Polar Urals #3: Crossdating

The three cores which account for 1032 being the "coldest" year of the millennium are 862450, 862470 and 862030. One other core (862460) is dated to the late 10th and early 11th century and contributes to early 11th century "coldness". The placement of these 4 cores has to be interpreted from the ring width information itself.

Figure 1 below shows the assigned start date versus identification – note that 862 is a site prefix and 0 is a suffix: thus the tree number is shown in digits 4 and 5. There is no information on sample locations or altitudes. This could easily be incorporated into WDCP records; being used to careful recording of geological information, I find the absence of this information to be very offputting. Doug Larson of the University of Guelph says that the assignment of identification numbers in field operations is nearly always connected with sample location: thus, cores with nearby sample numbers nearly always come from nearby locations. Note that 3 of the 4 critical trees: 862(45)0, 862(46)0 and 862(47)0 have highly anomalous dates relative to the implicit spatial arrangement of the identification numbers. (Presumably nearby) trees 40 and 41 have assigned start dates in the 17th century; conversely, the other trees assigned early dates have numbers below 10. Oddly, identification numbers 42, 43 and 44 are either not assigned or not reported.

Urals 1

FIGURE 1. Assigned Start Dates against Tree Identification Number. 862450, 862460 and 86470 are the anomalies.
The trees are dated by comparing ring width sequences to those of well-dated cores, building backwards in time from modern trees. The actual overlaps of these anomalous trees to well-dated trees are very tenuous, as summarized in Table 1. Tree 46 is dateable only with reference with trees 47 and 45: both of which dates are in question. Tree 47 is dateable only with reference to 2 (upstream) trees: 45 and 3. Trees 45 and 3 have more substantial overlaps, but quite different performance, as discussed below.

Tree "Start" "End" Length Upstream
46 936 1007 72 45, 47
47 966 1054 89 45,3
45 914 1130 217 2,3,4,6,10
3 1015 1162 148 2,4,6,7,10

Table 1: Particulars of Early 11th Century Polar Urals Cores.

The next earliest trees (6 and 4 respectively) are dated to start in 1052 and 1059. Beginning in the second half of the 11th century, there is modest replication. Because most trees at the Polar Urals site are relatively short-lived in dendro terms (average of 128 years), arguably a higher degree of replication is needed to ensure crossdating success.

I mentioned yesterday that COFECHA quality control failed using the Polar Urals data set as archived. I have been able to get COFECHA reports by two different patches: 1) by deleting all records which do not meet COFECHA (or Larson) requirements i.e. ones with more than one break in the core and/or with long NA intervals; 2) by making a lot of new identification numbers so that each questionable core is split into subsegments with no more than one break and no long NA intervals.

I’ve archived the results of the RW run under the first method here [COFECHA run]. If you go to Part 5, you will see anomalously low correlation values for cores 862450, 862460 and 862470: no other cores in the entire record have correspondingly low correlations. (The same applies for the RW run under the second method.) In the crossdating information sent to me by Phil Jones, the correlation values for 862450, 862460 and 862470 were likewise substantially lower than for any other series. In statistical terms, if one took the correlations for the modern cores (31 of them) as being exactly dated and being a type of bootstrap sample for the distribution of correlations in correctly-dated cores, the correlations for each of these 3 cores fail a dating significance test at nearly a 99% degree of confidence.

I’ll illustrate these dating issues with some other calculations that I’ve made. As I understand it, COFECHA “slides” the undated series against a “master chronology” of dated series and calculates correlations. I’ve written up some programs to do this in R (and to give some additional information). A simple correlation statistic has end-effect disadvantages (when the overlap goes down to very low numbers), so I’ve done the same calculations with t-statistics, making N the period of overlap between the master chronology and the series to be dated. Figure 2 below shows the t-statistics (essentially the correlation adjusted for degree of overlap) for a well-dated modern core (862462). You can readily see a marked spike in both the RW and MXD series at a start date of 1858 — which is the start date in the archived series. There are over 1000 correlations taken here — so that a t-statistic with 95% is not sufficient. In fact, the correct t-statistic is 99.99% significant.
Urals 1
Figure 2. Sliding t-statistics for core 862462. Top — RW; middle — MXD; bottom — average.

