Alberta #3

In February 2006, Luckman and Wilson archived their STD chronology for the Athabasca Glacier, Alberta site (STD fits each tree individually; RCS fits trees in groups.) Rob Wilson wrote in criticizing an earlier post for, among other things, not showing their STD version and for how I implemented the RCS emulation for Esper et al [2002].

Figure 1 below shows the "archived" Esper RCS ring width version ("archived" meaning the version that Science sent me in February 2006 after months of quasi-litigation) together with the LW05 STD ring width version (archived at WDCP in February 2006) and my emulation of the Esper RCS version using cana170w and cana171w with one regional curve. All curves have been smoothed and then the smoothed versions have been scaled – a common spaghetti graph methodology. There are some differences between the blue (Esper) and black (emulation) versions, but I don’t think that my emulation is "horrendous". (Esper et al 2002 does not contain any information on stratification of the site.) There are obviously significant differences between the Esper RCS version (blue) and the LW05 STD version (red).

Figure 1. Athabaska Glacier, Alberta (smoothed with 40 year gaussian filter, then scaled). Blue – Archived Esper RCS version; red – archived LW05 STD version; black – my emulation of Esper RCS version.

Next is a figure showing a more detailed comparison of my emulation of the Esper RCS series, which was done without dividing trees into "linear" and "nonlinear". Rob has criticized my emulation as being "horrendous", but why is it? I’ve attempted for months to obtain information on how Esper distinguished between linear and nonlinear trees. This should have been in the original SI. But even with an operational defintion, it is surely relevant to examine the effect of distinguishing between "linear" and "nonlinear" trees. The principal effect, regardless of the motivation, is to enhance 20th century levels. Doubtless there is a reason for this, but it’s not been provided so far.

Figure 2. Athabaska Glacier, Alberta RCS RW Versions. Top – Esper contained in Science email; bottom – emulation from cana170w, cana171w using bulk RCS fit. Correlation 0.80.

Rob said that "Significantly more low-frequency information was captured using the MXD data (See Appendix) but no significant gain was observed by using the RCS method on the RW data (analysis not shown)". Figure 3 shows a method that I like for checking the distribution of variance between low- and high-frequency: the distribution of wavelet variance by scale (la8 wavelet used here), in this case for two different "official" chronology versions, Esper RCS and LW05 STD (so that any inadequacies of my emulations are not material.) The graphs show very clearly that the variance share of high-frequency is much larger in the LW05 STD version than in the Esper RCS version. Figure 3 shows an objective method for quantifying statements about "gain in low-frequency information".

Figure 3. Wavelet Variance by Scale for RW Series, Athabasca Glacier, Alberta. Top – Archived LW05 STD chronology. Bottom – Esper RCS chronology.

The only point here, where I’m being critical of LW (as opposed to Esper et al) would be in their conclusion about the "gain" in low-frequency information, where I don’t see that LW05 has provided any support for this claim. I haven’t seen wavelet variance used by dendro people to quantify such statements and I think that it might be a pretty good way. I find these types of barplots to be far more informative than Fourier spectra on noisy series (but they reconcile to Fourier spectra).

The information shown here pertains to ring width site chronologies. The L97 and LW05 temperature reconstructions are primarily based on MXD chronologies; the ring width chronology is negatively weighted in the L97 temperature reconstruction.


  1. Paul
    Posted Mar 26, 2006 at 9:59 PM | Permalink

    I don’t see where the 20th century is the “warmest”, particularly the late 20th. Am I reading the graphs wrong?

    I also seem to see a MWP and a LIA, but how do we know those are tied to temperature? It seems logical to me that in warmer times trees grow better (but that doesn’t tell us what “warmer” is) and in cooler times trees don’t grow as well (but that doesn’t tell us what “cooler” is, either). Then again, it could have been a “wet” time (with no change in “warmness” or a “dry” time (with no change in “coolness”) that is driving these apparent differences in growth.

    But, reconciling these time periods to historical data, it would appear that it was “warmer” not “wetter” in the MWP and “cooler” not “dryer” in the LIA (although the MWP could have also been “wetter” and the LIA could also have been “dryer”).

  2. Steve McIntyre
    Posted Mar 26, 2006 at 10:04 PM | Permalink

    The LW05 data set has much more MW data than the earlier ones. The upspike at the start of the Esper version is not based on much data.

    These series are not the LW05 temperature reconstruction – that’s from MXD data.

  3. Posted Mar 26, 2006 at 10:20 PM | Permalink

    Do I understand well that the blue graph is your (Steve’s) honest version of what otherwise appears as the black graph? It’s probably “horrendous” because it disagrees with the scientific consensus. Your blue graph shows a striking discrepancy from the red graph especially around the 19th century. Incidentally, I don’t see any clear 20th century warming signal in either of the graphs.

