made by scientists. Ash and other particulate matter created a haze around the Earth in the upper atmosphere and effectively lowered the global temperature by about 0.9 degrees F.

    This is a clear case of cause and effect. (Less energy input into the system results in lowered global temperatures.)

    Also, the rate of which CO2 was added to the air was noticed by scientists to slow down for the next two years. From the article, "Many scientists previously thought the reduction in sunlight lowered the Earth's temperature and slowed plant and soil respiration, a process where plants and soil emit CO2. But this new research shows that when faced with diffuse sunlight, plants actually become more efficient, drawing more carbon dioxide out of the air."

    Again, a clear representation of cause and effect. (Diffuse sunlight leads to more efficient photosynthesis. Then, the more efficient photosynthesis leads to a drop in the atmospheric growth rate of CO2.)

    The lowered temperature also contributed to lower CO2 inputs to the system by slowing down plant and soil respiration. Cause and effect once again.

    Therefore, we have the dominant factors of a volcanic eruption and the resulting diminishment of sunlight reaching the Earth's surface. The diffuse sunlight allowed plants to conduct photosynthesis more efficiently (uses CO2). The lowered temperature slowed down cellular respiration (produces CO2).

    While temperature and CO2 did respond in kind, neither factor was directly responding to the other. A clear case of an outside factor(s) influencing both dependent variables.

    Also, it should be noted that this rapid decrease in temperature that persisted for two years, is almost as great as the gradual change in global temperature being attributed to AGW over the last 150 years (0.9 versus 1.4). I don't recall any environmental catastrophes during that time perioid.
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    Moderator Response: [muoncounter] You continue to take this thread off-topic. Pinatubo is well-researched and included in climate modeling. Your post has no apparent point.
  4. I have a comment pertaining to GC's post @ 197. But, first I would like to know if there is an official AGW hypothesis so I don't get accused of being in error.

    Thanks.
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    Moderator Response: This is the wrong thread for that. Look through the Arguments list to see if you can find a more appropriate thread.
  5. 204, apiratelooksat50,

    Thank you! You've provided a wonderful example of more evidence that the overly simplistic thinking that CO2 must always lag temperature is childishly flawed.

    The mechanisms involved are fairly easily understood, even if their interplay is at times surprising, but the point is made. One cannot simply say "this is what happened before, so it must always happen that way."

    The system is reasonably complex, and every factor affects other factors, which feedback on the system and affect everything else.

    One must understand how it all fits together to make a rational, intelligent statement about the system as a whole.

    The "CO2 lags temperature" statement is thus demonstrated to be insufficiently sophisticated to be used as an argument against the current effects of CO2 on climate.

    It's rather like a child who knows that 2+2=4, and so argues that it is therefore quite obvious that 2+3=4 and 2+4=4, and in fact 2+anything=4. It's clearly wrong, to anyone that understands 2nd grade math, although convincing the child of his naivety may be difficult.

    But your example does help to demonstrate the point.

    Well done.
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  6. Apiratelooksat50,

    It would be very helpful if you would take time to consider what you are going to type before you make your next post. So far you've been less than coherent, making it difficult to determine what point (if any) you are attempting to make.
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    Moderator Response: Also please look for the most appropriate thread on which to comment. Don't worry about your comment being overlooked because it's on a different thread. Most regular readers check the "Recent Comments" page you can get to from the link in the horizontal blue bar at the top of the page.
  7. apiratelooksat50 - AGW is not so much an hypothesis as an outcome from the current theory of climate. There obviously is no "official" version in science, but if you want to avoid strawman arguments, then its best to refer to IPCC WG1 reports. That way instead of claiming "AGW states this", you can instead say "the consensus view as expressed on pg xxx of WG1". This gets everyone on the same page immediately. For arguments about past CO2 level, you want Ch6 - paleoclimate.
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  8. Muoncounter @203 - The point of my post is to demonstrate that though CO2 and temperature are inexorably linked, this is a clear example of an external factor causing changes in both. It supports the orbital changes theory as an initiator of change, and gives further credence to at least the possibility of even more external factors influencing the rise and fall of temperature and CO2.