What happens with the 4 cores in question: 862030, 862450, 862460 and 862470?
862030 has a very strong RW t-statistic and moderately strong MXD t-statistic at the assigned start date of 1015. It is also an in-sequence numbered core.
Urals 2
Figure 3. Sliding t-statistics for core 862030.

Now look at 862470 dated against all cores except the other 2 “undated” cores 862450 and 862460. There is no spike indicating a compelling start date and the t values fluctuate at levels quite similar to fluctuations for incorrect dates in the above correctly dated cores. This is one of the 3 cores used to show that 1032 is the “coldest” year of the millennium.

Urals 3
Figure 4. t-statistics for core 862470 (supposedly dated 966-1054).

Next, let’s look at core 862450, dated 914-1130. This overlaps most of the same cores as 862030. However, here there is no distinctive upspike. The t-statistic for the assigned start date of 914 is slightly elevated, but not to the significance of well-dated cores. One must conclude that the date of 862450 is simply unknown and cannot be used to assert that 1032 is the coldest year of the millennium.
Urals 4
Figure 5. t-statistics for core 862450 (supposedly dated 914-1130).

Finally core 862460 is a very short core, dated 936-1007, and dated only by reference to 862450 (against which the correlations are unremarkable). Against reasonably-dated cores, as shown below, no dating emerges.

Urals 5
Figure 6. t-statistics for core 862460 (supposedly dated 936-1007).

In inquiries about the dating, the answer from Phil Jones has been that the Swiss do not make errors on these things and that 1032 is a very distinctive year. What seems to have happened is that core 862030 (reasonably well dated) had a low density in 1032. Similar low densities are not unusual in the Polar Urals record and comparable examples occurred in the 1980s in individual trees. It looks to me like cores 862450 and 862470 (which also have a ring with low density) were dated by lining up their low density rings with the 1032 ring of 862030 and the impact on RW COFECHA or COFECHA-type results were simply disregarded. Now there were 3 out of 3 cores with extremely negative MXD values in 1032 and the "coldest" year of the millennium emerged.

For a year that 6 degrees C lower than normal (as claimed by Briffa et al [Nature 1995]), you would expect an impact in the RW series, but there is nothing odd there. You would expect it at other Russian sites, but 1032 passess unnoticed there.

It seems to me that the evidence is overwhelming that the Polar Urals site has inadequate replication in the 11th century and that the majority of cores used to claim that 1032 is the coldest year of the millennium (and to show a cold early 11th century) are misdated.


18 Comments

  1. Spence_UK
    Posted Apr 5, 2005 at 8:55 AM | Permalink

    This is a genuinely fascinating look into the details behind some of the multiproxy studies.

    I have to admit I find it very easy to get “suckered into” straw-man political debates with people like John H and Peter H, which achieves very little except to raise the hackles. When comparing those pointless circular arguments to the very real, detailed (and useful) analysis here it really puts things in perspective.

    I have to admit also, that I had heard oft quoted the conclusion that 1032 was the coldest year of the millenium, but never actually looked at the graph. The first time I saw the graph with the one spike down in one of your earlier posts, my jaw almost hit the ground. That point screams out to me in 50 pt font “experimental error” or similar. I can’t believe they just published that without stopping, and thinking “That point doesn’t look quite right. Perhaps we should look a little bit closer”.

    The t-statistics from the cross correlations are very informative plots and show that the meaningless alignment of a erroneous rings is a considerably more plausible explanation than the idea that 1032 was some kind of isolated, anomalously cold year.

  2. John A
    Posted Apr 5, 2005 at 8:58 AM | Permalink

    Funny that no chronicler happened to mention a bitterly cold year in 1032AD. You’d think that someone would have noticed…

    Speaking as a layman, it seems incredible to me that there is any climatic information in these cores at all. They look to me like random noise through a narrow pass filter.

    Could 1032AD have been a drought in the Polar Urals region?

  3. Michael Ballantine
    Posted Apr 5, 2005 at 9:08 AM | Permalink

    SANITY CHECK! How does the earth lose and gain enough energy in one year equivalent to a 4C spike in the temperature?? A good question for the conference.
    In tree ring cores, how do you tell the difference between temperature and water supply local to the tree?

