Climate, paleoclimate, huevos rancheros, and general asymmetry

Yamal IV: Growth Curves and Sample Size

with 43 comments

Via Deep Climate, I found this post by Jeff Id at The Air Vent. Comments there and elsewhere lead me to believe there is some confusion about the related question of regional curve standardization and the reason for the importance of sample size in dendrochronology — dendroclimatology in particular — and while this post is only an indirect commentary on Jeff Id’s post, hopefully it will be more broadly useful or stimulate some interesting technical discussion.  For more information on regional curve standardization, this book chapter [PDF] is currently your best bet.

Jeff Id fits two separate exponential growth curves to the most recent 12 trees in the Yamal chronology and to the full Yamal series, and notes that they are different.  Let’s emulate this here.  Let me note first of all that this is an emulation — the published Yamal series uses a time-varying spline fit that I haven’t integrated in my own code.


What I’ve done is align the full Yamal set (blue) and the most recent 12 ring width series (red) by age, assuming no pith offset (that is, assuming the innermost ring in the core or cross section was the innermost ring in the tree).  The heavy lines are the mean regional curves.  The black line is the Khadyta River mean regional curve.

There are few interesting features, some of them I believe are noted by Jeff in his post.  The more recent Yamal trees had a somewhat lower growth rate when they were young than the average of the full set of living and subfossil trees; however, it is not at all out of the range of the full Yamal population.  The regional curve for just these twelve is therefore lower than that of the regional curve for the full population.  Another feature to note is that the red line (the regional curve for the 12 trees alone) rises at 100 years of age and again near 300 years of age, since these represent the ages of the most recent wider ring widths of several of the individual samples in this small set.  Finally, note that the Khadyta River trees as a whole are relatively young, and their growth falls for the most part lower than the regional curves for the Yamal full and recent subsets.

UPDATE: I’m adding here the spline curve fits


So what is the consequence of performing a separate RCS on the recent Yamal series only vs. the full Yamal set?


The 12-series only chronology is somewhat noisier overall, since it also excludes 5 other tree ring series that come into the second half of the 20th century but not all the way into the 1990s.  The influence of sample size on the chronology variance can also be seen in the 1600s, probably, when the year-to-year variability is reproduced but the small number of series (prior to 1660 or so, there are only 3 cores) influences the variance. The influence of the different regional curves — shown above — is more difficult to detect, since it is intermingled with the influence of the loss of the other 5 cores, but slightly higher levels in the 12-tree only chronology in the 1600s and parts of the 1700s might reflect it.  The most notable difference is therefore perhaps that the recent-tree only chronology is slightly lower than the full Yamal chronology starting in the early 1980s.

So what is going on?  In fact, you are witnessing the importance of overall sample size in the specific case of Regional Curve Standardization.  It is important to understand the importance of sample replication for two different (but of course complementary) purposes in dendrochronology, specifically when applying Regional Curve Standardization: [1] Adequate sample replication overall so as to accurately estimate the ‘true’ regional growth curve, and [2] sample replication  through time adequate to estimate the transient climate signal.  Remember that the goal of regional curve standardization is to remove a common age-related growth trend while preserving low frequency climate variability — to have any hope of estimating this you need a large number of trees whose actual period of growth was well-distributed over time.  The reason for this is that you need to avoid intermingling your climate signal of interest with your age-related growth trend.  You can imagine an age-related growth trend estimated by trees of more or less the same age that grew more or less at the same time could intermingle the time-related environmental signals with the age-related geometric growth patterns.  On the face of it then, Yamal is a good candidate for RCS since it has a large number of total trees whose actual time of growth is well-distributed over the length of the chronology.  Isolating the 12 most recent trees, however, runs the risk of intermingling recent patterns of temperature variability with the trees’ common growth signal.  The ‘regional curve’ from just these twelve trees is quite unlikely to be very representative of some significant fraction of the mean regional growth pattern associated with tree age.

The full Yamal regional growth curve is therefore likely to be a much better estimate of the ‘true’ regional growth curve common to trees from the region than a growth curve from a small number of trees growing over a period of anthropogenic climate change, because the climate signal of interest is a common feature of the growth of many of the trees.  The lower chronology values in the recent-only chronology is red above is a consequence of at least part of the temperature signal being subtracted because it is intermingled when the regional curve is calculated over only a few trees growing, at the end of their life, in a warming world.  Jeff’s post is a little hard to parse in places (for one thing, he keeps referring to ‘climatology’, but I think he mean ‘climatologists’ or the ‘climatology community’), but reading carefully, I think he might recognize this as a potential problem.

Now, the other important part of having multiple samples from the same site is maximize the signal to noise ratio (for our purposes, the signal is climate) at any given time.  Dendrochronologists have ways of traditionally estimated whether their chronology is sufficiently well-replicated and contains a common signal, including the Expressed Population Signal or Subsample Signal Strength.  Using 20 year windows with 10 years of overlap, the Expressed Population Signal for the 12-series only RCS chronology is consistently above the (arbitrary but historical) 0.85 level back to the 18th century (and, indeed, most of the way back to the earlier parts of the chronology before sample size is reduced to a few cores).  For 10 year windows with a 5 year overlap (not something I would consider particularly stable, but it allows us to look at very small slice of time), the EPS exceeds 0.85 from at least 1990 back to beginning of the chronology with only two decades in the 19th and 18th centuries with low interseries correlation.  Note that these windows are shorter than we normally use.

