A New Spaghetti Graph

Von Storch and Mann have both said that, in an MBH98-type reconstruction, it is impossible to allocate the impact of individual proxies. This is incorrect as we pointed out in MM05b. My posts on MBH98 Linear Algebra showed this more clearly (or at least in more detail). However, those posts only took the analysis back to the PC series. Since the bristlecones were represented in the PC series, this by itself did not segregate the bristlecone impact, other than indirectly through the PC series, and the connections have not always been as clear to others as they have been to me.

However, since the tree ring PC series are themselves linear combinations of the underlying tree ring networks, with a little more linear algebra, the approach of those posts can be extended to represent the MBH98 NH temperature reconstruction as a linear combination of the individual proxies, which, in turn, enables one to create classes of individual proxies and show the effect of individual proxies

Here I’ve done the calculations so that I obtain the MBH98 temperature reconstruction (working here only with the 15th century proxies) as a linear combination of the 95 individual proxies in the 15th century network. I’ve used 9 classes – by joint continent/proxy type class, distinguishing bristlecones from other North American tree rings. (I’ve grouped Gaspé with the bristlecones, because Mann fiddled with this series to get it into the 15th century network. ) Thus the classes are : Asia tree rings, Australia tree rings, European ice core; Bristlecones (and Gaspé); Greenland ice core; non-bristlecone North American tree rings; South American (Quelccaya) ice core; South American tree rings.

Figure 1 top panel shows the absolute contributions of each continent-proxy class to the MBH98 15th century reconstruction (bristlecones in red.). This vividly shows the noise of the other networks. If I overlaid the final reconstruction on this graphic, it overlaps the bristlecone contribution almost exactly. The bottom panel of Figure 1 shows all 9 series in a standardized format of the spaghetti graphs. What the Mann weighting system does is to pick out the bristlecones from the noise (by enhancing their weights). On another occasion, I’ll do a similar graphic without the bristlecones (which is the supposed “MM reconstruction”).

You can see quite easily how by enhancing the weight of the bristlecones and reducing the weight of all the other proxies, you can “get” a hockey stick. You have to work pretty hard to “find” the bristlecones out of this pig’s breakfast of noise; that was Mann’s “new” statistical method. If you take the bristlecones out of this system, there is no HS.

Figure: Spaghetti graph showing top- absolute contribution to MBH98 reconstruction (1400-1980 for AD1400 step proxies) by the following groups: Asian tree rings; Australia tree rings; European ice core; Bristlecones (and Gaspé); Greenland ice core; non-bristlecone North American tree rings; South American ice core; South American tree rings. Bottom – all 9 contributors standardized.


  1. Florens de Wit
    Posted Apr 1, 2006 at 3:42 AM | Permalink

    I am a little confused as to what kind of conclusion anyone is supposed to derive from this graph. One could argue that most proxies are useless because they contain little climate signal. Based on the same observation one could argue that the hockeystick methodology is correct to pick out the bristlecones because it is the only proxy that shows a climate signal consistent with a 20th century rise in temperature as measured by meteorological stations.

    It all seems to depend on whether you want to assume that proxies which show a signal that shows a trend in the 20th century actually also show a good correlation with local temperature at any other time, paired with the assumption that the measured global temperature is indeed accurate enough to be used as a training-set for the procedure

  2. Louis Hissink
    Posted Apr 1, 2006 at 3:47 AM | Permalink


    one observation – the top half of your graph indeed shows the disparity between HS and etc.

    The lower half…you changed the Y axis origins for the individual data sets and then overlaid them?

    I won’t comment further since I am now intrigued as to how you did that 🙂

  3. 2dogs
    Posted Apr 1, 2006 at 6:47 AM | Permalink

    Re Loius’ comment, am I correct in thinking the first graph has the proxy’s contribution to the reconstruction, and the second graph has the proxy’s standard score?

  4. Steve McIntyre
    Posted Apr 1, 2006 at 6:53 AM | Permalink

    #2. Louis, the units in the top graph are deg C and represent the contributions of the proxy classes to the MBH composite. In the bottom graph, each of these 9 series was scaled to 0 mean and sd-1 over the entire period. Y-axis limites were in each case was done by the software, but could have been speced. I did this up fairly quickly and thought the result was interesting. I could tidy it a bit more.

    #1. I’m trying to illustrate in these posts the difference between extracting a robust statistic (say a median) and data mining. The impression is given in MBH that the result comes from utilizing the information in a vast network, while the “active ingedient” is only the bristlecones and everything else is just fill. BTW giving excessive emphasis to one high-grade drill hole is a common trick of mining promoters.

