Wednesday, June 29, 2011

More proxy temperature reconstruction plots

This is a sequel to the previous post, where the list of data information, taken from the NOAA file, is printed. I have extended the time scale to 2000 years. This time I have used 41-year triangle smoothing. And I have experimented with inclusion and omission of instrumental temperatures.

This the plot over 2 millennia with HADCRUT3NH (with 11 year smoothing) in a background light grey.


More below the jump...



And here is the same plot, but without HADCRUT3, nor other reconstructions with instrumental components



And here is the 1 millenium plot, with smoothing and instrumental



and now the same without instrumental



49 comments:

  1. Hi Nick,

    Am I correct that the reason all the reconstructions differ from each other in previous centuries but converge on the same curve in the late 20th century is because they have all been calibrated in that period to the same instrumental data? Is it correct that in that sense none of them are truly independent of the instrumental data?

    Best,
    Alex

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  2. Nick, in the link below I cropped off the instrumental record. Without that part of the graph (and no longer animated) one can start to image a series of reconstructions that together look more like a combination of white and red noise over the entire period.

    I would think that it would be critical to those doing or who have done climate reconstructions to look closely at the reconstructions in the period where the instrumental temperature record has shown accelerated increases. Here I do not mean with newly selected proxies but rather with proxies that were previously selected for reconstructions. It affords an opportunity to obtain some out-of-sample testing.

    http://img600.imageshack.us/img600/3382/nsreconscropped.png

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  3. Alex,
    Yes, I think that's right. I think of it as extrapolation. You have the current period, where you know the temperature (thermometers) and tree-ring behaviour, or whatever. You see how well they are aligned there. Then you go back into the past, knowing only the treerings. Different extrapolations are likely to diverge as you go back.

    That's why I think most of the talk about the post-1960 "decline" etc is misplaced. Tree-rings aren't telling you about post-1960 temperature. As you're noting, that's the time when the thermometers are being used to align the tree-ring data. It's the earlier period where you are relying on treerings for temperature estimates.

    Of course, you need good alignment in the calibration to extrapolate well, and divergence detracts from that. But that is a different story.

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  4. Nick, what about the reference in Mann 2008 about divergence of the non tree ring reconstructions/proxies about which I quoted on another thread.

    Could the convergence of reconstructions in the instrumental period merely indicate that the process used for selection was not based on any a prior criteria, but rather that only proxies that had some reasonable agreement with the instrumental were retained for the reconstructions? Therefore a selection process biased towards convergence for in-sample testing (calibration/verification) shows rather predictably that the proxy response to temperature does not hold (divergence) with what might be considered testing out-of-sample.

    Divergence of the proxies amongst themselves and against the instrumental record have to be a cause for concern and certainly add more uncertainty to the reconstructions - assuming that the reconstructions are attempts to measure the same thing.

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  5. Kenneth,
    I'll look up the Mann ref - I can't where I am at the moment. There's obviously a general selection of proxy types for good alignment in the calib period (and verification) - that's really the only test of goodness that we have.

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  6. I also think that the divergence in the instrumental period is rather more problematic than those amongst reconstructions/proxies, since it would indicate that the proxies do not respond to the full extent of temperature variations. The muted response here would be in addition and independent of the contention that many reconstructions use methodologies that underestimate the temperature variations in synthetic data outside the calibration/verification periods.

    I continue to think that a reconstruction with all its proxy series displayed with the animation you have used here would be instructive.

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  7. Hi Nick,

    >>That's why I think most of the talk about the post-1960 "decline" etc is misplaced. Tree-rings aren't telling you about post-1960 temperature.

    That's only if we agree to the implicit assumption that the divergence is somehow anthropogenically caused, which is a long way from proved, at least as I understand it.

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  8. Nick: That's why I think most of the talk about the post-1960 "decline" etc is misplaced. Tree-rings aren't telling you about post-1960 temperature. As you're noting, that's the time when the thermometers are being used to align the tree-ring data. It's the earlier period where you are relying on treerings for temperature estimates.


    I think it is your faith in one particular explanation of the discordance of proxies and instrumental data that is misplaced.

    From an empiricists perspective, we know the proxies don't line up well with the instrumental data post 1960, but there does seem to be a good correspondence in the overlap region prior to that. All we can conclude from that is, post 1960 the tree ring growth is not temperature limited.

