Are Tree Rings Low Pass Temperature Filters?

I don’t know the answer to this question: I am not an expert in this area, and I haven’t the time or resources to track down the data to discover the answer. I even wonder if there exists controlled experimental data. It must be the case that the objections I make below are well known and have been considered by those who regularly use tree rings as proxies for temperature. I’m just hoping that some regular reader might know where to go on this matter.

Ulf Büntgen and a pal or two saw their “2500 Years of European Climate Variability and Human Susceptibility” published recently in Science (thanks to reader Sylvain Allard for bringing this to my attention). The abstract begins:

Climate variations have influenced the agricultural productivity, health risk and conflict level of preindustrial societies. Discrimination between environmental and anthropogenic impacts on past civilizations, however, remains difficult because of the paucity of high-resolution palaeoclimatic evidence. Here we present tree ring-based reconstructions of Central European summer precipitation and temperature variability over the past 2500 years. Recent warming is unprecedented, but modern hydroclimatic variations may have at times been exceeded in magnitude and duration.

The admission is “paucity of high-resolution palaeoclimatic evidence”, meaning no direct measures of temperature and precipitation exists. Thus, the reliance—I emphasize the word—on tree-ring data as a stand-in for what was not measured.

Then comes the key: “Recent warming is unprecedented”. Is it? How can we know? Well, by examining the reconstructions of temperature using tree rings: that is, by building statistical models of temperature as functions of tree-rings.

My question is this. Suppose, ceteris paribus, that temperature changes rapidly year on year. I leave “rapidly” undefined, as I do how the temperature changes (more in summer than in other seasons? equal change through all seasons? etc.; each possibly would presumably influence the way trees reacts to temperature). Can trees keep up with rapid temperature change?

My guess, based, it’s true, on vague biology, would be that the tree ring responds to this temperature change linearly when the year-on-year temperature change is slow, and it responds to the temperature change (say) logarithmically when the year-on-year temperature change is fast. That is, when temperature change is too quick, the tree can’t catch up and doesn’t respond as quickly to extremes. Tree rings would then, in effect, be a low pass filter on temperatures.

If that is true, then any reconstruction of temperature based on tree rings would always show less variability than would actual temperature measurements. The past would necessarily look calmer than the present, so to speak. Reconstructions would have more hockey sticks than at the Joe on a Friday night in January.

Now, if you knew how trees responded to rapid change, then you could of course incorporate this knowledge into your reconstruction models. But this removes these models from the land of simple regressions, and almost certainly, and unless the researcher is very careful, the results will be too certain in times of rapid change (the confidence or credible intervals should widen considerably when the regime switched from linear to logarithmic).

Then, too, we have the difference between estimates of the parameters of these models versus these models’ estimates of the actual observables (temperature). Use of the former—which is all you see in classical statistics—guarantees over-certainty.

Controlled experimental data would answer the question. Grow a strand of trees, paying attention to the ceteris paribus, then change temperature slowly, then rapidly and see what happens. Of course, since tree rings are laid down annually (I stand ready to be corrected here), this experiment will take some time.

You might then try to look to the wild where we have simultaneous (say) thermometer-based temperatures and tree rings, which must have been done. The problem here is observational bias. Chances are overwhelming that that ceteris paribus bit will not have been understood properly. I say this because it rarely is. This difficulty isn’t strong enough to bar these kinds of experiments, but it is sufficiently forceful such that we should always look at our results with some skepticism. Especially if our goal is to forecast temperatures changes of fractional degrees.

As I have said, all this is surely well known; thus this post is more a way for me to organize my thinking than any kind of review. I await enlightenment from you.


  1. Then there is always the divergence problem, where tree ”followed” the temperature fluctuation from about 1850 to the 1960s where they show a cooling trend which justify truncating the data series be we know that the data is bad. It must be bad since for the first 110 years the individual ring follow global temp and for the last 50 years they didn’t.

    This lead to this very precious quote by Malcolm Hughes (from MBH98):

    “The recent weaker correlation between tree growth and temperature clearly affects the reliability of our reconstructions of the past. Actually, it means past climate reconstructions (before the 1960s) are better than we thought they were. And, as a result of this, it means that we underestimated the differences between the present century and past centuries,” Hughes said.

  2. This reminds me of the “logic” that appears here:

    “The divergence problem is a physical phenomenon – tree growth has slowed or declined in the last few decades, mostly in high northern latitudes. The divergence problem is unprecedented, unique to the last few decades, indicating its cause may be anthropogenic. The cause is likely to be a combination of local and global factors such as warming-induced drought and global dimming. Tree-ring proxy reconstructions are reliable before 1960, tracking closely with the instrumental record and other independent proxies.”

