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Hot off the projector #3: Atmospheric CO2 to 800 kyr ago

Filed under: — david @ 12 December 2007

Just a few minutes ago Chappellaz et al presented the deepest dregs of greenhouse gas concentration data from the EPICA ice core in Antarctica, extending the data back to 800,000 years ago. In Al Gore’s movie you saw what was at that time the longest record of atmospheric greenhouse gas concentrations, back to 650 kyr, and their astonishing correlation with Antarctic temperature. This iconic superstar record has probably consumed as many eyeball-hours as any in climate science, alongside other classics such as the Jones et al. global temperature trends, the Moana Loa recent CO2 record, and the hockey stick. The Antarctic CO2 record has spawned countless internet rants about the CO2 lag behind temperature, and the circle of cause and effect between CO2 and climate. And the new data say …

The first point to write home about is that the correlation between Antarctic temperatures and CO2 continues unabated. One could imagine a world in which CO2 had no impact on climate, although if you buy that Dick Lindzen has a bridge he wants to sell you. In such a world, it could be that the correlation between CO2 and temperature since 650 kyr was just a coincidence, Mother Nature playing a cruel joke, and maybe in that case a little more data would cause the spurious correlation to start to unravel. That didn’t happen. CO2 continues to be high in warm times and low in cold times. There were no gasps of astonishment from the audience at the continued striking correlation. Ho-hum, of course it still works.

That being said, there are some interesting subtleties in the latest data. The CO2 concentrations were generally lower than average between 800 and 650 kyr. The lowest CO2 value ever measured in an ice core is now 172 ppm, from 667 kyr ago. If you average over the glacials and interglacials, there appears to be a very long-term cycle in atmospheric CO2, low from 600-800, peaking around 400 kyr ago in stage 11, the 50 kyr-long “super interglacial” when the Earth’s orbit was nearly circular as it is now, and then subsiding a bit since then. Perhaps this variability is driven by variations in rock weathering, the longest-term geological carbon cycle. Interestingly, there is no corresponding million-year cycle in Antarctic temperatures, when they are averaged in a similar way. CO2 is a dominant controller of global climate, but it is not the only game in town.

There were also millennial timescale wiggles in atmospheric CO2 and methane concentration during the descent from the stage 19 interglacial to the stage 18 glacial time. There are strikingly similar to the Dansgaard-Oeschger wiggles from 30-70 kyr ago in isotope stage 3. The duration is similar, about a thousand years, and the trajectories of the events are the same, with sharp warming and associated rise in greenhouse gases, then slower recovery. As in stage 3, they occur through the slow cooling transition between extreme climates, not in the full-blown glacial or interglacial states. These abrupt climate changes appear to be business-as-usual for the global climate system.

What would be really cool is if there were enough ice to continue probing back into the deeper past. Around 800 kyr ago, the climate cycles on Earth switched from being dominated by 40 kyr cycles, to the stronger 100 kyr cycles of the more recent times. The time period from 800 – 1000 kyr ago is called the mid-Pleistocene transition, and since the rhythms of the Earth’s orbit didn’t change, it must have something to do with the way that climate on Earth operates, maybe something about the carbon cycle. What would be really cool is if we could get CO2 and methane records back to say 2 million years ago, through this crucial transition time. Alas, 800 kyr is as far back as the useful ice in this location goes. The bottom tens of meters of the ice, like the bottoms of all ice cores, are too scrambled to interpret.

123 Responses to “Hot off the projector #3: Atmospheric CO2 to 800 kyr ago”

  1. 101
    Ray Ladbury says:

    Rod B. The photon doesn’t care, but the water content of the atmosphere varies considerably over time–varying from

  2. 102
    David B. Benson says:

    Al Tekhasski (97) says Where the additional noise comes from, nobody knows so far. But from Spencer Weart’s Discovery of Global Warming (linked on the sidebar):

    New evidence gave a particularly crucial role to changes in CO2 and other greenhouse gases. These changes were apparently driven not just by geochemistry and ocean circulation, but still more by changes in biological activity. And of course the biosphere depended in turn on climate — and not just temperature, but also trickier matters like fertilization of the seas by minerals eroded from glacial era deserts. Further peculiar influences were added to the list of possibilities almost every year. It would take much more study to determine just what combination of effects determined the shape of glacial cycles.