    Rob Wilson has recently argued that they are not as bad a proxy as I would have people think. Maybe yes, maybe not – we’ll see. Graybill, Fritts and Lamarche, blue chip dendro names, didn’t think so. Hughes of MBH has not tried to argue the point in any MBH responses to our criticism to date. realclimate has been remarkably silent on bristlecones. The issue of bristlecones was not even on the table, because Mann said that their results were robust to the presence/absence of all dendro indicators, so who would have thought to wonder about bristlecone validity as an important issue in assessing this study?

    But maybe Rob’s right. Maybe Graybill bristlecone chronologies are a reasonable temperature proxy. I’m not convinced about this – I don’t see how you reconcile the low MWP bristlecone values in his graph with the information in Miller et al [2006] on Sierra Nevada treelines, for example.

  5. jae
    Posted Apr 1, 2006 at 7:38 AM | Permalink

    If the bristlecones are a good proxy, it looks like they are the only tree ring series that are. The rest of them look just like random noise. Were these series adjusted by RCS?

  6. Dave Dardinger
    Posted Apr 1, 2006 at 8:30 AM | Permalink

    This is a killer set of graphs! Insofar as TCO has forced you to produce it, he’s proved his worth. The point being that here’s an ‘anti-iconic’ deconstruction of Mann et. al. Once it’s explained what the two graphs mean, there’s really no need to do any more. It’s obvious that the original hockey stick, at least, was nothing but a figment of the hockeyteam’s imagination.

    Of course, doing the same thing for other sets of the proxies (i.e. not just the 15th century set) might not be so clear-cut, but I expect they’ll be similar.

  7. Steve McIntyre
    Posted Apr 1, 2006 at 8:55 AM | Permalink

    I’ve got a lot of time for TCO’s questions. Not all of them are on the mark, but so what. This isn’t exactly one of the questions that he asked, but it was possible to use my implementation of Mann’s algorithm to improve the allocation of effects. I’ve drafted a very dry paper on the linear algebra of MBH, which is interesting to me (and underlies all my analysis) but it lacked a little punch and these graphs or their immediate descendants will probably do the job.

    Of the 95 proxies in this network, 37 have negative weights. Two of them have “natural” negative weights i.e. Quelccaya accumulation. (In terms of managing the proxy data seet, I think that any “natural” changes in orientation should have been dealt with in the collation of the data set and noted at the time, rather than trying to sort it out with unsupervised algorithms after the fact.

    The other 35 are tree ring series – where I don’t think that one could have assumed in advance that the series were inversely related to temperature. Ironically, it appears that Briffa’s Polar Urals temperature reconstruction is negatively weighted in the 15th century MBH98 reconstruction. It is not so strongly weighted that the reversal “matters”, since the only weighting that “matters” is the extraction of the bristlecones.

    It’s also possible that reversal of signs in the “noise” series matters a little more than the impact of any one series. Let’s suppose that (1) the bristlecones are not a signal – leaving that argument aside- merely supposing it for now; (2) there is a weak actual signal in the rest of the NOAMER network which is uncorrelated to the bristlecones. The Mannian PC algorithm is going to mine out the HS data before the weak actual signal. One way of isolating the HS series is not to flip all the actual signal series, but flip about half of them. That way the actual signal does not “interfere” with the extraction of the HS “signal”.

    The above graphics are also useful for visualizing small subset averaging and I’ve talked a lot about “active ingredients” in these small subsets. Let’s say that you’ve got 2 HS series in a 14-series network and that the other 12 are just a dog’s breakfast. THen the other 12 will cancel out to a very small amplitude average (since the variance of the mean of random data obeys a central limit law) and the HS will emerge out of it. But if you did a median, it would be more robust.

  8. Posted Apr 1, 2006 at 9:38 AM | Permalink

    These are nice graphs. My question is probably silly but I don’t understand why someone would ever claim that one can’t isolate the effect of particular proxies: cannot you simply use the same method WITH the given proxy or proxies and WITHOUT them and compare the two results? Even if the dependence of the result on the proxies were nonlinear, I could do this procedure. Moreover, the dependence is really linear.

  9. Posted Apr 1, 2006 at 9:51 AM | Permalink

    Moreover, the second article at Scholar.google.com that you obtain by searching for “bristlecone” and “climate”


    namely this article:


    explains that the bristlecone pine ring width is much more correlated with the amount of Carbon 14 created by cosmic rays than with climate. More generally, whatever quantity correlated with the tree ring width was growing (or decreasing) in the 20th century may be pictured on the hockey stick graphs extracted from the bristlecones.

    For example, the graphs based on the bristlecones may essentially measure the CO2 concentrations (plus errors) themselves.

    In the MBH methodology, you use them to reconstruct the past temperatures. Have you tried to run the same procedures but replace the temperature with something else we have measured in the last decades or century – such as the CO2 concentration? What result do you obtain?