    No evidence presented. Just terms like “likely”. Then shortly after…

    “The divergence problem is unprecedented, unique to the last few decades, indicating its cause may be anthropogenic.”

    As a physicist, I would say “How do you know? Where is your evidence?”. The evidence would suggest that trees most likely have a very non-linear response, and therefore tree ring thermometer proxies should be treated as unreliable. I’ve seen better evidence supporting the existence of UFOs.

  3. Matt,
    Maybe I can help. le tme play scientist. Todays model is; Science is fun, anyone can do it.
    My hypothesis is; The rings on trees are primarily determined by the conditions in spring when the sap rises. Therefore you are sampling the effects over a few-month or so interval. The growth of the tree (hence ring width) is influenced by temperature, moisture, light, Co2 level(its nutrient) and some other things that happen in this interval. Light(clouds), miosture (clouds,temperature gradients) and Temperature are highly correlated.
    Your job as statistician is to statistically ‘prove’ that recent approximately linear rises in Co2 are causing recent not so approximately linear rises in temperature. (I’ll give you a hint how to do it, all of us scientists do it this way; Use a Gaussian probability integral and invoke some rule about three sigmas. ) Feel free to throw in some PC, ARMA or whatever alphabet soup, it always helps. Don’t talk about stationarity or long tails on distributions please, it messes up the math.

  4. I do not know how variations in tree rings can be satisfactorily correlated with temperature. My understanding is that tree rings vary according to growing conditions during the year, with the broadest rings under the best growing conditions for the species in question. It would follow that any deviation from optimum conditions will result in narrower rings, so too hot or too cold will both result in narrower rings. As will other sub-opimal conditions such as drought or excessive precipitation.

  5. 1. You’ll notice that the study cited was somehow able to tease two variables (temperature and moisture) out of a single measured parameter (tree ring width).

    2. The “supporting online material” reports that the tree ring data is processed with a high pass filter …

    Three independently developed oak chronologies from Great Britain and Northern
    Germany (10), from Central Germany (11) and from Slovenia (12) were re-processed here,
    i.e., 20-year high-pass filtered, and then used for comparison with our new high-frequency
    oak data, both at the regional-scale and the CE network level (Fig. S6).

    … although in two other places a “20-year low-pass” filter is mentioned.

    The supporting material (warning: Heavy Statistics) is available here.

  6. robm says
    Sorry for the sarcasm that took over my previous post.
    I know that most researchers out there are doing their best do deal with this very difficult problem.
    My real point was that I would also consider that the data may be under sampled in that the rings may respond to what is happening in a short window (growing season) where the confluence of temperature / moisture is important. Even if they do respond to temperature it is likely not the annual mean. Would this not tend to increase the variability?

  7. If I may restate the question in a more “engineering” context: quantify the accuracy and precision of trees (i.e. tree rings) as temperature measurement systems.

    My guess: it is conceivable that they’re accurate, at least for growing-season temperatures, but it’s hard to imagine that there is much precision.

  8. Regarding your tree growing expiriment, Is a 2000 year old tree as sentsitive to these variables as a 200 year old tree? It may take a very long time before you have a reliable dataset.

    Regarding the divergence probem. Doesn’t this scream that either tree growth is perhaps less senstive to temperature than was once thought. At the very least, it should increase the margin of error / the width of the confidence intreval to a place where 2 degrees of change is within the margin of error.

  9. Forward modelling of tree ring growth is the cutting edge…

    So they are now combining GCM reconstructions and psuedo proxy data and baysian methods.
    No references ready at hand, just some tidbits picked up at the last AGU.

  10. sylvain: ” It must be bad since for the first 110 years the individual ring follow global temp and for the last 50 years they didn’t.”

    I wonder if that is true?

    Is it possible that for 160 years the trees are right, but the thermometers have been contaminated by UHI and moving them all to airports?

    Anecdotally, the 1930s heat and droughts were way worse than perceived heat in the 1990s.

    Australia is another example where the Quensland floods are blamed on AGW, but in fact where worse in the 1970s and 1800s.

  11. I’ve often wondered how the PC’s were associated with temperature. We have 4 (maybe more) variables associated with the width of a tree ring: sunlight, temperature, water and nourishment. All together they combine to form the tree ring width. Effectively, one has multiple unknowns and one equation. Presumably (hopefully), a PC analysis magically separates the variables. Even so, how does one know which PC(s) are most associated with temperature? I heard that at one time there was an intended study which attempted to eliminate temperature variation say by comparing trees in Alaska with trees in Thailand or other places where temperatures are most stable (and an available record). Does anyone know if this was ever done?