My take home message is this and it is intended to be general: it is important to understand the two complementary parts of the importance of samples size in developing RCS chronologies for climate reconstruction. Lots of ring width series are necessary to develop an accurate regional curve.  The number of chronologies needed at any given point in time to capture the transient climate signal can be estimated using EPS.   Strong average interseries correlation between cores can mean that even relative few trees collectively capture a significant portion — again, as estimated from established metrics — of the climate variance and allow for adequate signal to noise ratios in the mean chronology.  Replication gives us increased confidence in the value of the mean chronology, but a strong common signal is an important part of the equation.


Written by delayedoscillator

October 17, 2009 at 9:35 pm

43 Responses

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  1. As you may have noticed, there is a discussion about the modern H&S 17-tree sample, and whether that sample was selected with different criteria than Schweingruber Khadyta.

    One point of confusion is whether these samples would have been selected by the same H&S criteria as the sub-fossil series, i.e. both length (# of years) and sensitivity (higher interannual variability).

    Of course, higher sensitivity aids in cross-dating, which is not an issue with the “live tree” samples. But it also seems that it allows a clearer climatic signal. So would it not be reasonable that modern samples would be chosen the same way so as to permit a more homogeneous comparison with sub-fossils? H&S 2002 does not seem clear on this point. Or was this possible inhomegeneity handled a different way?

    Deep Climate

    October 17, 2009 at 9:53 pm

    • Hi DC,

      I unfortunately can’t speak to HS beyond what they’ve written in their paper, but it certainly would seem to be reasonable to use segment length and mean sensitivity on living as well as subfossil materials (at the very least, on the principle of similar treatment). For what they actually did and why, however, you’ll have to ask them — I’d just be guessing, and I am not familiar enough with the paper to comment offhand.


      October 18, 2009 at 3:01 pm

  2. BTW, the Briffa chapter link is broken (concatenated with your WordPress path).

    Deep Climate

    October 18, 2009 at 4:52 am

    • Should be fixed now, thanks,


      October 18, 2009 at 5:38 am

  3. Nice job. I think it’s equally important to note that in dendro literature the exponential curve used in this form of RCS is not a physical certainty. In corridor standardization polynomial fits are common. The reason it becomes important is that there could be physical reasons for trees to expand their growth in later life. i.e. reduced competition from higher light capture due to physical size, reduced competition for fertilizer created by shading the neighbors etc.

    These other possibilities might tend toward a slight U shape in ring width over the life cycle of the tree. If you used hundreds of trees this U shape would still create a strong uptick in RCS standardization with an exponential. I wouldn’t be surprised if we see some unprecedented papers from this effect (if it exists) in the near future.

    My own opinion is that the mean is still the best method for standardization. Sure there would be a slight distortion of signal at the recent end but nothing compared to the obviously incorrect Briffa Yamal. It might be best to simply chop the youngest 75 years off every tree in the series and 150 years off the earliest of the reconstructed growth curve and take the mean.

    I picked those 75 and 150 numbers visually after pouring over this data for hours. IMHO, that type of method is about the best that can be done from the two standardization methods I’ve read. It’s probably going to turn into a post when I get time but you can imagine it will have good match to mid-series variance without strong unprecedented ends. The milder endpoint uptick will likely be a better match to the not huge uptick in Yamal instrumental temp also.

    No matter what though, trees make lousy thermometers.

    Jeff Id

    October 18, 2009 at 11:31 am

    • Hi Jeff,

      Thanks for stopping by. A few comments and replies:

      [1] The negative exponential fit is not the only one (or even necessarily the most common) used for detrending and standardization. Quite commonly splines are used. Indeed, in the example above, I develop the RCS chronologies using a 67% spline. There is also the Hugershoff fit (generalized negative exponential). You don’t see polynomials very much. There is a rather large literature on this I hope you’re digging into.

      [2] I’m not clear what you mean by ‘U shape’ in this particular context? Are you referring to growth responses to temperature? How are you relating this to detrending and standardization?

      [3] Not sure what you mean by ‘unprecedented papers’ — do you mean we might actually see some submissions to the peer-reviewed literature from your cohort? As I said, there is a rather large body of literature on these issues, and divergence and low frequency standardization are frequent topics of presentations and discussions currently at professional meetings, so hopefully these future unprecedented papers will incorporate much of this.

      [4] Mean standardization can have similar problems as I’ve described above — your theoretical detrending curve (straight line long-term mean) may intermingle ring width with climate signal, particularly if there is a long-term trend in the climate variable of interest (as oppose to, say, decadal-scale variability). I am happy to hear, however, that you think that removing the juvenile period and then detrending with the mean is a potentially good approach — there are examples of this in the literature.