    To Sphaerica @204:
    I've never stated, nor do I think that temperature always precedes CO2. I do think they are linked and driven by other more dominant and stronger variables.

    Try reading this which states in the summary.

    "The energy transfer processes that occur at the Earth’s surface are examined from first principles. The effect of small changes in the solar constant caused by variations in the sunspot cycles and small increases in downward long wave infrared flux due to a 100 ppm increase in atmospheric CO2 concentration on surface temperature are considered in detail.

    The changes in the solar constant are sufficient to change ocean temperatures and alter the Earth’s climate. The effects on surface temperature of small increases in downward LWIR flux are too small to be measured and cannot cause climate change. The assumptions underlying the use of radiative forcing in climate models are shown to be invalid. A null hypothesis for CO2 is proposed that it is impossible to show that changes in CO2 concentration have caused any climate change, at least since the current composition of the atmosphere was set by ocean photosynthesis about one billion years ago."
    Author: Roy Clark
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  9. " The point of my post is to demonstrate that though CO2 and temperature are inexorably linked,"

    Yes. However, rising temperatures are NOT the cause of this CO2 rise. Eventually those carbon feedback will also cut in (very slow feedbacks) and FURTHER raise the temperature. You seem to have ignored so far the fact isotopic signature of CO2 in atmosphere is fossil based whereas isotopic signature in ice bubbles from past show CO2 from carbon cycle.

    Try reading some peer-reviewed literature on the subject.
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  10. Muoncounter @203 - The point of my post is to demonstrate that though CO2 and temperature are inexorably linked, this is a clear example of an external factor causing changes in both. It supports the orbital changes theory as an initiator of change


    There's got to be a name for the "if X can cause Y, Y must always be caused by X" fallacy.

    This guy apiratelooksat50's teaching science to kids, right?

    Grrr ...

    So apiratelooksat50 accepts mainstream science (orbital changes can initiate change) but rejects the fact that increased CO2 can initiate change ...

    due to ideology.

    That's the only possibility. There's no logical connection between the two positions.

    Rockfalls can kill people, therefore guns can not kill people.

    An exactly congruent analogue to his point.
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  11. 208, apiratelooksat50,

    appinsys is a joke. If that's where you go for "information" then you are a lost cuase.

    The link you submitted is hysterical. What is most laughable (aside from the fact that his argument is so far out of the mainstream as to be the equivalent of alchemy) is that he went to such lengths to disguise his litany in the form of a published, peer-reviewed paper.

    Please don't quote from such nonsense and expect to be taken at all seriously.
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  12. apiratelooksat50's Roy Clark cite is from Energy and Environment, a "journal" that openly admits it is politically driven.

    Is this what science teacher apiratelooksat50 believes should be the future of science? Journals explicitly stating their political bias and saying they'll publish damn near any paper that fits their *political*, not scientific, gateway?
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  13. @gallopingcamel: "Enough of the straw man approach."

    Yes, please stop using strawman arguments.

    "It may surprise you when I assert that CO2 "always" correlates with climate as it affects the energy balance through the well understood process of capturing long wavelength radiation."

    You may assert it, but in fact you'd be wrong if by "correlating with climate" you mean exactly correlating with temperature. CO2's effect on temperatures is not direct. Sure, the energy imbalance may closely follow the amount of CO2, but the effect of the energy imbalance are anything but linear.

    "Where we diverge is in the magnitude of the effect in relation to other things that influence climate, such as water vapor, clouds, aerosols, cosmic rays etc."

    We do diverge on that. The problem is that you have no evidence to support your position.

    "What should be red flags to those of you who are so sure that CO2 is the magic bullet of climate change is the inability of the modelers to explain past climate change and their lack of predictive powers."

    That's not a logical argument. Why would uncertainty in models change the basic physical properties of CO2?

    Also, their "lack of predictive powers" is highly subjective. In fact, models have worked pretty well so far, and there is no lack of explanation for past climate change.

    Again, it's quite simple: CO2 used to be a feedback, now it's a forcing. You have yet to even come close to challenging this simple fact.

