Tornetrask #2

Here is a type of diagram which I often do on tree ring data. I’ve never seen anything like this in the tree ring literature, but some of you may be interested.

The top panel simply plots the cumulative growth of each tree in a network on a time scale. The slope of the plot for each tree indicates its growth rate. It’s a pretty simple and obvious thing to do, so you’d think that people would do it all the time, but they don’t. There are a lot of datapoints plotted here – 18,851.

The middle panel is the Tornetrask RCS ring width "chronology" (my calculation which is pretty close to the figure in Briffa et al, NATO 1996), which is essentially the mean growth after removing the "age-related" trend. In RCS standardization, the negative exponential model is fitted to all the measurements, rather than to each core individually. In "conservative" standardization, a negative exponential model, or as a default a stright or negative-sloping straight line) is fitted to each individual tree. The bottom panel shows the implied amount of "adjustment" from the age-adjustment – negative values "gross up" the site chronology, rather than the opposite. (Maybe I should reverse this in future presentations). I think that there are all kinds of interesting statistical issues involved in these "standardization" processes, which, as far as I can tell, have never been considered by real statisticians. Cook is by far the best of the dendrochronologists at statistics, but the whole field needs housekeeping. I’ve been working on this from time to time and have some interesting results, but obviously have some other irons in the fire.

I’m showing this graphic because of the recent interest in my Tornetrask post and it illustrates some thoughts that I may not have articulated, but influence my views on some of these matters. [Note: the graphic below and a few comments have been updated on Mar. 20, 2005. In doing this graphic before for web-version, I didn’t remove NA data. You see the effect of a long NA patch in a core in the 12th century which is perfectly level. I’ll post a bit about NA in these records in connection with Polar Urals where it is pervasive. The plotting function didn’t plot values after an NA value. The update does – that’s why it’s a little denser in this version.]

Just looking at the top panel, I find the relative linearity of growth in many cores to be quite striking. Obviously some cores have a juvenile growth spurt – this is an effect that is allowed for by the negative exponential models. But a lot of cores don’t seem to have much of a juvenile effect. For example, look at the "alpha" trees in the first millennium: they start off as fast-growers and keep growing fast until they die. The modern "alpha" trees are also fast growers from the start( I mis-described one tree in the prior version.)

Secondly, the recruitment of new trees is obviously not homogeneous. There are some big gaps, e.g. the 16th century and from the late 18th century on. Impressionistically, periods of long-term high RW "chronologies" seem to be somewhat biased to periods of low recruitment and vice versa. It makes one wonder about whether the negative exponentials are really modeling this the right way.

You can see that the age-adjustment factor has been increasing in the past 150 years and is presently at the highest level in the entire record (because of the lack of young trees sampled.) The contribution of the "alpha" tree to the 20th century chronology will be remarkably high because its modern growth is high relative to its age.


FIGURE 1. Tornetrask. Top panel – Cumulative ring width by individual core; middle – RCS "chronology" (smoothed); bottom; the implied age adjustment in the RCS chronology. [Amended Mar. 29, 2005]

The diagram for the Tasmania site, also beloved of multiproxy studies, has some quite spectacular aspects to it – I’ll try to tidy it up and post it up in a week or two.


  1. N. Joseph Potts
    Posted Mar 29, 2005 at 7:45 PM | Permalink

    Examples like this (and most others under discussion here and elsewhere) point up the sheer arrogance of any scientific specialist (say, a climatologist) to possess or even command in others (as people with big staffs like Mann’s could do) in claiming any sort of exclusive mastery over the vast range of sciences that one must bring to bear in producing a restrospective estimate of hemispheric or global science.

    There is NO specialization more specific than “scientist” that could lay any claim to authority over the kind of spectrum required for “climatological” feats like the hockey stick. And to be a scientist is first and foremost to embrace a certain attitude toward observations and their interpretation. This is the very test that Mann, many other climatologists and, indeed, many other “scientists” fail so manifestly.

    As a society, we’ve really advanced but little beyond witchcraft and superstition. With but few exceptions, such as present company.

  2. Larry Huldén
    Posted Mar 29, 2005 at 11:29 PM | Permalink

    The rightmost parts of the panels are hidden by the links etc. on the right !

