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,
References:
WILLIAM D. SELLERS. 1968: CLIMATOLOGY OF MONTHLY PRECIPITATION PATTERNS IN THE WESTERN UNITED STATES, 1931–1966. Monthly Weather Review: Vol. 96, No. 9, pp. 585–595. http://docs.lib.noaa.gov/rescue/mwr/096/mwr-096-09-0585.pdf
V. C. LaMARCHE Jr. and H. C. FRITTS. 1971: ANOMALY PATTERNS OF CLIMATE OVER THE WESTERN UNITED STATES, 1700–1930, DERIVED FROM PRINCIPAL COMPONENT ANALYSIS OF TREE-RING DATA. Monthly Weather Review: Vol. 99, No. 2, pp. 138–142 http://docs.lib.noaa.gov/rescue/mwr/099/mwr-099-02-0138.pdf