    If you want to publish many papers, you should probably learn that there is no difference between effects and motivations. The difference between linear and nonlinear trees is the same as the difference between good, politically correct climate scientists and those who are in the pockets of oil industry: the former group gives the good conclusions while the latter group gives politically incorrect, insulting conclusions.

    Remember: if you hate a tree, say that it is nonlinear. If you love a tree, say that it is a bristlecone.

    If you learn a more convincing explanation of the difference between linear and nonlinear trees, I hope you will share it with us so that no one is misled.

  4. Steve McIntyre
    Posted Mar 26, 2006 at 10:27 PM | Permalink

    #3. No, you’ve got it wrong. The blue graph is the site chronology for Alberta used in Esper et al 2002 (it has nothing to do with me). THe black is my attempt to replicate Esper’s blue series, based on archived data (which is archived) and without distinguishing between linear and nonlinear trees (There may be other unreported stratifications that contribute to the differences.)

    The L97 and LW05 reconstructions primarily rely on MXD chronologies rather than ring width chronologies (and negatively weight RW in the regression equation.) But think back to Briffa’s “adjustment” of Tornetrask. In that case, the MXD series trended down in the 20th century, so he “adjusted” it upwards to the RW series which did not trend down.

    So Rob would defend their reconstruction on the basis of their regression, which I haven’t discussed yet. But I’m troubled by why the relationship between temperature and RW/MXD as a combination is so inconsistent between sites.

  5. Posted Mar 26, 2006 at 11:36 PM | Permalink

    OK, thanks. There are too many people in this game whose exact acts I would have to learn to understand it. Because I’ve never heard about “Rob” (Wilson?) before, I will probably leave this job to others. 😉 Good luck, Lubos

  6. TCO
    Posted Mar 27, 2006 at 10:51 AM | Permalink

    I don’t understand what “capturing more information” is. The information is in question, no? Is high variance better than low variance? What we really care about is the truth, no? what matches reality? If an invariant low frequency result is WHAT OCCURRED, then that’s fine. So…I don’t see how looking at the variance over the proxy reconsutruciton period tells you anything.

    Looking at which parameter matches the instrumental record better tells you something. Gives you an argument for how the parameters track temperature. Then you use those same correlations and move backwards and make a reconstruction. Hopefully, the X and Y parameters don’t leave the range of what occurred during the instrumental time. Otherwise, your calibration is out of range.

  7. TCO
    Posted Mar 27, 2006 at 10:57 AM | Permalink

    And if they don’t track in the future (divergence problem) then that shows that your regression was useless. Is just random correlation at a specific site. It also hurts a bit that you need a different regression for each site…although there might be reasons for this to happen…and you might be still able to get information this way. Just need to watch the divergence issue and maybe look at the amount of instrumental time and the strength of the correlation, etc.

  8. jae
    Posted Mar 27, 2006 at 11:08 AM | Permalink

    Steve: I suspect the reason that you get no answers about “linear” and “non-linear” trees is that this is just a little more “scientific” way of selecting between cherries and other fruits. Linear trees are “in line with” what is desired. I’ll bet a case of beer on it.

  9. Mark
    Posted Mar 27, 2006 at 11:27 AM | Permalink

    Part of the problem with using weights from current times to get aggregates in past times is stationarity. The K-L transform (PCA) requires stationary statistics. This means that all variables need to maintain constant statistics for the weights to apply. This is probably why they fail r2 outside of their calibration period.

    Which leads me to…

    re #1: EXACTLY! How do we know that the same correlation applies today as 1000 years ago? We don’t. Was the moisture in the ground (and humidity in the air) constant over the last 1000 years? What about cloud cover? How about soil nutrition? All of these things clearly can have an impact on tree growth yet nowhere are they accounted for. It’s just assumed they are all constant and the only impact is temperature. In other words, those things that can corrupt a correlation if they vary widely are assumed constant when in fact they likely are not.


  10. TCO
    Posted Mar 27, 2006 at 11:33 AM | Permalink

    You are too chicken little pessimistic, Mark. It’s almost like you don’t want to find out the answers. Like the people who think that you have to measure each individual instrument site for micro-site UHI.

  11. Mark
    Posted Mar 27, 2006 at 1:14 PM | Permalink


  12. TCO
    Posted Mar 27, 2006 at 2:07 PM | Permalink

    Mark, no.

    New topic. The comment about the negative weighting of RW is interesting. I like that they are using multiple parameters (could be a way of getting over precip confoiunders, etc.), but it sure seems to call into question others who use a positive weighting. I don’t rule out a different system for different species/sites. but if so, you need a lot of good foundational work (more of it) to gibe with such an approach.

