Lamarche and Fritts 1971

While the Hockey Team like to talk about "moving on", in most scientific disciplines, articles of substance usually remain of continuing interest, since there had to be some interesting insight to have created the substance in the first place.

I’ve been backtracking through some of the tree ring literature to try to fully understand how the notion of a linear relationship between ring width and temperature became part of Mannian methodology. I wrote up a first installment about 10 days ago. I don’t promise that there’s any particular order in these notes.

Today I’m posting up on Lamarche and Fritts [1971], a paper by two very important tree ring guys, entitled "Anomaly patterns of climate over the western United States 1700-1930, derived from principal component analysis of tree ring data." (Mon Weather Review 99, 139-142.)

As far as I can tell, this is the first article in which principal component methods are applied to tree ring data. It’s interesting to see what they had in mind when they did this. (In passing, one of the implied representations of MBH98 was that they were carrying out analyses on series that had already passed muster in peer reviewed literature, but, of course, the Mannian tree ring PC series had never been published in peer reviewed literature.)

Access to this article is much facilitated by a new and commendable free online service by the American Meteorological Society in which past issues of their publications, including Monthly Weather Review, are online. Lamarche and Fritts is here.

It is trite that a singular value decomposition of a matrix is purely numerical and does not consider any potential geographic structure on the location of the columns (if these are, for example, time series from geographic locations.) However, if the data set does have a geographic structure, then you can plot the eigenvector coefficients on a map and then contour the map. Lamarche and Fritts [1971] cite Sellers [1968], also available at AMS online, as having done this successfully for precipitation in the western US. In fact, MBH98 itself does this for its temperature PC analysis, showing 5 contoured maps of eigenvector coefficients. Lamarche and Fritts described the process as follows:

When applied to time series from a spatial array of m data points, the analysis results in a set on m eigenvectors. Each eigenvector can be plotted an contoured to display the spatial variation exhibited by the component. The resulting mapped pattern has been termed a "characteristic anomaly pattern" (Grimmer, 1963) A limited number of such patterns may explain most of the variance in the original data. Furthermore, the dominant patterns can also have clear-cut physical explanations.

Their Figure 1 showed 4 contoured eigenvector coefficient maps for precipitation (4 different months) and 8 contoured eigenvector coefficient maps for tree rings – 4 different eigenvectors by 2 different period.) One of the tree ring examples is shown below:

Lamarche and Fritts Figure 1 – Pattern A – middle panel showing contoured eigenvector coefficients for first eigenvector 1931-1962.

Lamarche and Fritts then show the "amplitudes of the eigenvectors" [i.e. principal component series in my usual terminology] as below – none of which has a hockey stick shape,

Figure 2. Amplitudes of the first four eigenvectors of tree growth [SM: PC series]. The eigenvectors were calculated from data for 1700-1930; the heavy line indicates dependent data; the light line, independent data (see also table 2).

Lamarche and Fritts observed that all but two of the chronologies begin before 1600 AD. However only the indices for the period 1700-1962 were used.

Lamarche and Fritts use 49 tree ring chronologies, but do not list them. Fritts [1991] used 65 chronologies (again without listing them) and the publication listing them is inaccessible. I was unsuccessful in inquiries to several people at the University of Arizona in getting a list of the sites, but noticed one day that Janice Lough in Australia had coauthored a paper with Fritts and, through her, was able to get a list of these 65 sites, which seem to include the 49 sites. 15 sites are used directly in the MBH98 network. The 1971 cutoff in MBH PC network excludes most Fritts sites (although the Fritts reconstruction is used – extended past 1962 by MBH98 inserting Briffa values after 1962 – without annotation.) Some of the Fritts sites have names that I recognize and later versions might be used for some of them. (Similarly, many of the sites used in Cook et al 2004 as precipitation sites were used in MBH98, as I observed in a post early last year.)

