Upside-Down Quadratic Proxy Response

David Stockwell has suggested a discussion of nonlinear responses of tree growth to temperature. I’ve summarized here some observations which I’ve seen about bristlecones, limber pine, cedars and spruce – all showing an upside-down U-shaped response to temperature. The implications of this type of relationship for the multiproxy project of attempting to reconstruct past temperatures by assuming linear relationships between ring widths and temperature are obvious.

The assumption of a linear response between proxies (especially ring widths) is stated clearly in MBH98 as follows:

Implicit in our approach are at least three fundamental assumptions. (1) The indicators in our multiproxy trainee network are linearly related to one or more of the instrumental training patterns. In the relatively unlikely event that a proxy indicator represents a truly local climate phenomenon which is uncorrelated with larger scale climate variations, or represents a highly nonlinear response to climate variations, this assumption will not be satisfied.

This assumption is asserted in MBH98, rather than proven. Here’s what some source literature says:

Bristlecones and Limber Pine
Schoettle [2004] Figure 4 shows an upside-down U relationship between temperature and conifer seedling growth for three species, including Great Basin bristlecone pine, limber pine and balsam fir.

Original Caption: Figure 4“¢’‚¬?Relative temperature response of net photosynthesis of seedlings of three conifer species. The optimum temperature for photosynthesis for each species is that temperature that the maximum rate of photosynthesis was recorded. To enable comparison among species, photosynthesis is expressed as a percentage reduction from the maximum rate.

Schoettle observed that there were sharp declines in bristlecone net photosynthesis with increasing temperature (and a lesser decline in limber pine):

How can limber pine uncouple its growth from the environmental differences from the upper to the lower tree line? The rates of most physiological and biochemical processes are a function of temperature. Limber pine seedlings from four of five populations from Wyoming, Nevada and California revealed a typical photosynthetic temperature optimum (15 àƒ⣃ ‹’€ à…⽃) but an unusually broad response curve with a variation in photosynthetic rate of only 12 percent from the maximum over the temperature range of 10-35 deg C (Lepper 1980). This is in contrast to the sharper temperature response of photosynthesis of balsam fir (Abies balsamea (L.) Mill., Fryer and Ledig 1972) and Great Basin bristlecone pine (then called Pinus aristata Engelm. but now recognized as Pinus longaeva Bailey) according to Bailey (1970) Mooney and others (1964) where photosynthesis fell 63 percent and 87 percent, respectively, below the maximum rates within the range of 5 deg C below and 20 deg C above the optimum temperature for photosynthesis (fig. 4). Strong variation in photosynthetic capacity between mature trees at the elevational extremes (Schoettle, unpublished data) also suggests considerable adaptive physiological variation for limber pine.

Some other interesting observations in Schoettle [2004] (not exactly on point but collated here since I found the points interesting):

It is thought that during the Pleistocene glacial periods there was nearly continuous habitat for bristlecone pine between the New Mexico and Arizona stands, suggesting that the Arizona stand is a relic of a formerly larger distribution (Bailey 1970). The current southern distribution of bristlecone pine appears limited by suitable habitat, however it is not known what limits bristlecone pine from occupying apparently suitable habitat to its north. The distribution of this species may reflect a dependence on summer monsoons, restricting it from occupying higher elevation sites in northern Colorado. Rocky Mountain bristlecone pine (referred to as bristlecone pine hereafter) has a narrow elevation range and is primarily a high elevation species occupying dry sites from 2750 to 3670 m elevation (Baker 1992)…

The origin of bristlecone pine stands throughout Colorado is related to episodes of drought and presumably peak fire occurrence (Baker 1992). Bristlecone pine is a long-lived species that regenerates well after fires. Baker (1992) reports that bristlecone pine regenerates well only on recently burned sites and therefore attributes the persistence of old stands of bristlecone not to climax stand dynamics but to the long lifespan of the individual pioneer trees in the absence of competition and fire. However, Baker’s data reveal some bristlecone pine regeneration in most of the sampled bristlecone pine stands. This raises the question of how much regeneration is necessary to sustain bristlecone pine on sites with little to no competition…

Vegetation in bristlecone forests is influenced primarily by elevation and soil pH and secondarily by substrate, soil texture, topographic position, and geographic location (Ranne and others 1997). Although bristlecone pine is a pioneer species after fire, its role in mediating the environment to facilitate the establishment of late successional species has not been fully explored. In the subalpine zone, bristlecone pine forests tend to have relatively clear boundaries with bristlecone pine densities abruptly falling as elevation decreases and moisture regimes change.

Larson, Kelly and Matthes of the University of Guelph have been studying cedars for over 15 years with remarkably interesting results. The cedars in question occur in cliffs along the Niagara Escarpment which stretches through southern Ontario from Niagara to the Bruce Peninsula. The "forest" is about 600 km long and 100 meters wide. They have pointed out many similarities between these cedars and bristlecones – both of which have strip bark forms, are very long-lived and live in very adverse environments. Kelly et al [1994] (including Hockey Team member Ed Cook) reported an "optimum" temperature above and below which growth decreases:

The strong negative correlation between tree growth and mean monthly temperature shows that tree ring growth is specifically inhibited by hot July and August maximum temperatures in the preceding summer. T. occidentalis may respond to excessive late summer temperatures by slowing down physiologically in a way that influences growth potential in the following year. This agrees with observations made by Matthes-Sears and Larson [1990] on the net photosynthesis of T occidentalis in response to changing leaf temperatures. In that study, net photosynthetic rates in Thuja were shown to peak at 20 degree C and decline with continued increases in temperature leading to markedly reduced rates of photosynthesis beyond 30 deg C. The exact physiological mechanisms in T occidentalis that explain this response to high temperatures are not know, but they likely involve increases respiration, lower net photosynthesis [Fritts, 1966, 1976] and the resultant loss of photosynthetic reserves.

White Spruce at Northern Treeline
The decline of ring widths with increasing temperatures was reported in D’Arrigo et al [2004], about which I reported briefly here:

A few tree ring studies indicate recent growth declines at northern latitudes. The precise causes are not well understood. Here we identify a temperature threshold for decline in a tree ring record from a well-established temperature-sensitive site at elevational tree line in northwestern Canada. The positive ring width/temperature relationship has weakened such that a pre-1965 linear model systematically overpredicts tree ring widths from 1965 to 1999. A nonlinear model shows an inverted U-shaped relationship between this chronology and summer temperatures, with an optimal July–August average temperature of 11.3 deg C based on a nearby station. This optimal value has been consistently exceeded since the 1960s, and the concurrent decline demonstrates that even at tree line, trees can be negatively affected when temperatures warm beyond a physiological threshold.

D’Arrigo et al. [2004] go on to say:

We chose TTHH for this case study because it is a well-established temperature sensitive site, where the data for ring width (including raw measurements as well as standardized indices) show decline since the 1960s despite a concurrent rise in Arctic temperature [Chapman and Walsh, 1993; Hansen et al., 1999]. At nearby Dawson, Yukon Territory (see section 2), temperature has increased along with the Arctic warming (see Figure 4), while precipitation has not changed significantly. These observations suggest that persistent higher temperatures may have induced a stress on the trees. The stress may be due to temperatures rising above an optimum level for growth at this site. Above a certain level, net photosynthesis declines as the effects of thermally increasing respiration overcome the diminishing response of photosynthesis to temperature increases [Kramer and Kozlowski, 1979].

Original Caption: Figure 3. Results of a linear relationship between temperature and tree rings. Actual (solid line) tree ring width indices for TTHH chronology are shown. Estimates (dashed line) based on using Dawson temperatures as predictors over 1901–1964 period are shown. (These temperatures are based on adjusted data from Vose et al. [1992]. Use of adjusted data was recommended by D. Easterling (Scientific Services Division, National Oceanic and Atmospheric Administration’s National Climatic Data Center) and L. Vincent (Canadian Meteorological Service) (personal communication, 2004).) Horizontal line is tree ring index mean over 1901–1999. Variance accounted for by linear regression model is 33% (ar2), adjusted for degrees of freedom. Model is based on temperature variables: Year t-1 is April, May, July, and August; year t is May–August. Note that regression estimates for 1965–1999 overpredict ring width values. Analyses using unadjusted data indicated some differences relative to those reported herein (with less of a disparity between actual and estimated tree growth) but the same overall conclusion: i.e., that radial growth at this site is overpredicted by the linear model based on temperature.