    To go beyond that and say "most of the talk. ... is misplaced" requires—for an empiricist— not only a plausible explanation that e.g. anthropogenic factors dominate post 1960, you must be able to demonstrate that none of the alternative hypotheses are equally plausible as the one you personally clearly favor.

    The problem is, if for example the non-temperature limited growth were due to a shift in the elevation of the tree line as the climate warmed and cooled (which also explains the shift in and out of temperature limited growth), it would make tree ring proxies an unreliable measure of temperature.

    Until you can explain the discordance between tree ring and temperature data in the post 1960 era, the interpretation of tree rings as temperature proxies remains very much in question.

    ReplyDelete
  9. Carrick and Alex,
    I'm not saying what explanation should be favored for the divergence - I'm just saying that it doesn't mean that temperature actually declined. It doesn't trump the thermometers.

    Yes, it diminishes faith in proxies, to an extent,especially if the reasons aren't anthropogenic, or otherwise special to this time period.

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  10. Carrick, Alex and Kenneth

    Why would you simply engage Mick over the issue of divergence? Why not take it upon yourseles and consult with dendrochronogists.

    Your own skepticism is pretty meaningless if you don't try and understand the problem beyond the information presented here.

    ReplyDelete
  11. Sorry I meant 'Nick'

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  12. "Why would you simply engage Nick over the issue of divergence? Why not take it upon yourseles and consult with dendrochronogists."

    Anonymous, if you take the time to read Mann (2008) you will see that divergence is not limited to tree ring proxies and reconstructions. If you have any links that might explain these divergences, please make them available here.

    What Nick has presented in his animated graphs shows very clearly to me that one could readily explain the proxies/reconstructions with a signal that is mixture of red and white noise prior to the instrumental period. The closer agreement of the proxies with the instrumental record during that period could be explained by those doing reconstructions selecting proxies based on how well they reasonably follow the instrumental record. If the selection process involves in-sample testing, as opposed to a criteria for proxy selection devised a prior, than the series prior to the instrumental period becomes, to a certain extent, testing out-of-sample. The divergence in the instrumental period would indicate to me that even with in-sample selection it was not possible to find proxies that always matched the steep increase in the later day modern temperatures.

    Nick, you seem to addressing an issue that I do not believe the posters here are not posing. We all agree that the instrumental record best measures the temperatures in that period and the divergence is problematic for the proxies, not the instrumental record.

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  13. Let me try that last paragraph again:

    Nick, you seem to be addressing an issue that I do not believe the posters here are posing. We all agree that the instrumental record best measures the temperatures in that period and the divergence is problematic for the proxies, not the instrumental record.

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  14. Nick:
    These animations are useful, but perhaps you have the bandwidth to do even better. I'm sure *you* understand this, but:

    a) Real science has error bands, and while the NOAA file sadly doesn't show them, at least some of the papers do. A lot of the arguments over these spaghetti graphs would be seen as silly if more people understood the attached error bands.

    b) The best shot at this I've seen is in the 3rd graph (c) in AR4 WG I Chapter 6, or p.467 of the book.

    I have no idea what software they used to produce that.

    Seeing your animations, I keep wishing for one that 1) computes the background as in AR4, then flips between specific reconstructions as you do, on top of the background, ideally with error bands.
    This is nontrivial compared to lines of course.

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  15. "What Nick has presented in his animated graphs shows very clearly to me that one could readily explain the proxies/reconstructions with a signal that is mixture of red and white noise prior to the instrumental period"

    Or that the temperature did not change much, which was the point of MBH and successors

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  16. John #14,
    As you say, it wouldn't be easy, either graphically or in gathering the numbers. Even the papers that give usable error bounds probably don't calculate them on the same basis.

    One reason why I rather like the spaghetti plots, despite their confusion, is that they do give an error bar effect intrinsically. After all, an error range is meant to show how things might vary if you could do it again letting the things that could vary randomly do so. Insofar as these calcs are independent, they include that variation. They also have underlying reasons for varying, but it's quite likely that the random dominates.

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  17. Anonymous: Why not take it upon yourseles and consult with dendrochronogists.