      [5] You’re not going to get very far tossing off unsupported or inflammatory statements like ‘obviously incorrect’ and ‘No matter what though, trees make lousy thermometers’ — That is not the intellectual tone I want around here and I would encourage you in scientific discussions to avoid such things. I was tempted to snip these since I have no intention of getting dragged into battling phantom or untrue claims such as these. Neither of these statements is supported by any citations. There is no evidence I am aware of that the RCS approach at Yamal is ‘obviously incorrect’. And there are good examples of temperature-sensitive tree ring width chronologies (to say nothing of MXD chronologies, which tend to have a quite strong summer temperature signals). Look at Table 1 from Wilson et al. (2007), for starters.

      Wilson, R., et al. (2007), A matter of divergence: Tracking recent warming at hemispheric scales using tree ring data, Journal of Geophysical Research, 112(D17), doi: 10.1029/2006JD008318


      October 18, 2009 at 2:47 pm

  4. Well thanks for letting it through moderation.

    Your point 5 reads like so many AGW blogs when presented with a differing opinion and is needlessly argumentative. I don’t know if you require citations from peer reviewed work to be confident yourself but RCS is very simple. My statement is supported by my own work as well as Briffa’s own literature. I’ve also been privy to some comments by dendro’s on the subject so I am confident in what I say.

    The RCS standardization in Yamal is incorrect for a variety of reasons including core count. The error becomes ‘obvious’ when the result differs so far from the mean which you point out that others use. I really appreciate that point you made about the mean BTW, the field is new to me.

    The ‘unprecedented’ result is an artifact of the fit nothing more. My statement is therefore fully supported both by my work and Briffa’s own writings in literature as well as several others who recommend minimum core counts. I don’t feel like digging them up at the moment but Briffa has written quite a bit about the problems and dangers with RCS particularly at the endpoints. I expect you have read them anyway from your knowledge of the subject.

    I thought I explained U shape well enough. I mean to say that trees under static conditions of climate may typically grow faster in later years due to several competition related factors of which I listed 2. Were this hypothesis the case RCS will typically make a hockeystick from older trees.

    I will leave any references to the quality of thermometer trees out of my writings here.

    Jeff Id

    October 18, 2009 at 3:30 pm

    • Hi Jeff,

      Many of the points you raise in your response to me here about sample size and other aspects of RCS I’ve addressed in this very post, and my results and conclusions differ from yours. Other points from your original post on your own blog are hypotheses in need of testing (I encourage you to do so!). I find that strong statements like ‘obviously wrong’ should be supported by citations. In any case, I look forward to your peer reviewed articles on these subjects in the future.

      As to tone, well, I’ve now had a chance to skim your blog, and I can’t say I find your tone all that appealing either. Guess I’ll just have to be content as one of ‘a bunch of PhD’s would be looking for jobs’ if I hadn’t been so poorly trained from ‘an early age’.


      October 18, 2009 at 3:50 pm

    • Hi Jeff,

      One more thing: You are more than welcome to make ‘references to the quality of thermometer trees [sic]’ — but I would appreciate it if you would keep the style of this blog evidence-based and inquisitive, and provide new evidence and citations to the literature. Sweeping statements that ‘trees make lousy thermometers’ are simply not supported by the available, published data. If you want to claim otherwise, it should be a statement you can back up, not an opinion you toss on the end of a comment.


      October 18, 2009 at 3:54 pm

  5. I realize that the tone of tAV is a bit rough. I try to stay out of the politics but find that my temper is occasionally lost and I vent. Also, I don’t like several works in paleoclimate. They are simply not supportable in my opinion. That doesn’t help the tone either.

    Regarding peer reviewed papers in climate, it is my great hope that climatology doesn’t become that kind of hobby. I will probably be participating in a couple of papers either way. Fixing the Steig antarctic temperature reconstruction is one which has been very entertaining.

    While my tone is strong, I don’t make statements that I can’t back up typically. And as an engineer accepting a tree as a thermometer is impossible without verification. That’s not to say there isn’t a temperature component to the signal, just that there are many other non-separable influences as well and the assumption of linearity is unreasonable IMHO. See Dr. Loehles peer reviewed literature on the subject.

    Also, the calibration of multiple noisy series is highly problematic and very interesting to me, as a PhD you may have some insight as to the biasing created by MVregression LSfits and CPS on noisy signals and how to overcome them.

    Rather than beat up on a whole field I’ll leave it there for today.

    Thanks again for letting my posts through. I’ll check back soon and will consider adding this blog to my blogroll.

    Jeff Id

    October 18, 2009 at 5:01 pm

    • Hi Jeff,

      Thanks for your comments. Some things we’ll naturally disagree on. The tone thing can be hard, for myself as well I realize — my thoughts on it, as well as things that I think get in the way of useful discussion and exploration, are here.

      One thing I consider a priori unacceptable is derogatory comments about working scientists.