    Al Tekhasski further says … the CO2 follows changes in temperature, and therefore cannot play “leading role” in climate changes. You need to carefully read the Hansen et al. paper about three times so that you understand that currrently, you misunderstand. I pointed out your misunderstanding, yet you (fairly clearly) do not comprehend.

    Also read the Wunsch chapters I provided a link to. But you might do well to begin with Spencer Weart’s Discovery of Global Warming.

    Instead of attempting to make much out of a cross-correlation for which you one time say is an 800 year lag and another time a 700 year lag. (This is a easy parameter estimation problem, to find that lag which maximizes the correlation coefficient.) And you have yet to state what that correlation coefficient is. You ought to do that before claiming any particular significance can be attached to it. Further, you ought to further do some significance testing.

    I am sorry, but so far you have made untrue claims (from which it seems you have retreated to a mere cross-correlation). Then you vastly over-simplify the climate system by treating biological activity, etc., as mere noise. You don’t bother to indicate how good your correlation is. And you don’t seem to have bothered to look at any of the literature.

    I don’t think anybody should take you seriously as it stands.

  3. 103

    RE #100, I think such ad hominem attacks are unnecessary. You may not be interested in how many people are dying via AGW or will die over its entire course, but I am. And some ballpark attempts at such stats would complement the many economic calculations surrounding GW and its mitigation that most are so focused on.

  4. 104
    Rod B says:

    Lynn (103), I meant it as a serious but good-natured barb. But since you’re sticking with serious, the analysis you’re quoting is all huff and puff, a little smoke and mirrors, comparable to calculating the number of deaths caused by Big Macs. It’s worthy of an Paul Ehrlich screed but not much else.

  5. 105
    Hank Roberts says:

    We’ll see the statistics eventually.
    For current risks climate isn’t ranked high. Time will tell.

    Clinicians should emphasize the primary prevention of coronary artery disease (CAD) …. investigating behavioral risk factors for CAD such as tobacco use, dietary fat and cholesterol intake, and inadequate physical activity. …

    Coronary artery disease is the leading cause of death in the United States, accounting for about 1.5 million myocardial infarctions and 520,000 deaths each year.
    —end excerpt—-

    That’s why the nutrition information is now published at the burger place, so you can make your own risk decisions, informed.

  6. 106
    Al Tekhasski says:

    Dear David, your power of deduction is truly amazing. If you re-read again your citation from the historical overview, it just says exactly what I said (only with some elaboration on possible spectrum of forces that might affect fluctuations of CO2), that “nobody knows so far”.

    Then you say: “you one time say is an 800 year lag and another time a 700 year”. I guess you are not familiar with the fact that timing scale in all ice record is “tuned” to one or another degree. Do you happen to know how accurate it is? More, as far as I remember from appropriate literature, globally-accessed proxy records yield the estimation of time lag as 800 +-600 years. This is the consensus of climatology at this date. Therefore, any number between 200 and 1400 years is as good as 700 or 800, especially for the sake of establishing the causal relationship between two time series. Picking on 100 years is called “nitpicking”.

    You are truly correct that I am simplifying. In science, it is called an analytical approach: consider major signal/effect first, and neglect (for a while) secondary effects. Then include corrections if necessary.

    On the other hand, you say that I neglected biological activity and denigrated it as “noise”. If you are so sensitive to this, I would recommend to use your own recommendation and look into works of C. Wunsch for analysis of what is regular in glaciation cycles, and what is noise. In a particular work,

    he shows that “the fraction of the record variance attributable to orbital changes never exceeds 20%”, and “all records are consistent with stochastic models of varying complexity”. Similar conclusions have been reached for every available proxy record. In short, almost all the signal in ice data is noise. That’s why I, as you correctly mentioned”, “don’t bother” much.

  7. 107

    Rod B posts:

    [[What does an infrared photon care if a H2O molecule has been there for a long time or just showed up after a different vapor molecule vanished into a liquid? How does the photon even know the history? It seems water vapor maintains a fairly consistent concentration — variable a little by location with minor ups and downs over a day’s/week’s/month’s period. Why is the fact that vapor molecules are replaced with other vapor molecules over a week or two such an AHA! moment for AGW?? What am I missing?]]