There are three bristlecone series in the Fritts collection, all in earlier versions than used in MBH. (Ironically, one of these obsolete series is used in Moberg et al 2005 – which then ALSO uses an updated version of the same series.) These particular bristlecone series are from Methuselah Walk and do not have the HS pattern of Sheep Mountain and Campito Mountain.

Mann did NOT ever publish a contoured coefficient map of tree ring eigenvector coefficients. Do you suppose that he ever did one? If he did, he would have noticed that the map did not contour in any sensible way. For example, the coefficients for series within a few miles of each other were hugely different under Mannian methodology.

I’ve not researched the topic of constrained PC analysis in which the eigenvector coefficients were penalized if they failed to meet smoothness conditions. I don’t see any reason why you couldn’t do something like that and I’m sure that somebody has in some context. I’ll take a look at it. I’ll also post up a contoured map of Mannian tree ring eigenvector coefficients to see what they look like. Contouring can be a bit tricky, particularly if there are some subtle details that you want to show. So I may not get back to this for a while, but will try to rememebr to do it,




  1. Dave Dardinger
    Posted Apr 17, 2006 at 11:16 AM | Permalink | Reply

    So how much of the variation is explained by the 4 PCs? Could a hockey stick be lurking down in PC5 just waiting to be trained to the surface temperature record?

  2. John A
    Posted Apr 17, 2006 at 12:49 PM | Permalink | Reply

    Why do the eigenvectors look a lot like Dave Stockwell’s random numbers with some persistence thrown in?

    Did Lamarche and Fritts come to any startling conclusions about these unremarkable results?

  3. TCO
    Posted Apr 17, 2006 at 1:51 PM | Permalink | Reply

    Read the paper, John. It’s linked.

  4. John A
    Posted Apr 17, 2006 at 2:58 PM | Permalink | Reply

    I’ve read the paper. I’m none the wiser as to what it is supposed to show. The least they could have done is show a map showing precipitation regimes or something.

  5. TCO
    Posted Apr 17, 2006 at 5:46 PM | Permalink | Reply

    I asked Fritts a few days ago to stop by here and contribute to the discussion. However, he said that he is taking care of a sick wife and has little time (I get impression he is rather old).

  6. bender
    Posted Jul 21, 2006 at 3:20 PM | Permalink | Reply

    As I delve into the Climate Audit blog, I am continually impressed by the quality of analysis and the high level of critical thinking. I thought I could contribute on (1) the climatic signal in the lost cedars of Gaspé – and you beat me to it. I thought I could contribute on (2) the topic of problems of spatiotemporal PCA as applied to tree rings – and you beat me to it. Hats off. I think you are doing a very good job given the adversity you face. The only thing I can do is reiterate (3) my comment on

    bootstrap sampling of proxies prior to RegEM training, to get a true idea of (i) how truly variable the proxies are, (ii) how flaky the calibrations are, and (iii) how huge that reconstruction confidence envelope really is

    Don’t overlook this point. (But I am willing to bet that I will soon find you’ve already figured this one out too.)

    Carry on.

  7. bender
    Posted Jul 21, 2006 at 3:37 PM | Permalink | Reply

    Re #2 The eigenvectors look like random numbers because the key driver of growth in those tree species on those site types is moisture limitation. That’s why they do the analysis on precip data (Pattern A) and on the tree-ring data (Pattern B).

    If these eigenvectors can be interpreted as precip anomalies (due to ENSO, PDO, bidecadal solar, etc.) – and I’m not saying they can – then you would not expect to see a hockey stick in the other eigenvectors which are not shown.

  8. bender
    Posted Jul 21, 2006 at 3:39 PM | Permalink | Reply

    Re #1
    Your answer is in Table 1.

  9. bender
    Posted Jul 21, 2006 at 4:01 PM | Permalink | Reply

    Re #4

    The least they could have done is show a map showing precipitation regimes or something.