  12. DAV:
    There is absoluely no reason to assume that PC’s will reflect tree growth variables. They are as likely to cluster trees that respond to growth variables in similar ways as to identify a temperature variable. This is part of the puzzle that McIntyre and McKitrick famously unravelled and why Bristlecone Pines are so notorious.

  13. bernie,

    Indeed. Theoretically, PCA can resolve the hidden variable problem but there is still the underlying assumption that the resultants of the hidden become independent as a result. But what if the response to moisture was modulated by temperature (a definite likelihood) instead of just being mixed with the temperature response? Then it would be next to impossible to separate them without rigorous control as there would then be multiple levels of hidden variables and insufficient information to even identify them.

    Just the same, I really would like to know the justification behind the assumption that tree rings are a reasonable proxy for temperature. How does anyone know that they could be?

  14. DAV:
    If you are really interested I would go to Climate Audit and check out their references. Steve McIntyre has really done a good job looking at this issue. I do have the supposedly seminal book and will try to dig it out.
    In my experience with factor analysis real interdependence among so called independent variables is almost by definition a limit on the likelihood that the variables can in fact be isolated through PCA – but my linear algebra is extremly rusty.

  15. I’ve spent a fair amount of time examining the dendroclimatological literature. If you go to the basic texts, they acknowledge the multiple factors that affect tree rings, but then emphasize how they believe they can isolate temperature effects. Fundamentally, they believe that (summer) temperature is the dominant factor affecting the tree ring values at the “tree line” — the highest latitude or altitude at which that particular tree can grow. In these conditions, the “degree days” (or some similar measure) in the summer above the minimum temperature required for growth is the controlling factor in the tree growth for that year. Other variables are less important, as, for example, sufficient moisture could not be used for growth if the summer were too cool.

    We have at least a possibly plausible argument here. But it rapidly goes downhill after this. Many tree ring data sets used in prominent climate reconstructions came from sites nowhere near the tree line (e.g. Gaspe cedars in the original hockey stick). Or, even if the trees are near the modern tree line, they may not be near past tree lines.

    Many of the most prominently used tree ring series come from the California mountains (Sierra and White) and the Russian Ural mountains. In both cases, we know that the tree lines were hundreds of meters higher in Medieval times than now. Yet many of these series show low growth in Medieval times compared to the 20th century. Remember that the basics of dendroclimatology acknowledge pretty directly that tree lines are a good indicator of temperature. Yet when the tree ring data disagrees with the tree line data, the tree ring data gets used, violating two of the discipline’s own precepts — that rings are a reliable proxy for temperature only when taken from the tree line, and that tree lines are a good proxy for temperature.

    I don’t yet have a good feel for your real question in the post, as to whether the tree response low-pass filters the temperature profile, even in those conditions (assuming they exist) where temperature is the dominant factor. It would not surprise me if this were true, but I have not stumbled across anything good on this one way or another.

    On the other hand, I have seen, in both the peer-reviewed literature and on blog posts, what I believe to be convincing mathematical analysis showing that the reduced variance in the past compared to the present in these types of reconstructions is a mathematical artifact of the reconstruction techniques. Data series are selected or weighted based on their correlation to some temperature series during the instrumental period, then pre-instrumental temperatures are computed in reverse based on these selected/weighted series. The selection/weighting is in large part actually random (even if there were an underlying real relationship, the happenstance matching of “noise” dominates). Outside of the instrumental period, all of the randomness tends to average out, dramatically reducing the variance in these periods. And voila! A hockey stick!

  16. Speaking as a forest biometrician with much familiarity with tree growth models, some special caveats need to be mentioned.

    Diameter growth on any tree is theoretically a sigmoid growth function. No tree puts on constant radial growth year after year. Trees grow by adding a layer of new wood at the cambium, under the bark. Each year a larger surface area is added. If growth is constant, the rings get narrower. But growth is never constant. There is significant deviation from ideal (model) sigmoid diameter growth in individual trees regardless of the weather. Even when sigmoid growth models are used, the natural variation adds statistical error.

    Diameter growth in a function of tree-to-tree competition. Dense stands exhibit narrow rings on individual trees, sparser stands may have wider ring growth, yet both stands may have equivalent gross growth. That’s why only open-grown trees are supposed to be selected for ring studies. But nobody knows what the tree density surrounding an individual tree was 100, 200, 500 years ago. Competitors could have arisen and died without leaving evidence of their presence so long ago. More error.