    "As "apiratelooksat50" and others including myself have pointed out many times, the uncertainties are great."

    Not so great that we cannot have a pretty good idea that CO2 sensitivity is between 2.5 and 4C.

    "We are trying to measure changes of a few tenths of a degree in measurements that oscillate over very wide ranges from night to day and summer to winter."

    Appeal to complexity

    "What we know about climate change is vastly exceeded by what we don't know. "

    Again, appeal to complexity. Just because you don't understand the science doesn't mean it isn't true.

    "Those who express certainty that CO2 is driving modern climate come across as zealots rather than scientists."

    Well, the evidence supports it, so it is very likely to be true. Of course, certainty is for fanatics, but that doesn't mean we can't evaluate the chances of something being true or not. To argue otherwise is simply not logical.

    When a lot of evidence points one way, and virtually no evidence points the other way, then chances are the one supported by evidence is true. Again, that may not be a very romantic view (I suspect most contrarians get a kick out of being the underdog), but it's the truth.

    "You have it backwards. It is up to the proponents of AGW to make better case for the hypothesis."

    Nice try. As others have pointed out, the case of AGW has been made. It is up to you to disprove. So far, you've been doing an extremely poor job at it. Perhaps it's time to reevaluate your position?

    "Like the above esteemed scientists"

    That's sarcasm, right? Singer and Lindzen are far from being esteemed scientists. They are scientists-for-hire who've been shown to be wrong time and time again.

    "Trenberth's "rebuttal" of Lindzen & Choi 2010 was a fine piece of nit picking but failed to change the main conclusions of the paper."

    Actually, Trenberth's rebuttal left Lindzen & Choi in tatters. But keep rooting for the "underdogs," I'm sure they'll be vindicated in the third act, right?
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  14. @apiratelooksat50: "It supports the orbital changes theory as an initiator of change"

    Yeah, except we have a pretty good idea that orbital changes aren't responsible for the current warming.
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  15. Apiratelooksat50,

    The fact that your cite, Roy Clark, thinks the current gaseous composition of the atmosphere has held steady for the last billion years should tell you all you need to know about his competence (which is nil). The quality of your arguments suggest you aren't really thinking about the information you're assimilating, but simply repeating it uncritically.

    Nice Jimmy Buffet reference though.
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  16. 1. It is easy to obtain confirmations, or verifications, for nearly every theory — if we look for confirmations.

    2. Confirmations should count only if they are the result of risky predictions; that is to say, if, unenlightened by the theory in question, we should have expected an event which was incompatible with the theory — an event which would have refuted the theory.

    3. Every "good" scientific theory is a prohibition: it forbids certain things to happen. The more a theory forbids, the better it is.

    4. A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice.

    5. Every genuine test of a theory is an attempt to falsify it, or to refute it. Testability is falsifiability; but there are degrees of testability: some theories are more testable, more exposed to refutation, than others; they take, as it were, greater risks.

    6. Confirming evidence should not count except when it is the result of a genuine test of the theory; and this means that it can be presented as a serious but unsuccessful attempt to falsify the theory.

    7. Some genuinely testable theories, when found to be false, are still upheld by their admirers — for example by introducing ad hoc some auxiliary assumption, or by reinterpreting the theory ad hoc in such a way that it escapes refutation. Such a procedure is always possible, but it rescues the theory from refutation only at the price of destroying, or at least lowering, its scientific status.

    Karl Popper, "Conjectures and Refutations", 1963
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    Moderator Response: This belongs on the thread "The Science Isn't Settled." Anyone who wants to tespond, do so there. Responses here will be deleted.
  17. apiratelooksat50 - I have posted a response on Is the Science settled?
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    Moderator Response: Thank you for redirecting the discussion!
  18. Why are you pointing to 0.6% of an area to refute the effect over the whole? What makes it more important than the other 99.4%
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  19. gallopingcamel

    The problem you have is that while we're talking about global warming, you're only focusing on some regions. And as I've already pointed out to you, regional factors can have a considerable impact on regional temperatures. To suggest that this is not what the theory states only shows that you haven't done your homework. You might want to read this FAQ, and then read the whole of chapter 11 for more information on regional climate change. Note also that uncertainties and difficulties are clearly stated.