    Residence time affects how much we can change something. If we doubled water vapor overnight, nearly all the excess would be gone in less than a month. But carbon dioxide stays in the air for centuries. We can’t affect water vapor (and neither can nearly anything else aside from temperature), but we can affect carbon dioxide.

  8. 108

    Well, I’m not so interested in whether I would die from GW, but more how many we are killing. I know this would be exceedingly difficult, even impossible to calculate, even given various parameters. I understand that according to WHO 160,000 per year are dying from GW-induced vector disease spread at present. And they have attributed half the 30,000 heat deaths in Europe the summer of 2003 to GW. I don’t think they are attributing any deaths due to malnutrition and related diseases due to crop failures in part due to GW. And I don’t imagine they are attributing farmer suicides due to crop failues in India or Australia to it. Or a portion of victims of mega-cyclones, storms, floods, and other extreme weather events enhanced by GW and its various effects. Or thinking that it was that last “umph” of the storm that did the killing or greatest damage…the last part mainly enhanced by GW. Or the reduction of people’s finances due to GW harms, that prevent them getting medical attention, leading to earlier deaths.

    And then no one, I’m sure, is calculating how many will be killed in the future from GW-related problems. And since a portion our CO2 emitted today can last in the atmosphere up to 100,000 years, there may be people dying even then from its effects, or other GW effects set into motion earlier, though the population might be greatly reduced by then (assuming worst-case scenario). (Of course, we should also subtract lives saved by GW effects, in any calculation.)

    I’m sure the information will be forthcoming as scientists are better able to calculate these stats in the decades and centuries ahead, but by then it would probably be too late to then start tackling GW more seriously with the vigor required to make a difference, and all we could say is “sorry,” or we wouldn’t even be around to say sorry when the greatest harms from today’s emissions go into effect.

    I guess some reasons I’d like to know, is so I can explain to people the various GW harms in a more thorough way. Some think it’s only the polar bears who will suffer (and some don’t care about the bears if it means reducing their GHGs), or a tiny bit of land loss due to sea rise (some blame victims for building too close to the shore). It’s hard for most to grasp the entire enormity of GW and all its effects.

    An analogy sometimes I use is it’s like shooting bullets up into the air (they actually do that in S. Texas on July 4th), which come down much later and kill people. But that’s not a good analogy, since only rarely a person gets hit and dies, and with GW we know people are dying already, and the death rate would likely increase over time. It’s somewhat more certain than random shootings.

  9. 109
    Rod B says:

    Barton, thanks. The words often used (to which I was questioning) are like ‘water vapor lasts only a few weeks’ which implies that it can’t be important as a GHG because it is short-lived. Maybe the implication is inadvertent or just poorly worded. I think you are saying that the concentration of water vapor stays, over the long term, relatively constant; and the “half-life” of any particular H2O molecule is completely irrelevant. That I can understand. Is it correct to assume that you also contend (I may or may not agree with, but I’m trying to understand the argument) that, while water vapor is the “strongest” GHG, it does not provide a direct (or at least major) forcing function, as opposed to indirect feedback influence, because a consistent concentration cannot “force” temperature changes? Or am I over simplifying it?

  10. 110
    Ray Ladbury says:

    Rod, How do you put more water vapor in the atmosphere and have it stay there? Raise the temperature. This is the reason why H20 is best looked on as a feedback. CO2 on the other hand stays there–as a gas–for a very long time in pretty much whatever quantity we choose to put it into the atmosphere.

  11. 111
    Hank Roberts says:

    Rod, your question about the distinction between forcing and feedback is answered well by the presentation beginning here:

    —briefest possible excerpt—-
    it is important to distinguish between the two. A radiative forcing results from changes that are external to the climate system and may be either natural or anthropogenic in origin. For example, anthropogenic emissions of CO2, changes in solar flux, and the reflection of sunlight from volcanic aerosols are all examples of radiative forcings. A radiative forcing initiates a change in climate that is distinct from the system’s internal variability. A radiative feedback, on the other hand, arises from the response of the climate to either external forcing or internal variability.
    —-end excerpt—-

    My little snippet isn’t enough to fully answer you, but the full posting and links Dr. Soden provide make this pretty clear.

    Short answer on water vapor: the level of water vapor in the atmosphere can’t be controlled by human activity, it’s going to do what it’s going to do. Fossil fuel use is controllable by choices.