    Got it. We can just agree to treat dendrochronologists as (unlike the rest of us schmucks) infallible demigods whose judgements are never to be questioned... unless you're another dendrochronologist. (You can do that, I choose not to.)


    Your own skepticism is pretty meaningless if you don't try and understand the problem beyond the information presented here.


    Like Kenneth I actually have done my homework, and I believe I have a fairly decent grasp of the underlying empirical issues.

    Eli:
    Or that the temperature did not change much, which was the point of MBH and successors


    Was that really the point? Here I thought it was to dispassionately attempt to reconstruct global mean temperature.

    MBH isn't in particularly good agreement with the later reconstructions in any case. If it were in deed the gold standard for later reconstructions that some people like to suggest it to be, the newer papers would have a been a waste of time in any case.

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  18. Nick: As you say, it wouldn't be easy, either graphically or in gathering the numbers. Even the papers that give usable error bounds probably don't calculate them on the same basis.

    I agree with Nick here. I think you'd have to process them using the same methodology before you could put them on the same graph.

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  19. Off topic. You probably already know this, but HadSST3 is now available.

    http://www.metoffice.gov.uk/hadobs/hadsst3/

    ReplyDelete
  20. Carrick:
    From an empiricists perspective, we know the proxies don't line up well with the instrumental data post 1960, but there does seem to be a good correspondence in the overlap region prior to that.

    The point is that our knowledge is not restricted to the overlap period. For example, we can use tree proxies to reconstruct past ENSO cycles. We find that the peaks and through line up pretty well with independent evidence over at least a couple of centuries. We can also spot historical volcanic eruptions. This indicates that tree proxies do record climate information in the pre-instrumental past.

    Got it. We can just agree to treat dendrochronologists as (unlike the rest of us schmucks) infallible demigods whose judgements are never to be questioned...

    Well, we could start with actually reading their papers, before deciding ex cathedra what they can and can't do?

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  21. Dendrochronologists may not be demi-gods , but they are individuals who have worked in the field for years. This includes multiple degrees with the accompanying constant professorial and peer criticism, continuing reading and research and the peer publication process with the stress of revieve and criticism. No wonder they are always wrong!

    The focus by Carrick, Ken ( and others) on a single day in 2008 reminds me of Groundhog Day.

    I suspect some don't know that dendrochronologist's work is respected and used by historians, archaeologists and researchers in historic climate other than temperature. Are they always wrong in these fields too?

    John McManus

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  22. John McManus, dendrochronologists, as a general class, would not be directly involved with the results of dendroclimatologists. The former are more interested, generally, in using the precise dating properties of tree rings to record historical events such as volcano activity and other cataclysmic events, while the latter is more likely to attempt relate tree ring widths and densities to a climate variable.

    It has been my view that dendroclimatologists put out their results, but are much less inclined to push them as the end all in recording past temperatures. That has been more in the realm of some climate scientists such as Mann.

    You lost me on the one day in 2008. My take away message derives from what Nick Stokes has provided in total in his animated graphs.

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  23. Kenneth and Carrick
    I used Google scholar and got some links pretty quickly to papers from 2008 and 2010 that discuss the issue you are so concerned with (so concerned that you haven't actually gone and looked yourself).

    They state that the divergence problem is a site specific problem. One that is not consistent amongst trees of the same species or consistent across locations in at similar latitude. It also only affects the northern hemisphere and 'tree line' trees. It is a problem that crops up from time to time, it is not a problem with the physical basis for dendrochronology or the use of rings for climatological purposes.

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  24. "The point is that our knowledge is not restricted to the overlap period. For example, we can use tree proxies to reconstruct past ENSO cycles. We find that the peaks and through line up pretty well with independent evidence over at least a couple of centuries. We can also spot historical volcanic eruptions. This indicates that tree proxies do record climate information in the pre-instrumental past."

    To be useful for reconstructions of past temperatures the assumptions are that proxies are responding in a linear fashion to temperatures and in a quantitative manner. That tree rings can qualitatively respond to climate affecting events was shown in a paper as I recall authored by Rob Wilson. He showed that most trees in his study responded to volcanic events recorded independently in history. What was most obvious to me was that those responses were quite different in scale.

    I did not see a link to your ENSO comment but it suggested that that relationship might well be more qualitative also.