    Trees can sustain injuries that affect growth, such as top and branch damage, that are difficult to detect 200 years later, especially a few feet off the ground where the rings are sampled. There are very few pristine, undamaged trees. I know, having searched for such across broad acreages. Open grown trees at high elevations are always damaged. A heavy winter snow can snap off branches and the tree will exhibit reduced diameter growth for a few years, even if growing season conditions are ideal.

    Trees, especially conifers, exhibit epigentic traits. That is, individual trees can alter their morphology in response to changing conditions over long lifetimes. Those conditions can include competition and damage from a variety of agents that have nothing to do with growing season temperatures. Similarly, average growing season temperatures can vary widely from year with no noticeable (measurable) effect on growth.

    Ring width has all but been abandoned as a temperature proxy. Instead, the latest technique is sampling rings for O18 ratios, under the assumption that O18 varies with temperature. Regardless of the ring width, the O18 ratio is supposed to have recorded growing season temperature. But that theory is fuzzy and mushy, and O18 ratios in living trees correlate very poorly with known growing season temperatures. In other words, it calibrates with much error at best.

    Trees are not thermometers, but even thermometers have some serious measurement error problems.

    Tree ring studies are a fad akin to phrenology and other discredited pseudosciences that has not dissipated as it should have decades ago.

  17. Mike D. says:
    1 February 2011 at 10:44 pm

    I think broadly he is in the right of it.

    Let us be clear Dendrochronology is perfectly sound science, count the tree rings to tell you how long the tree lived before it was felled or died. Combine that with radiocarbon dating and you can get a very good idea of the date of that piece of wood.

    Better still if it is a large piece of wood, and the English have built their houses out of wood for thousands of years, and reused the timbers time and again, it is possible to compare local samples by ring width because most timber used in England for housing was locally sourced. This allows you to date the mighty oak beam in your local pub fairly accurately by comparing its rings with other timber of similar age to narrow the likely date of felling.

    And consulting the local records which, which go back a thousand years, yes timber was that important to local economies, and you can get a very precise date.

    And you will find quite a few of those massive beams that hold up the floors in your local pub are well over a thousand years old. Ain’t recycling wonderful?

    So I concur with Mike D, treenometers are pretty well on the level of phrenology, alchemy or whatever is the current fashionable fraud, which these days is dressed up in pseudo scientific claptrap.

    The question is why such charlatanism took such a hold upon the imaginations of supposedly educated people. I have no answer to that except to say that it always has done.

    And that is the difference between Western philosophy which tries to deal with the external world and it’s Eastern counterpart which essentially deals with human perception, emotion and mysticism. That is a seductive mix, I have known scientists of greater intellect, I am sure, than mine, to be drawn into it: and lost forever.

    So do not waste your time Mr. Briggs in trying to understand such a fraud: if you do so you will end up in a mirror maze because there is no way to find the truth because there is no truth to find. And do not be so arrogant as to suppose that it cannot happen to you.

    Whereas the real question is how this? how can such sloppiness and lack of intellectual rigour have become so common? They answer is they always were, the hard truth has a difficult time getting established. But it does in the end.

    And when new tools, the computer with it’s ability to process vast amounts of data and crunch them to provide amazing correlations here there and everywhere the imperfections of the technique are lost in the enthusiasm for using them. And a belief that it is possible to extract meaning from things when in fact there is none.

    So let me pose the problem in your own terms. Suppose I cast a die a vast number of times
    there will be runs when the number six does not turn up. Of course all unaware I could use many methods of statistical analysis to show that this run was somehow significant, important or whatever. Amazing stuff since only the numbers one to five turn up so nobody even knows there is a six. But there it is. If I do not know what I am dealing with and not all the statistical analysis in the world can help me. And the truth is that the run was just a part of a random series of numbers and has no meaning at all.

    And almost all these modern techniques which seek to interpret data, temperature, tree rings or what you will, never address the question of whether there is any meaning in the huge mass of the data: it is just assumed that there is. But there is no reason to suppose that is true.

    So beware Mr. Briggs. Getting involved in the detail of fraudulent logic and pseudo scientific balderdash is the the primrose path to perdition. You need only to consider the basics as so ably set out by Mike D above.

    Kindest Regards

  18. Surely the calibration can be run in reverse. Select a time interval in which the temperature, be it annual or seasonal, has no trend. (Perhaps the last decade). Examine the constancy of tree ring parameters currently used for thermometry in this period.

    If the correlation between temperature and tree ring parameter is high, then surely it is a candidate for palaeo studies. One small problem – how does one derive a sensitivity when there is no trend?

    Which is just another way to show that signals buried in noise can tell many stories to imaginative authors.