      I was most interested in this part of your message:

      accepting a tree as a thermometer

      The fact is, no one thinks this. It is a straw man. Like most other proxies, tree rings represent, if you will, the environment filtered through a set of biogeochemical and physical processes. Abstractly, you might say dendroclimatology is a signal detection problem (and I disagree that they are necessarily non-separable), and in many proxies part of this problem is dealing with multivariate, potentially non linear, and occasionally non-stationary relationships between environment and proxy. This is why multiproxy approaches are the ones that give us the most confidence about our knowledge of the past.

      For this reason, the whole ‘treemometers’ nonsense is just that — it is a straw man and can only reflect a lack of understanding of how dendrochronology actually works. I realize this is just a hobby for you, and but I encourage you if you are interested to read some of the fundamental texts in the field.

      Perhaps I’ll get around to a post on this issue, broadly speaking. The other issues you raise — about statistical aspects — are something I’ll continue to post on from time to time, but research on these issues appear regularly in the peer reviewed literature.


      October 18, 2009 at 9:27 pm

  6. It certainly is a hobby and I’ll keep reading, however I am fully aware of the requirements of metrology having spent a certain amount of time designing instruments. It is more difficult than dendro’s realize to separate competing signals. Unexplained competing signals are next to impossible.

    If you are a paleoclimatologist yourself (I am wondering who I’m talking to) , I would hope you consider some of the basic criticisms I’ve put forth on calibration and preferential sorting of data. There are reasonable ways to use the data which are far more convincing than some of the signal hunting that get’s through peer review.

    Do you have a preferred proxy?

    Jeff Id

    October 18, 2009 at 10:18 pm

    • Hi Jeff,

      Obviously we won’t agree on this, and I’m not sure as to the utility of making sweeping statements about what ‘dendro’s [sic] realize’ Such statements are likely to be wrong both in premise and in the broadness and diversity of the community they claim to sweeping characterize. I encourage you, however, to participate in future discussion on specific papers or approaches, so that such sweeping (and in my professional experience, incorrect) statements aren’t necessary.

      As to having a preferred proxy, it depends on what you mean — all proxies have advantages and disadvantages, at least a few of which in most cases tend to be unique to the particular proxy. So, our best understanding of the past comes from deriving that understanding from as many proxies as possible.

      [sorry for the delay in moderating my comment cache, I’ve been traveling]


      October 22, 2009 at 7:38 pm

  7. d.o, nice blog. I think this blog is sorely needed. Thanks to Jeff Id for leading me to it.

    “For this reason, the whole ‘treemometers’ nonsense is just that — it is a straw man and can only reflect a lack of understanding of how dendrochronology actually works.”

    Actually, it reflects frustration in how dendrocronology is being misused.

    Like Jeff Id, I also come from an engineering background. My intention here is not to criticize working scientists, but rather to share a difference in perspective.

    From an engineers perspective, measuring mean global surface temperature to an accuracy of, say, +/- 0.5C at a point in time would represent the largest, most expensive and most ambitious engineering undertaking in human history. It would require that instruments be placed on at every intersection of a grid with cell dimensions that I’m guessing would need to be <1 mile. This would necessarily include the surface of the ocean as well as all along the topography of Mount Everest.

    Of course in the practical world, we have a much more sparsely populated instrument grid, so we can use mathematical techniques to infill for missing data. But as anyone who has visited the microclimates of San Fransisco could attest, hideous levels of errors get introduced as the grid becomes more sparse. The current instrument grid is extremely sparse.


    Dendroclimatology is an important science and is extremely useful. The problem is that some have over reached with claims that are unsupportable. The dendro community has not made any attempt to correct those who are making these wild claims. Failure to publicly correct the over-reachers is hurting the reputation of the dendro community.


    October 22, 2009 at 6:50 pm

    • Hi Arbie,

      To address your two points

      [1] In essence, this is one of the reasons climatologists measure anomalies. If you are interested in why this works, here are a few places to start:

      But otherwise, this is off topic.

      [2] Again, sweeping statements about what scientists have or have not done don’t really interest me, since they are invariably wrong as yours statement is wrong. You’ll notice that other things I have failed to personally attempt to correct include the shortsighted cancellation of ‘Firefly’ and ‘Keen Eddie’ and mixing plaid and stripes. In all seriousness, however, I think what you’re looking for is the peer reviewed literature and comment-and-reply system.


      October 22, 2009 at 7:51 pm

  8. Pardon me, but either you’re making an extremely fine distinction (which I don’t understand, and would like to have clarified) or you’ve retreated quite a bit from your complaint about Jeff’s “inflamatory” comment. If I understand your most recent position, it is that that “no one thinks” that “trees are thermometers.” If so, then what could possibly be offensive about the assertion that they’re “lousy thermometers.” Is it the suggestion that they’re thermometers at all? I’d understood your original complaint to be based on precisely the opposite presumption–that they were, in fact, an entirely useful means of measuring temperatures.

    If, indeed, you believe it is crucial for people to bear in mind all of the caveats you recite in your most recent post about the ability of dendroclimatology to measure past temperatures, I would think that you would find equally infuriating the remarkable claims being made about the precision and certainty of the climate reconstructions based upon it. For all I know, you have voiced such objections; I only know that I’ve never heard any such warnings, from any dendro, against placing too much confidence in those reconstructions.