Original Caption Figure 4. Comparison of observed July–August averaged temperature values (thick line) with physiological optima (straight thin line) computed for TTHH site. Because there are relatively few years in which observed temperature exceeds the threshold prior to 1965, the correlation between ring width and temperature is generally positive (Figure 2).

D’Arrigo et al [2004] go on to say:

As noted in text, elevational differences between Dawson and the TTHH site imply that summer temperatures could be 3.5 deg C lower at the tree site [Jacoby and Cook, 1981].Our results indicate that the tree growth decline at TTHH is consistent with increases in the average July–August temperature over its optimal value (Figure 4). Unlike the systematic error in the linear model (Figure 3), which highlights its lack of cointegration (ADF with constant and no time trend is 2.25, p > 0.38), cointegration implies that there is no systematic error in the quadratic model. The lack of a systematic error suggests that higher July–August temperatures (beyond the trees’ physiological optima) are consistent with the growth decline at TTHH after 1965.These results, combined with those for the ECM, suggest a mechanism for the quadratic relationship between ring width and July–August temperature. Early in the growing season, soil moisture can be sufficient for growth even at somewhat higher temperatures. For example, the coefficient associated with June temperature in equation (3) is positive. As summer progresses, soil moisture usually dwindles. The lack of moisture is especially stressful at high temperatures. Without a persistent increase in precipitation (the precipitation time series are stationary), the persistent increase in temperature over time beyond the 11.3 deg C threshold has a negative effect on ring width. Toward the end of the growing season when soil moisture probably is near the growing season low, the lagged values in the ECM generally have a negative effect on ring width. This would indicate that warm temperatures have a negative effect on ring width in the absence of sufficient soil moisture.

How can this direct evidence of a relationship between temperature and ring width which is not only non-linear, but non-monotonic and reversing within the very target temperature range, be reconciled with the linear assumption of MBH98 and other multiproxy studies? Beats me.

A.W. Schoettle, 2004. Ecological Roles of Five-Needle Pines in Colorado: Potential Consequences of Their Loss In: Sniezko, Richard A.; Samman, Safiya; Schlarbaum, Scott E.; Kriebel, Howard B., eds. 2004. Breeding and genetic resources of five-needle pines: growth, adaptability and pest resistance; 2001 July 23–27; Medford, OR, USA. IUFRO Working Party 2.02.15. Proceedings RMRS-P-32. Fort Collins, CO: U.S. Department of Agriculture, Forest Service, Rocky Mountain Research Station.

P. Kelly, E.R. Cook and D.W. Larson, 1994. A 1397 tree ring chronology of Thuja occidentalis from cliff faces of the Niagara Escarpment, southern Ontario. Cdn J For Res 24, 1049-1057.

Matthes-Sears U and D.W. Larson, 1990. Environmental controls of carbon uptake in two woody species with contrasting distributions at the face of cliffs. Cdn J Bot 68, 2371-2380.

D’Arrigo, R. D., R. K. Kaufmann, N. Davi, G. C. Jacoby, C. Laskowski, R. B. Myneni, and P. Cherubini (2004), Thresholds for warming-induced growth decline at elevational tree line in the Yukon Territory, Canada, Global Biogeochem. Cycles, 18, GB3021, doi:10.1029/2004GB002249.


  1. John Hekman
    Posted Oct 10, 2005 at 5:22 PM | Permalink

    “T. occidentalis may respond to excessive late summer temperatures by slowing down physiologically in a way that influences growth potential in the following year.” So in addition to being non-linear in its response to temp, the ring growth depends on temp in the previous year, which means you need to model it as auto-regressive, otherwise the coefficients will be biased.

  2. TCO
    Posted Oct 10, 2005 at 9:43 PM | Permalink

    How would one evaluate if the danger of this non-linear response was significant to MBH or not?

  3. Steve McIntyre
    Posted Oct 10, 2005 at 10:14 PM | Permalink

    The main issue is this: if the proxies downturn with warmer temperaure, how can you determine whether a medieval proxy was on the warm or cold side of the pantleg. Ergo, how can you establish any confidence intervals. My impression is that there is no evidence that any of these multiproxy studies differ significantly from weighted averages of red noise (with a little cherrypicking).

  4. TCO
    Posted Oct 10, 2005 at 10:20 PM | Permalink

    If one can determine that the series is only in one half of the parabola, one would not need to worry about the maxima. (or visa versa).


  5. Steve McIntyre
    Posted Oct 10, 2005 at 10:30 PM | Permalink

    But how would you know for the 11th century?

  6. TCO
    Posted Oct 10, 2005 at 10:34 PM | Permalink

    I thought I was conducting this Socratic dialogue…damnit!

  7. Paul Penrose
    Posted Oct 10, 2005 at 10:38 PM | Permalink

    Re #2:
    Beats me, but if you find that one of the stated assumptions of a study has been even partially refuted, then I think you have to question the results of the study. At least until the study can be revisited in light of the possibly busted assumption. I doubt that Peter or anybody else on the hockey team will see it that way though; they are true believers in AWG.

  8. Paul Penrose
    Posted Oct 10, 2005 at 10:39 PM | Permalink

    I wish I could edit my own comments after I submit them. Just after I pressed the submit buttion I realised I typed “AWG” (American Wire Gage) instead of “AGW”.

  9. Mike Coffin
    Posted Oct 10, 2005 at 11:43 PM | Permalink

    All these studies seem to assume that the genomes of tree populations are fixed. For example, there doesn’t seem to be any allowance made for the possibility that a population of trees could adapt to changes in temperature. There is surely variation in temperature tolerance within populations, and there is surely variation in temperature, so one would expect that natural selection would change the genome over time. For example, after a temperature drop, the *average* growth pattern might slow down for a time, but after the population is depleted of cold-intolerant trees, the average growth could rise again.

    Is this issue unimportant because that the times in question are short compared to the typical generation? Or is there evidence that the genome is largely static? Or is it just not considered? (Or maybe I just missed it?)

  10. Rob Wilson
    Posted Oct 11, 2005 at 1:52 AM | Permalink

    The potential non-linear response that Steve mentions is potentially very worrying. I have noted a recent decrease in response to climate in recent decades for many tree-ring chronologies around the world. See also work by Briffa. No one reason, however, appears to be the cause for this observation and that different conclusions and hypotheses can be made for different regions throughout the Northern Hemisphere.
    Some possible reasons are:
    Trees have hit a thermal threshold – i.e. to warm (as Steve mentions)
    Moisture stress – too dry (Alaska a good example)
    Increased late winter/early spring snow-pack (Vaganov work in Siberia)
    Pollution effect on growth
    Urban heat island effect on instrumental data
    Maximum vs. minimum temperatures and their affect on mean temperatures

    If the ‘non-linear response’ mechanisms predominate, then there are obvious repercussions for tree-ring based reconstructions. For example, if a tree-ring chronology cannot model recent warming, it is possible that a similar loss in sensitivity occurred in earlier warmer periods (e.g. MWP). If the ‘other effects’ predominate, then these effects can ‘theoretically’ be quantified and adjusted for.

    As a dendrochronologist, it would be a very boring world if there were not such problems to try and overcome. All proxies have their limitations. Such problems can only be addressed at the regional scale.

    Does this mean that we should NOT use tree-ring data in large scale reconstructions of climate? NO. However, the potential limitations of such reconstructions need to be clearly stated. We may never be able to overcome all these difficulties – at least by focussing on tree-ring data alone. The future for robust large scale reconstructions is the multi-proxy approach. But again, the limitations of each proxy type need to be taken into account.

  11. John Davis
    Posted Oct 11, 2005 at 2:16 AM | Permalink

    Is it just me or is there something really strange about Figure 4. I’ve heard of global warming…

  12. John Davis
    Posted Oct 11, 2005 at 2:22 AM | Permalink

    …the second Figure 4, that is.

  13. Louis Hissink
    Posted Oct 11, 2005 at 6:27 AM | Permalink


    The first graph yopu show is not, I must repeat NOT, a graph between temperature (X axis) and conifer seed growth.

    It is a graph depicting seed growth versus temperature departures from optimum.

    Not temperature.

    The distinction is crucial.

  14. John Davis
    Posted Oct 11, 2005 at 6:53 AM | Permalink

    re #13
    Louis, I don’t understand your comment.
    The graph has a linear temperature scale along the bottom, and % decrease in photosynthesis rate (presumably = growth)along the vertical axis. It’s just normalised, that’s all.