  3. Paul Linsay
    Posted Mar 30, 2005 at 8:30 AM | Permalink

    I’ve always followed the hockey stick with interest but never saw the raw data before or ever looked into how the analysis is done. Having spent many years analyzing other data you could never get me to believe that it’s possible to extract any kind of temperature proxy from this. Presumably the temperature is related to the local derivative of the cumulative ring width.

    Just to make one point of many that suggested themselves. At any given time there are trees with very different RW slopes, trees that are all of the same species and living in the same spot (correct assumption?). This means that the trees are responding very differently to some underlying factor that is not temperature, which is presumed to be the same for all trees. Since the trees respond so differently to this underlying factor, what reason is there to think that they will all respond to temperature in the same way? Why won’t small changes in the underlying factor(s?) cause changes that swamp any signal from temperature?

  4. John G. Bell
    Posted Mar 30, 2005 at 1:59 PM | Permalink

    My eye shows about 19 of 58 cores with a juvenile growth spurt. None of the cores after 1600 have this feature. The spurt might be due to a genetic difference or perhaps something like sunlight competition; a tree’s fortune being dependant on shade cast by other nearby trees, most likely an early life event. Do these cores always capture the full life of a tree? Probably some don’t and wouldn’t that make RCS standardization an unobvious method of choice?
    How you standardize a core with a spurt does seem particularly important due to the AD1500 “alpha” tree.
    The “alpha” tree you spoke of does seem to be unique. Can you quantify how much influence this one tree has?

    When I supersize my browser the full panel becomes unhidden. You might also click on the graphic to view it in it’s own window. Above work under FireFox at a high resolution.

  5. John A
    Posted Mar 30, 2005 at 3:25 PM | Permalink


    I’ve shrunk the diagram slightly. There should be a sign on this weblog saying “this weblog is best viewed in 2048×1600”

    By the way, the next time Phil Jones suggests that oak trees in the 11th Century were deliberately grown north of where they do today, give the man an acorn. Then say “go plant this 150 km north of the current treeline and see if it grows”.

    Then please e-mail the picture of his face looking at the acorn to climateaudit AT

  6. Steve McIntyre
    Posted Mar 30, 2005 at 8:24 PM | Permalink

    Larry, I haven’t quantified the effect of the “alpha” tree. The “robustness” of various dendro standardization methods is an interesting question – in fact, all the statistical methods involved in dendro “chronology” calculations need a big housekeeping. I’ve spent a lot of time on this in the past year and have a lot of thoughts in inventory but haven’t worked up much yet.

    I’ll post up some info on the Polar Urals site in a day or two to give more food for thought.

    One would really like to see maps of where the samples were taken. If geologists were doing this, they would be much more methodical and everything would be better documented (I haven’t seen any evidence that dendro people routinely make proper sampling maps, but I don’t know that they don’t either.)

    I think that I’ve read somewhere that the Tornetrask Scots pine are to the north of their modern range and are a relict (like some other long-lived sites), which would toe them to the Finnish oaks, but I don’t recall the reference.
    Regards, Steve

  7. Steve McIntyre
    Posted Mar 31, 2005 at 7:46 AM | Permalink

    I amended the “grass” diagram as the first one (which I’d prepared fresh for the website) didn’t show values after an NA value. The amended one has more detail, although anyone’s impressions are unlikely to be altered. Steve

  8. John G. Bell
    Posted Mar 31, 2005 at 6:13 PM | Permalink

    The updated “grass” diagram now has one core with some years of negative RW values. That’s not raw data, it’s bloody :). What is a NA value? Not available? The core I speak of lasts from AD900 to 1450 or so. A negative slope is unexpected, right? Perhaps, an unavailable ring width is indicated by a negative value in the data? Sounds like a standard programing trick to me :). Better to replace the negative RWs with zero. Not right but not so wrong.

  9. Dave Dardinger
    Posted Mar 31, 2005 at 10:05 PM | Permalink

    Re Comment 8.

    Unless he’s already corrected what you mentioned, I think you’re being taken in by an optical illusion. When I hold a paper to the screen the line looks flat, not negative. But with all the other lines trending upward, that one flat one looks like it’s declining.

