AGW Observer

Observations of anthropogenic global warming

Timing of carbon dioxide and temperature in Vostok ice core

Posted by Ari Jokimäki on October 17, 2009

It is well known that carbon dioxide (CO2) concentration generally lags temperature in Vostok ice core records, see for example papers listed here. Some time ago I was writing another post that used Vostok ice core records and I decided to check how was the timing of the peaks seen there (data for CO2 is here and for temperature here). I also checked the timing of the “valleys”. Figure 1 shows the peaks I checked marked with letters and valleys marked with numbers. I checked pretty much all the peaks that are seen, but in the case of valleys there were lot of difficulty to find corresponding minimums so I ended up checking only ten most obvious ones. In my analysis, in order to avoid cherry picking accusations, I have generally favoured temperature leading, so that when there’s uncertainty about exact peak/valley timing, I have selected the one that favours the earlier peaking of temperature. See the appendix for notes on individual peaks and valleys.

co2lead
Figure 1. The Vostok ice core records for carbon dioxide concentration and temperature with peaks and valleys marked as explained in text. Data for temperature is from here and for carbon dioxide from here. Temperature values has been scaled (T’ = T * 10 + 200) to show up more clearly in combined view of the two. It makes no difference because it is the timing we are interested here and the timing is not affected by the scaling.

Timing of the peaks and valleys

Table 1 presents the timing of the peaks in CO2 and temperature, and their difference (in years so that present = 0):

    Name CO2 (earliest...latest)      T (earliest...latest)        Difference (Min...Max)
    A    -415434 (-417160...-414085)  -410483 (-417969...-409995)  4951 (-3884...7165)
    B    -384909 (-386579...-383504)  -383641 (-384159...-383134)  1268 (-655...3445)
    D    -342998 (-344735...-340165)  -341930 (-342401...-341462)  1068 (-2236...3273)
    E    -323485 (-324189...-322827)  -322638 (-323695...-322426)  847 (-868...1763)
    F    -303953 (-304590...-303334)  -303316 (-303558...-303077)  637 (-224...1513)
    G    -292474 (-293002...-291769)  -292732 (-292976...-292490)  -258 (-1207...512)
    H    -277298 (-277925...-275218)  -276830 (-277036...-276622)  468 (-1818...1303)
    J    -255233 (-256053...-253880)  -254767 (-254972...-254560)  466 (-1092...1493)
    K    -238199 (-238935...-237831)  -237975 (-238084...-237866)  224 (-253...1069)
    L    -212281 (-217271...-211929)  -217244 (-217356...-217131)  -4963 (-5427...140)
    M    -202212 (-203191...-199025)  -202169 (-202275...-202065)  43 (-3250...1126)
    N    -191057 (-191592...-189335)  -190934 (-191043...-190822)  123 (-1708...770)
    O    -181617 (-182447...-180779)  -181382 (-181502...-181259)  235 (-723...1188)
    P    -169870 (-175440...-166299)  -169531 (-169638...-169425)  339 (-3339...6015)
    Q    -160494 (-161037...-155707)  -159548 (-159651...-159444)  946 (-3944...1593)
    R    -149157 (-150303...-145435)  -150972 (-151076...-150868)  -1815 (-5641...-565)
    S    -128399 (-128652...-128300)  -128357 (-128405...-128309)  42 (-105...343)
    U    -84929 (-85727...-82858)     -84576 (-84638...-84515)     353 (-1780...1212)
    V    -57068 (-57799...-51174)     -57289 (-57362...-57215)     -221 (-6188...584)
    W    -49414 (-51174...-48229)     -51159 (-51230...-51086)     -1745 (-3001..88)
    X    -39880 (-44766...-27062)     -42225 (-42298...-42152)     -2345 (-15236...2614)
    

Positive difference means that CO2 leads. 15 peaks out of 21 have positive nominal difference, so 71 ± 10 % of the peaks seem to be lead by CO2. However, note that none of the peaks have positive minimum difference, so in strict interpretation we can not claim for sure any of the individual peaks to show CO2 leading. Note also that this is only very rough analysis, for example the uncertainties in age determinations have not been included here. However, uncertainties are expected to make the minimum-maximum difference bigger, so they would not change the nominal values.