  15. Steve McIntyre
    Posted Oct 11, 2005 at 8:15 AM | Permalink

    Re #10. Hi, Rob. Thanks for dropping in. For others, Rob Wilson is an excellent dendrochronologist, who has co-authored with Esper, D’Arrigo and other luminaries, whose attitudes towards me ranged between disdain and loathing long before climateaudit. Rob seems to have broader shoulders. I have corresponded with him prior to any real notoriety and he was always very generous with his time with me. He is earnest about trying to doing a good job and his comments should be read carefully.

    Rob, you say:

    However, the potential limitations of such reconstructions need to be clearly stated.

    That’s the nub. In the canonical multiproxy reconstructions, you do not have a "clear" statement of this and other problems, but you typically have the opposite. Where is the "clear statement" in MBH98-99, Jones et al [1998], Crowley and Lowery [2000] or even, for that matter, in Esper et al [2002] or Moberg et al [2005] of the "bad behavior" of late 20th century proxies?

    We agree that there are many examples of chronologies which do not reflect recent warming. If this is due to any of the nonlinear effects, you agree that the ability of the tree-ring chronologies to pick up a similar MWP event would be compromised. Of the 3 "Other Effects", the 2nd – inaccurate instrumental data (an alternative suggested by Kullman) – would also have policy significance and would compromise the practice of splicing proxy and instrumental records, which is a common rhetorical device in paleoclimate studies.

    So the only non-problematic alternatives are (1) and (3). Briffa hypothesized an "unknown anthropogenic" effect about a decade ago, but has not produced anything. I just about gagged when I read his paper which essentially said that by simply hypothesizing such a thing, he was entitled to ignore the problem. You’ve at least tried to talk about the issue a little more pragmatically, but if you look at the literature squarely, there’s precious little to show for this. This leaves the change in min-max-mean relationships, that you advocated in one of your articles. Again looking squarely at the literature, I wouldn’t say that this is a magic bullet for the issue or that it has been adopted by in the literature.

    You say:

    As a dendrochronologist, it would be a very boring world if there were not such problems to try and overcome. All proxies have their limitations. Such problems can only be addressed at the regional scale.

    I agree that it would be boring with dendrochronologists if there were no problems to overcome. If the debate were contained to common rooms, then I would have no beef. But there’s been a lot of selling of dendrochronological results without many warning labels attached.

    Having spent a lot of time looking at multiproxy studies, the "active ingredients" in some of them are still tree rings. Sure MBH98-99 has corals and other odds and ends, but the hardcore issue of the MWP-modern relationship is driven by tree rings. I agree that Moberg et al [2005] isn’t driven by tree rings, but there are some very strange proxy decisions there and no discussion of how the proxies are selected from the universe of proxies.

    Anyway, nice of you to drop by. If you’ve got time to respond to any of this, it would be nice, but I know that you’re busy. Cheers, Steve

  16. Posted Oct 11, 2005 at 8:22 AM | Permalink

    Re: #10

    Does this mean that we should NOT use tree-ring data in large scale reconstructions of climate? NO. However, the potential limitations of such reconstructions need to be clearly stated.

    In ideal conditions, where methods like MGH98 are used to select proxies that respond appropriately to the instrumental record of temperature, a limitation would be that the proxy is a valid indicator of temperature within the range of the calibration. As any user of scientific instrumentation knows, measurements outside the calibration range cannot be relied on particularly when there is extreme non-linearity. But: 1. without evidence that proxies stay within their calibration range, they are useless as indicators within the range and 2. no conclusions about the temperatures outside the range (such as MWP) are valid. I am guessing your argument is that case (1) might be established with other proxies. I would add that it is not enough to state limitations, the limations must inform conclusions, e.g. tree-ring proxies are unreliable, but don’t you worry about that, they show no MWP.

  17. TCO
    Posted Oct 11, 2005 at 9:02 AM | Permalink

    What I mean is, is there a mathematical/statistical way to say that that the change in slope is a problem/is not a problem?

  18. Posted Oct 11, 2005 at 9:12 AM | Permalink

    Re: #17. Without evidence that the temperature is within the calibration range, (and that defeats the purpose of the proxy), there are two choices of temperature for every proxy value (imagine a horizontal line through the hump). It seems to me the model is intrinsically non-deterministic for predicting temperature.

  19. Steve McIntyre
    Posted Oct 11, 2005 at 9:50 AM | Permalink

    For a model like this, you certainly can’t take the standard error of the residuals in a calbration period and say that those will give you confidence intervals for the entire period. It’s hard to see how you would reduce the confidence interval below natural variability.

    I think that the approach of Naurzbaev that I commended in an eartilce could resolve this and there are circumstances where a sharp quadratic could be an advantage. If you have a relatively short-lived species like larch, a sharp quadratic would suggest that it would move up and down a mountain or north and south to keep to its optimum. This would enable some low-frequency conclusions which would be of interest. Unfortunately most dendro reconstructions do not report ample altitudes and their own reconstructions jumble different altitudes altogether (see Polar Urals).

  20. Dave Dardinger
    Posted Oct 11, 2005 at 10:06 AM | Permalink

    re 17 & 18

    If we had data on the altitudes of the various trees in a proxy set it would probably be possible to see what side of the growth curve we’re on. Higher trees should be cooler so if trees higher in altitude are growing better in a given year than the lower ones it likely means the temperatures are on the hot side while if lower ones grow best we’re on the cooler side.

    Of course this just adds to the need for data sets to be posted, preferably with all the information gathered, not just the items the collector thinks is of interest for a given study. Who knows what will later be found to be important?

  21. TCO
    Posted Oct 11, 2005 at 10:12 AM | Permalink

    So collect altitude and do a multiple regression. Box, Hunter, Hunter is at the library…

  22. Steve McIntyre
    Posted Oct 11, 2005 at 10:21 AM | Permalink

    Information on altitude of individual samples is not available.

  23. TCO
    Posted Oct 11, 2005 at 10:32 AM | Permalink

    Are you being deliberately obtuse? The order was spoken to the field in general. And the altitude info in the trees is readily obtained by conventional surveying instruments.

  24. Posted Oct 11, 2005 at 11:02 AM | Permalink

    Perhaps if you had altitude data, you could develop a proxy based on the differential growth of upper and lower trees, i.e. Temp=f(u-l). This would at least create an expectation of monotonic response to temperature. Not a regression with altitude. There are other issues though. Actual response curves (in the presence of competition) seem to be fairly flat on top, with steep edges restricting the range of temp response. Also, I got the impression that trees for this purpose were generally selected from the upper treeline, but the mixed bag of responses does not suggest the upper vs. lower pattern will be very reliable.

  25. Posted Oct 11, 2005 at 1:41 PM | Permalink

    Couldn’t the difference between the tree rings and the temperature record of Dawson partly be due to urban warming in Dawson? The thermometer in Dawson is recording a anthropogenic local warming which is not present at the tree ring sites?

  26. Douglas Hoyt
    Posted Oct 11, 2005 at 5:50 PM | Permalink

    It seems like assuming a linear fit between temparature and ring width when it is really an upside-down quadratic has too major effects:

    1. Warm years and warm periods are interpreted as cool, so a period like the MWP would disappear.

    2. Warm years and cool years are lumped together so the overall variability of climate in the reconstruction is reduced compared to the real climate.

    No MWP and low climate variability – seems to describe MBH’s reconstruction pretty well.

  27. John S.
    Posted Oct 11, 2005 at 8:40 PM | Permalink

    It would be very interesting to see what happens if you could extend the negative branch of figure 4. At the moment, I would say that a linear approximation of those quadratic curves over the range shown would be ‘near enough’ (particularly for the limber pine and fir, maybe not for the bristlecone) given other sources of error in proxy reconstructions. It’s negative, but it’s still close enough to linear which is the key requirement.

    An interesting consideration in this is whether temperatures below 10 degrees C (which seems to be the lower limit of the graph based on the comment about 15 degrees being the optimum) are observed or likely to have occurred over the life of the trees.

  28. Willis Eschenbach
    Posted Oct 11, 2005 at 10:15 PM | Permalink

    It’s one of those blindingly obvious ideas, that every organism has a preferred temperature for growth, and thus that every organism grows more slowly both above and below that temperature. But I never considered the far-reaching implications for historical temperatures and tree ring widths.