    But by all means, if you can show that the AMO or any other factor can explain recent trends in global temperatures, please provide the evidence.
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    Moderator Response: I deleted GC's comment because it is off topic for this thread, and because he knows perfectly well how to find the appropriate threads.
  20. To Trueofvoice @215;
    Nice catch on the JB reference. First person on any of these sites to do that. Do libs not listen to Buffett? ;)

    Also, Roy Clark was not referring to the climate holding steady, but instead to the establishment of the current climate and it's basic ranges of gaseous concentrations. It took billions of years of photosynthesis from cyanobacteria and blue-green algae to oxygenate the atmoshpere.

    Thanks for being civil.
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  21. Pirate,

    Clark is completely wrong in his assertion of atmospheric gas concentrations being "set", and his timeline is off as well. I'm not going to say more here because I'm already dragging the thread off topic.
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    Moderator Response: Yes, that is off topic for this thread.
  22. @apiratelooksat50: "Do libs not listen to Buffett?"

    What's a "lib," and what does it have to do with climate science?
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  23. 222, archisteel,

    I'm pretty sure a LIB is a Little Ice Blanket, a technique used by scientists to combat global cooling during the LIA. I read that on some really, really trustworthy and informative site, like WUWT, so it must be true.

    Don't ask what a LICk is, though... you don't want to know.
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  24. Found this on the website "Ice age now", phwoaarr, 1010ppm.
    What are they thinking ?? This has to be lunacy, surely ?
    http://www.iceagenow.com/1010ppm–lets_go_for_it.htm
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    Moderator Response: [Daniel Bailey] Magic 8-ball says: Yes.
  25. Very good, apologies for the bad link, I must have been delirious with the thought of 1010ppm.
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  26. When I look at this graph, for most warming periods, I don't see much of a lag between temp and co2. The explanation of the lag during warming seems reasonable enough, but it seems unnecessary. There doesn't seem to be much of a lag during warming. I don't even seem to get the basic argument you are debunking here. Most of the time, the two seem to rise fairly concurrently.

    The lag seems to occur when there is a general cooling long-term trend. CO2 is the longest lasting GH gas from what I have read, and so may take longer to decrease as temps decrease from other causes.

    Overall, I must be really lost. I don't even see what is being debunked here.
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  27. #226: "I don't even see what is being debunked here."

    That's actually a good thing.

    To look at the Vostok graph, spanning 400000 years, and claim to see a 'lag' on the order of less than 1000 years makes this one a pathetically thin argument. But that's the hand that deniers play: cherry-picking here, over-interpreting a trend there and forcing a one-size-fits-all conclusion. Pay no attention to any other independent evidence and ignore the physical mechanisms. Sprinkle liberally with 'of course its natural' and 'it can't be us' or 'you can't trust those scientists' and you see the full picture.

    How these guys can convince anyone with an open mind that they are right is absolutely stunning.
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  28. Anne Marie,

    If temp. drives CO2 and then CO2 also drives temp., then they reinforce each other and should result to upward spiral and runaway greenhouse effect. Why didn't that happen? If past climate change was dominated by reinforcing positive feedbacks, why did the warmings stopped and reversed into coolings so many times? What was the cause of the reversals? There must have been a stronger negative feedback or stronger negative forcing at work.
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  29. Dr Doom The reason there isn't an upward spiral is because (i) the radiative forcing due to CO2 is only logarithmic in the concentration and (ii) the uptake of CO2 by the oceans depends on the difference in partial pressure between surface ocean and air as well as on the temperature of the surface ocean, the higher the partial pressure in the atmosphere, the more difficult it is for the oceans to de-gass and the easier it is for CO2 to go from the atmosphere into the surface oceans. This means that there comes a point where a new equilibrium is reached and the temperature stops changing (until the forcings change again). This is the negative feedback to which you refer (although it only becomes stronger as CO2 levels rise).
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  30. Dikran, if CO2 forcing is logarithmic, then there is a limit to its climate sensitivity. What is that limit? Since CO2 increased 37% from pre-industrial level and temp. increased 0.7C last century, the CO2 doubling sensitivity must be less than 1.9C (0.7/0.37 = 1.9) It would be 1.9C if it were linear but since you said it was logarithmic, it must be <1.9. This is smaller than IPCC predicts.
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  31. Dr. Doom (i) the logarithm has no limit, ln(x) -> infinity as x -> infinity, and hence there is no limit to climate sensitifity. (ii) the sensitivity is generally expressed in terms of a doubling of CO2 exactly because the relation is logarithmic, which means it is exactly the same for any doubling of CO2, i.e. it is the same from 100ppm to 200pmm as it is from 200ppm to 400 ppmv etc.