    The idea of eigenanalysis is to interpret precipitation patterns, NOT show them. The precipitation patterns could be reconstituted as the linear combination of the spatial loadings in Fig 1, the temporal scores in Fig. 2, weighted by the eigenvalues in Table 1. And what would THAT tell you that you didn’t know already? Sometimes the West is dry and sometimes it isn’t. The question is “why?” and analyses like these have since led to the discovery of ENSO etc.

    I’m none the wiser as to what it is supposed to show.

    It shows, visually (but does not quantify) the relationship between spatial patterns of precip anomalies and spatial patterns of tree growth. In the western US, precip anamolies influence tree growth.

    The reason this paper is important is not its insight. It is important for the same reason that a robust critique of MBH98 is important – it tried to set a methodological precedent.

    LaMarche was ahead of his time and may have slipped one through in a relatively minor journal. Mann was not ahead of his time, and somehow managed to publish in the most prestigious journal there is, on one of the most controversial conclusions of our time.

    That shows you how slowly the corrective wheel of science can turn.

  10. bender
    Posted Jul 21, 2006 at 4:08 PM | Permalink | Reply

    Re: contour plotting of PCA scores & loadings

    Contouring can be a bit tricky, particularly if there are some subtle details that you want to show. So I may not get back to this for a while, but will try to rememebr to do it

    Did you do this yet? If not, let me know. Are you using R for your eigenalyses? If so, I have some contour generation code for use with spatiotemporal PCA in R that may save you a day’s worth of tinkering.

  11. TCO
    Posted Jul 21, 2006 at 4:22 PM | Permalink | Reply

    You seem smart.

  12. bender
    Posted Jul 21, 2006 at 7:13 PM | Permalink | Reply

    Re #11.
    I’m not. It’s just that I’ve done this kind of work before.

    Quick backgrounder for anyone who cares. Unlike HT, I did my work solo, as a student under the watchful eye of a very critical statistician. I did not work on continental or global scale multiproxy data, but fairly dense networks of tree-ring data. When I first saw MBH98 I could not make heads or tails of their methods. I still can’t. I figured I wasn’t cut out to be a tree ringer, so I set that aside. Now I work on my first interest, insect outbreak models. So I know something about “nonlinear positive feedback-caused chaotic strange attracting runaway death-spiral tipping points” (ha ha), and I think I have some sense for how much uncertainty must underlie process-oriented GCMs. Even though I actually know very little about physical climatology.

    I also have looked at a lot of tree-ring chronologies. And what I know is that there is not a single species north of 49° that is not infested periodically by some bug. Dendroclimatologists HATE hearing that.

    My motivation is simple: (1) As long as you have pseudo-scientists & policy people insisting there is no uncertainty, the good science aimed at reducing that uncertainty gets marginalized. (2) Any insurer understands that uncertainty itself costs. When society buries its head in the sand about the true cost of uncertainty, the price tag, when the bill comes in, can be much higher than it would have been otherwise.

    On AGW I am agnostic because I am unqualified to speculate.

    What I advocate is a clear expression of the hypothesis. The AGW trick is to convince people that there are only two camps, to get you to commit to the A>0 camp (which is not a huge leap of faith), and then tell you again and again that what righteous AGW advocates believe is that A>>àŽⲬ where àŽⲠgets ratcheted up over time. To hypothesize that A>0 is trivial. It’s all about estimating the true magnitude of A. To an agnostic there are three camps.

    Apologies for the length of the posts, including this one. There are just so many interesting ideas and data sets here that it is a very stimulating environment.

    “If you choose not to decide, you still have made a choice.”

  13. fFreddy
    Posted Jul 22, 2006 at 12:20 AM | Permalink | Reply

    Re #12, Bender

    I also have looked at a lot of tree-ring chronologies. And what I know is that there is not a single species north of 49° that is not infested periodically by some bug. Dendroclimatologists HATE hearing that.

    Forgive my ignorance, but what is the significance of these infestations ?

