In part one, I summarized briefly three principal analytical problems in using tree ring widths to infer long term paleoclimatic trends. I noted that any one of the three would be a major problem, but that taken together, they are fatal to confidence in the validity of long term climate reconstructions. In this second part I’m going to go into some more detail on the second problem, given that the first issue (as described in the cited Loehle and Kingsolver papers) is straightforward and well-described therein. However, first a couple more notes on that first issue of nonlinear response functions.
Restating that issue, if ring response is a +/- unimodal function of climate, then one cannot be sure which “side” of the optimum response that the ring widths of pre-calibration years fell on, and accordingly, cannot confidently use them to infer a single climatic value for any given time point. The best one can do is to estimate a bimodal response–and even then only if the climatic and ring width values during the calibration period cover a broad enough range of climatic states to allow this; that is, that they sample rings on both sides of the optimum. Such an estimate would certainly be a valid and useful piece of information, but it would not be the definitive estimate of a single value arising from an assumed linear relationship between climate and ring response. Furthermore, I have yet to see a single paper that takes this approach. Rather, studies universally assume a linear relationship between climate and ring response and then invert this relationship in order to predict past climate states. The point is that this assumption/practice is not justified, either empirically or theoretically; it constitutes a serious conceptual mistake in tree ring analysis. As I stated in part one, it is therefore disconcerting that it took so long for someone (i.e. Loehle, 2009) to point it out. Better late than never of course, but a number of the horses are already out of the gate.
One more point on this issue. The argument has been made explicitly or implicitly more than once, that a linear relationship between climate and ring response observed during the calibration period justifies the assumption of a linear relationship in the past. No it does not! This is in fact part of the point; the fact that all the observed ring responses during the calibration period fell on the “left” side of the optimum, and therefore approximate linearity, does not in any way guarantee that they did so in the past. There is no analytical method currently available for doing this, and it is not clear that it is even possible. [I have some ideas on how that problem might be approached but won't get into that issue here. It is by no means clear that the problem is fully tractable however].
Now on to the second issue: problems with standardizing (or “detrending”) ring responses in order to remove the long term effects of changing tree age/size, thus leaving (presumably) only the effect of the climatic variable of interest. The problem here is that this is done by ad-hoc curve fitting procedures that cannot in any way guarantee an accurate result. An empirical “curve” (almost always a straight line or a negative exponential curve) is fit though each ring width series (obtained from a tree core), that curve being assumed to represent the effects of changing tree age/size on ring response. The residuals from this curve are thus taken to represent the effects of climate. There is no question that as a tree changes in age/size with time, that the ring characteristics also change. Ring widths typically, though not constantly, decrease with increasing tree size, for example. There are two main approaches to this “detrending” and it’s important to understand their basics.
The first, and historically oldest, method, fits a separate curve to each ring series individually. [I call this "Individual Curve Standardization" (ICS) for convenience, since there is no commonly used acronym in the literature for it.] It is immediately clear that the longest term effects of age/size, and climate, are (potentially) irretrievably confounded in this approach, and thus not fully resolvable. This issue was most clearly described in 1995 by Cook et al. The second method therefore tries to address this problem, by instead assuming that there is one fundamental age/size effect for a given species in a given, defined area, that can be approximated by a single curve fit to the ring series from the set of trees sampled therein. This method is known as “Regional Curve Standardization” (RCS). It is awkwardly described in the literature (e.g Briffa, 1992a) as resulting from “stacking” cores by their “cambial” ages, taking means, smoothing those means, etc. etc. More simply, RCS is the fitting of a single curve (or spline) to the ring cambial ages (years from tree center) of all cores in a defined area, followed by a detrending of each ring series with that single curve. [Sometimes two curves are generated if there are distinct groups of trees defined by clearly different long term growth patterns see e.g. Esper et al (2002)].
The RCS approach dates to Erlandsson (1936), but was used rarely until revived by Briffa et al (1992a). It has been generally assumed that the method largely solves the problems of the ICS method as long as certain requirements are met, the principal ones being that (1) the fullest possible range of tree ages is sampled in the field, and (2) that the sampled trees constitute a single biological population with respect to their response to climate. However, the first requirement in particular is clearly often not met, as inspection of the tree ages in many sites archived at the ITRDB shows. Clearly, field workers have almost always tried to sample the oldest trees at the expense of younger ones. This is very understandable, given that a common goal is to carry a chronology as far back in time as possible, but it creates real problems for the RCS method. Also, RCS approaches were rarely used before 1992, and only scatteringly since, so there was very likely no general awareness of the importance of the issue. More recently, Briffa and Cook have emphasized its importance however, so hopefully field sampling strategies will change. The second requirement (single biological population) also becomes questionable as the regional area encompassed by the tree sampling is increased, due to potential differences in site quality (e.g. soils and topography) and genetic differences between widely scattered sampling sites. Therefore, even the recognized requirements of the RCS method range from clearly unmet, to questionable and undemonstrated. And this does not include the unrecognized issues with the method (which there are; more on that later).