    For any organism, not just trees but any organism, the curve of growth versus temperature will resemble an inverted quadratic, an upside-down “U” shape. I can think of no way to distinguish, based on tree ring width alone, which of two skinny tree rings from the 1750s was caused by excess heat, and which by excess cold. I can’t even fit an inverted quadratic to the dataset, because there’s no way to tell whether a given width goes in the too hot pile or the too cold pile. There may be a way, but I’ve given it some serious thougt, and I sure can’t think of one. I just don’t think the information is there in the data to distinguish too hot from too cold.

    Never mind the confounding factors like too much or too little precipitation, or a late cold spring followed by a hot summer, or a year with perfect conditions except an early frost. Never mind that even in the best case ring widths only relate to summer temperatures, not winter. Never mind that microclimates often mean that one tree has two good years, and another a few hundred metres away has to bad years. Never mind any of that.

    One fact, the simple observation that growth versus temperature shows an inverted “U” shape, means that the science of paleodendrochronological temperature reconstruction, that is to say reconstructing past temperatures from tree ring widths, is dead. Mort. Muerte.

    At best, even if someone tomorrow figured out some way to distinguish between hot years and cold years based on tree ring width, every single study would still have to be redone. In addition, the uncertainty ranges would be on the order of 50-100% larger.

    A new science may emerge out of the ashes, based on something like a ring-by-ring analysis of trace elements to distinguish a hot year from a cold year from a wet year from a dry year from a cold, wet year from a hot, wet year … tough, but possible.

    Or we could get a new science from new studies looking at the difference between treeline and the lowest elevations, for example. The problem with this approach is that at the extremes of any organism’s range of tolerance for any given variable, other variables become much more important. Either heat stress, or cold stress, or dehydration, for example, increases the risk of a given insect infestation slowing a tree’s growth and showing up in the ring width. In other words, when we consider the extremes of the range, the signal gets lost in the effects of the confounding variables on an already stressed organism. Might be a detectable signal there, but my guess is not.

    But the old science, that of reconstructing historical temperatures by analysing tree ring widths, that one can join numerology and iridology as a part of science that didn’t stand the test of time. It will take a while for folks to notice, but that science is a dead man walking.

    Dang, the de-construction of an entire branch of the tree of science … don’t see that every day.


  29. Dave Dardinger
    Posted Oct 11, 2005 at 10:42 PM | Permalink

    Well, Willis, it’s not quite that bad, but I don’t think the existing analysis looks too good. Let me switch my hat around and make a couple of points in favor of tree-ring proxies for temperature. First, as I pointed out earlier, if we have information available on the elevation of individual trees, then comparing trees with high and low elevation should allow us to tell which side of the inverted U we’re on. Second, it’s probably no accident that it’s trees near the tree-line which are touted as good temperature proxies. The tree line is, to a large extent, a measure of the lower limit of temperature which trees can survive at. Therefore, the odds highly favor a tree near the tree-line being on the low-temperature side of the growth curve almost all years. The tree line therefore serves as a dendro-chronological temperature rectifier.

    But, of course, all that being said, there still remains the problem that other things like fertility and precipitation need to be considered.

  30. Brooks Hurd
    Posted Oct 12, 2005 at 12:33 AM | Permalink

    Re: 28, Willis

    A new science may emerge out of the ashes, based on something like a ring-by-ring analysis of trace elements to distinguish a hot year from a cold year from a wet year from a dry year from a cold, wet year from a hot, wet year … tough, but possible.

    This is certainly possible, and not too tough, however it would not be cheap.

    Dendrochronologists would need to take special care in preparing samples for such an analysis. In addition to wet chemistry, surface analysis techniques such as AES or ESCA would provide trace component analyses.

  31. John A
    Posted Oct 12, 2005 at 12:36 AM | Permalink

    OK, which dendrochronologist is going to say “The game is up. We don’t know anything about past temperatures”?

  32. Willis Eschenbach
    Posted Oct 12, 2005 at 2:54 AM | Permalink

    Re: 29 Dave, thanks for the analysis. You say:

    First, as I pointed out earlier, if we have information available on the elevation of individual trees, then comparing trees with high and low elevation should allow us to tell which side of the inverted U we’re on.

    Unfortunately, not so. The key is to realize that for any given tree, the widest ring is not necessarily the warmest temperature. It’s the best temperature. Here’s the problem. Some years, even the trees on the treeline are too hot for optimal growth. And some years, even the trees at the low elevations are too cold for optimal growth.

    There is no way I know of to distinguish these years from the reverse, to distinguish the hot from the cold based on the ring width. If you know a method to distinguish between two skinny tree rings of identical width, and you can tell which one is skinny because it was too hot and which one is skinny because it was too cold, I’d be very interested to know how that method works.

    Finally, in general we don’t have elevation information for individual trees, just for the stand where the group of trees were.

    You also say:

    Second, it’s probably no accident that it’s trees near the tree-line which are touted as good temperature proxies. The tree line is, to a large extent, a measure of the lower limit of temperature which trees can survive at. Therefore, the odds highly favor a tree near the tree-line being on the low-temperature side of the growth curve almost all years. The tree line therefore serves as a dendro-chronological temperature rectifier.

    A couple of points about that.

    First, the treeline is not the limit of the tree’s ability to tolerate temperature. It is the limit of the tree’s ability to tolerate the combined high altitude stressors, which include things like high UV, thin atmosphere, low relative humidity, infrequent or too much precipitation, landslides and unstable soil, wind damage, large temperature swings, insect infestation, poor soil nutrients and lack of topsoil, snow damage, low absolute CO2 levels, increased slopes, and other factors.

    Thus a tree at the treeline may or may not be a good temperature proxy, not only because of the number of confounding factors, but because of their relative importance to an already-stressed tree. A small change in any one of these can cause a large change in the growth rate of a stressed tree.

    Second, I grew up in the high mountain forests, and I’ve seen many years where the entire forest, from the lowlands up to the tree line, suffered from the heat. Plants need more water when it is hot, and if they don’t have it, their growth suffers. You can see the signs of this heat stress in the forest if you know what to look for, the tips of the branches change colour, and the whole tree kind of droops.

    This “more heat than water” stress can hit especially hard at the treeline, because there is typically not much water in the soil, not much leaf litter on the ground, and the air tends to be dry. So even though the treeline trees don’t get as hot as the lowland trees, they can suffer greatly from heat stress, which affects their growth just as surely as a cold year.

    I know that in those years, the trees at the treeline would have had skinny rings because they were too hot. Again, I say, if you can distinguish that hot year skinny tree ring from a cold year skinny tree ring, I would like to know how.

    Finally you say

    But, of course, all that being said, there still remains the problem that other things like fertility and precipitation need to be considered.

    To which I can only say, absolutely. In particular, as I mentioned above, the temperature is not the critical factor at the hot end. It is the combination of the heat and the available moisture. If a year is dry, not in an absolute sense but compared to the temperature, the tree’s growth will suffer even if the temperature is fairly low.

    Like I said, I can’t figure out how to distinguish the hot years from the cold years in the tree ring width data. And without that, the science is dead.


  33. 2dogs
    Posted Oct 12, 2005 at 4:04 AM | Permalink

    Would it be useful if we estimated the optimal temperature for the given species, and then used non-tree proxies to test whether or not to reject the hypothesis that the tempature is above the optimal level for a given year? In the (unlikely?) case that the other factors such as precipitation could be accounted for, could the tree ring data then be used to refine the temperature estimate for the accepted years?

  34. Willis Eschenbach
    Posted Oct 12, 2005 at 5:03 AM | Permalink

    Re #33, this is an interesting approach, and theoretically possible. The difficulty is threefold:

    First is the lack of other proxies in that exact area with comparable data resolution (1 year plus perhaps some autoregression) and comparable spatial resolution (very local). If we had that, we might be able to decide whether the ring was skinny because it was too hot or because it was too cold. Unfortunately, however, we don’t in general have such proxies, which is why we use (or tried to use) tree ring width data.

    Second, the “optimal temperature” you refer to depends on other factors such as elevation and precipitation. A summer during which a tree in the wet lowlands might flourish could be too hot a summer for a tree in the drier foothills, and at the same time be too cold for a tree at the treeline. What is the “optimal temperature” in that case?

    Third, as you say, the confounding effect of precipitation is very difficult to account for, as it affects both the year to year growth and also the optimal temperature for each tree.

    There is also an additional philosophical question here. Can you improve upon some proxy data by using the tree ring data, if you are using the proxy to order the tree ring data from hot to cold? Seems like circular reasoning somehow, might be possible, but I’d have to be convinced that it could improve whatever accuracy the other proxy started out with.