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  25. "They state that the divergence problem is a site specific problem. One that is not consistent amongst trees of the same species or consistent across locations in at similar latitude. It also only affects the northern hemisphere and 'tree line' trees. It is a problem that crops up from time to time, it is not a problem with the physical basis for dendrochronology or the use of rings for climatological purposes."

    What about the Mann (2008) observation and graph that I noted above which states that divergence is seen in non tree ring reconstructions? Do you have a link to the paper from which you draw your comment above?

    I was aware of the rationale used by some climate scientists to explain/limit the divergence problem (and others related to algorithms used to remove the tree age effects on the tree ring widths), but I find it interesting that in the Mann 2008 tree ring reconstructions that his proxies must have had a sufficient diverging types to make the entire reconstruction diverge. Would you suggest eliminating those diverging proxies and go with those that do not? Have any papers been published with the results of that preselection process?

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  26. Kenneth:

    http://www.buentgen.com/uploads/2/2/0/9/2209799/buentgen_etal.08_trace_dp.pdf

    Try using google scholar 'dendrochronology divergence'


    "but I find it interesting that in the Mann 2008 tree ring reconstructions that his proxies must have had a sufficient diverging types to make the entire reconstruction diverge."

    Why do you say this?

    "Would you suggest eliminating those diverging proxies and go with those that do not?"
    Not necessarilly as the divergent part is not the part you are using for your reconstruction.

    "Have any papers been published with the results of that preselection process?"
    Don't know

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  27. Carrick

    "MBH isn't in particularly good agreement with the later reconstructions in any case. If it were in deed the gold standard for later reconstructions that some people like to suggest it to be, the newer papers would have a been a waste of time in any case."

    you can compare it in Nick's new layout... Looks ok to me.

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  28. Anonymous,the tree ring divergence problem in the review you linked is the one that I think covers all the purported potential causes of the divergence. I have excerpted what I consider to be two telling comments from that review.


    "This has also implications for the use of tree-ring data taken from freely available data pools (e.g., ITRDB) for large-scale modeling purposes: Before being included in climate modeling studies, metadata about the specific sampling strategies for an underlying tree-ring data set should carefully be considered...


    ..This review reveals that future dendroclimatic research should not ignore potential complex and nonlinear growth responses to a changing climate system, which may challenge the current
    interpretation of the principle of uniformity as well as methodological biases that emerge from tree ring detrending and chronology development."


    I judge that part of the problem of pre-selection of samples to be used in tree ring reconstructions is that it biases the samples for good performance in the instrumental period. Discarding samples that have obvious and readily explainable problems is not my issue here, but rather that of ignoring the larger population of samples that might be indicating that general response of tree rings to temperature is not what is indicated by a selection process based on reasonable correlations in the calibration/verification periods. I am not all certain that some climate scientists comprehend the full implication of the selection process from a statistical point of view. Good statistical practice would require having a prior selection process and criteria based on reasonably good science and not selecting samples posterior.


    A posterior selection process could lead to what we see in divergence in both part of the instrumental period and between proxy responses. This is a point that I have not seem addressed by climate scientists or dendroclimatologists. Part of this problem could be alliviated by bringing proxy sites used in the original reconstructions up to date. I see no current efforts along this line.

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  29. The seemingly different views on the divergence issue shown in Mann (2008) might be due to not having a common link to that paper and thus below is a link:



    http://www.pnas.org/content/105/36/13252.full


    Look closley at Figure 2 in that paper and note the caption which states in part:


    "Comparison of CPS: hemisphere screened (A); “no dendro” (B); and EIV full global (C) and “no dendro” (D). NH reconstructions (colored curves.."



    I clearly see divergence in all four graphs, i.e. no dendro and dendro. Under Results: Validation Exercises look for a link to the SI and then look at graph S4 where you will see NH, SH and global reconstructions and all having a divergence problem.