These problems point to a more general issue in the field however. Namely, it is based almost entirely on empirical data analyses of various types, with little or no theoretical foundation. The field has made almost no use of the power of simulation analysis to answer critically important questions regarding the limitations of various possible analytical approaches, which such types of analysis are particularly insightful for. If analyses of complex systems are performed piece-meal, based on empirical data analyses from some arbitrary set of realizations of that system, one will often obtain a set of results that is not underlain (and hence explainable) by any unifying conceptual framework. Dendroclimatology fits this description pretty well; it is almost entirely an observational science, with little basis in rigorous and systematic experimental analysis, be that on actual trees, or in simulated model systems (each of which has its own strengths and weaknesses).
It should go without saying that such an approach will have limited power to solve certain types of problems, and that it will also likely lead to potentially serious confusions and disagreements arising as different researchers apply different analytical methods to different data sets. This manifests itself, for example, in “spaghetti graphs” of the past temperature of continental and larger regions, each single strand differing, often substantially, in its time course from many of the others. It is (apparently) assumed by most or all that this represents a type of ensemble and that the “truth” therefore lies somewhere in the middle of the individual strands. But this assumption is defensible, as with any ensemble approach, only if each strand is one realization of an unbiased, stochastic process, with the signal gradually emerging from the noise as more ensemble members (strands) are added. But this requirement has not been even close to demonstrated (or even attempted as far as I can tell), and in fact is very unlikely to hold true, for the reasons discussed here and elsewhere. There is simply no way to know where the truth lies in (or outside of?) the spaghetti pile, given commonly used analysis methods. It’s frankly just a pile of spaghetti, without much real meaning. How are we supposed to have strong confidence in what the pile represents?
Inexplicably, although the RCS method has been generally believed (though again, not conclusively demonstrated) to be superior to ICS in retrieving the long term climatic signal (or at least no worse than it), at least since Cook et al. (1995) or Briffa et al. (1992a), this has not stopped a number of researchers from using the ICS method anyway. This includes studies by those two authors themselves (e.g. Briffa et al 1992b; Cook et al., 2004), and at least five or six other large (continental to global) scale reconstructions, right up to the present (e.g. Pederson et al., 2011), not counting a number of others at regional and smaller scales. One can only guess as to the rationale behind this, because in few if any of those papers is it made clear why this choice was made, and there is no set of agreed-upon rules or guidelines anywhere that clearly defend and delineate under what conditions the ICS method should and should not be used to detrend tree ring series.
Additionally, I argue that the RCS method also has one very serious unrecognized flaw, and is therefore by no means a complete solution to the problems with ICS detrending. Although this latter point is recognized in several places in the literature (e.g. Briffa and Melvin, 2010), this unrecognized issue means that the extent/magnitude of the method’s problems is worse than is currently recognized. That topic will be covered in part three.
[note: Craig Loehle points out in the comments that tree size is the better predictor of ring size than is age. I agree with him; I use the phrase “age/size” in the above discussion mainly because, historically, detrending has been done by fitting curves to tree ages, and most people are used to thinking in those terms. The two measures are highly correlated, but it is size that is the better predictor]
(see Part 1 for links to the Loehle and Kingsolver papers; you’ll have to use Google Scholar for the others, sorry: many (but not all) of them are freely accessible)
Briffa KR, et al. (1992a) Fennoscandian summers from AD 500: temperature changes on short and long time scales. Climate Dynamics 7:111-119.
Briffa KR, et al. (1992b) Tree-ring density reconstructions of summer temperature patterns across western North America since 1600. Journal of Climate 5:735-754.
Briffa KR, Melvin TM (2010) A closer look at Regional Curve Standardization of tree-ring records: justification of the need, a warning of some pitfalls, and suggested improvements in its application. In: Dendroclimatology, Progress and Prospects; Hughes MK, Swetnam TW, Diaz HF, eds. Springer, Heidelberg.
Cook ER, Briffa KR, Meko DM, Graybill DA, Funkhouser G (1995) The ‘segment length curse’ in long tree-ring chronology development for palaeoclimatic studies. The Holocene 5:229–237.
Cook ER, et al. (2004) Long-Term Aridity Changes in the Western United States. Science 306:1015-1018.
Erlandsson S (1936) Dendrochronological studies. Geochronology Institute Report 23, University of Upsala, 1–119.
Esper J, Cook ER, Schweingruber FH (2002) Low-frequency signals in long tree-ring chronologies for reconstructing past temperature variability. Science 295: 2250-2253.
Kingsolver JG (2009) The well-temperatured biologist. The American Naturalist 174:755-768.
Loehle C (2009) A mathematical analysis of the divergence problem in dendroclimatology. Climatic Change: 94:233–245.
Pederson GT, et al. (2011) The unusual nature of recent snowpack declines in the North American Cordillera. Science 333: 332-335.