  35. Rob Wilson
    Posted Oct 12, 2005 at 8:42 AM | Permalink

    I am leaving for 2 weeks fieldwork soon, so I will keep this brief (ish).
    We must not forget that all proxies have their problems. If we get too hung up on the problems, then we might as well not bother with palaeoclimate reconstruction. This of course would be a ridiculous situation.

    As I said previously, we need to understand the limitations of each particular proxy type.

    Trees can be sensitive to temperature, precipitation and many other environmental variables. Site location is therefore paramount for the successful identification of a climate sensitive tree-ring chronology. As a general rule of thumb (it may not always be so however), upper tree-line (including high latitude tree-line) for a particular tree species is controlled by temperature, while lower tree-line is controlled by moisture.

    Therefore, if we imagine a hypothetical elevational transect of trees from lower to upper tree-line, the ring-width series from low elevation trees should correlate with precipitation, while the high elevation RW series will correlate with temperature. At intermediate elevations, there will be conflicting influences from both precipitation and temperature.

    Elevation of the sampled stand, as mentioned in previous posts, is very important. However, there is a degree of leeway with regards to elevational zones. For example, from my work with spruce in central Europe (Bavarian Forest), the low and high elevation zones can be quite broad (i.e. Low = 350-700m / High = >1200m). Within these zones however, the closer you are to the forest border, the stronger the climate signal in the tree-ring records.

    Fine – that is easy – the obvious strategy would be go to tree-line. Well, unfortunately, it is not that easy. The oldest trees are generally not found at present day tree-line, but may be found 100-200 m downslide – representing the tree-line during the Little Ice Age. Therefore, these older trees may not be as sensitive to climate now, as they were 200 years ago, because their local environment has ‘improved’.

    Also, present day tree-line (e.g. European Alps) may be an anthropogenic artefact of animal grazing and is lower than it naturally should be if climate was the only controlling factor.

    Despite these problems, tree-ring based temperature proxies from the Alps show strong coherent trends at all time-scales and favourably compare well with completely independent annually resolved proxies like documentary archives.

    When sub-fossil or historical material (of different or unknown elevation) is mixed with living material, the overlap between the living and sub-fossil/historical material must be scrutinised. If they portray the same signal, there should be strong coherence. If not, then the sub-fossil/historical material simply does not present the same climate signal as portrayed by the living data.

    Growth rates in the raw RW series can be different if there are different populations of samples (i.e. living and sub-fossil wood). However, traditional detrending methods reduce the raw data to indices of unit mean and variance. So long as there is strong coherence between the two populations, the detrended indices can be combined to develop a robust mean function chronology.

    It is not so simple when using detrending methods like RCS. However, the data can be divided into different populations, separate regional curves generated for each group and separate RC detrending performed. The resulting detrended indices for each population group can then be combined and a final chronology developed.

    Finally, I agree that some caution is needed when interpreting individual years – for example, an extreme dry year may well affect high elevation trees also. However, we (dendrochronologists) model MEAN response over a calibration period. Hence, as there is noise (influence of other factors at the inter-annual scale), TR based reconstructions of climate generally range between 30-60% of the climate variance explained. However, when smoothed over a few years to decades, these values can increase to 80-90%. So as I said, one needs to understand the limitations of the proxy type.

    I could go on. It is all in the literature. As far as I am concerned, we hide nothing.

  36. Posted Oct 12, 2005 at 9:03 AM | Permalink

    Rob, Many thanks for your clear explanation. Not being familiar with the literature, I appreciate your summary. The non-linearity in growth was too obvious for researchers not to have thought of it. Have a good trip.

  37. TCO
    Posted Oct 12, 2005 at 10:52 AM | Permalink

    Rob, given the critical importance of site selection and the supposed ability to use site selection to overcome endemic methodology problems, do you feel that site selection is sufficiently well described in experimental studies or that tree-guys take a “trust me” attitude?

  38. Steve McIntyre
    Posted Oct 12, 2005 at 12:13 PM | Permalink

    Re #35 and 36: David, you’re letting Rob off the hook too easily here. Rob hasn’t dealt with the issue here at all, although he’s discussed other topics. I haven’t suggested that the issue isn’t latent in the literature – I cited D’Arrigo et al. as an article in which the upside-down U response was articulated. But there are no implemented reconstructions (to my knowledge) that are based on anything other than a linear response. There are calibration-verifications that work OK in the 19th-20th century transition, but the verifications on post-1980 proxies typically have very poor results. If these poor verifications are reported at all, they are then ignored. There’s an important forthcoming article that I can’t discuss here that falls prey to exactly these problems.

  39. Posted Oct 12, 2005 at 1:01 PM | Permalink

    Re #36. I realised after I wrote it that my comment might have been interpreted as letting Rob off the hook, but that was not my intention at all. Rob raised a lot of issues. One is that that while researchers might have thought of the issue, what have they done about it, and are their conclusions justified (the bias issue)? Second, people of vast experience like Rob might appreciate the limitations, but what is done by such people to restrain researchers who don’t and make unsupported claims on faulty methology (the due dilligence question)? Not many people have time to study the literature. Third, Rod has suggested that various strategies reduce the problem – averaging, site-selection – and the efficacy of each of these is a separate study. I don’t agree with this strategy. I think the first task in any modelling exercise is to specify the model correctly, and a linear model with temperature is an obviously mis-specified model. Averaging and sample selection can then help reduce random residuals.

    If I can find something to get a hold of it is the statement that

    TR based reconstructions of climate generally range between 30-60% of the climate variance explained. However, when smoothed over a few years to decades, these values can increase to 80-90%.

    But your results suggest much less, like 10% of temperature, would be typical. Also, it would be a simple matter to show a significantly better quadratic fit than linear of proxies to 20th century temperatures, and would be an important rebuttal of their assumptions. But it doesn’t sound like this, and its implications are in the literature at all. Which means someone has to do the work, and explore the consequences.

  40. Rob Wilson
    Posted Oct 12, 2005 at 2:57 PM | Permalink

    Perhaps I am missing something here.
    Yes, we (me included) model our relationships linearly in the knowledge that the relationship MAY be non-linear. But this is a practical necessity. I do not see how using a quadratic relationship that a valid reconstruction can be developed. If one works with a single tree-ring chronology which can be modelled well using a quadratic relationship with local temperatures, how does such a model ‘decide’ whether low index values in the chronology are related to cooler conditions (as would be implied from the linear modelling), or warm conditions (where growth is depressed due to temperature being above a thermal threshold).
    I am no statistician and am all ears if anyone can point me in the right direction for such a method. I am sceptical though. The non-linearity issue has been discussed since the 1970s, and so far no one has managed to come up with a new methodology that is significantly better than the linear approach.
    I will enjoy reading your suggestions in 2 weeks.

  41. Ed Snack
    Posted Oct 12, 2005 at 3:09 PM | Permalink

    Rob, you’re begging the question. Is it that you are modelling the relationship as a linear one, and yet you know that this is incorrect, that your justification appears to be "Well, at least we can get results that way" ? This approach surely requires significant caveats on the use of any results.

    You point out yourself the exact problem, "If one works with a single tree-ring chronology which can be modelled well using a quadratic relationship with local temperatures, how does such a model “decide’ whether low index values in the chronology are related to cooler conditions (as would be implied from the linear modelling), or warm conditions (where growth is depressed due to temperature being above a thermal threshold)." One thing though is quite clear, to assume cooler conditions as the linear model does is unjustified and unjustifiable. This is the "Assume we have a can-opener" approach criticized by Steve. If the quadratic response is approximately correct, and all current reconstructions are based on a linear relationship, then all paleo-reconstructions based on dendro records are quite simply unreliable.

  42. Steve McIntyre
    Posted Oct 12, 2005 at 3:28 PM | Permalink

    Re #40: if you felt that there was a true upside-down U relationship between ring width and temperature (and there is no a priori reason why the pant legs should be symmetric), then the pro forma reconstruction would have two branches as well – a high reconstruction and a low reconstruction. Both branches would have to be displayed. The more extreme the result, the further the branches from the mean. The reconstruction would be bimodal (but only bimodal). You would then have to advocate acceptance/rejection on other rounds.

    For example, in the 1670s, the narrow widths would yield both a high reconstruction and a low reconstruction. There’s lots of ancillary evidence to argue that the 1670s were cold and thus you could plausibly argue for the cold branch.