    October 22, 2009 at 7:31 pm

    • The reason the whole ‘treemometer’ nonsense is, well, nonsense, is that no one thinks that trees are thermometers. No one. So this is nothing but a straw man and does not reflect reality. Tree rings and other proxies are the result of often complex biogeochemical and physical processes, and our recognition of this informs our field, laboratory, and analytical practices, and our ultimate use and interpretation of the data.

      Let me repeat — if you say that scientists think trees are thermometers, you are making a false statement. Tree ring proxies and other paleoclimate archives allow us to make estimates (and estimates of uncertainty of the estimates) about past climate and environmental change, but those of us who collect and develop these proxies never forget that we are dealing with often complicated systems.


      October 22, 2009 at 7:58 pm

  9. “Tree ring proxies and other paleoclimate archives allow us to make estimates (and estimates of uncertainty of the estimates) about past climate and environmental change, but those of us who collect and develop these proxies never forget that we are dealing with often complicated systems.”

    I think you need to continue to press this point. The fact is that IPCC is presenting the hockey stick with error bars that suggest that the reconstruction is as accurate as an instrument measurement.


    October 22, 2009 at 8:47 pm

  10. DO, you stated “Abstractly, you might say dendroclimatology is a signal detection problem (and I disagree that they are necessarily non-separable), and in many proxies part of this problem is dealing with multivariate, potentially non linear, and occasionally non-stationary relationships between environment and proxy. This is why multiproxy approaches are the ones that give us the most confidence about our knowledge of the past.”

    I understand the point of multiproxy approaches that give the most confidence. I see that you disagree that the signals are necessarily non-separable. As far as I can tell, the bone of contention will be “multivariate, potentially non linear, and occasionally non-stationary relationships.” In particular, non-stationary relationships in a complex biogeochemical and physical system would indicate to an engineer that the problem(s) is potentially intractable. The question I would ask is that if the system is complex with occasional non-stationary relationships, what methodology or criteria would allow us to assign confidence to their separability?


    October 22, 2009 at 10:07 pm

    • Man, what is it with the engineers that have commented here? 😉 The engineers I know in real life are major problem solvers, eager to take on challenges. Why the continued nihilism then with regard to paleoclimatology? I suspect it really doesn’t have to do with the technical issues themselves, which I personally find fascinating and engaging.

      A short, but by no means complete list: [1] good field practice, particularly site and microsite selection and replication replication replication, [2] multiple proxies, even from the same archive (so, ring width, density, and stable isotopes all from the same tree rings or same site), [3] building large proxy networks, [4] explicit error characterization including new methods for detection and attribution of any changes in climate and growth relationships, [5] integrating models and proxies for a number of approaches (inverse, probabilistic). I’m sure there are others, but I actually have to go work on a few of these now 😉


      October 23, 2009 at 4:20 pm

  11. DO “Why the continued nihilism then with regard to paleoclimatology?” I imagine because when we tackle a new problem, and say we have a solution it has to work. However, the biologist in me agrees with your statement of {1} – {5}. My biology problem is that we have seen by some authors {3} in good stead, {1} some adherence, {2} and {4} abysmal, and less than openess and completeness on {5}. My engineering side agrees with my biology side that nihilism is appropriate for these works. I am glad you went to work on a few of these, perhaps you could list some others, when you tackle them, such as non-stationary relations in a statsical procedure that assumes stationarity. 😉


    October 23, 2009 at 8:59 pm

    • Heh 🙂 There are a couple of approaches to deal with non-stationarity, although I favor [1] avoiding it, 🙂 [2] identifying it, and [3] accounting for it in error (covariance) estimates

      But, there are other approaches being developed now to explicitly deal with this.


      October 24, 2009 at 6:40 pm

  12. The problem is that you cannot avoid it if it occurred and you have not measured it. 😉 I know this to be true and assume this applies because you favor identifying and accounting for it in error covariance estimates, rather than measuring it. 😉 Avoiding, generally means that you use post facto sorting, a real no no for proper accounting for anything other than exploratory work. 😉 Thus I would assume you HAVE to develop other approaches to explicitly deal with this. 😉


    October 25, 2009 at 12:41 am

    • John,

      You seem to misunderstand.

      [1] Avoiding situations where nonlinearities are likely to arise by good field and laboratory practice occurs during study design and fieldwork
      [2] identification of nonlinearities and attempting to account for them is what we call ‘data analysis’. I encourage you to familiarize yourself with the literature on the subject of climate-growth relationships in dendrochronology.

      Finally, I hope that your substitution of emoticons for periods doesn’t convey an underlying condensation. This comment thread has wandered far off topic and I am unlikely to allow it to continue if I think there is little point to having it.


      October 25, 2009 at 3:18 pm

  13. The spline-curve fit raises a particular problem with Yamal dataset – the oldest trees are predominantly modern. This means there is not a good spread of old growth available across the chronology to derive a common growth signal for recent times.

    There are of course good reasons to think that the plot will be flat for older trees, from your spline plot from 200 years old onwards. This would mean replacing the latter end of the spline curve with a flat line – as plotted you are likely to remove the modern signal in an RCS chonology.