    Again you are missing the point that you mentioned the equilibrium sensitivity, there hasn't been enough time for that equilibrium to have been met since the start of the 20th century; hence you can't use the temperature difference to directly estimate climate sensitivity.

    It is quite obvious from your comments that your grasp of what climate sensitivity actually is is fairly weak. I suggest before posting more messages you familiarise yourself with the basics by reading the relavant posts and follow up the links provided. I would start with How sensitive is our climate, read all three versions, basic, intermediate and advanced.
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  32. Dikran,

    With due respect, your comments policy states "No ad hominem attacks. Attacking other users or anyone holding a different opinion to you is common in debates but gets us no closer to understanding the science."

    Your statement "It is quite obvious from your comments that your grasp of what climate sensitivity actually is is fairly weak" sounds like a personal criticism. If you don't think it's a personal criticism, then allow me to reply:

    "It is quite obvious from your comment that your grasp of what logarithm function actually is is fairly weak."

    A natural logarithm function y = ln (x) has a limit on y such that as x approaches infinity, y approaches a finite value. In climate sensitivity, y is temp. and x is CO2. As CO2 increases indefinitely, temp. approaches a finite value. What is that finite value? That's what I was asking.

    Now, if you're saying there is no limit to temp., then it is not a logarithm function. It may be linear, exponential or polynomial. But you claim it's logarithmic so what is it really?
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  33. Dr Doom you're avoiding the point. Your example in #230 is a basic calculation of transient sensitivity as Dikran pointed out. The equilibrium sensitivity is higher than that, and well confirmed by palaeoclimate to be so. And there's plenty room for enough doublings for us to get uncomfortably hot, trend to infinity or not...

    But we should be glad that the gain in the positive feedback between CO2 and temperature is significantly less than 1 (though it is still unquestionably a positive feedback) - otherwise we would not be here having this discussion.
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  34. Skywatcher, I asked the question so I know what my point is. You may have a different point but this is my point: people suggested that CO2 sensitivity is logarithmic. That means it has a limiting value. I want to know what that value is. I don't mind if that value is 1C or 100C. People here are so eager to prove that it must be high. That is not my point. I just want to know what it is.

    Now, if there is no limiting value, fine. If there is, what is it? That's all. This is science not propaganda.
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  35. Dr Doom My comment was not intended as a personal attack, but constructive advice, I appologise for not making that more apparent. Your post demonstrated a lack of understanding of the difference between equilibrium and transient climate sensitivity, until you appreciate the difference between the two, you would not be able to understand the flaw in your argument, and hence you need to do some background reading.

    Now your grasp of mathematics also appears to be a little shaky; the logarithm does not approach a finite value as x tends to infinity, it approaches infinity as x tends to infinity, as I pointed out here. If you don't believe me, look it up.
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  36. Well there is a limit - when the atmosphere is only water vapour and CO2. Beyond my skills to calculate it however. Perhaps just consider CO2 at 10,000ppm (at the concentration it is toxic)?

    Dr Doom, considering your pseudonym, you may find the CO2 series at Science of Doom. Rather more detail than a blog comment will allow.
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  37. Dikran,

    Apology accepted and your point well taken. Please refrain from concluding “you don’t understand.” I do. Just explain your point and focus on the argument and not on me.

    In the logarithm function y = ln (x) where y is temp. and x is CO2. The CO2 sensitivity is the derivative dy/dx defined as the change in temp. per unit change in CO2. This approaches zero as CO2 approaches infinity. It means that temp. is becoming less and less sensitive to CO2 as CO2 increases.