What about valleys then? Table 2 presents the timing of the valleys in CO2 and temperature, and their difference (in years so that present = 0):

    Name CO2 (earliest...latest)      T (earliest...latest)        Difference (Min...Max)
    1    -354372 (-356838...-352412)  -353838 (-354400...-353273)  534 (-1988...3565)
    2    -333627 (-335290...-332293)  -333602 (-334101...-333106)  25 (-1808...2184)
    3    -280361 (-281200...-279543)  -281602 (-281875...-281332)  -1241 (-2332...-132)
    4    -257792 (-258477...-257247)  -262131 (-261865...-261865)  -4339 (-4618...-3388)
    5    -246090 (-247447...-245483)  -246917 (-247135...-246700)  -827 (-1652...747)
    6    -222958 (-223446...-221612)  -224351 (-224536...-224164)  -1393 (-2924...-718)
    7    -138226 (-139445...-137986)  -138193 (-138308...-138078)  33 (-322...1367)
    8    -89363 (-91691...-88051)     -90128 (-90209...-90048)     -765 (-2158...1643)
    9    -65701 (-66883...-63687)     -65756 (-65855...-65655)     -55 (-2168...1228)
    10   -17695 (-19988...-13989)     -19610 (-19696...-19525)     -1915 (-5707...463)
    

Valleys seem to be leaning towards temperature leading. 7 out of 10 valleys have negative difference, three of them even so that the maximum difference is also negative. 70 ± 15 % of the valleys seem therefore to be lead by temperature. However, even in valleys some minimums show CO2 leading in nominal values, although only one of them (valley 1) has substantial positive difference.

There is an interesting string of events, where CO2 seems to lead all the time: 354372 years ago, CO2 concentration started to increase (valley 1). Then, 534 years later (353838 years ago), temperature started to increase. Following that, 10840 years later (342998 years ago), CO2 concentration started to decrease (peak D), and 1068 years later (341930 years ago), temperature started to decrease. CO2 concentration started to increase again (valley 2) 8303 years later (333627 years ago), and 25 years later (333602 years ago), temperature started to increase. 10117 years later (323485 years ago), CO2 concentration started to decrease (peak E), and 847 years later (322638 years ago), temperature started to decrease.

Another, shorter string of events also shows CO2 leading whole time; in valley 7 CO2 leads by 33 years, and in the subsequent peak S, CO2 leads by 42 years. It needs to be noted, that these are of course very small time differences. However, another interesting thing here is that two largest climate changes seen in Vostok ice core, the change from valley 2 to peak E and the change from valley 7 to peak S both seem to have CO2 leading through the whole climate change.

Mean for the timing differences are 32 years in peaks and -994 years in valleys, but for three largest climate changes (peaks E, K, S and valleys 2, 5, 7) the mean is 371 years for peaks and -256 years for valleys. General picture seems to be that temperature starts the warming events, but CO2 then takes the lead and only when CO2 has started to decrease, temperature starts to cool.

Although all of this is very uncertain, at least next time when someone claims that CO2 always lags temperature in Vostok ice core records, you can wave this in front of them and ask: “are you sure?”

Appendix. Some notes on individual peaks and valleys

Peaks

A – There is some uncertainty about where the corresponding peak of temperature is. Highest peak has been selected, but there is another, slightly earlier peak (max. at -417419) which would lead CO2 peak. Value for earliest peaking has been selected from this earlier peak.

B – Temperature is double-peaked. Earlier and higher peak has been selected.

C – It is very unclear what is the CO2 peak here. There are two minor peaks. Earlier one matches temporally much better (and leads temperature by about 700 years). Later peak is so much later (peaks almost 10000 years later than temperature peak) than temperature peak that it wouldn’t make sense as a matching peak. However, earlier peak is so small that it really isn’t much of a peak at all, so this whole entry has been rejected.

D – Both peaks are quite round.

E – Temperature peak is quite difficult. It first reaches a peak only 3 years later than CO2 peak but it then drops a bit and soon reaches even higher. Highest peak has been selected, but the value for earliest peaking has been selected from the earlier peak.

H – CO2 peak is quite wide but there doesn’t seem to be much question about the time of the maximum peak.

J – Temperature is double-peaked, earlier has been selected.

L – CO2 is double-peaked, higher and later has been selected. However, considering timing of other peaks, it would seem that the earlier peak would really be more correct here, so the value for earliest peaking has been taken from the earlier peak.

M – Temperature is double-peaked, earlier has been selected. Later peak would be about 900 years later than the CO2 peak.

O – Temperature is double-peaked, earlier has been selected. Later peak would be about 700 years later than the CO2 peak.

P – Temperature is double-peaked by quite wide margin, earlier has been selected. CO2 peak is very wide, possibly corresponding to both peaks of temperature. Whole width of the CO2 peak has been used in calculation.

Q – Temperature is double-peaked by quite wide margin, earlier has been selected.

R – Very minor peak. CO2 is double-peaked, higher and later has been selected.

T – No obvious CO2 peak is evident, so this entry has been rejected.

X – Temperature is double-peaked by quite wide margin, earlier has been selected. CO2 peak is very wide, possibly corresponding to both peaks of temperature. Whole width of the CO2 peak has been used in calculation.

Y – Temperature seems to peak here without corresponding peak in CO2, so this entry has been rejected.

Valleys

1 – Temperature peak is quite wide.

4 – Both temperature and CO2 are double-peaked, later has been selected for both.