    Although there are few earlier trees as long lived as the modern trees, there are larger trees. I can’t find an application of RCS chronology based on a size rather than age growth curve. Yamal might be a prime candidate for such an approach.

    Tom P


    October 25, 2009 at 7:51 am

    • Hi Tom,

      You might be interested in this article:

      A theory-driven approach to tree-ring standardization: Defining the biological trend from expected basal area increment.

      Click to access Biondi&Qeadan2008TRR.pdf


      October 27, 2009 at 11:52 am

  14. DO,

    You have a problem with somebody pointing out that you don’t know the difference between engineers who solve problems and engineers who find problems?

    So about that Yamal field data. 2 cores per tree are required. have a look at the record for me and see if you can tell if that were done.. 2 cores 90 degrees apart. That’s the protocal right?

    Steven Mosher

    October 26, 2009 at 5:09 am

    • Hi Steve,

      [1] I’m incredibly uninterested in carrying on a wide-ranging blog comment section on something I followed with an emoticon

      [2] Generally, yes, that is standard protocol, although there are situations where you might take more (I do this frequently) or less. I don’t know any more than you do about the Yamal collection (from reading the published literature and looking at the data file), and therefore it would be irresponsible of me to speculate further. The proper people to direct this question to would be the original collectors.


      October 26, 2009 at 11:25 am

  15. Thanks DO.

    So If I am to understand your rules you are allowed to disparage people as long as you follow it with a smiley face? just kidding.

    WRT Yamal. If you cannot tell from the data file and the metadata whether or not 2 cores were taken do you roll the dice and hope so or do you exercise analytical caution?

    Steven Mosher

    October 26, 2009 at 8:31 pm

    • Feel better now, Steve?

      As I said, repeatedly, if you want to know more about the data, you can always inquire to the authors.


      October 27, 2009 at 11:50 am

    • DO,

      you avoided both of my questions. First it has nothing to do with how I feel. So, whether I feel better or not is immaterial. In fact, I can’t say how I felt when I read it. The issue is your POLICY. is it or is it not your policy not to allow disparaging remarks, either with or without a smiley face?

      Second. I asked if you cannot tell from the data file and metadata if there were two cores taken do YOU:

      A: roll the dice.
      B: exercise analytical caution?

      Let me make this clearer. what did YOU do? I think you
      did A. I think you just threw the data in the hopper. You didnt exercise caution, you didn’t contact the authors. Now, on the supposition that I have contacted the authors what do you suggest that I do? The science of dendrochronology requires at least two cores per tree. We’ve all seen cross sections of trees we know how rings vary even in a given year. So, if the meta data doesnt tell you if you have two cores and the researcher wont tell you, what is your scientific decision with regard to the usability of this data and the confidence you can put in your results?

      Those are clear questions. I would expect direct answers about the questions and not a post about my feelings or what I might do. What would YOU do?

      Steven Mosher

      November 5, 2009 at 10:07 pm

      • Hi Steve Mosher,

        Good to see you again, was getting worried that you hadn’t been around after your initial flurry of comments.

        [1] My policy is clearly posted, twice really. If you want to discuss my blog policy, please take it back to that thread. Off topic posts will be snipped.

        [2] My exercises with the data from Yamal have been to test statements made at other blogs (namely, the Air Vent) and that have popped up in comments here. I’ve described everything I’ve done in the posts. If I were to plan to publish original research (as opposed to doing ‘blog science’) on the Yamal data, these metadata might become more important to me. I can’t tell from the core designations alone much about the provenance of the individual data series. Two cores (or radii in the case of cross sections) is standard operating procedure, but there are exceptions where more or less might be collected, and in how this would be reported. Incidentally, as a first order assumption, within-tree variability is usually much smaller than between-tree variability.

        [3] I’m not going to respond positively to demands nor a combative tone. If you are interested in general inquiry on these subjects, please consider that in writing future comments.


        November 5, 2009 at 10:49 pm

  16. Tom P, you can find what you seek in Melvins PHd thesis. he discusses modifications to RCS. See my posts on CA or read his thesis its only 271 pages.

    Steven Mosher

    October 26, 2009 at 8:33 pm

  17. Sorry, didn’t note I used all emotes. But I also didn’t want to appear too hard headed. An accusation (often true) sent in my and other engineers’ direction. The question is the measurement of non-linearity and non-stationary. There are times when one cannot measure. One example is temperature in proxies before use of thermometers. At that point, as you say, avoiding situations where they are likely to occur is dependent on good field work and laboratory pratices. I am familiar with data analysis and in that you have included good laboratory practices, as you should, an effort to avoid non-linearity is not the same as actually avoiding non-linearity, or for that matter non-stationary sampling. With the ability to measure, non-linearity and non-stationary problems can be lessened. Without measurement, it is an assumption. One can increase one’s confidence with good fieldwork, true. Also, have statistical models with known properties as a basis for understanding the limits of the field, or lab work, and even the assumptions is necessary. There are many climate-growth relationships in dendrochronology. Several do not have measuremtns that extend into the time periods that are under consideration. At that time in-situ comparison to site factors are limited, if existant at all, so efficacy of good site selection, or good field protocols have limited effect past periods of measurement. I am learning and familiarizing myself with the literature. But as you know, there is a lot of literature. In engineering, being able to justify assumptions is required. Most, if not all, questions posed of dendrochronology concern the justification of methodology and assumptions. That is the direction of my questions.