  12. 112
    Rod B says:

    Lynn (108), I agree that GW, if it proceeds as predicted by some, will eventually — sometime between next month and next millennia — cause much human suffering and death. But that’s about as far as scientific accuracy allows. The problem is that this scientific assessment does not create desired responses from the populace: it’s (maybe) too far in the future and too indefinite to cause a reaction. So the next political step is to conjecture to the demon level, make everything sound more precise, and surround it in sophisticated-sounding scientific jargon — granted well-intentioned and not fraudulent — to wake up the people to the danger. The WHO has some secret science and understanding that they can fairly accurately predict of the people that died during one summer in Europe, how many died from excessive heat and how much of that excessive heat was the result of global-scaled warming due to increases in CO2?? (Would that have been last year’s increase or maybe last decade’s??) Gimme a break.

    You go on to say, “….I don’t think they are attributing any deaths due to malnutrition and related diseases due to crop failures in part due to GW. And I don’t imagine they are attributing farmer suicides due to crop failures in India or Australia to it. Or a portion of victims of mega-cyclones, storms, floods, and other extreme weather events enhanced by GW and its various effects. Or thinking that it was that last “umph” of the storm that did the killing or greatest damage…the last part mainly enhanced by GW. Or the reduction of people’s finances due to GW harms, that prevent them getting medical attention, leading to earlier deaths….”

    Give them a little more time and a little more head count and, without a doubt, they will. Why? Because they must to get the desired reaction and call to action. And this is true for nearly everything big that government/society wishes to change. I understand that and, in fact, fully support it, so long as I am fully convinced of the necessity.

    I am not (yet?) convinced of the GW scenario. I understand you are and might fully support all of the above assessments. And I fully understand and accept your belief and support for that, and respect your passionate concern. But it’s like claiming 3000 SIDS death from second-hand smoke (they do) or 22,376 cardiac deaths due specifically to eating Big Macs (they’re not there yet but give ’em time.) It ain’t science; and it ain’t accurate.

  13. 113
    Al Tekhasski says:

    Rod asks:
    “while water vapor is the “strongest” GHG, it does not provide a direct (or at least major) forcing function, as opposed to indirect feedback influence, because a consistent concentration cannot “force” temperature changes?”

    In daily operation of the atmosphere, water vapor and temperature field are dynamically coupled, meaning that the temperature and vapor mutually adjust to each other on hourly-daily-weekly time scale through interaction on surface boundary, and via condensation into clouds or rains. In climatology, they call this coupling as “feedback”, which has very little to do with known technical terminology, and creates a lot of confusion. The “forcing” created by water vapor (as a GHG agent) must be calculated from models of general circulation, and is initially unknown. Obviously, temperature is not a solo factor that determines water vapor fluxes. For example, sea surface contamination may vastly reduce supply of vapor into air. Or extent of sea-ice coverage. Or deforestation. Therefore, it is possible that other processes could “force” temperature drifts via GH effect from water vapor, and possibly stronger than the weak background effects from trace gases.

  14. 114
    Al Tekhasski says:

    Lynn says: “Or the reduction of people’s finances due to GW harms, that prevent them getting medical attention, leading to earlier deaths.”

    Wouldn’t the carbon tax vastly decrease people finances by eventually taxing every ptoduct on the market? The whole AGW scare is already affecting gasoline prices, which reduces my ability to pay for medical attention and quality food. Is this what you are advocating?

  15. 115
    David B. Benson says:

    Al Tekhasski (106) — Thank you for the link to the Wunsch 2004 paper. That saved me having to hunt it down today.

    The paper is quite good, with regard to the weakness of orbital forcings. However, a further analysis via random walks seems desirable. For example, consider a one-dimensional random walk with reflecting barriers as crudely approximating the longer temperature records. Feller (1968) is the book I have which treats this case, where the transition probablity to the left is p and to the right is q = (1-p), except at the reflecting boundaries. The main point to note is that various statistics depend upon the ratio p/q. Now suppose that orbital forcing slightly varies p and hence q. This is then magnified in the ratio. So it is certainly possible to set up a simple model in which climate variablity is treated as random and yet orbital forcing drives the general nature of the record. In such a model I would suspect that the power spectral estimates would look like those in the Wunsch paper.

    Climate variability is not noise, in the traditional sense. Even the Wunsch paper puts “noise” in quotes. I only object to this term as misleading, not to models which contain random components.