    The paper discusses the divergences under Results: Validation Exercises immediately preceding the graphs and notes:



    "However, in the case of the early calibration/late validation CPS reconstruction with the full screened network (Fig. 2A), we observed evidence for a systematic bias in the underestimation of recent warming. This bias increases for earlier centuries where the reconstruction is based on increasingly sparse networks of proxy data. In this case, the observed warming rises above the error bounds of the estimates during the 1980s decade, consistent with the known “divergence problem” (e.g., ref. 37), wherein the temperature sensitivity of some temperature-sensitive tree-ring data appears to have declined in the most recent decades. Interestingly, although the elimination of all tree-ring data from the proxy dataset yields a substantially smaller divergence bias, it does not eliminate the problem altogether (Fig. 2B). This latter finding suggests that the divergence problem is not limited purely to tree-ring data, but instead may extend to other proxy records. Interestingly, the problem is greatly diminished (although not absent—particularly in the older networks where a decline is observed after ≈1980) with the EIV method, whether or not tree-ring data are used (Fig. 2 C and D)."

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  30. This did not post on my first attempt.

    The tree ring divergence problem in the review you linked is the one that I think covers all the purported potential causes of the divergence. I have excerpted what I consider to be two telling comments from that review.


    "This has also implications for the use of tree-ring data taken from freely available data pools (e.g., ITRDB) for large-scale modeling purposes: Before being included in climate modeling studies, metadata about the specific sampling strategies for an underlying tree-ring data set should carefully be considered...


    ..This review reveals that future dendroclimatic research should not ignore potential complex and nonlinear growth responses to a changing climate system, which may challenge the current
    interpretation of the principle of uniformity as well as methodological biases that emerge from tree ring detrending and chronology development."


    I judge that part of the problem of pre-selection of samples to be used in tree ring reconstructions is that it biases the samples for good performance in the instrumental period. Discarding samples that have obvious and readily explainable problems is not my issue here, but rather that of ignoring the larger population of samples that might be indicating that general response of tree rings to temperature is not what is indicated by a selection process based on reasonable correlations in the calibration/verification periods. I am not all certain that some climate scientists comprehend the full implication of the selection process from a statistical point of view. Good statistical practice would require having a prior selection process and criteria based on reasonably good science and not selecting samples posterior.


    A posterior selection process could lead to what we see in divergence in both parts of the instrumental period and between proxy responses. This is a point that I have not seem addressed by climate scientists or dendroclimatologists. Part of this problem could be alleviated by bringing proxy sites used in the original reconstructions up to date. I see no current efforts along this line.

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  31. John McManus: The focus by Carrick, Ken ( and others) on a single day in 2008 reminds me of Groundhog Day.

    And this comment reminds me of something Carl Spackler might say. :D


    Anonymous: you can compare it in Nick's new layout... Looks ok to me.

    Looks can be deceiving. ;-)

    If you want to test the degree of agreement between two curves, you don't look at them visually, you use a statistical test, like Pearson's cross-correlation

    Here's a comparison against Ljundqvist's reconstruction.

    I used a 500-year time window in computing the correlation coefficient, and am plotting the correlation coefficient against the center of the the time window. I am using Pearson's correlation---which adjusts for variance---because I am not convinced that the different reconstructions can be trusted to be properly calibrated outside of the calibration region. This fixes things like the variance loss associated with the regularization scheme used in many of the reconstructions as well as issues with sparse geographical sampling....I can go why I would expect this to affect the overall calibration (scaling) if you're interested.

    When I was trained to study time series, another thing we were also trained to look at
    were the spectra associated with the time series. It shows an interesting picture. I would grade series that are able to retain high-frequency information as superior to those that reduce the high-frequency components of the temperature fluctuation spectrum to white noise.

    (My take away from the limited analyses I've done is yes there is a MWP, but it was cooler than the current climate, Loehle probably gets the right shape, but his calibration constant is off from other methods. Other methods suffer from variance loss and de-correlation of the high frequency components of the temperature fluctuation spectra..which likely reflects on more on the proxies they use than the overall method for reconstruction.)

    Anyway you look at it (besides on a spaghetti graph) reveals MBH98 to not be in agreement with much of anything, other than maybe a red noise series.

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  32. Nick,

    I tried to stick error bars into spaghetti charts awhile back over at the Blackboard: http://rankexploits.com/musings/2010/comparing-proxy-reconstructions/

    Also, your early baseline period seems to do weird things to Moberg vis a vis a later baseline.

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  33. Zeke,
    Yes, baselines are tricky here, because the proxies move relative to each other quite a lot on a decadal scale. So 30 years is a bit short. But with the Loehle series stopping in 1935, a longer period means going further away from the calibratrion period. I see you used 1880-1930 - I could try that.