    October 27, 2009 at 11:19 pm

    • Hi John,

      Thanks. Yes, fundamental to earth science of all kinds is the assumption of uniformitarianism ( Good site/microsite selection and study has been the best way to try and minimize potential nonlinearity/nonstationarity. This is why temperature divergence is troubling and a critically important area of research (speaking only for myself here, of course), but there are also issues potentially related to tree age, non-climatic influences (many of these will be site specific). Again, field practice has always been considered important in these cases, as is building networks of proxy sites. Detection is the next step (responders/nonresponders, comparison to other proxies, other archives, other sites, other species, modeling, etc.), but is so are investigations into whether divergence is ‘real’ (n the biological sense, you might say) or ‘just’ an artifact of data (both instrumental and proxy) treatment. Third, ‘real’ divergence would suggest an advantage to reconstruction techniques that can account for non linear relations and pull up confidence intervals and parameter estimates or probabilistic interpretations of the data that reflect this.


      October 28, 2009 at 1:39 pm

  18. Firstly, I thank you for bulling through your frustration with people who you doubted were capable of carrying on a civil discussion, and the temptation to dismiss them as irredeemably useless debate partners. This is depressingly rare conduct these days.

    Secondly, I hope you will indulge some questions born of profound ignorance. I understand the impulse to dismiss such questions with the brush off “I recommend you read the literature,” but the truth is, no one has the time and energy, much less the talent, to become an expert on everything, and yet, [snip — politics] it has become important for us non-experts to consider how much faith to put in the experts. Put another way, its not unreasonable for those outside the field to reject the argument from authority.

    So, my first question is why (and whether) it is unreasonable to think that the “divergence” problem is the result of a de-coupling of CO2 from environmental temperatures. I believe that there is little controversy over the propositions that (1) CO2 causes increased plant growth, and (2) the amount of atmospheric CO2 has greatly increased in the past 100 years or so. If temperature and CO2 were perfectly coupled, that would be immaterial, but my understanding is that this is neither a reasonable assumption nor a demonstrated fact.


    November 3, 2009 at 9:51 pm

    • This is a great question, I’m happy to provide a bit of background.

      Outside of controlled experiments and those using juvenile trees, any influence of CO2 on tree growth has been quite difficult to detect. Even the Free Air CO2 Enrichment (FACE) experiments tend to see difference in ring width between control and enriched CO2 plots fade after a few years. This is probably because other factors quickly become limiting. In mature trees, the influence of CO2 on ring width has been very difficult to detect — it is not even seen next to natural CO2 vents. I recognize not everyone has time to read a scientific paper, but if you do, I recommend Korner’s Tansley Lecture from the ‘Journal of Ecology’ titled ‘Carbon limitation in trees’. The most interesting message from this paper, in my mind, is this:

      ‘It is concluded that, irrespective of the reason for its periodic cessation, growth does not seem to be limited by carbon supply. Instead, in all the cases examined, sink activity and its direct control by the environment or developmental constraints, restricts biomass production of trees under current ambient CO2 concentrations.’

      So, while it is a reasonable hypothesis that rising CO2 levels might decouple temperature controls from tree ring growth in certain environment (high elevation of semiarid regions, in particular) there is no strong support for this hypothesis thus far.

      Again, great question, thanks for asking.


      November 3, 2009 at 10:25 pm

  19. Thank you, that was very helpful. I took the time to read the full abstract and a few related sources I could Google up, but, unfortunately, the full article was behind a pay wall. This was a bit frustrating, because I am curious about the period and method of study of historical concentrations of NSCs–especially because I am curious about the levels of atmospheric CO2 studied–given the hypothesis, I’d expect a discontinuity at the point where growth stops being CO2 limited. From the abstract, Korner concludes we’re past it, but I can’t tell if he has any inkling of when that happened. Anyway, have I got it right so far?

    My next question has to do with what seemed like a rather sensitive question–the model of the relationship between temperature and ring size. (Forgive me if I’m mistaken, but it seemed like you bristled at the mention of a “u shape”.) If I have it correctly, the accepted model posits a monotonic relationship, but this contradicts my intuition. Personally, I would expect that organisms well adapted to their environment would display a bell-curved response, with optimal growth corresponding to historically average (on evolutionary time scales) conditions. Or, even if that’s mistake, I would assume that at some sufficiently high temperatures growth would be stunted. Regardless, this would seem to me to create a pretty serious–if possibly surmountable–problem, since some technique would be required to determine whether a narrower ring is the result of temperatures that were too high or of temperatures that were to low. So what reasons do we have for rejecting my intuitive model?