    Let me rephrase my question: At what CO2 level will the sensitivity become close to zero or insignificant?

    This is of interest to me since when this CO2 level is reached, adding more CO2 will no longer increase temp. Please no ad hominen. Let’s just discuss science.

    Scad, thank you. It's not there.
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  38. Dr Doom

    In a scientific discussion it is perfectly reasonable to point out when someone doesn't understand something. In scientific discussion if someone suggests you don't understand something, standard practice is to assume that they are right and go and check, rather than to take it as a personal insult. Scientists tend to have this sort of defensiveness knocked out of them pretty quickly by the peer-review process, which is all about poking holes in your science.

    As I have already pointed out, the fact that climate sensitivity is described in terms of the effect of a doubling of CO2 already takes this into account. For a logarithmic function, you get the same change in the logarithm for any doubling of x, regardless of the value of x.

    The sensitivity per doubling of CO2 is the same, regardless of the starting concentration.

    Now in practice, I suspect that the logarithmic law holds while CO2 is a trace gas, and will breakdown once it is a substantial fraction of the atmosphere. However that point is so far down the track as to be wholly irrelevant to the discussion of AGW, as scaddenp points out it will have reached toxic concentrations by then, so the greenhouse effect wouldn't be our primary concern.
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  39. Dikran,

    In scientific discussion, you don't presume ignorance or lack of understanding. You explain why the argument is flawed. Focus on the argument not the person.

    I presume you understand my point. If CO2 sensitivity is logarithmic, then the sensitivity dy/dx is diminishing and approaching zero. At a certain value of x (CO2), increases in CO2 will no longer increase temp. I think it is important to know what that value is. In essence, that is a physical limit on y (temp.)

    Now, I understand your point about doubling CO2 will always increase temp. by the same amount. However, in reality you cannot do this forever because to get the same temp. increase down the road, you need almost infinite amount of CO2. In reality, there will be a diminishing CO2 sensitivity.

    We can speculate that the ‘physical limit’ on temp. is far down the road. But it is better to calculate this value than to speculate. An accurate calculation of the sensitivity of doubling CO2 does not tell us anything about where the ‘physical limit’ is, whether it is near or far the current temp.

    Since this website is about answering the skeptical arguments on climate change, I suggest you take a look at this issue because it is one of the skeptical arguments. They say IR absorption is already over 90% implying that we only have less than 10% to go to reach the limit.
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  40. DrDoom#237/239: "y = ln (x) where y is temp. and x is CO2. The CO2 sensitivity is the derivative dy/dx defined as the change in temp. per unit change in CO2."

    This may be the source of your continued misunderstanding. The logarithmic function in question relates radiative forcing to relative CO2 concentration:

    delta F = 5.35 ln [CO2(t)/CO2ref],
    where t is time and CO2ref is a baseline value, usually taken as ~280ppm. Forcing F is measured in watts/m^2

    delta T = lambda delta F, where T is temperature

    The sensitivity parameter lambda can be seen as the derivative of T wrt F, not T wrt CO2 as you have repeatedly claimed.

    The function ln x is indeed concave down; it is in fact unbounded, with a derivative that approaches (but does not reach) zero as x increases. But to find a time derivative of temperature, dT/dt, we need the function CO2(t).

    Taking measured values of CO2 over time, we find that CO2(t) is strongly concave up. Temperature as a function of time is thus both increasing and concave up; a net positive forcing, regardless of CO2 concentration, causes temperature increase. Increasing the forcing (increasing the CO2) increases the rate at which temperature changes.

    Further discussion of this particular point is more appropriate to the thread linear warming.
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  41. " They say IR absorption is already over 90% implying that we only have less than 10% to go to reach the limit."