  13. bruce
    Posted Mar 27, 2006 at 2:37 PM | Permalink

    TCO, love your work! (especially the stuff after a couple of glasses LOL), but re these last few posts (from #10 on which all got a bit too cryptic for me to follow) can I refer you to a recent post on another thread that said: “It’s not hard…………divide them up and avoid the kitchen sink tendancy…….Just tell a simple straightforward story and follow the rules.)”

  14. TCO
    Posted Mar 27, 2006 at 2:42 PM | Permalink

    🙂 That’s why publications for the literature are better. I will try though…

  15. Mark
    Posted Mar 27, 2006 at 2:50 PM | Permalink

    TCO, you do not make any sense then.

    By definition, any K-L weight calculation requires stationarity. We cannot guarantee such a statistical thing since we do not know past conditions at each site. This is not analogous to removing micro UHI, this is the PRIMARY requirement for the calculation. In the absence of stationarity, the weights are valid ONLY during the training period. Look it up, non-stationarity requires adaptively changing weights, which is not possible since our correlation is against a record that is only supported over a century or two, not ten.

    Furthermore, to claim any correlation with temperature requires that we know for sure we are measuring temperature. We do not. For all we know, we are measuring . How can you claim anything else in the absence of evidence? No criteria for removing extraneous influences has ever been posited, yet somehow I’m being pessimistic? I want the answers, but I want them based on solid mathematics. The kind they teach in introductory statistics classes would probably suffice.

    Soo, in other words, you need to reevaluate which version of statistical analysis you’re studying, as this one is flawed.


  16. Mark
    Posted Mar 27, 2006 at 2:55 PM | Permalink

    Oh, I might add, even saying the weights are valid during a training period in the presence of non-stationary statistics is a stretch. If the statistics change too much (“too much” is sort of a subjective statement but suffice it to mean “enough to prevent the weights from converging”), the usefulness of the weights will certainly be diminished over the entire period of calibration.

    There are methods for dealing with non-stationary environments. There are also ways to deal with multiple non-random variables (though I am not proficient with these).


  17. TCO
    Posted Mar 27, 2006 at 3:16 PM | Permalink

    It’s always been implicit in the use of proxies that we don’t have direct observations during the olden times. That’s what the proxy does. If you find that the proxy is little affected by precip during the training period and there was a wide range of precip, then that makes it more reasonable. If you find the opposite, it makes it less. I also hold some hope that the use of more variables (RW, MXD, elevation, etc.) allows to factor out the different causes. For instance the chestnut about low elevation being a precip proxy and high elevation being temp. Why not run both together?

  18. Mark
    Posted Mar 27, 2006 at 3:26 PM | Permalink

    TCO, I realize this, but that was NOT my point. My point is that any variations need to be taken into account if you want the statistics to work out. They (being the reconstructionists) are applying a stastical method that REQUIRES stationarity. In the absence of stationarity, or in the presence of multiple changing variables, the weights are not sufficient to combine the data. That’s a fundamental definition of the method. Nowhere is any selection criteria (that I know) actually demonstrated other than output statistics. I.e. these seem to correlate now, therefore they must correlate for all time. Why? Because!

    I did not say it was not possible to remove the variables, I said it is not being done.


  19. Neil Fisher
    Posted Mar 27, 2006 at 3:31 PM | Permalink

    Re: linear vs. non-linear trees. I suspect that this refers to trees that show a linear relationship to temperature over the calibration and verification periods. That is to say, we have, say, 1mm RW “calibrated” to, say, 25C, 0.8mm “calibrated” to 20C, 1.2mm “calibrated” to 30C etc. If this is indeed the case, then here is another major flaw in these reconstructions. I’m sure the reference is on this site somewhere that shows such linearity does not exist – IIRC, it’s closer to an inverted U. Therefore, any trees that actually show such linearity are clearly being affected by other factors – they should be selected to be thrown out, not kept!

  20. jae
    Posted Mar 27, 2006 at 3:40 PM | Permalink

    I don’t rule out a different system for different species/sites. but if so, you need a lot of good foundational work (more of it) to gibe with such an approach.

    No 12. This is the crux of the problem in “dendroclimatology,” IMO. As you know, the whole basis for the tree ring-based temperature reconstructions is that tree growth and/or latewood ring density is positively correlated with temperature. And I’m very suspicious that there is no foundation for the whole premise.

  21. Mark
    Posted Mar 27, 2006 at 4:23 PM | Permalink

    Or a poor foundation at best, jae.

    The more I dig in to the tree-ring hypothesis (untested, therefore only hypothesis), the sicker I get about seeing it used as fact.


  22. TCO
    Posted Mar 27, 2006 at 5:09 PM | Permalink

    No correlation is way of an overstatement. Steve has read enough papers to disagree with this statement.

    Now if we want to get into confounding factors and the like, then fine. But that’s a different case from saying there is no relationship.