    Anomalies work best with stationarity, and that is particularly lacking with HADCRUT. The further back you go for the baseline, the more it rises relative to the proxies. I think that is arguably more correct - the period around 1900 and before is as close to stationary as it gets.

    I could try the error bars, as you did. It's hard to show more than one at a time, but the dynamic display helps there. I'm still not sure whether they can be truly compared, though.

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  34. Kenneth

    You need to speak to real dendro's to get an answer to your question. That was my original point.

    You won't find the answers here. My guess, becaue it's clear you have been going on about this for a few years is that you don't really want to know youjust want something to complain about.

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  35. Carrick

    thanks, I suppose MBH98 is completely wrong then.

    Great

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  36. "You need to speak to real dendro's to get an answer to your question. That was my original point."

    Anonymous, I must admit I have a difficult time following what your attempting to say with your replies.

    Would I be correct in saying that speaking to a real dendro may be difficult and that I would be better to continue to search the dendro literature and look for papers that shows evidence and reasonable theories for divergence and how that divergence explanation would make more sense than merely assuming the reasonably good fit in parts of the instrumental period derives from a posterior selection process that succeds fairly well in-sample but diverges out-of-sample?

    I think by saying the answer does not lie within the realm of this blog, you actually mean that you cannot answer my queries. I accept that, but I can continue to hope that others with countervailing views might engage.

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  37. Just to add to my inclination that dendroclimatologists do in-sample posterior testing in selecting proxy candidates for reconstructions, read the following comment by Jim Bouldin at Realclimate:

    "The Russians state that they use 224 series in their chronology, chosen based on being the longest and most sensitive of the larger set of series, with sensitivity defined by inter-annual response to instrumental temperatures. It is thus highly likely that they chose their 17 modern cores based on these same criteria. This is perfectly valid dendroclimatic practice, and indicates that the 12 cores Briffa used in the modern chronology are sensitive to temperature."


    http://www.realclimate.org/index.php/archives/2009/09/hey-ya-mal/comment-page-10/#comment- 137375

    If such a practice is widespread in selecting proxy candidates it would bias the proxies to agree reasonably well with the instrumental period temperature. Unfortunately one would properly need an a priori selection process to overcome this potentially fatal statistical weakness. Obviously an a priori selection process could be tested for validity by comparing the ultimate temperature sensitivity of the proxy during the instrumental period. However, if that process were then used to select criteria based on the ultimate sensitivity it would become a posterior selection and as flawed statistically as a system that selects posterior the proxy sensitivity directly.

    One could say that it would make little sense to use proxies that were not temperature sensitive for a reconstruction, or sufficiently so, during the calibration and instrumental period, and that would be a true statement. On the other hand, the more valid selection a priori system would force the issue of making an effort to determine whether a proxy can be validated without in-sample and posterior testing.

    A good test for temperature sensitivity for proxies, already selected and used in temperature reconstructions with in-sample testing, would be to obtain some out-of-sample results by updating the samples to present time. I have not seen this addressed as an important issue in the literature.

    In theory using separate calibration and verification periods would provide some measure of out-of-sample testing, provided that the analysts could show that they did not "snoop" the verification results and/or select based on the verification results.

    If anyone reading this thread can suggest links to where dendroclimatologists or others working in related fields have dealt with these issues, I would greatly appreciated their efforts.

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  38. hey Nick.

    http://stevemosher.wordpress.com/2011/07/11/taminos-method-regional-temperatures/

    If I get time this week I'll be putting tamino's code into RghcnV3.

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  39. Steven,
    Yes, I saw your note there. I'll look to see how it worked out.

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  40. I am posting in 2 parts to overcome the character limit. Part 1 is below.
    I have recently downloaded all 1209 Mann (2008/2009) proxies to compare side by side for series coherence and to model with arima and arfima. That will keep me busy for a while and thus in the meantime I wanted to relate what I found in analyzing Mann (1999) proxies. The paper is linked below. That link leads to links for the proxies.

    http://holocene.meteo.psu.edu/shared/research/ONLINE-PREPRINTS/Millennium/DATA/PROXIES/


    The proxy data were a frustrating case of determining exactly which 28 individual series were used in the all important International Tree Ring Database (ITDB) PCs #1, #2 and #3 from North American (I was unsuccessful). I also could not find the Morocco proxy and three of the Quelccaya (ice core with 18O and accumulation) appeared to have incorrect starting dates listed.