  10. Steve McIntyre
    Posted Apr 1, 2006 at 10:22 AM | Permalink

    It’s amazing what google scholar does. I’ve read all the other articles in the first page and cited most, if not all of them in our E&E 2005 paper, but I didn’t pick up the Sonett and Suess paper.

    I haven’t done the exercise that you suggest, but I’m sure that MBH methods will produce a HS type reconstruction against any upward trending series. Thus it will undoubtedly reconstruct past CO2 variations, the population of England, the price of silver with equal facility and, in each case, with “significant” RE statistics. (or for that matter, monthly tech stock prices ending in 2000).

  11. Steve McIntyre
    Posted Apr 1, 2006 at 10:30 AM | Permalink

    #8. I agree with you. It’s hard to think why they would say such things, but they did. See the citations in our EE 2005 article.

    As to the linearization, I guess they just didn’t think through the linear algebra. But it was one of the first things that I noticed. We mentioned this in our 2003 article – everything was linear. But it’s a lot of work going from that to controlling the data well enough to apply the information. Also there’s an important presentational gain in going from 415 series to 9 regional aggregates. I probably should have thought of doing this long ago, but I didn’t think of it and it is a little intricate to implement accurately.

    In the case of von Storch, I guess that he just assumed that, with so many proxies, individual proxies wouldn’t matter. That’s the exact point of difference where my different background came into play. I didn’t assume that – in promotions, you think of salesman distributions (10% of the salesmen do 90% of the sales) – not normal distributions. So I hypothesized right from the outset that a few proxies were probably driving this. If I’d stuck to this insight more systematically, I’d have saved myself a lot of time, but not explored interesting byways.

  12. JerryB
    Posted Apr 1, 2006 at 11:02 AM | Permalink

    An interview of Paul Damon at http://www.agu.org/history/sv/contrib/PaulDamon may provide a bit of interesting history pertaining to tree ring research, 14C research i.e. radiocarbon dating, and some of the bumps along the way.

  13. Paul Linsay
    Posted Apr 1, 2006 at 3:01 PM | Permalink

    #9: A bit of speculation: Cosmic rays, hence C14, are anti-correlated with cloud cover (http://www.dsri.dk/~hsv/Noter/solsys99.html) Fewer clouds, more sunlight and warmth and wider tree rings. Which effect is dominant has to be determined by the biology of BCPs. It would be interesting to see the figures from the article to see if wide rings are anti-correlated with C14 production.

  14. MarkR
    Posted Apr 1, 2006 at 3:25 PM | Permalink


    Many thanks for the graphs.

    Could I suggest a form of presentation that would make it clear to non specialists like myself and no doubt many others.

    1 Show the normal absolute, and/or standardised contributions statistical graph for each region, with a key, but exclude the bristlecone.

    2 Show the normal absolute, and/or standardised contributions statistical graph for each region, with a key, and include the bristlecone.

    3 Show the Mannian data mining data method graph for all the data, and include the bristlecone.

    4 Show the Mannian data mining method graph for all the data, but exclude the bristlecone.

    That should make it crystal clear to anyone who can read a graph how the inclusion or exclusion of the Bristlecone affects the result, and how un-robust? the the results of Manns analysis are in relation to the inclusion or exclusion of any data set using any normal method of analysis, unless the data is enhanced by the Mannian data mining technique, in which case the results will appear robust because any/all data sets will produce a hockey stick.

    Also it would highlight how it is the Mannian data mining statistical technique which can produce a hockey stick out of any data.

    Also big labels saying “With Bristlecone, “Without Bristlecone”

    The reason I make this point is that at some stage someone is going to have to publish a graph in the mass media, but before that happens, a busy journalist is going to have to understand what it means, and believe that his readership will also get it.

    Hope this is helpful.


  15. Louis Hissink
    Posted Apr 1, 2006 at 10:20 PM | Permalink

    Re #4


    No, it’s ok as it is – was curious about both having 0 but scaled differently.

    Thanks for the clarification.

  16. Hans Erren
    Posted Apr 2, 2006 at 1:33 AM | Permalink

    re #14
    I’ll second that request.

  17. Pat Frank
    Posted Apr 2, 2006 at 3:52 AM | Permalink

    “If I overlaid the final reconstruction on this graphic, it overlaps the bristlecone contribution almost exactly.”

    When I looked at Figure 1, I was struck immediately, almost shocked, by how much the BCP series looked like the MBH98 reconstruction. I’d sure like to see them scaled to a common zero and total intensity, and plotted over one another; especially with a difference residuals plot.

    If I understand your plots correctly, Steve, the top panel shows all the various series scaled to MBH98 normal. The BCP series, in addition, is just offset to the center line of MBH98 to show its extreme similarity to MBH98. The bottom panel includes all the series, including the BCP series, all at normalized intensities, with a common zero line. Is that about it?