  14. ET SidViscous
    Posted Jul 22, 2006 at 12:35 AM | Permalink | Reply

    stress on the trees

  15. fFreddy
    Posted Jul 22, 2006 at 2:57 AM | Permalink | Reply

    So big infestation leads to low growth, yes ?
    And how reliably do bug infestations correlate with weather ?

  16. TCO
    Posted Jul 22, 2006 at 3:21 AM | Permalink | Reply

    I would imagine that it will be a confounding factor with temp and that it will increase tree to tree variability.

  17. TCO
    Posted Jul 22, 2006 at 3:22 AM | Permalink | Reply

    My impression (casual, from reading the dendro forums and tree ring page) is that these guys ought to be collecting a lot more samples, given what they are trying to do.

  18. bender
    Posted Jul 22, 2006 at 6:17 AM | Permalink | Reply

    Re: #15
    Short answer: Weather influences insect population dynamics significantly, but the degree and form of the effect varies from system to system. Statistical evidence is hard to come by, but that’s not surprising given the way these systems work. There is no ‘one size fits all’ answer.

    Longer: People have tried to make the link between all kinds of weather indices and insect outbreaks and they usually don’t pan out. It is thought that this is because of the action of other variables in the system (the forest, insect predators, etc.) – that weather is far from the only driver, such that the correlations are typically weak. That being said, there are many systems, and situations, where drought can act as a trigger to insect outbreak. The idea is that (1) insects like the warm weather, and (2) they do well on the weakened, drought-stressed trees. The spruce bark beetles currently in Alaska are a great example. All insects are cold-blooded and in temperate areas are limited by temperature, so as we move out of the Holocene most forest-dwelling species are expanding their range with the retreat of the glaciers.

    Dendrochronologists like Tom Swetnam know all about this, and so people trained in dendrochronology at LTRR & elsewhere generally have a good appreciation for the potential importance of insects in affecting ring width, density, and character. (In fact his 1993 published work on western spruce budworms tried to make the link between budworm outbreaks and wet summers.) But I would not say that the appreciation for millenial-scale variability in outbreak dynamics is very good. Insects are viewed as a random noisy nuisance which they are happy to be rid of (usually by cherry-picking hypothetically insect-free sites). One problem is that the signal associated with some insect species, often periodic, has a way of fading in and out in time and space.

    The argument against insects as a key driver of ring characteristics goes like this: we’ve never seen any on this tree species in this particular site type in the 20th century, so therefore they were never here, and therefore weather is the primary driver.

    The problem is that we now know that climates vary naturally. We know that insects move in when a region warms up (spruce beetles in Alaska, mountain pine beetle in British Columbia, hemlock wooly adelgid in the NE US). So in theory it is possible that these insects, though absent now from the system, were at one time prevalent.

    A dendroclimatologist will argue that the proof is in the pudding: weather variable ‘X’ correlates with ring width/density, therefore it causes it. The problem is, as you know, that these correlations are never all that strong, and they even go through phases of strengthening and weakening. Maybe the weakening is the result of some other limiting factor kicking into play? Who knows what. But where there’s uncertainty, there’s doubt.

    I can’t comment on the specific case of BP as it is a system I don’t know anything about. But I was interested to learn about 10 year cyclic outbreaks on cedar leaf miners on northern white cedar in eastern Canada (Jacoby’s lost Gaspé cedars). The outbreaks can be quite intense and are triggered by drought – such as the most recent outbreak from 2000-02 in Ontario. Dead cedars in Guelph not 10km from where Kelly et al did their cliffside cedar studies. This insect has never been seen at high elevations in Gaspé … in the 20th century. But that doesn’t mean it wasn’t there during the MWP.

    I’m not suggesting insects everywhere are the major driver and that dendroclimatologists are in gross error. I’m suggesting that they shouldn’t be so quick to dismiss insects, as there is a chance they could be compromising reconstruction quality during some parts of the tree ring record.