    “Do you happen to know how accurate it is?” Yes. But first of all, not all records are orbitally tuned, but ice core records are perforce tuned one way or the other to turn the known depth into an approximate time scale. For example Barnola et al., analyzing the Vostok ice core, set the CO2 optimum of the Eem at 136.5 kya while Petit et al. set it at 128.4 kya. New results firmly date the temperature maximum of the Eem at 135 kya (unless it is 134 kya, I can’t find my source just now.) Given this, the dates in those two works (and also in Fischer et al.) need further adjusting.

    My understanding of the 800 +/- 600 year lag is from the onset of a major deglaciation until the CO2 begins to rise, not for the entire deglaciation nor for the entire record. Hansen et al. provides more information. In particular, any number between 200 and 1400 years is not equally good. Try doing some reading.

    But most important, the physics of the relationship between global warming (so-called greenhouse) gases and temperature is soundly understood. What is not is all the sources of climate variability nor, yet, the extent to which such can be understood. But in any case, from the physics, there is no surprise in why and how temperature and CO2 closely track. Hansen et al. provides the energetics of why this must occur. Try doing some reading.

  16. 116
    James says:

    Re #114: [Wouldn’t the carbon tax vastly decrease people finances by eventually taxing every ptoduct on the market?]

    No, because all the carbon tax plans (that I’ve seen, at least) specifically make the tax revenue neutral. That is, it either replaces some existing tax, such as sales taxes or VAT, or the money collected gets rebated to the people (much like Alaska does with oil revenues). Thus there’s no net effect on people’s finances, though of course there are individual winners – those who figure out ways to reduce their carbon footprint – and losers. But then that’s the whole point, to give people a financial incentive to reduce their emissions.

  17. 117
    Rod B says:

    Hank, Al, et al: thanks.

  18. 118

    RE #112 & “The WHO has some secret science and understanding that they can fairly accurately predict of the people that died during one summer in Europe”

    One of the factors that has a GW signature on it was that the death rate was greatly enhanced due to the nights not cooling off much, giving people a chance to recouperate from the heat stress during the day. In a non-GW world, therefore, a similar heatwave would not have killed as many people. And then again, it is that last bit of heat, and heat during the night, that does the person in, that part which is most attributable to GW. They might not have added that consideration into the calculation.

    Not to mention that science is way too conservative in such estimates. I’d like a ball park figure from a false-negative avoiding (medical) perspective, not a false-positive avoiding (scientific) perspective. Just for my own person sense of what might be going on, and what to expect from the future. Not at the level of scientific certainty or of evidence for criminal conviction or even civil case win (preponderance of evidence).

  19. 119
    David B. Benson says:

    William Astley (69) — The Adams et al. paper discusses a cooling event about 8.2 kya, seen in the Greenland ice core record. This event led to the abandonment of agriculture on the Anatolian plateau, and possibly elesewhere. The event appears to be contemporaneous with the supereruption of Kurile (now a lake) and so the pluvian/super-pluvian eruption may have triggered the cold interval of about 200 years.

    The paper also remarks on a strong arid event about 4000 years ago “across northern Africa and southern Asia.” This event brought Mesopotamia’s first empire, the Akkadian, to an end in warfare and the distruction of Ur III.

    Something similar happened to the Mayans, according to Jared Diamond. If you wish to worry, worry about the effects of both drought and flooding. Both seem to be happening now.

  20. 120
    Rod B says:

    Lynn (118), you say “…..I’d like a ball park figure from a false-negative avoiding (medical) perspective, not a false-positive avoiding (scientific) perspective….”

    I don’t fault that. I just say the self-assured and near arrogant estimates of epidemiological stuff with this looseness is not accurate — pretty much a SWAG. But for one with your background and interest to take that wild estimate with a “100% margin of error” and nonetheless say ‘just possibly something might be there…maybe, and I’d better keep my eyes on it’ is perfectly proper (IMO) from even a scientific viewpoint. There’s nothing unscientific about following hunches, especially if those hunches could be highly leveraged, meaning potential for extraordinary effect if proven correct, as GW is. I’m simply bothered with taking a WAG, however “confident” the WAGer is, and dressing it up in glittering accuracy to try to prove something. The old bury ’em with stats and math — and don’t worry about reality as long as there are piles and piles of numbers — until they succumb.