    What a graphic! Your point that all the rest of the proxies merely add noise (and hence a visual authenticity) is perfectly displayed.

    Questions: Is scaling everything to a normal sd before averaging valid in proxy production, or do people weight each given regional series by the number of trees in that series before averaging? Also when averaging, say, an O-18 proxy with a tree ring proxy, are they weighted by their native sd’s? Silly questions, perhaps.

  18. Posted Apr 2, 2006 at 11:21 AM | Permalink

    Dear Steve,
    thanks, we’re on the same page.

    Another silly comment of mine: I feel that these whole sectors of science are done without the physics approach – especially without smart experiments designed to find something out.

    Has someone picked 20 bristlecones, give some of them more CO2, some of them more heat, some of them more moisture, some of them more Carbon 14, and so on, and just experimentally measure how the different quantities influence their tree ring width and growth?

    The people in these fields just wait for random decisions of Mother Nature, which are always rather fuzzy and ill-defined, and then try to extract the signals and invent random correlations. It’s like if physicists in the 1940s were waiting when enough Uranium gets together and an accidental explosion of the atomic bomb occurs.

    Best wishes

  19. Posted Apr 2, 2006 at 11:48 AM | Permalink


    The paper above argues in favor of CO2 fertilization of bristlecones. It compares two “races” of the tree and shows that they both increased the water-use efficiency W, but they distributed the extra carbon differently among different parts of the trees.


    Organic carbon, clay, and mean air temperature accounted for 83% or 55% of the growth for two types of bristlecones in the article above.

  20. Paul Linsay
    Posted Apr 2, 2006 at 1:56 PM | Permalink

    #19: But notice the earlier statement “Because of bristlecone pine’s intolerance to shading…” indicating that it is sensitive to sunlight or equivalently cloud cover. They don’t seem to take that into account in their mean annual growth rates.

  21. Steve McIntyre
    Posted Apr 2, 2006 at 5:38 PM | Permalink

    Luboà…⟬ I did a post on the Tang et al article last summer here http://www.climateaudit.org/?p=329 . I thought that it was a pretty interesting article.

  22. TCO
    Posted Apr 2, 2006 at 8:28 PM | Permalink

    1. When you say that you’ve “gotten the MBH reconstruction with the 15th century proxies”, to what extent did you follow the procedure in the overall MBH HS?
    2. How much work involved in doing the same experiment with all the proxies? And how relevant would it be?
    3. Why did you pick the 15th century? Does it help your story over other time frames?
    4. From the chart it looks like the bristlecones are giving a lot of weighting. About (negative) 25% over much of the time period. Would it be possible to say how much of the HS index comes from each group? I think this is a different issue than just total weighting, but not sure. How about just averaging over time and saying how much each group and in particular the bcps weight the reconstruction? Would actually be interesting to see a table of this proxy by proxy.
    5. The negative weighting of so many series is fascinating. It sure points out how much some of these are just chaff.
    6. Is it possible to show the same thing for the overall experiment (the way MBH was run…not just the 15th century stuff). So we can tell what is affecting things within the HS itself?
    7. Fascinating that you stick up for the concept that proxies are just peices of the puzzle and that the HS is a linear combination, but that some of the howler monkeys (maybe even Ross) want to say that it is impossible to isolate flaw extents, or to savage me for being interested in it, or to “inform me what I didn’t know (haha)” that some flaws that are small in extent are still interesting for embarressment/caution reasons.
    8. What the hell are SH proxies doing in a NH reconstruction?
    9. What’s going on in your “standard way of showing” bottom graph? What’s the axis? Did you normalize each series by its own variance?

  23. jae
    Posted Apr 4, 2006 at 1:19 PM | Permalink

    I suppose someone has already mentioned this, but just in case: Even if you allow the BPs, foxtails and other questionable series to be included in the reconstructions, the fact that they ALONE impart a hockey stick curve to otherwise relatively trendless data PROVES that the reconstructions do not represent the NH, let alone the global trend. They reflect a “localized phenomonen.” Hmmm, it seems that I have seen that argument used before by certain scientists concerning the existence of the MWP… So, it doesn’t really matter a bit what caused the striking growth patterns of these localized groups of trees, relative to the notion of NH or global warming.

  24. Steve McIntyre
    Posted Nov 23, 2007 at 3:00 PM | Permalink

    Bump. Here’s the sort of analysis that I’d like to do if we can get regression coefficients from RegEM TTLS. We can then group the proxies by continent and class and calculate the contribution of each group and compare that to the contribution of Graybill bristlecone chronologies. As you seen in the graphics of this post, everything other than GRaybill chronologies is pretty much noise in the MBH98 network.

    If RegEM TTLS is yielding results “remarkably similar” to MBH98, my guess is that the graph allocating contributions will be “remarkably similar” to what I’ve shown here.

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