    Given the importance of BP to MBH98 it might be interesting to know something about the insects of BP. As I say, I don’t know thing myself. High elevation sites are often too cold for defoliating insects. On the other hand, climates do vary …

    (On the uptick of BP growth in the 20th century: has a nitrogen pulse been excluded yet? That it is only in the NE US BP is interesting. Looks like there are actually two upticks – 1950, 1980 – coinciding with eastern spruce budworm outbreaks.)

    This is one of my areas of research (but NOT BP), and so I can say firsthand that the state of knowledge evolves continually.

    Long answer to a simple question. :(
    Wish that nature were simpler.

  19. TCO
    Posted Jul 22, 2006 at 7:40 AM | Permalink | Reply

    What do you think of the popular Tree Ring site and what do you think of the listserv at U of A (for dendro stuff). What is your impression of smarts and statistics ability in dendro? No offense, but are we sorta talking “girls in marine biology” vice physicists here?

  20. Steve McIntyre
    Posted Jul 22, 2006 at 8:15 AM | Permalink | Reply

    #18. I spent a day with Pete Kelly and Doug Larson and Ross at Guelph in the summer of 2004. They were very intrigued with our work and vice versa. I was very interested in the work that they were doing on cedars. They were very critical of the lack of ecological attentiveness of nearly all dendro people. They viewed SChweingruber’s sampling as more less equivalent to a drive-by shooting.

    On cedars, they said that cedars grow best in cool moist environments, neither too cold nor too hot. Their cedars and bristlecones hae some points in common (they have an article comparing the two, noting the very long lives). I thought that it would be interesting for a non-Hughes person to sample bristlecones and even suggested it to Kelly. They are busy with cedars, but could probably make time for bristlecones if the project turned up, but wouldn’t promote it themselves. I’m sure that outside sampling of bristlecones would be hotly contested by the Team.

    Jacoby and Cook refused to identify the location of theirGaspe samples, when I tried to locate the site for re-sampling.

  21. TCO
    Posted Jul 22, 2006 at 8:30 AM | Permalink | Reply

    That’s fine. Not optimum, but fine. If you have the general location, just go out and find a stand that has good characteristics on your own. If it differs, because of going to a different stand, then this is an inditement of the original sampling also (that it differs stand to stand).

    I actually think you get more info in some ways from doing this then from explicitly chekcing their work. Of course, best to do both. But in any case, if you all come up with same answer from a different stand that is powerful. If it is different then it focuses the debate on why, on how sampling needs to be better documented, etc.

    Of course, I’ve said this like 10 bazillion times. But I’m still right. Ask Weggie. He’ll back me up. He’s a real scientist.

  22. fFreddy
    Posted Jul 22, 2006 at 8:32 AM | Permalink | Reply

    Re #18, bender
    Thank you – very educational.

  23. Dave Dardinger
    Posted Jul 22, 2006 at 10:05 AM | Permalink | Reply

    re: #22

    Second that e-motion. There have been a lot of very good posts here the past few days. It may be because with Steve gone the trolls haven’t been quite as active. OTOH it may be that some new blood of the big-gun variety have been doing some posting, or more of it.

    Actually the level of troll activity makes an interesting analogy to insect infestation in trees. If there’s a high level of activity, the tree has to spend a lot of its energy just fighting off the attack while if the attack declines then after a latent period the tree gets back to putting out leaves and building wide tree rings.

  24. TCO
    Posted Jul 22, 2006 at 10:36 AM | Permalink | Reply

    Am I a troll or a big gun? Or hoi palloi?

  25. Dave Dardinger
    Posted Jul 22, 2006 at 11:41 AM | Permalink | Reply

    If the bridge fits….

  26. fFreddy
    Posted Jul 22, 2006 at 1:26 PM | Permalink | Reply

    Re #25, applause !

  27. TCO
    Posted Aug 4, 2006 at 5:57 PM | Permalink | Reply

    The dendro list serv has some discussion on the hearings. I like observing there. Have not really joined in. Have to say (in contrast to Dano) that I’m not blown away by sophistication of discussion there. We are not talking Steve and Zorita and Cubash.

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