  4. Greg F
    Posted Apr 5, 2005 at 9:23 AM | Permalink

    Steve,
    It would be helpful if you included a link to the data sets your using from WDCP.

  5. Steve McIntyre
    Posted Apr 5, 2005 at 11:01 AM | Permalink

    Spence – thanks for the kind words. I hate to say how much time I’ve spent on the Polar Urals dataset. I’ve had a very hard time figuring out how to represent the interrelationship between replication and dating issues. I’m working this with Tornetrask analysis into an article on the impact on Jones et al [1998]. One of the defects of terse journal arguments is that you don’t get to show the number of plots that are sometimes necessary to illustrate what’s on your mind. Websites definitely help in this respsect.

    John – the correlations between well-dated cores e.g. 862462 yield very a distinct upspike in the t-statistic and, while I can’t formulate a theory of statistical significance, on a practical basis, I don’t have any problem accpeting that 862462 is dated correctly based on the highly significant t-statistic relative to alternative placements. The neat trick proposed here is to use t-statistics instead of simple correlations (which helps a lot with end-effects which noise up the corresponding graphs with correlations.) This is a completely obvious gimmick but I don’t see it in COFECHA and I didn’t think about doing it until a couple of days ago. The other advantage is that you can argue that well-dated modern cores are a type of "bootstrap" for assessing statistical significance for questionable past datings. The t-statistics for the questionable cores fail the bootstrap significance test.

    Greg – the ring width measurements are at ftp://ftp.ncdc.noaa.gov/pub/data/paleo/treering/measurements/asia/russ021w.rwl and the max density measurements are at ftp://ftp.ncdc.noaa.gov/pub/data/paleo/treering/measurements/asia/russ021x.rwl.
    There are no site chronologies.

    Michael – you can’t directly tell the difference between temperature and precipitation effects. For example, the majority of sites in Mann’s AD1400 network which supposedly evidence temperature change are used in Cook et al [2004] as evidence of precipitation change. I agree with the sanity check – however the referees at Nature evidently did not think the same way.

  6. Michael Ballantine
    Posted Apr 5, 2005 at 1:38 PM | Permalink

    Steve – I know you can’t tell the difference but the hockey team seems to think so. It’s such a basic observation, and so damaging to the hockey team’s temperature graphs that no one but me commented on it when you posted it. ( http://www.climateaudit.org/index.php?p=136 ). Talk about a hot potato!
    How about ruling out any core sample that does not have an independent indicator to show whether water or temperature is the sensitive factor. Opps! That probably eliminates over 99% of all cores ever used in these studies. Maybe this time we’ll get a dialog going on this rather elimentary point.

  7. Chas
    Posted Apr 5, 2005 at 2:27 PM | Permalink

    I dont suppose that this is possible; but might the poor cores have been measured the ‘wrong way round’??

  8. John G. Bell
    Posted Apr 5, 2005 at 4:02 PM | Permalink

    Re #7
    Steve, if you don’t flip the data in these cores and see if they fit you’ll break my heart.

  9. John G. Bell
    Posted Apr 5, 2005 at 6:53 PM | Permalink

    Here are my flips. Please excuse the format. I put it in a readable condition by hand so…

    Some shell scripts
    grep 862450 russ021w.rwl | awk ‘{ print $12, $11, $10, $9, $8, $7, $6, $5, $4, $3 }’ | backwards > russ021w.jgb
    grep 862460 russ021w.rwl | awk ‘{ print $12, $11, $10, $9, $8, $7, $6, $5, $4, $3 }’ | backwards >> russ021w.jgb
    grep 862470 russ021w.rwl | awk ‘{ print $12, $11, $10, $9, $8, $7, $6, $5, $4, $3 }’ | backwards >> russ021w.jgb

    The backwards script out of K&R’s UPE:
    #/bin/bash
    # backwards: print the input in backward line order
    awk ‘ { line[NR] = $0 }
    END { for (i=NR; i > 0; i– ) print line[i] } ‘ $*