    Dr Doom, this has nothing whatsoever to do with the subject of this thread but it is a common misconception. Please see CO2 effect is saturated thread. If the article doesnt answer your question, I suggest you continue there. The Science of Doom article (well the whole sequence of articles) does deal with this in some detail.
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  42. Dr Doom I didn't presume ignorance, you demonstrated ignorance here (trying to estimate equilibrium climate sensitivity using a timespan over which equilibrium couldn't possibly be reached), here (thinking a logatithmic relationship implied a finite limit) and now here (CO2 absorption is saturated). In each case the issue you raise has been answered; it is not my fault that you have taken the answers badly. There is no shame in not understanding something, we all start from that position and none of us should object to being told that we don't understand something. It is part of normal science. I am not making this personal, just trying to help you to realise that you are starting from a set of misconceptions, which appears to be preventing you from moving forward.

    Now I know that dy/dx tends to zero as x increases for log(x). However I have already told you that this does not mean that log(x) tends to a finite value (and given a reference). I have already explained to you that CO2 radiative forcing is described in terms of doublings for precisely this reason (as x gets larger the increase you need to get a constant increase in forcing doubles). To show you this is true, using the rules of logarithms

    log(2x) = log(2) + log(x)

    which implies that

    log(2x) - log(x) = log(2)

    In other words, if you double x, its logarithm changes by a constant amount, i.e. log(2). This is true for any value of x.

    A logarithmic relationship does not imply an upper limit on temperature (y). Such a limit will ocurr in practice because the logarithmic law probably only applies to trace gasses, however this limit is way too high to have any bearing on AGW.

    As scaddenp points out, the idea that CO2 already abosrbs 90% of IR radiation emitted by the surface is a skeptic argument based on a fundamental misunderstanding of how the greenhouse effect actually works. It is not absorption at the surface that matters, it is absorption in the upper atmosphere that matters. As well as the SkS link that scaddenp provided, there is also an excellent explanation of this by Spencer Weart at RealClimate.
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  43. I stopped reading the comments because the personal references continue. I’m not the subject of this blog so my knowledge or ignorance is irrelevant. What matters is the explanation why an argument is right or wrong.

    Point #1
    There is not enough time in the 2oth century to attain equilibrium sensitivity. 100 years are not enough? If you start at the end of 20th century up to present, that’s 11 years. Still not enough? Mind you, Schwartz initially estimated the time constant at 5 years. Later he adjusted it to 8.5 years. Other estimates are 15 to 17 years. All are below 100 years. Are they all ignorant?

    My simple calculation of climate sensitivity is < 1.9C. In scientific studies, the lowest estimate is 0.5C. Various studies put the lower bound at 1.5C. IPCC claims < 1.5C is unlikely. But may I add not impossible. Gregory put it at 1.6C with 90% confidence level. Schwartz put it at 1.9C plus or minus 1.0C. Right smack my simple calculation. All these figures are within my estimate. Are they all ignorant?

    Point #2
    As already demonstrated, a logarithmic function indeed as a limit of zero on dy/dx. Do you still need proof that this is true?

    Point #3
    Is the CO2 effect saturated? Clearly my answer is no. Or else I wouldn’t be computing the CO2 sensitivity. I would have just said it’s futile because the sensitivity is zero. You misunderstood my point. My question was, is there a saturation effect as implied by the CO2 sensitivity which is logarithmic? Obviously it is not saturated now but will it ever be? If there is no such thing, dy/dx should not converge to zero. It should not be a logarithmic function. Let’s develop a non-logarithmic function.

    Hulburt did not falsify the CO2 saturation hypothesis. To quote this website:

    “the details of the absorption in the lower troposphere do not matter since heat "is spread around and transferred upward by convection". In other words, what govern the energy balance of the earth is the radiative balance in the upper troposphere and CO2 concentration there does matter.”

    So it’s the CO2 concentration in the upper troposphere that matters, not the lower troposphere. It didn’t say whether there is a saturation CO2 concentration in the upper troposphere. Definitely there is less CO2 molecules in upper than in lower troposphere. But if there is a clear cut answer, scientists should say that CO2 saturation is physically impossible. If so, it means CO2 can absorb more than the solar flux of 342 W/m^2. There is no limit. Not even by the finite solar energy. If there is, what is the limit?