    I have linked to graphs described below of the individual series that made up the proxies. I show the series as annual data and a 10 year 2 sided moving average. The annual data is used because it shows some interesting characteristics of the series.

    In the first link I have graphed the annual series for 14 proxies used in Mann (2009). The series are listed below and appear in the 7 row by 2 column matrix of graphs starting with 1 on the upper left and 2 upper right and then down to left for 3 etc. :
    1. Fennoscandia1, 68N 23E, Start 914, Type MDX 2. Fennoscandia4, 68N 23E, Start 914, Type MDX
    3. Fennoscandia6, 68N 23E, Start 914, Type MDX 4. N. Patagonia, 38S 68W, Start 869, Type TRW
    5. Tasmania, 43S 148E, Start 900, Type TRW 6. Polar Urals1, 67N 65E, Start 914 Type MDX
    7. Polar Urals4, 67N 65E, Start 914 Type MDX 8. Polar Urals6, 67N 65E, Start 914 Type MDX
    9.France, 44N 7E, Start 988, Type TRW 10. Greenland, 77N 60W, Start 553, Type Ice Core O18
    11. Quelc.1, 14S 71W, Start ~ 488, Type Ice Core Acc 12. Quelc.1, 14S 71W, Start ~ 488, Type Ice Core O18
    13. Quelc.2, 14S 71W, Start ~ 488, Type Ice Core Acc 14. Quelc.2, 14S 71W, Start ~ 488, Type Ice Core O18
    The second link shows the same series in the same order with a 10 year two sided moving average.
    http://img143.imageshack.us/img143/966/mann1999annprox.png
    http://img143.imageshack.us/img143/966/mann1999annprox.png

    What is readily seen in the annual graphs is that some series appear to be truncated at the lower proxy responses, others show a very visible change in variation from smaller to larger when proceeding from early to late in the time period and finally some series show oscillating character early in the series.

    When a 10 year MA filter is applied most of these distinguishing features in the annual series are muted. The 10 year MA series look very much like a mixture of white and red noise to me. Perhaps when I plot some simulations of white and red noise I will change my mind. I see nothing of a feature of the handle of a hockey stick in these series and, of course, the blade is not in place without adding the instrumental series to the end.

    I had some puzzlement about the 3 PCs noted above that is best shown by presenting the 3 PCs listed as just that in the Mann link from above. These three series are shown in the link below:

    http://img705.imageshack.us/img705/2011/mann1999pc123.png

    Surprisingly PC1 bends downward in most recent years in the series while PC2 and PC3 are rather flat throughout the series time period.

    The next three series are will display in the link below are from the Mann link above and are identified as the fixed PC1.

    http://img705.imageshack.us/img705/2011/mann1999pc123.png

    I am confident that I understand these three series, but I do not understand how we got the PC series we see in this link from the PC1 in the previous link. Maybe an interested poster here knows. The PC1 was transformed in Mann (1999) by replacing the period from just after 1600 to 1980 with that of another TRW series. The reasoning was as follows: (See Part 2 next post)

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  41. Below is Part 2:

    The reasoning was as follows:

    The PC1 showed an unrealistically greater TRW response for part of 1600 to 1980 time period which Mann (1999) attributes to CO2 fertilization of trees at high altitude. The enhanced TRW growth then levels off and Mann (1999) attributes that to a saturation effect and rationalizes the replacement of that part of PC1 with another TRW series by way of saying that whatever the reason for enhanced growth and leveling off it must be "unnatural" and thus was removed.

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  42. Kenneth,
    The two links to images are identical - I think you missed the smoothed one.

    When you say
    "The 10 year MA series look very much like a mixture of white and red noise to me. Perhaps when I plot some simulations of white and red noise I will change my mind. I see nothing of a feature of the handle of a hockey stick in these series"
    isn't the handle expected to look like noise? Flat - no signal?