    The same for the MXDs using russ021x.rwl
    ———————–8<———————-
    862 1 Polar-Ural (historisch) WIDTH_RING LASI –
    862 2 Russia Siberian larch –
    862 3 FRITZ SCHWEINGRUBER – flipped by jgb

    862450 79 63 26 18 7 12 26 53 12 45
    862450 60 45 -999 77 86 38 19 21 13 30
    862450 19 25 26 29 22 14 21 46 17 18
    862450 17 21 23 30 27 47 44 30 27 28
    862450 22 33 22 57 25 65 35 21 22 30
    862450 40 9 37 8 12 16 20 23 12 18
    862450 17 28 7 29 19 20 29 17 52 20
    862450 52 30 22 48 60 61 55 61 47 27
    862450 47 31 34 26 49 30 68 83 54 83
    862450 127 96 70 83 103 102 63 62 40 70
    862450 89 92 67 102 76 18 42 36 44 88
    862450 132 47 31 69 93 64 37 32 77 50
    862450 48 67 46 44 44 100 50 74 41 84
    862450 69 50 50 19 63 165 89 55 44 10
    862450 112 121 59 39 24 14 25 45 31 20
    862450 16 23 17 76 30 22 24 34 14 18
    862450 26 21 53 65 108 174 33 99 102 102
    862450 105 108 132 174 19 39 42 182 141 135
    862450 70 100 119 78 143 244 183 128 114 79
    862450 58 172 69 118 167 128 147 101 59 102
    862450 73 44 142 99 86 47 99 86 75 13
    862450 14 42 63 59 32 168 62 999

    862460 29 16 26 7 17 12 50 47 52 77
    862460 36 54 51 26 45 49 9 57 43 21
    862460 31 30 23 34 28 15 38 32 38 54
    862460 31 17 12 25 36 29 37 42 42 80
    862460 51 31 57 17 73 126 128 64 49 36
    862460 53 16 55 48 90 67 53 34 25 9
    862460 -999 23 24 25 18 16 16 21 14 24
    862460 33 44 999

    862470 48 87 79 72 109 85 82 43 55 51
    862470 81 176 40 114 106 70 57 138 112 59
    862470 101 73 18 36 45 46 62 37 10 14
    862470 92 58 79 84 55 98 45 67 45 111
    862470 94 91 73 34 82 47 74 124 91 79
    862470 33 43 15 51 51 54 47 51 65 110
    862470 86 46 45 31 64 44 18 17 21 16
    862470 13 28 40 18 24 18 19 16 14 18
    862470 19 17 14 40 27 34 24 22 31 999
    ———————–8<———————-
    862 1 Polar-Ural (historisch) DENSITY_MAXIMUM LASI –
    862 2 Russia Siberian larch –
    862 3 FRITZ SCHWEINGRUBER – flipped by JGB

    862450 50 41 61 46 37 40 49 69 60 85
    862450 72 71 -999 77 74 85 60 79 55 68
    862450 58 56 75 75 72 66 66 99 72 63
    862450 57 64 89 93 82 86 88 76 78 67
    862450 75 84 69 93 80 77 86 69 79 83
    862450 81 62 82 56 59 64 70 73 58 67
    862450 49 73 70 70 73 63 55 58 81 73
    862450 78 70 72 84 85 74 77 84 78 56
    862450 70 58 74 68 60 84 75 88 65 70
    862450 78 73 81 65 75 70 81 94 45 83
    862450 83 67 86 67 66 63 78 63 70 82
    862450 80 78 77 74 83 64 81 62 61 73
    862450 68 85 73 58 75 70 54 58 70 83
    862450 59 76 68 73 71 83 76 73 73 53
    862450 85 68 68 75 77 54 60 78 80 63
    862450 76 61 71 72 55 83 75 64 51 62
    862450 61 62 79 50 67 72 76 73 87 69
    862450 75 77 62 68 79 69 80 88 74 79
    862450 77 87 76 64 76 79 79 77 74 79
    862450 77 70 78 78 80 75 71 68 80 80
    862450 74 77 92 70 77 71 73 86 80 68
    862450 81 76 66 61 64 72 64 999

