## More on Urals and Tornetrask

I’m finally trying to finalize my presentation on Jones et al [1998] for the US GCRP workshop in November, which is necessarily mostly about the Polar Urals and Tornetrask reconstructions. Bot MXD chronologies and RW chronologies are supposed to correlate to temperature. So an obvious quesiton is how do they correlate to eachother. I’ve plotted scatter plots up separately before. Here I present them together with some color coding to show key dates.

The figure below shows scatter plots for RW chronology against MXD chronology (both RCS versions, both my calculations) for Polar Urals and Tornetrask. The Polar Urals chronology incorporates the 1999 update from russ176.

Figure 1. Scatter Plot RW chronology versus MXD chronology. Red – 20th Cent; blue- 19th Cent; green – other.

The individual distributions of RW and MXD are not normal, but it’s particular easy to see that the combined distribution is not bivariate normal. At Polar Urals, other than a tail towards the origin for low values, there seems to be relatively little relationship between MXD and RW values, with MXD values seeming to max out, while there is much greater upwards variation in RW values. There seems to be a "tail" towards the origin, with 19th century values over-represented in the tail. Here’s another example which I posted up before here:

Jaemtland RQ and MXD distributions

The form of bivariate distribution between RW and MXD seems to be surprisingly characteristic. I’ve been browsing the literature on copula functions to think about methods of representing this type of distribution, but I don’t know how to do it at present and the dendro community doesn’t even seem to have noticed the problem. It’s hard to see how both RW and MXD chronologies can have a strong relationship to temperature and still generate this type of joint distribution.

A calibration-exercise involving the 19th century will give more weight to the transition from the tail to the body of values than is justified by the data overall, making the relationships seem better than they really are. There are also a lot of values outside the range of the calibration period.

The differences at Tornetrask are odd. At Polar Urals, the calibration-verification period values seem to be a little to the high left of the body of values, while at Tornetrask they seem to be a little to the lower right.

The "Briffa Adjustment" at Tornetrask (see here) was an arbitrary upward adjustment of MXD values in the 20th century because the MXD chronology was lower than the RW chronology. But the MXD values look very much in a plausible range, hardly arguing for any "adjustment". Or it would be just as plausible to adjust the MXD values for Polar Urals downwards in the 20th century.

### 6 Comments

1. TCO
Posted Oct 23, 2005 at 4:27 PM | Permalink | Reply

(made this point before)

I wonder if there is something in RW being extensive and MxD being intensive that would influence limits (high and low) differently.

2. TCO
Posted Oct 23, 2005 at 4:57 PM | Permalink | Reply

I know you like to think aloud a lot and make some unclear references to other posts, work…but:

A. unclear what you mean by calibration period data
B. unclear what a “Briffa” adjustment is or what this has to do with topic

On other notes (more general, strategic and “soft”)
1. Shouldn’t there be some numerical analysis of covariation for RW, MxD? r value, other metric, etc?
2. Same issue but wrt centuries. p test? (to see if seperate populations)
3. I do sorta (r-sq by eye) see a shallow correlation of RW with MxD in both graphs. It may not be surprising that the intensive density variable has less range than the RW from a physiological standpoint. I mean think about humans: they vary in size much more than in density. There is a certain type of structure that makes up the flesh and it has a fixed density.
4. Would be nice to connect in with a framework that discusses the physiological (or other) basis(es) for the different RW/MxD effects. How about a 2 by 2 matrix (bizness weenie consultant like) that shows high/low for each component. Then you can think about what would put you in each of the 4 blocks and think about how that matches with the general data and anything else we know.
5. Do you have a link to the original paper?
6. What is the general story on what the two seperate sites tell us? Are there varaibles that differ by sites for instance and can we analyze data to understand things from the comparison?
7. This is just me trying to understand you: but what is basic thread of what author’s found in the work? What is your basic thread in your commentary? (i.e. could be as simple as they found a correlation and you argue that it’s overstated because of selective methods).
8. Link to the original paper?

3. TCO
Posted Oct 23, 2005 at 4:59 PM | Permalink | Reply

Oh forgot this one: how well do they do at the Feynmanesque “control the rat experiments for rat experiment confounders”. For instance age effect?

4. Steve McIntyre
Posted Oct 23, 2005 at 11:03 PM | Permalink | Reply

Hi, TCO. I’ve inserted a link to the Briffa adjustment and added in a scatter plot from the Jaemdtland data which I have on hand. This kind of distribution pattern seems characteristic: the MXD data is left skewed; the RW data is right skewed; and the copula is sort of lobate. The Jaemdtland plot is for ALL measurements not just the chronology. But the chronology distribution will also be left skewed for the MXD; right skewed for the RW and lobate for the bivariate. Until I can do copula functions, I’m a bit stymied in modeling the bivariate distribution. As I say, the dendro people just ignore this and implicitly assume that all distributions are normal and presumably that the joint distribution is bivariate normal. It’s obviously a lot more work to try to figure out how to fix things than it is to point out the problems. I’m probably not going to use this in any presentation. I was mostly interested in seeing where the 19th and 20th centuries were relative to the rest of the data.

On a Bayesian basis, other than in the “tail”, knowing the MXD or RW doesn’t seem to be much help in knowing the other measurement. It looks to me like RW has more discrimination; I get this impression by the more recent studies, you hardly ever see MXD being studied. I suspect that it was a bit of a fad, which didn’t pan out (but it’s been fossilized in the two influential Briffa studies which live on.)

5. Steve McIntyre
Posted Oct 23, 2005 at 11:04 PM | Permalink | Reply

TCO, if you go to the right frame on Jones et al 1998, you’ll pull up past posts on Tornetrask and Urals, which I’ve talked about a lot – next to MBH98.

6. John G. Bell
Posted Oct 27, 2005 at 1:37 PM | Permalink | Reply

Steve, I’ve run across a fine book published by the University of Arizona Press in 1984: “Tree Rings and Telescopes: The Scientific Career of A. E. Douglass”, by George E. Webb. The ISBN is 0-8165-0798-8. It filled me in on a good bit of the history of the science of dendrochronology. Douglass found the solar cycle in RW’s back in 1913 with an invention of his he called a periodograph. The cycles were most clear he found in European wet-climate trees. His explaination for this phenomenon was that “radiation (possibly of short wavelength), that is especially favorable to trees growing generally under cloudy skies.” However, it seems that Douglass sought trees that were most sensitive to rainfall as a rule. Much of the tree ring data he collected, and his work was on a grand scale, will show this bias.

OT – A book I’m now reading “Ubiquity: Why Catastrophes Happen” by Mark Buchanan, ISBN 0-609-80998-9 is hard to put down. You might enjoy it if you have the time.

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1. [...] would be worthwhile when one is seeking to combine RW and MXD series as well. A while ago, I posted up some plots showing joint distributions of RW and MXD measurements for Jaemtland – no special [...]