  21. 121
    David B. Benson says:

    My recalled dates for the Eemian interglacial are wrong by about 10 kya:

    According to one of the studies linked below, the Eemian interglacial lasted from 127.3 kya until 116.5 3 kya with the optimum between 126.4 and 124.1 kya. (All dates +/- 3 kya.) Assuming the maximum temperature exactly in the middle, it was at 125.3 kya.

    There were two periods of sea highstand, at 123 +/- 1 kya and again at 121.5 +/- 1 kya, with a pronounced sea lowstand of 4–10 meters below the maxima during the intervening cold period.

    Note that it appears that the sea highstands come near and after the end of the temperature optimum period, if these datings are to be believed. (These are uranium/thorium isotope ratio dates, so likely to the trustworthy within the stated error bars.)

  22. 122
    David B. Benson says:

    Apologies for the messy format. This is just to demonsttate how difficult it is the obtain precise, world-wide unifrom, dates for events only so long ago as the Eemiam interglacial.

    Best estimate Region Highstand Reef (R) Intra-Eemian Age of Intra- Ref.
    maximum value (m) Beach (B) sea-level Eemian sea-
    highstand interval Notch (N) drop? level drop (ka)
    highstand Egyptian
    125-120 coast, NW +6 to +9 R, B Y ~122 s1,s2,s3a
    Red Sea
    highstand South Sinai,
    125-118 N Red Sea +3 to +6 R N s5a
    highstand Eritrean +10 to +19 one ~125 and
    125 ± 7 coast, SW R Y (2x) one younger s6a
    Red Sea (regional uplift) event
    124-119.5 Possible
    (small second max. Barbados up to +7 R Y lowstand s7
    at 115-114.5) ~122.5
    >0m: 128-120
    highstand after Western N (but hiatus
    isostatic correction: Australia about +4 R reported5) s8,s9
    highstand Australia +
    127-122 global above +2 R N s10
    129-120 Bahamas up to +6 R Y ~125 s11
    132-118 ~125 s12
    Bahamas +2 to +6 R, N Y
    130-117 ~121 rescaled (s9)

    Table S1. Summary of literature-based estimates concerning the timing of the MIS-5e
    maximum highstand interval and the possible presence of interruptions of that maximum
    highstand. The overall apparent age range of the maximum highstand is around 128 until
    119 kyr BP, with an average sea-level position around +4 (-2/+2) m. Within that period, a
    brief erosive event/sea-level drop seems to have occurred around roughly 122 ±1 kyr BP.
    Reference numbers correspond to those in the main text.

  23. 123
    Nylo says:

    I will agree with Al Tekhasski that the correlation shown doesn’t prove at all that CO2 concentration lead to temperature changes in the past. The lag between T and CO2 strongly supports the opposite, with temperature changes CAUSING CO2 concentration changes.

    This of course doesn’t mean that an atmospheric CO2 increase cannot cause some warming. It probably does. But it is not demonstrated by those graphics and that correlation, by any means. It is posible that CO2 acted as a positive feedback, as has been stated. But only with those graphics, it is as well possible that it didn’t. You cannot use the correlation to prove your point. No way. You need something different if you want to prove that CO2 leads to temperature changes. So from that point of view, the original post is highly misleading and a bad service to science. The prehistorical data doesn’t prove at all that CO2 lead to temperature changes.

    This said, Al Tekhasski is also wrong to say that, because of the lag, it is imposible for the CO2 to influence the temperatures. No, that also cannot be concluded from those graphs. The graphs only say that temperature changes led to CO2 changes in the past, and doesn’t provide a clue about whether CO2 acted in return as a positive feedback or not. It cannot be concluded from the graphs. IMHO it did, although it is not clear to what extent. Maybe it only led to an aditional 5% or 10% increase of the temperature. Maybe it did as much as 50%. It cannot be concluded from the graphs in any degree.

    Our scientific knowledge on GH effect however doesn’t only rely on these graphs. We know for sure that an increase of CO2 by external causes other than temperature changes, like the human activities, by itself, without considering additional factors like cloud formation, insolation and the like, should cause some warming. This wasn’t the case in the past, because CO2 concentration was mostly led by the temperature. But now we are changing that, and we can expect CO2 to have initiated the process of the temperature change.