  19. The questions I have are (1) how is it possible to measure a tree ring within a claimed precision of 1/10 of the diameter of an individual tree cell, and (2) how is measurement error dealt with when calculating error bars on the reconstructions?

  20. WRT the divergence problem, you’d think trees would like all that extra CO2 (but perhaps that only affects their vertical growth…)

  21. One is tempted to wonder, especially after reading the brief but informative comments from “Mike D” above, whether any of those who place such great store upon the findings of “dendrothermometry” have ever actually done any gardening? 🙂

  22. In the comments here:

    Paul Dennis said…
    Before I add anything further to the debate I should say that I’m an Isotope Geochemist and Head of the Stable Isotope and Noble Gas Laboratories in the School of Environmental Sciences at the University of East Anglia. I’ve also contributed to and published a large number of peer-reviewed scientific papers in the general field of palaoclimate studies.

    I don’t say this because I think my views should carry any more weight. They shouldn’t. But they show there is a range and diversity of opinion amongst professionals working in this area.

    What concerns me about the hide the decline debate is that the divergence between tree ring width and temperature in the latter half of the 20th century points to possibly both a strong non-linear response and threshold type behaviour.

    There is nothing particularly different about conditions in the latter half of the 20th century and earlier periods. The temperatures, certainly in the 1960′s, are similar, nutrient inputs may have changed a little and water stress may have been different in some regions but not of a level that has not ben recorded in the past.

    Given this and the observed divergence one can’t have any confidence that such a response has not occurred in the past and before the modern instrumental record starting in about 1880.”

  23. No correlation (measured by the Pearson correlation coefficient) between two variables doesn’t imply there is no relationship between them. For example, plot a scatter diagram and compute the correlation coefficient for the following data set.
    {(x,y)} = {(0,0), (1,1,), (3,2), (5,1), (6,0)}

    a jone,

    So let me pose the problem in your own terms. Suppose I cast a die a vast number of times
    there will be runs when the number six does not turn up. Of course all unaware I could use many methods of statistical analysis to show that this run was somehow significant, important or whatever …

    I think you are bluffing!

  24. The same misleading trick is used for carbon dioxide levels, where ice core data covering thousands of years is spliced on to modern direct measurements. See for example the very first diagram in IPCC AR4 SPM, where the IPCC starts as they mean to continue – by misleading policy makers with false comparisons.

  25. MikeD says: “Ring width has all but been abandoned as a temperature proxy. Instead, the latest technique is sampling rings for O18 ratios, under the assumption that O18 varies with temperature. Regardless of the ring width, the O18 ratio is supposed to have recorded growing season temperature. But that theory is fuzzy and mushy, and O18 ratios in living trees correlate very poorly with known growing season temperatures. In other words, it calibrates with much error at best”.

    In the case of tree rings, the hockey stick team combed through 1000s and 1000s of series to find a few that correlated somewhat with the instrument record. They declared that these few series represented ‘temperature responders’ — magic flutes as McIntyre calls them. They then used the temperature responders to project back in time before the ‘calibration period’. Then immediately after the calibration period, ring widths began to diverge from the instrument record. Indicating to most applied scientists that the correlation during the calibration period was specious.

    I’m quite certain one could do the exact same ‘trick’ with dO18. Given a large enough population of O18 series, one could establish a calibration period and select only those series that roughly correlated with the instrument record during the calibration period. You would then have a new group of magic flutes. Of course, the new magic flutes would likely begin to diverge immediately after the calibration period, but if you were to select the end of the calibration period to be within a few years of today’s date, then no one could call you out on divergence for many year. You could then run the new magic flutes through the Mannian short centered PCA method (that mines for hockey sticks), being sure to add the active ingredient (a few series that exhibit strong hockey-stick-like behavior) and presto — a new hockey stick reconstruction using no tree rings!

    Parlor trick complete.

  26. Land use changes are known to be one of the biggest drivers in local climate changes. In the early middle ages, agricultural innovations like the mouldboard plow and the horse collar allowed the cultivation of much heavier soils than in Roman times. As a result, by 1300 AD so much land had been cleared that many parts of Europe were inhabited for the first time (and the only time – the Black Plague and Little Ice Age depopulated many of these villages, which were never resettled).

    Why this is on-topic is the question whether this led to a positive feedback (forcing) of the temperature. Certainly we know from tree ring (and pollen count, etc) that it was warmer then. How much was natural variation and how much was because forest had been cleared is an interesting question.

    I guess this isn’t entirely on-topic, but it certainly adds to the mystery around what the actual climactic variation was.

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