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  43. Nick, thanks for picking up my error in posting the 10 year 2 sided MA (5 years on each side). The correct link is below:

    http://img818.imageshack.us/img818/170/mann199910ymaprox.png

    I must concede to your lawyerly tendencies on the HS handle and rephrase my comment by noting that I was referring to lack of lower frequency variations on the original HS as compared to those of the proxy features. The higher frequency signal is there in the original HS and these proxy series. Also the original HS slopes downward at a steady incline until the instrumental record is attached to the end with the blade sloping upward.

    I think it best for me to show a simulated white and red (and LTP) noise series here soon. When I modeled these proxies they differed in both red and white noise and LTP content.

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  44. In finishing the Mann(1999) proxy analysis, I ARFIMA modeled the 14 long proxies used in Mann(1999) with fracdiff in R, library(fracdiff), and then used the coefficients obtained from the models with the R function fracdiff.sim to simulate several ARFIMA series for each proxy. In order to assure that the proxies and simulated proxy series were at the same scale, I used anomalies and then divided by the standard deviation for each proxy and simulated series. In both cases, I used a two sided 10 year moving average to better view the intermediate frequency structure of the proxies and simulations. I used the R default which generates the innovations with white N(0,1) noise. I have linked the results as follows:

    The first link is a table with the best model I obtained (maximum likelihood) for each proxy showing the model and coefficients. An ARFIMA (1,d,1) or (0,d,1) fit the models. In 2 cases the fractional d was effectively 0 and in some cases the ar1 and ma1 coefficients were close to zero.

    The second link is the 14 proxies series normalized in the manner described above in a 7 row by 2 column array of individual graphs. The order of the proxies is from the table reading down and appear in the matrix starting from left to right and then down.

    The next 14 links show 14, 7 row by 2 column, matrixes of 14 individual simulations for each proxy obtained by using the proxy parameters from the table. I used 14 simulations to fill a 7 by 2 matrix in order to keep all the graphs the same size for ease of comparison. The links are in the order of the proxies in the table.

    I will let the observer decide how well the models simulate the structure we see in the proxy series. I think it is quite good.

    http://img196.imageshack.us/img196/8540/mann99proxsimtable.png
    http://img685.imageshack.us/img685/4794/mann99proxproxnorm.png
    http://img11.imageshack.us/img11/691/mann99proxsimfenno1.png
    http://img51.imageshack.us/img51/3950/mann99proxsimfenno4.png
    http://img37.imageshack.us/img37/2683/mann99proxsimfenno6.png
    http://img69.imageshack.us/img69/9332/mann99proxsimpatagonia.png
    http://img225.imageshack.us/img225/9207/mann99proxsimtasmania.png
    http://img193.imageshack.us/img193/6499/mann99proxsimural1.png
    http://img402.imageshack.us/img402/2003/mann99proxsimural4.png
    http://img192.imageshack.us/img192/5852/mann99proxsimural6.png
    http://img683.imageshack.us/img683/5156/mann99proxsimfrance.png
    http://img189.imageshack.us/img189/1002/mann99proxsimgreenland.png
    http://img812.imageshack.us/img812/6470/mann99proxsimquel1acc.png
    http://img695.imageshack.us/img695/8761/mann99proxsimquel1o18.png
    http://img824.imageshack.us/img824/3880/mann99proxsimquel2acc.png
    http://img641.imageshack.us/img641/8509/mann99proxsimquel2o18.png

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  45. The final entry in the table was cut off. It should have been as follows:

    Quel2 O18 1,d,1 0.06 -0.25 0.14

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  46. Nick, when you removed the instrumental series from the Mann (2008) and (2009) reconstructions was it the Luterbacher instrument series or a contemporary series like Had CRU or both?

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  47. Kenneth,
    I didn't modify any data sets. When I said "nor other reconstructions with instrumental components" I simply omitted Mann2008g and h from the set plotted, as shown by the legend.

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  48. The y-axis for the simulated and real M99 proxy series is labeled upward from positive negative. That orientation makes no difference for the simulated proxies, but could for the actual M99 proxies if one is looking for the blade of the hockey stick. I, therefore, judge it prudent that I show the M99 proxy series with the corrected y-axis orientation. I apologize if this error has confused anyone.

    http://img685.imageshack.us/img685/5038/m99proxycorrected.png

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  49. Nick, thanks for the details on your no instrumental components in the graphs.

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