    But your decision for the Medieval Period would be a lot trickier. In some periods, it would be hard to exclude the warm branch. In fairness, you would have to show both and, if one branch were higher than the 20th century and one branch were lower, you would have to state that you can’t draw any conclusions about the relative position of this period to the 20th century based on the inability to exclude the warm branch.

    Another form of evidence might be the altitude of the trees. If they are relatively high (e.g. MWP) then you could use that to argue for the warm branch; if they are low (LIA), then cold branch. But you’ll need some evidence beyond the ring widths themselves to decide.

    It’s a little unfair to expect volunteers here to resolve a conundrum that has seemingly plagued dendro reconstructions for 30 years. Even if we are unable to resolve the conundrum, that does not prove that the conundrum does not exist or that dendrochronologists are entitled to ignore the problem.

  43. TCO
    Posted Oct 12, 2005 at 3:32 PM | Permalink

    I’m not convinced that there is no way to account for the quadratic shape effect. We’ve already discussed altitude. There may be other things RW, MXD combos, derivatives, etc. Year to year comparisons, etc. Don’t know the answer, but would like it looked at.

  44. John A
    Posted Oct 12, 2005 at 4:19 PM | Permalink

    What about the straightforward wellknown fact the pretty much all tree species in temperate regions only grow for 6-8 months of the year?

  45. TCO
    Posted Oct 12, 2005 at 4:23 PM | Permalink

    That’s not news. It’s an understood limiation of the proxies. Perhaps some quantification of the degree of the danger ought to be made and included with the reconstructions. Should be possible to do some comparison of summer-year correlations. This is a stats thing. It can be done. Still have a danger that relation will change over unobserved time. But at least you have first order estimate.

  46. Posted Oct 12, 2005 at 9:07 PM | Permalink

    Re: #40 Much as I appreciate the reply I am coming at this as a scientist in a related field with concerns that uncertainty in reconstructions is being understated, and I haven’t heard anything to make me feel better. First you say everyone knows its a problem, then that its under control, and proxies are 80-90% accurate, then you say there is no alternative to linear assumptions anyway. With respect, I find all those statements hard to believe. Steve, if you could suggest some longish proxy records that might show a recent downturn I will practice my R skills and do a reconstruction along the lines you describe in #42.

  47. Paul
    Posted Oct 12, 2005 at 10:54 PM | Permalink

    There’s another more subtle issue that is being missed here. Not only is the temperature response an inverted parabola, so is a tree’s response to water. Too much or too little will stunt its growth. That’s obvious. But this means that the response of the tree rings is the -> product

  48. Paul
    Posted Oct 12, 2005 at 11:01 PM | Permalink

    [the last comment got truncated for some reason.] But this means that the response of the tree rings is the PRODUCT of the two curves. The response of a tree’s growth to soil fertility is also going to be an inverted parabola which itself will have to be multiplied into the growth curve for tree rings. The net result is that tree ring growth is going to be a very nonlinear function of all the growth factors that determine the vitality of a tree.

  49. Willis Eschenbach
    Posted Oct 15, 2005 at 4:45 AM | Permalink

    My Big Fat Tree Ring Analysis

    Well, I got to thinking about what Rob said about common results in tree ring studies, viz:

    Finally, I agree that some caution is needed when interpreting individual years – for example, an extreme dry year may well affect high elevation trees also. However, we (dendrochronologists) model MEAN response over a calibration period. Hence, as there is noise (influence of other factors at the inter-annual scale), TR based reconstructions of climate generally range between 30-60% of the climate variance explained. However, when smoothed over a few years to decades, these values can increase to 80-90%. So as I said, one needs to understand the limitations of the proxy type.

    So, being an investigative type of fellow, I thought I’d look at some studies to see what’s what. Here’s a typical study:

    Neil Pederson, G. Jacoby, E. Cook, D. Peteet, and K. Griffin. 2002. Evidence That Southern Range Margin Trees in the Hudson Valley, NY Experience Heat Stress. Dendrochronology, Environmental Change and Human History – 6th International Conference on Dendrochronology. August 22nd-27th 2002. Québec City, Canada

    Each study population is located at or near a southern range margin and growing at relatively low elevation. The Shushan white spruce outlier is located in a boreal swamp in Cambridge, NY. These trees are growing at 140 m above MSL. Of the 34 trees used in this analysis, minimum tree age ranges from 80 to 187 years. The red spruce grow at 260 m above MSL in a red maple-black tupelo dominated swamp at the Lincoln Mountain State Forest in Greenfield Center, NY. Minimum age range for the 19 trees used in the chronology for this population is from 48 to 143 years. The northern white-cedar grow in a tidal swamp forest at the RamsHorn-Livingston Sanctuary in Catskill, NY at roughly 3 m above MSL. Minimum age range for the 16 trees in this chronology is from 70 to 191 years.

    Growth chronologies were developed using standard techniques (Fritts, 1976; Cook and Kairiukstis, 1990). Residual chronologies were used for climate analysis in order to reduce the influence of stand dynamics. Each growth series was regressed against 20 months of monthly climate (prior March through current October). Monthly climate variables used were average minimum and maximum temperatures and total precipitation. The Kalman filter analysis technique was used to determine if the relation between climate and growth were time stable (Visser, 1986).


    Growth of white spruce was primarily positively correlated to minimum monthly temperatures, though two significant negative correlations were found for the prior March and current June. The five positive months accounted for 15.8% of growth variation while the two negative months account for 14.8%. Six months of minimum temperatures were significantly correlated with red spruce, three positive and three negative. The positive months account for 14.1% of growth variation while the negative months account for 19.3% of the variation. Four months of minimum temperatures were significantly correlated with northern white-cedar, one positive and three negative. The positive months account for 9.9% of growth variation while the negative months account for 28.8% of the variation.

    Growth of white spruce was also primarily positively correlated to maximum monthly temperatures. The three positive months accounted for 12.2% of growth variation while the two negative months account for 5.4%. Seven months of minimum temperatures were significantly correlated with red spruce, two positive and five negative. The positive months account for 9.2% of growth variation while the negative months account for 29.2% of the variation. Eight months of minimum temperatures were significantly correlated with northern white-cedar, three positive and five negative. The positive months account for 18.3% of growth variation while the negative months account for 20.7% of the variation.

    There were few significant relations between precipitation and growth for each population. Only the prior December was negatively significantly correlated to white spruce growth. Red spruce growth was negatively correlated to prior May precipitation. Prior March and current July precipitation was positively correlated to northern white-cedar growth. Kalman Filter analysis shows that most relations between climate and growth are time stable, although some relations are changing through time. For the most part, significant trends were negative (indicating increased heat stress), though some trends were found to be positive.

    Now to me, a result that explains 10% of the variation doesn’t mean much. After all, that’s an r2 value of 0.01, not exactly a giant number … so I thought, let me do a tree ring analysis myself and see what I find. I took the records of a stand of Scots pine trees at 200 metres of elevation, 85 trees in all. I’ll only tell you where they are if I get a subpoena, Michael Mann got his and I want mine. As described in the study above, I used the residual chronologies to come up with an average tree ring width for the year. I used the period 1797-1994 as my comparison period, 206 years.

    Again as described above, I regressed the Scots pine tree ring widths against “against 20 months of monthly climate (prior March through current October)”. Here are my results:


    Growth of Scots pine was positively correlated to average monthly temperatures. Current October, January, and December, and previous October and July, were all significant at 99% (f-test, v1 = 9, v2 = 196). Together they account for 26% of the variance of the tree ring data.

    Now, this is about the same kind of result that the folks who did the study above got. Most of the 20 months were not significant, but some of them were, and between the significant ones, they account for some reasonable chunk of the variation, in this case 26%. What’s not to like, doesn’t this show that tree ring analysis really works?

    Um … well … I hate to say it, but what’s not to like is that the trees are in Finland, while the temperature record comes from … Armagh Observatory in Ireland … so unless I want to name my research paper “Telecommunication of Irish Temperature Variations in Finnish Scots Pine”, I have to assume that I have run afoul of the problem that Steve delineated elsewhere on the site. The problem is that if you take autocorrelated records and compare them, you will find all kinds of “significant” results that aren’t significant at all.

    Of the 20 months that I regressed against (for a longer period and with more trees than the study above), five of them are significant at the 99% level, and three are significant at the 99.9% level. In anyone’s world you’d have to say that this was a significant result, but it’s not, it’s just chance that the previous July’s Armagh temperature alone explain 16% of the Finnish tree ring variation.