  10. Steve McIntyre
    Posted Mar 31, 2005 at 11:52 PM | Permalink

    NA- not available. The core in question is horizontal over the NA values; the impression of a negative slope is either an optical illusion or the plot is slightly tilted for some reason. I think that it’s an optical illusion. I haven’t determined the reason for the prolonged NA values. I have sorted out some NA issues in Polar Urals. There were two cores with archived values of 0 for over over 400 years (the life of the Polar Urals trees is usually only a couple of hunder years.) After many inquiries, it turned out that they had mistakenly assigned the same id number to two different cores (in 2 cases). They never explained to me how they handled this in RCS calculations as presumably the relatively high values of “700” year old trees would affect the RCS calibration. I suspect that it’s posssible that there are different cores with the same ID number.

    One unusual feature of the Polar Urals dataset (and to a lesser extent Tornetrask) is the many cores with some NA values. After many inquiries, Phil Jones said that they broke the cores for densitometric studies, resulting in rings being unavailable for measurement but not actual “missing” – if you follow the distinction. He said that they counted the rings, but did not measure them before breaking them. I asked a specialist about this and he said that numerous breaks show that the core is not oriented right and is proceeding at a tangent; also that cores break cleanly and no more than one ring should be lost. So there are many remaining quality control issues at these sites.

  11. Dave Dardinger
    Posted Apr 1, 2005 at 7:46 AM | Permalink

    So how do they measure the distance between rings? Do they rotate the core until the rings are parallel in the microscope first or do they just measure the distance from ring to ring even if there’s a tilt in the rings? if the latter they’re off by a factor of Cos(tilt angle). Of course at low angles it doesn’t matter much, but if they indeed aren’t aimed directly at the center of the tree it will make the younger rings look increasingly wider as you approach the center.

  12. John G. Bell
    Posted Apr 1, 2005 at 8:09 AM | Permalink

    Dave – Exactly right. It was an optical illusion. A good one I think.
    Steve – I wondered about the total lack of juvenile growth spurts in cores after 1600 and think it might be caused by drilling orientation on live trees so often missing their true centers. That would make me think those trees older and at a later stage of their life. Perhaps only by decades. Just a guess.

  13. John G. Bell
    Posted Apr 1, 2005 at 1:25 PM | Permalink

    Might a person extracting cores select from among the healthier live trees with the thought that they will more accurately record the weather, but in fact introduce a bias in that earlier cores from dead trees included trees in their decline with with smaller RWs in their last years? Could the AD1500 to 1600 gap be a result of so many 500 or so year old trees fitting into that category? AD1600 is not quite a light switch for live/dead cores but almost. conservatively 5/45 to 13/14. Keep in mind that this is by eye and I am proven subject to optical illusions

  14. Steve McIntyre
    Posted Apr 1, 2005 at 9:54 PM | Permalink

    Dave – I’m going to post up something about NA values, which are more of a problem at Polar Urals than Tornetrask. In doing densitometric studies, Schweingruber’s group broke the cores and, if you can imagine, did not measure ring widths. Jones said that they counted the missing rings. I asked a specialist about this – he said that there should never be more than 1 broken ring and, if you have more than 1 break, the core is at a tangent. At some of the Urals cores, there are 7 breaks and up to 59 years missing at a break. Some of the cores definitely seem to be at a tangent. I’m not sure whether this has a material effect. The same specialist said that the data collection appeared to be hit-and-run, which may explain why there don’t seem to be any sampling maps.

    John Bell, I’ve seen a report discussing modern sampling bias of a quite extraordinary type, which I’m going to post up. When they do samples, the cut-off point seems to be a 10 cm (or sometimes 8 cm tree). Also it seems that once trees get to a certain size, they are more prone to die. Sites have both fast-growing and slow-growing trees. So the cutoff point will not pick up slow-growing modern trees, whereas the fossil trees do not have the same bias. This has an effect on Briffa’s RCS method, but would not affect standardization with individual effects. The issue may be very serious.

  15. TCO
    Posted Sep 18, 2005 at 12:39 AM | Permalink

    Here is a type of diagram which I often do on tree ring data. I’ve never seen anything like this in the tree ring literature, but some of you may be interested.

    Why not share this with the community by publishing.

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