    Mark, you and I are likely not so far apart. I just want to get away from the extreme of some people on this site who say that because we didn’t validate the proxies with instruments during the 1200s that we can’t look at the proxies. I mean…sure…in some sense that position is right…but if you take that position, you’re sticking your head in the sand and not looking at useful detective work.

    As far as the issue of level of precip variation, I think this should be looked at during the instrument period. a. how much of a dependance was seen during this time? b. can one select trees that have less dependance on this (the Lamarch hypothesis). c. was precip variation over the period of the instrumentation period large or small? d. in the end, we may not know (without independant precip proxies or at least extra mixed ones), that some radical precip variation did not take place. But I think one can still do the analysis regardless and just note that a confounding factor was not controlled for. Much of Steve’s criticism does not depend on the issue of a confounding precip variable. They are issues even if we accept linear temp response. e. I would think that the bigger concern is CO2. We KNOW that those conditions are different from the proxy period to the calibration period.

  23. Mark
    Posted Mar 27, 2006 at 6:10 PM | Permalink

    Mark, you and I are likely not so far apart. I just want to get away from the extreme of some people on this site who say that because we didn’t validate the proxies with instruments during the 1200s that we can’t look at the proxies.

    That’s not what I’m saying, TCO. Not at all as a matter of fact.

    The way the algorithm works is to calculate weights over a correlation period (I do the same thing with radar or communications signals). It is then assumed that the statistics that were present during the “training period” are the same over all time. Flaw #1 as we do not know this, though it is required for the algorithm to work. Then, they take the weights and recombine past proxies, still relying on constant statistics, and perform cross-validations. The cross-validations fail, likely because the statistics are not the same.

    The method used by the so-called dendroclimatologists is to select their tree-rings based on current correlations (er, recent). This method suffers simply because we do not know for sure that the correlation that may be strong now, was also strong in the past. The fact that the r2 is low, and near zero, supports a conclusion that the correlation was not the same in the past.


    PS: a more common method in my field is to solve the optimal weight equation w = R^-1 * p (I use Gram-Schmidt), where R is the sample correlation matrix and p is the sample cross correlation vector. These weights are calculated over short blocks to remove the correlated signals, typically noise from a jammer. Obviously, in climatology we want to keep the correlated signals, but the process is the same. We use short blocks in order to guarantee stationarity. If I ran the algorithm adaptively over time in a non-stationary environment, I’d never get a convergence on the weights, and my output would be garbage. This presents a problem in climatology as we are forced to assume the extraneous variables are constant outside of the calibration/verification period when in fact, they may not be. It is a conundrum I do not have a solution for.

  24. jae
    Posted Mar 27, 2006 at 6:41 PM | Permalink

    Now if we want to get into confounding factors and the like, then fine. But that’s a different case from saying there is no relationship.

    Yes, I understand that confounding factors are an extreme headache (probably insurmountable). But even beyond that, the only relationship I’ve seen between tree growth (or latewood density, I can’t remember) is a U shaped one, where there is an optimum temperature. Now how does that help in using tree rings as proxies? If there is no linear response between growth (density) and temperature, tree rings are not suitable “thermometers.”

  25. TCO
    Posted Mar 27, 2006 at 6:55 PM | Permalink

    Well…maybe you can use extra variables to help with that (elevation, MXD). Or maybe you can work in a region where you don’t have much curvature.

  26. mark
    Posted Mar 27, 2006 at 7:07 PM | Permalink

    I think we need to figure out a way to isolate all the relevant variables. I.e., there needs to be a way to show that the variation in soil moisture or nutrition is not impacting width OR, use such information to provide “adjusted” widths/densities with the variable removed from considerations. Sort of a normalization process.

    I find the impact of CO2 concentration in the air to be the most interesting, btw, as that’s plant food. How do we get around CO2 causing temperature causing tree-ring width changes? It’s a cart before the horse proposition.


  27. bruce
    Posted Mar 27, 2006 at 7:58 PM | Permalink

    Re #24: Err jae, I think that when you say

    the only relationship I’ve seen between tree growth (or latewood density, I can’t remember) is a U shaped one, where there is an optimum temperature.

    you actually mean: “the only relationship that I’ve seen between tree growth (or latewood density, I cant’ remember) and temperature is an inverted U shaped one, where there is an optimum temperature.”

    My point is, as has often been noted here, tree rings will be thin in unusually cool (and dry) seasons, thickest in seasons where temperature (and moisture, and light, and whole lot of other variables) are optimal, and thin again at elevated temperatures, especially if drought conditions prevail and the trees are stressed.

    Can you please confirm that that is what you meant.

  28. jae
    Posted Mar 28, 2006 at 6:57 AM | Permalink

    re: 27 Yes, that’s exactly what I meant. Thanks.

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  1. […] the reconstruction used in Osborn and Briffa 2006, and discussed previously at the blog here, here, here,, with a Rob Wilson criticism here and my reply here. Its predecessor chronology from Luckman […]

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