    862460 56 55 58 42 47 48 64 60 69 66
    862460 71 61 76 74 76 75 45 77 69 60
    862460 80 68 61 69 79 69 74 78 67 81
    862460 82 64 74 79 72 64 78 69 74 84
    862460 76 80 80 68 77 81 74 83 85 77
    862460 85 73 69 81 84 75 80 79 85 64
    862460 -999 70 80 81 83 84 82 79 64 78
    862460 71 82 999

    862470 81 86 77 90 91 66 79 61 60 84
    862470 70 81 50 68 73 73 87 74 78 77
    862470 94 89 29 75 84 58 87 86 63 70
    862470 82 59 61 75 88 64 73 78 70 76
    862470 58 66 75 68 77 60 74 67 77 62
    862470 58 56 68 80 60 67 65 83 71 78
    862470 72 72 72 74 87 70 67 74 79 55
    862470 60 76 77 62 78 53 76 75 46 77
    862470 69 56 47 67 50 67 48 52 53 999
    ———————–8<———————-

    Hope I got it right. What format would be right?

  10. Steve McIntyre
    Posted Apr 5, 2005 at 9:21 PM | Permalink

    I flipped the RW series for 862450 and 862470 and did a similar t-test. I didn’t get anything significant.

  11. John G. Bell
    Posted Apr 7, 2005 at 3:06 PM | Permalink

    Steve,
    Kramer’s “Physiology of Trees” 1989 has a bit about false rings. A false ring can have many causes but the result is two rings in one year’s growth. One interesting cause is a hard freeze after a mild winter.
    You are more likely to see this in the earlier rings.

    I imagine a sample with a false ring would defeat the method you use unless the false ring is quite close to one of the ends of the core. One way to overcome this would be to ripple an NA for two consecutive data points through the set. If you are lucky you will only have to run half the resulting data sets before you get a match. No you don’t have to thank me for this grand idea. :) I’ll create the datasets if you’ll point me to the required format. I could then zip them up and attach them if you’ll give me an email address.

  12. John G. Bell
    Posted Apr 8, 2005 at 10:58 AM | Permalink

    Steve,
    Here is 862142 from russ021w.rwl with a addition of a false ring inflicted on the tree in the year 1905. Does it still match? Seems like an easier method to see the impact of a false ring. I don’t know how useful a test this is but you might wan’t to try it before my idea in #11.
    By the way, what is going on with 862481 & 862482? nearly 800 years of zeros and this from live cores? Are zeros treated like a -999 in the data and do they indicate the data is not available or some other thing?
    ————-8<—————
    # 862142w.mod – 2 rings in 1905, 20 & 26 replace 46
    30 30 65 61 63 42 58 66 38 52
    28 50 36 53 20 26 31 42 35 44
    28 61 52 77 46 71 37 62 87 41
    52 94 88 105 84 89 76 78 88 57
    21 32 35 80 61 77 81 104 103 95
    59 29 69 105 71 79 44 18 49 39
    68 53 68 122 99 101 123 67 56 59
    39 53 62 84 91 95 33 36 20 43
    30 23 55 44 56 11 55 42 52 72
    32 80 81 89 79 57 29 79 77 74
    63 999

  13. Spence_UK
    Posted Apr 8, 2005 at 11:50 AM | Permalink

    I would have thought that Steve’s method would be reasonably robust to one false ring. This would produce a spike in the t-stats of (I assume) around half height, but if you look at the magnitude of the spike in 862030 then you can imagine half height would still stand out a fair bit. In addition, and the real giveaway on this point, is that there would be two neighbouring high values as the next value along would have a strong t-statistic response as well.

    This could be further boosted if the ring widths have any kind of shaping to the noise envelope (which one would expect if they are temperature-sensitive).

    This assumes the false ring is central. If it is not central, then obviously the result would be clearer, as you postulate John. If there are multiple false rings, then Steve’s method becomes less accurate. Not sure how you would accommodate this though, but not knowing a great deal about dendrochronology, I’m not sure how frequent such events are.

  14. Steve McIntyre
    Posted Apr 8, 2005 at 12:34 PM | Permalink

    Re #12- John, if you look at Polar Urals #2, I discuss 862461 and 862482. They used the same ID number for different trees. The WDCP format (which is rather inconvenient) merged the two records and put 0s in between. I asked Briffa how they handled this in their age-width calculations, but he failed to respond.