    And this doesn’t begin to deal with the problems with tree ring chronologies, wonky mathematics, inverted parabolic trend lines … after finding 3 results significant at the 99.9% level in unrelated data, I’d have to see some real strong correlations before I’d believe any of these studies.


  50. John A
    Posted Oct 15, 2005 at 5:42 AM | Permalink

    Willis, bravo!

  51. Posted Oct 15, 2005 at 8:32 AM | Permalink

    Re: #48 Yes non-linearity could come from any limiting variable.

    Re: #49 Here is another one (here Lindholm, M., Lehtonen, H., KolstràƒÆ’à‚⵭, T., MerilàƒÆ’à‚⣩nen, J., Eronen, M. & Timonen, M. 2000. Climatic signals extracted from ring-width chronologies of Scots pines from the northern, middle and southern parts of the boreal forest belt in Finland. Silva Fennica 34(4): 317–330.

    Climate explains close to one half of the variance in the north and about one third in the south. The percentages for central and eastern chronologies are considerably less,
    about 12 and 17 percents respectively.

    Pines from the central region
    show highest sensitivity, although the signal is
    not clear and unambiguous.

    Nice paper actually showing relationships of growth with latitude, temperature and rainfall. Though, variance in growth explained by climate should be less that variance in temperature explained by growth, for the simple reason that two variables (precip and temp) contribute to predicting growth, but only one variable (growth) contributes to predicting temperature. So the variances as quoted should grossly overestimate reconstruction skill.

  52. Posted Oct 15, 2005 at 8:43 AM | Permalink

    Re: #49 While I agree the correlations are low, the collelation in weather conditions between Amargh and Finland would be also be a likely explanation, and so is not proof the correlations are spurious.

  53. Dave Dardinger
    Posted Oct 15, 2005 at 9:40 AM | Permalink

    re #52

    I was thinking something similar. I’m sure our warmer friends would say that this indicates we’re therefore seeing a more global signal in Willis’ study. Which means, I suppose that if I did the same thing using Finnish tree study and the climate date for here in Arizona I’d find a truly global signal….

    Just kidding. I realize the difference between local and global correlations. Still it would make a good paper to run the same tree-ring sample against weather data in a number of locations and see what the correlations look like. If you get the same general pattern just with different months being highlighted, for instance, it would argue against there being any real signal in the data [some caveats needed as there can also be a time-delay as weather patterns move], whereas if there’s a distinct reduction in correlation vs distance it would argue there was a real signal…. Surely this has already been done if dendroclimatic analysis is a real scientific enterprise. Does anyone have a reference for this sort of study?

  54. Steve McIntyre
    Posted Oct 15, 2005 at 10:19 AM | Permalink

    Re #49: Hi, Willis. Nicely put. Your earlier post about the effects of drought up and down a mountain were very well put as well. The unique role of bristlecones in MBH98 is completely bizarre in this respect: they compete with sagebrush; it’s seems obvious to me that a simple demarcation saying that lower border trees are precipitation proxies and upper border trees are temperature proxies is just arm-waving.

  55. David Stockwell
    Posted Oct 15, 2005 at 9:42 PM | Permalink

    Re: #49, #53, here you go, you are not alone.

    Decreasing teleconnections with inter-site distance in monthly climatic data and tree-ring width networks in a mountainous Alpine area C. Rolland A1 Theoretical and Applied Climatology, January 2002

    Summary The similarities in time series recorded at sites which are distant from each other are called teleconnections. In this paper, the loss of such correlations with inter-site distance was investigated for both climatic and dendrochronological data sets, with 70 tree-ring chronologies. A dense network of weather stations was studied in the southeastern French Alps, covering complex climatic gradients over three departments.

    The teleconnections between precipitation series were found to be higher than those observed for temperature over short distances, but the maximum threshold distance was lower (193 km) compared to a positive correlation distance that exceeds 500 km for temperature. The maximum temperatures had stronger teleconnections than minimum values (522 km versus 476 km), since the latter are linked more with other site factors, such as slope, exposure and local topography.

  56. Willis Eschenbach
    Posted Oct 17, 2005 at 4:55 PM | Permalink

    I just read an article in Nature magazine on the big European heat wave of 2003. Among the points they made was that the extreme heat wave caused the growth of virtually all trees to slow markedly, all over the region.

    This, of course, means that future dendrochronologists (if they are not extinct by then) will conclude that the summer of 2003 was colder than usual.

    As I mentioned before, I see no way around this problem. Merely saying, as someone did above, that:

    At the moment, I would say that a linear approximation of those quadratic curves over the range shown would be “near enough’ (particularly for the limber pine and fir, maybe not for the bristlecone) given other sources of error in proxy reconstructions. It’s negative, but it’s still close enough to linear which is the key requirement.

    does not even begin to approach, much less to solve, the problem. The problem is that in the dendrochronological record, 2003 will go down as an extremely cold year, and no amount of hand-waving about “near enough” and “close to linear” will change that erroneous conclusion.

    And of course, it’s not limited just to 2003. Any and every very hot year will be recorded by the dendrochronological “thermometer” as a cold year. What kind of bogus thermometer is that?


  57. JerryB
    Posted Oct 18, 2005 at 6:47 AM | Permalink

    Ah, another dendro teleconnection: June, and July, were relatively cold at the South Pole in 2003, and that obviously stunted the growth of European trees. QED.

  58. Hans Erren
    Posted Oct 18, 2005 at 7:00 AM | Permalink

    re 55
    How persistent are teleconnections? Decades, centuries, milennia?

  59. Steve McIntyre
    Posted Oct 18, 2005 at 10:19 AM | Permalink

    Re #27: John S., the problem with your observation that the biological growth could be approximated over the illustrated range as negative relationship to temperature is that the active ingredient in MBH98 is increased bristlecone growth in the 20th century, which is assumed in a Mann world to be evidence of global warming.

  60. John Hekman
    Posted Oct 18, 2005 at 10:27 AM | Permalink

    Re: #54. Steve, if bristlecones compete with sagebrush, and if these bristlecones are located on places with names like “Sheep Mountain”, and if the anomalous growth started in the mid-19th century, then maybe sheep herding led to elimination of sagebrush, which led to less competition for bristlecones.

  61. Steve McIntyre
    Posted Oct 18, 2005 at 1:31 PM | Permalink

    Re #60: John, look at the discussion of this very topic in our E&E article. While Graybill and Idso attributed the anomalous bristlecone growth to CO2 fertilization, this is not the only possible explanation of anomalous growth and all alternatives have to be considered in order to establish the anomalous growth as being climatic-related. There is much evidence of a pulse in growth of woody plants in the American Southwest after the introduction of commercial sheep herds eliminated herbaceous competition. This has not been specifically discussed for bristlecones, but there is definite evidence of commercial sheep grazing near several bristlecone sites, including the White Mountain sites. I started posting up some site information earlier this year and then didn’t pursue it. I’ve got some notes on various sites which are interesting.

    I was thinking about the sheep eating other herbs, rather than sagebrush. I just googled the terms and Natinal geographic has a fresh article on sheep and sagebrush,, in which the sheep are used to aid sagebrush growth by eating competitors such as spotted knapweed. That’s more what I had in mind: if the sheep aid sagebrush growth by eating competitive weeds, then presumably the same weeds would be competing with bristlecones on the adjacent substrate. I’m not trying to make definitive statements on this, but surely if one is basing world climate history on this sort of stuff, a specialist should report on the matter prior to any conclusions being drawn.

  62. John Hekman
    Posted Oct 18, 2005 at 2:05 PM | Permalink

    Thanks Steve. Very interesting. Also, there have been articles in the last few years about Malibu and other towns here in Southern California using South American goats, along with their South American goat herders, to control brush on fire-threatened hillsides. Make a note: in a few years we will hear about the higher growth rate of the California oak trees in those areas as a result of human-induced climate change!

  63. John Hekman
    Posted Oct 18, 2005 at 2:11 PM | Permalink

    Here’s a good example of what goats can do in Malibu and Berkeley:

    I think you are right that grazing has to be considered as a variable in some of these tree growth spurts. Also, logging was quite extensive in many of these areas. And I bet the people looking for trees to take a core from used logging roads to get up the mountainsides.

  64. John S
    Posted Oct 18, 2005 at 3:15 PM | Permalink

    Re #59

    Ahh. So we are really in a period of AGC – it’s just the thermometer records which are messed up. The high-quality proxies are giving a perfectly clear signal!