5 – Temperature is double-peaked. Later has been selected, because that’s when temperature really starts rising.

6 – Temperature is double-peaked. Later has been selected, because that’s when temperature really starts rising.

7 – CO2 is double-peaked. Later has been selected, because that’s when CO2 really starts rising.

10 – Temparture peak is wide and the lowest peak is much earlier than when the temperature actually starts to rise. The point where temperature starts to rise has been selected.

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4 Responses to “Timing of carbon dioxide and temperature in Vostok ice core”

  1. Al Tekhasski said

    Dear Ari Jokimäki:
    Your analysis is faulty, and uses quite outdated technique. Your technique is inadequate to the task of finding time-shifted correlation between two functions that are subject to substantial noise. The adequate technique is to use the so-called correlation function that should be known to every engineering student. I am sure you know who Dr. James Hansen is, the one who is the Director of NASA Goddard Institute and the leading proponent of AGW. Please examine his publication, Hansen et al, “Climate change and trace gases”, published in Phil. Trans. R. Soc. A (2007) 365, 1925–1954. On figure 1(a) he shows exactly the data you are using, and on Fig1(b)the corresponding correlation function is shown, which has a single peak of 92.5% at a lag time of 700 years. Are you trying to say that J. Hansen and his co-workers are wrong, and there is no time lag?

  2. Ari Jokimäki said

    Thanks for the feedback. I know that my analysis is not adequate to determine for sure the whole lead/lag situation. I just simply looked at the timing of the minimums and maximums in the data, and found that in nominal values surprisingly many were lead by carbon dioxide. In internet discussions, I had faced claims that temperature leads carbon dioxide at all timescales, so in that sense it is proper to point out that even by such a naive analysis as this one I’m presenting, we can find evidence that puts some doubt for that kind of claims.

    I’m not arguing against overall lag of carbon dioxide concentration, but I am wondering if my analysis does show that while something else generally starts the warming events, carbon dioxide then takes control. This is the general picture that has been put forward by Hansen and others, and can be seen in papers I have listed here. However, my analysis also includes a suggestion that cooling events are started by weakening of the carbon dioxide concentration. That is something I don’t remember seeing discussed in the papers but I would have to check that.

    But yes, my analysis is very simplistic, and you are correct to point that out. Far more accurate (less noisy) data would be needed to perform this kind of analysis for real. I perhaps should have emphasized this more in my text, but I did make a note on the uncertainties. This is just a preliminary look at the surprising finding, or at least to me it was surprising as I expected to find temperature leading practically every peak and valley.

  3. Al Tekhasski said

    Please keep in mind that time resolution of Vostok CO2 data series is about 1500 years on average (1460 to be precise), with standard deviation of 1200 (!). More, there is substantial uncertainty in dating of each sample. With this kind of jittery and under-sampled data noone should expect any direct correlation between individual peaks and valleys.

    You also suggest that “cooling events are started by weakening of the carbon dioxide concentration”. This is not supported in the data set. If you examine the Vostok data more carefully, you will see that after every rapid deglaciation there is a period of time (2000-3000 years!) when CO2 keep rising while T goes down. Look at 212k-215ky range, or 231-233ky range, or 114-126 ky range where CO2 was flat to up, while T was gradually down. Or most recent chunk of data, 2.3k – 5ky. This contradicts to your suggestion, and is more consistent with the idea that CO2 chart is a delayed copy of T.

  4. Ari Jokimäki said

    Please keep in mind that time resolution of Vostok CO2 data series is about 1500 years on average (1460 to be precise),…

    Yes, that’s what the minimum and maximum values stand for in the tables above.

    …with standard deviation of 1200 (!). More, there is substantial uncertainty in dating of each sample. With this kind of jittery and under-sampled data noone should expect any direct correlation between individual peaks and valleys.

    Yes, I noted the uncertainty issue above.

    However, considering that overall lag should be the 700 years, and assuming that the peaks follow that overall value, then the peaks generally should be concentrated around the 700 years of lag with half of them below it and half of them above it. Here we have the situation where only 4 peaks out of 21 are below the 700 lag, and 15 of them are even showing CO2 leading. That is the strange situation here, peaks are clearly leaning to the side of CO2 leading.

    You also suggest that “cooling events are started by weakening of the carbon dioxide concentration”. This is not supported in the data set. If you examine the Vostok data more carefully, you will see that after every rapid deglaciation there is a period of time (2000-3000 years!) when CO2 keep rising while T goes down. Look at 212k-215ky range, or 231-233ky range, or 114-126 ky range where CO2 was flat to up, while T was gradually down. Or most recent chunk of data, 2.3k – 5ky. This contradicts to your suggestion, and is more consistent with the idea that CO2 chart is a delayed copy of T.

    Again, I’m not arguing against the overall lag of CO2, I’m arguing that peaks and valleys show the lead/lag situation differently.

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