    I’ve put this dataset (and all tree ring datasets into R tables arranged in 4 columns ID, year, age, RW (or MXD). So if anyone wants R versions, I can send. Steve

  15. John G. Bell
    Posted Apr 8, 2005 at 2:54 PM | Permalink

    Spence,
    In my simple state of ignorance I often just try stuff out and look at the results. If my extra ring in 862142 causes it not to match with the other Polar Ural cores, perhaps one or more of Steve’s three rejected cores suffer from that actual defect. If that defect were found, the core might find a real home in the chronology. Yes I know you couldn’t put it in based on the significance test as computed. The test would overvalue a match. A core might be saved from the trash bin and fit into the 17th century! Obviously that wouldn’t counter Steve’e argument.

    Another question. Could a core that tapes two parts of the chronology together with a mid section not overlapping those two parts contain a two ring for one year defect and cause some other good cores not to match in that part of the chronology?

    As far as how frequent? Great question. Some one should write a paper.
    If you don’t know, can you not deal with it? :)

    Are the methods used robust when faced with a core with two tree rings in a year? Easy to try out I’d think.

  16. Spence_UK
    Posted Apr 9, 2005 at 12:31 PM | Permalink

    John,

    Thanks for the reply. I was just kind of thinking out loud in comment #13 on what effects might occur. One of the problems with this kind of thing is that it introduces masses of permutations, which means the demands on statistical significance become so stringent any real signal is likely to get thrown out by the noise.

    Interesting thought about 17th century – I assume that it should be possible to create (as Steve puts it) a kind of “master record” and test one core against the whole record. The danger of this kind of thing is that if an erroneous set is entered into the “master record”, you really run into trouble! On the flip side, through integrating multiple cores into the record, it should be possible to improve the signal to noise ratio.

    As mentioned earlier, I’m don’t know much about dendrochronology, so I’m likely to make schoolboy mistakes when discussing it!

  17. John G. Bell
    Posted Apr 9, 2005 at 2:01 PM | Permalink

    Spence, your explanation in #13 should have cued me in. Steve’s method is obviously robust when exposed to a double ring year in a core. You explained it well. Thanks

    It could even match a core with a NA data gap the wrong size.
    You’d get two reduced spikes with a gap between them the size of the error in years. It would tell you what was going on.

    Do cores like the above end up lighting barbecues with the data going into the bit bucket? Do these sorts of errors get massaged out of the data before use? Is it thought they aren’t significant?

    So if a core doesn’t quite fit, and you just toss that data away, don’t you loose the ability to determine your confidence in the result? Doesn’t the process of selecting cores for a chronology do just this?

    Sorry in advance if I’m asking silly questions.

    Steve, I think you are doing great work. Thanks for taking the time to repeat in #14.

  18. TCO
    Posted Sep 18, 2005 at 2:59 PM | Permalink

    I was going to urge you to write a short note when I saw this:

    I’m working this with Tornetrask analysis into an article on the impact on Jones et al [1998]. One of the defects of terse journal arguments is that you don’t get to show the number of plots that are sometimes necessary to illustrate what’s on your mind. Websites definitely help in this respsect.

    Steve, I think your publishing strategy needs work. You’ve been working on this stuff as long as and as much as a grad student for his Ph.D. You should have a wealth of publications of different level of abstraction (some small points, some more review). some addressing MBH, some general method notes, some new things you’ve found in the data that aren’t even related to GW debate.)

    You should publish this as a small note. And it’s not such a big deal about the usage of this in reconstructions other than that is why it makes it mildly worth while to do the work. But the main point should be around your examination of this study itself. Don’t let the battle with the forest prevent you from killing a tree.

    I’m serious. This should be published yesterday. and if they don’t want a note in the original journal of Polar Urals, publish it in Tree Ring Surveys (or whereever).

    also, this is more strategy: be very clear about what claims you make and differentiate them for speculation as to implications. And follow the Notice to Authors and proofread like a martinet. I’ve gotten way faster publication by doing this.

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