  65. John Thau
    Posted Oct 18, 2005 at 7:40 PM | Permalink

    Try antipode comparative analysis. Unfortunately there’s not too many 2700m + regions with data, like you have in Asia and the Western North America,in the southern hemisphere

  66. JerryB
    Posted Oct 18, 2005 at 8:30 PM | Permalink

    John Thau,

    I, for one, do not understand your comment. Would you please elaborate?

  67. Phil B.
    Posted Oct 18, 2005 at 9:24 PM | Permalink

    Re #60 & 61 John and Steve, There is a 60 minute video called “In the shadow of White Mountain”. You can view the video at It has AGW flavor but you should find it interesting.
    I had several points to make about the grazing hypothesis.
    1. In figure 3 of Graybill and Idso 93, the strip bark shows the hockeystick, but the full bark doesn’t. It not clear how a grazing hypothesis would explain this fact.
    2. I have not been to the Sheep Mountain site, but I wouldn’t graze sheep at either the Schulman or Patriarch bristlecone Groves. Nothing but rocks, poor soil, and the bristlecones.
    3. Sheep mountain may have been named for the native Bighorn sheep not for the domestic sheep. I am trying to determine that history.
    Phil B.

  68. Steve McIntyre
    Posted Oct 18, 2005 at 10:15 PM | Permalink

    Re #63: actually I think that it was more likely that the roads were to old 19th century mining camps. I tracked down site information on a number of bristlecone sites by looking through ghost towns of the Old West, which is something that vaguely interests me. For example, the britlecone pine site Timber Gap is actually shown on a 19th century map to Mineral King California. One thing that few dendrochronologists probably are aware of is that little underground mines use timber for roof support; so if you’re running a little silver or gold mine at 9000 feet, you might use some nearby bristlecone even if it’s not timber that you’d take to Los Angeles for building houses. I’ve clipped some infor on that. I’ll try to revive these posts because they were interesting,

  69. Steve McIntyre
    Posted Oct 18, 2005 at 11:49 PM | Permalink

    Correction on sheep and sagebrush: says “Big Sagebrush is good forage for sheep and wildlife on winter ranges”.

    My understanding is that Methuselah Walk and Schulman Grove are lower than Sheep Mountain and that there might be more vegetation at higher altitudes since there’s a but more moisture. Also, in some cases, the commercial sheep herds ate the herbs down to their roots. It’s possible that the modern appearance of these sites may differ from the 19th century appearance. There’s much evidence of landscape change elsewhere esulting from overgrazing. John Muir of the Sierra Club absolutely hated commercial sheep – “hoofed locusts” and Carl Purpura, a naturalist of the day, wanted to kill the commercial shepherds for desecrating the mountains. If the vegetation is “mined” out by commercial overgrazing by sheep, according to my sister, a landscape architect in Colorado, even wild bighorns could maintain a desolate appearance.

  70. John Thau
    Posted Dec 4, 2005 at 2:03 AM | Permalink

    Jerry, I was hypothesizing the comparison of opposite points in the southern hemisphere with equivalent vegetation and elevation with, for example the White Mountains in California. I would guess the closest would be near say Mt. Kenya or Kilo in Africa.

  71. Steve Sadlov
    Posted Feb 7, 2006 at 9:10 PM | Permalink

    I reckon there were sheep herds all over the Eastern Sierra and the Western Great Basin from about the 1860s until the early 20th century.

    Note also the following unique factors in that part of California, vs say, the Alps:
    * Massive wildfires caused by dry lightning. Prior to about 1940 most of them became absolute monsters and simply went until they burned themselves out.
    * The Summer Monsoons. Incursions of cT air masses which affect the East Side of the Sierra and Great Basin dramatically. And their strength varies greatly from year to year. So, did the MWE increase or decrease them? One may be able to tell from other proxies further south and east, on into Mexico.
    * Rainshadows, dramatic impacts of predominent Wintern jet stream direction on amount, type, depth of snow and continuity / overall duration of the snowpack.

    I personally do not agree that with Bristlecones, higher sites are more sensitive to temperature than moisture in this setting. The soil is of a type not found in places like the Alps and the typical relative humidity is far lower – the lowest extremse of humidity are simply unheard of in Central Europe. In fact, daily, day to day and annual large variations in temperature are a way of life in the US SW. Any tree in such a setting is innately adapted to it. Whereas, moisture, wind and depth of and development of soil strongly influence the health of high altitude trees in such a setting.

  72. Posted Nov 2, 2007 at 2:40 PM | Permalink

    Sorry, link not working. Try this:

  73. Posted Nov 3, 2007 at 5:37 AM | Permalink

    Sorry again, comment on wrong forum, was supposed to be sent to “What other data series could be plugged in?”

  74. Geoff Sherrington
    Posted Nov 3, 2007 at 6:43 AM | Permalink

    If you own a forestry company and your wish is for maximum growth rate for quickest return on investment, you already know that the U curve is inverted. There is only one point at which optimum is achieved. All other points are lowered by factors such as: nutrition, competition from other plants, shading/excessive light, water, pests and diseases, fires, temperature (hot and cold), distance from optimum locale, lightning, soil profile variation, strangler vines, polyploidy and possible genome adaption in the life of the tree – to name just a few. In commercial practice, those that can be manipulated are, if it is cost-effective, like aerial fertilising. There are even super-trees that are selected for superior performance and seed harvest to improve the genetics, as in race horses. I have believed that rings can be counted for a chronology, but I have never been convinced that they are a proxy for temperature, as I have written here before of some simple complications like knots and branches too close to the core. Seems to me that proxies for temperature earlier than times of measured temperature are a frustrating exercise in circular logic.

  75. John M.
    Posted Nov 3, 2007 at 7:17 AM | Permalink

    To be fair though I think the argument you would get from the dendro people is that only very specific stressed environments result in tree growth that is primarily temperature dependent and that most trees cannot be used as proxies for that reason. If they have a long enough calibration period where they can compare growth rates with temperature records I think there can be some value to the technique but there is no way a single dendro study should ever have been trumpeted as concrete proof that the LIA and MWP didn’t actually happen when there is so much documented historical evidence for those events having taken place.

  76. MarkW
    Posted Nov 3, 2007 at 8:58 AM | Permalink


    Therein lies one of my bigger complaints against dendroclimatologists. They tell us that only in certian, narrowly defined climates zones, do trees act as thermometers.

    Well if the climate needed is so precise, how do we know that over the millenia, the climates have stayed constant enough for the trees to remain good “thermometers”

    We know that there have been huge swings in precipitaion levels, lasting decades, even centuries.

    Additionally, there is the problem of the fact that the way temperature affects tree growth is U shaped. Are the temperatures in question on the uphill side, or the downhill side of the U. That is, if growth is increasing, is it because the temps are getting hotter, or because they are getting colder?

    I don’t believe that we will ever be able to puzzle out enough of the confounding factors to be able to use trees as thermometers.

  77. Posted Jun 10, 2008 at 11:10 PM | Permalink

    There’s another more subtle issue that is being missed here. Not only is the temperature response an inverted parabola, so is a tree’s response to water. Too much or too little will stunt its growth. That’s obvious. But this means that the response of the tree rings is the -> product

  78. Steve McIntyre
    Posted Oct 20, 2008 at 8:31 PM | Permalink


  79. Mark T
    Posted Oct 20, 2008 at 11:41 PM | Permalink

    I’m guessing you’re bumping because of the few recent, and relevant, mentions of linearity?


  80. Steve McIntyre
    Posted Oct 21, 2008 at 7:46 AM | Permalink

    I get tired of thread after thread on other topics being hijacked on this topic.

  81. Mark T.
    Posted Oct 21, 2008 at 8:47 AM | Permalink

    Hehe, some of us are quite convinced the entire reconstruction argument lives or dies on linearity. 🙂


  82. Mark T.
    Posted Oct 21, 2008 at 11:08 AM | Permalink

    I know. I specifically thinking of your statement in one of the other threads to that end. In fact, I replied to that one as well. 🙂

    Even the dendros agree that the mixture of influences on tree growth changes with time, creating linearity issues (which translate to stationarity issues as well). I believe there is even an email response in the Peter Brown thread (from Peter Brown) that states this explicitly. That alone throws out any possibility of using one set of weights to cover the entire proxy range. Yet, in the very same thread, Peter Brown insists that Mann’s use of the proxies is “one of many legitimate means of developing temperature signals at a global perspective.” You can’t have it both ways, either the temperature signal is non-linear, which means linear methods are inappropriate, or it is linear, which means linear methods may work. It can’t get any more fundamental than this.


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