    For those who wish to reply, please no more personal references of “ignorance” or whatever positive or negative personal attributes. Just address the arguments. Don’t be too defensive, I’m not trying to falsify AGW. I’m just interested in climate science.
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    Response:

    [DB] Playing the "injured bird" routine just smacks of tone troll.  DM aready went this route with you, so please just focus on the science.

    Ignoring previous comments due to the perceived tone is specious.

  44. # 243:
    "There is not enough time in the 2oth century to attain equilibrium sensitivity. 100 years are not enough?"

    Riddle me this: Is the atmospheric CO2 concentration in equilibrium? Has it stopped increasing? Therein lies your answer.
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  45. Dr Doom

    Point #1 Full equilibrium temperature is only reached after the thermal inertia of the oceans is achieved. That takes thousands of years. The estimate given by Schwartz is for short term perturbations of the climate system, e.g. due to volcanic eruptions, not long term changes in forcings due to e.g. a rise in atmospheric CO2. Schwartz certainly is not ignorant, but your interpretation of his work is clearly incorrect (further discussion of Schwartz' work belongs on the thread I linked to above).

    Your calculation may be in the range considered plausible by the scientific community, however the method used to obtain the estimate was based on faulty assumptions, as explained earlier in the thread. The fact that your result is plausible doesnt correct the error in the reasoning. In science it is not enough to get the answer right, the chain of reasoning by which it was obtained and the assumptions used must also be valid.

    Point #2 the fact that dy/dx tends to 0 as x tends to infnity does not imply that there is a meaningful limit to CO2 radiative forcing, at least not one that has any bearing on a discussion of climate.

    Point #3, as I have already explained, CO2 radiative forcing does not saturate, no logarithmic function saturates because as dy/dx tends to zero as x tends to infinity, at that point y tends to infinity. So if you really insist, you could say that a logarithmic relationship saturates at infinity.

    You write: "If there is, what is the limit?"

    I have told you repeatedly that there is no limit, other than the trivial limit you will get when the atmosphere is 100% CO2 and contains all of the available carbon and oxygen on the planet.
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  46. 243, Dr. Doom,
    My simple calculation of climate sensitivity is < 1.9C. In scientific studies, the lowest estimate is 0.5C. Various studies put the lower bound at 1.5C. IPCC claims < 1.5C is unlikely. But may I add not impossible.
    This is a gross distortion of the facts. You say "various studies put the lower bound at..." but then make no mention of the median expected sensitivity, or the upper bound. It strikes me as just so much gamesmanship to be that blatantly manipulative with a presentation of the facts.

    "But I may add not impossible?"

    Meaning what, exactly? It's not impossible that I would find a million dollars on the street tomorrow. What's your point?

    If you want to be engaged, you must do so with more honesty. No one wants to get into the mud with someone who seems to enjoy it.
    It didn’t say whether there is a saturation CO2 concentration in the upper troposphere.
    More gamesmanship. My college chemistry text never explicitly stated that gremlins don't live in the spaces between electrons. Do I also need to worry about that? Or do scientists need to conduct multiple studies of your issues just to put your personal concerns at ease (as well as designing and building an Interspacial Gremlin Detection Apparatus to lay my own fears to rest)?

    But I can answer that question. Science is warning of climate change due to increasing CO2 in the atmosphere. This, by fairly simple logic, leads one to the obvious conclusion that CO2 in the upper troposphere is not saturated, and will not be in the near future, because if that were the case no climate change would occur. No explicit statement statement to that effect is necessary.

    There are also myriad paleoclimate studies (see here and here and here and here and here and here and here and here and here and just about every paper that you bother to look at here) that demonstrate that CO2 levels have been much, much higher in the past (by a whole order of magnitude), along with global mean temperatures, further evidence that if there is a saturation point, we're currently nowhere near it.
    But if there is a clear cut answer, scientists should say that CO2 saturation is physically impossible.
    Why? Who cares? The point is that it's not saturated, we're increasing CO2 levels, and it's dangerous.

    Your questions appear to be only so much "how many angels can dance on the head of a pin" speculation, of no value to anyone attempting to understand the relevant science.

    Make a valid point, or pose a worthy question. The positions you've presented appear to be distractions with no merit whatsoever.
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