    Another question I have is whether the accepted model posits a relationship between ring size (and density) vs. average anual temp., annual temp. during the growing season, both, or perhaps some other kind of temperature metric. I guess it’s pretty clear these aren’t entirely orthogonal, so perhaps the better question is which temperature metric is believed to give the best signal, and how strongly is that metric believed to correlate to other temperature metrics of interest?

    Again, I appreciate you taking the time to talk to answer questions that may seem to you like a four year old repeatedly asking “Why?”.


    November 4, 2009 at 7:41 pm

    • I should have given you a better link — I believe the entire article can be found here:

      Click to access 2003koerner_tansley.pdf

      As to your second point, the ‘u shape’ I was doubtful of was actually Jeff’s suggestion that old trees (for some reason) put on a later growth spurt in the Yamal set (his U shape is therefore juvenile growth, midlife, and old age vigor). The inverted U shape you’re talking about here is perfectly reasonable. Standard methods assume that we’re operating more or less on the linear part of the climate/growth relationship, but the entire response space is probably something trapezoidal. One hypothesis (one of the earliest, in fact) for divergence is indeed that growing season temperatures on average have risen to some optimum level for northern tree line species. (this tends to be less of a concern, near as I can tell, in semi arid conifers, which have strong precipitation/drought signals, although in the wettest of the wet years there is a tendency to not capture those extremes). There are ways dendrochronologists have sought to avoid ending up with a reconstruction from a chronology in the nonlinear (optimum) range of temperature-sensitive trees’ growth/climate space — good field practice, various forms of cross validation, assessing the stability of a relationship, etc.

      If divergence really is a shift in the environment to an optimum range of the climate/growth relationship (and we’re not convinced that’s it at all, yet), it still isn’t insurmountable — but it would require different techiques for detection and estimating past climate. Nonlinear inverse problems are a feature of lots of fields, so the problem would be challenging but by no means insurmountable.

      For high latitude trees, you’re generally talking about a summer (growing season) temperature signal in both ring width and density. For this reason, many hemisphere-scale reconstructions are ‘warm season’.

      Thanks for the interesting questions.


      November 5, 2009 at 12:55 pm

  20. DO I looked at the FACE about a year ago. One of the comments I have from looking at the equipment and quicky write-up, and confirmed from the little research I did that FACE did not keep the C:N:P ratio constant. This is proper for CO2 only study, it is not necessarily true for non-stationary problems due to die-off.Do trees that die young, or die old differ from the standard curve, and in what a priori manner do they do so? IN particular this is in reference to the theoretical underpinnings to RCS. Trees die, yet without a standard curve with offset to express the age limits of a tree species, the extrapolation is that a species would live forever. From the practical point, leaf growth is also influenced by rain, and nutrients. With timberline tree loss (changes) documented in the peer reveiwed literature, how many years, and how much will the increased nutrients and increased water supply from the rotting roots affect the basic theoretical model, and how can this be implemented in actual studies? Does this specie(s) have a symbiotic fungal relationship that behaves in a logarithmic or semi-log relationship to provide nutrients or growth potential for the tree?


    November 4, 2009 at 10:38 pm

    • Hi John,

      Yes, they (the biogeochemists) were actually interested in how those nutrient pools were different as a result of the higher CO2 levels. It would be interesting (although non trivial) if one were interested primarily in the basal growth to hold more things constant, wouldn’t it?

      One thing to keep in the back of your mind with the FACE experiments is that most are with very young trees, so scaling up individual-to-ecosystem responses from these experimental settings is potentially tricky. Korner and colleagues did a mature forest FACE experiment:

      From their abstract: ‘Although growing vigorously, these trees did not accrete more biomass carbon in stems in response to elevated CO2, thus challenging projections of growth responses derived from tests with smaller trees.’

      The rest of your points are interesting and probably represent several lifetimes of work in biology 🙂 Fundamental questions like why do trees get old? why do trees die? why do certain species live on average for a certain span of time? The question (for dendrochronology) is are these processes relevant at the time scale of climate (or do they influence the mean state, mean basal area increment, etc.). The adage ‘live fast die young’ applies pretty well in many cases. And, there are papers here and there in the literature looking at whether there is different climate sensitivity of old vs. young trees, i.e.

      Maybe if there are tree biologists lurking around they could chime in with some thoughts.


      November 5, 2009 at 1:23 pm

  21. Hi DO,

    Nice discussion. References to Dr. Koerner’s work were excellent.

    In your original post you show the plot of raw ring growth vs age. Is is correct to assume that temperature reconstruction from this data is based on the physics of photosynethesis and the biological process of the specific species of tree? If so, it seems as though there would be little debate around reconstruction of “Growth Energy” (is there a term for this?) vs time from tree rings. The questions start occuring when we start assigning relative contribution of each bio-physical component (light energy, CO2 concentration, and temperature).

    The low sensitivity of ring growth to CO2 concentration for mature trees would lead me to believe that its variability is easily accounted for in reconstructions. How do you distinguish between temperature related growth and light energy (irradiance and wavelength) related growth and as a result enhance the climate signal? At a purely physical level, they are highly correlated through a “chaotic” system which would make statistical regression extremely challenging.


    November 5, 2009 at 11:34 pm

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