I’m going to keep after explaining the essence of the detrending problem in dendroclimatology, even if it appears to be the beating of a dead horse, because I think the issue’s still not completely clear to some (maybe a lot of) people, and because reader “kch” has given me an idea on a different tack with a question in part one of this series, on the role of experimentation. The roles/importance of experiments versus models in scientific practice constitute a never-ending source of contention/confusion it seems.
First a restatement of the essential problem, which is one of signal extraction (or, noise removal if you like). One’s ultimate objective is to extract the environmental (typically, climatic) signal from raw measures of ring size (typically, ring width) from a set of trees sampled at a single site (excluding thereby all those issues related to how to derive a larger scale reconstruction from the collection of such sites, which are separate issues). This signal is however, potentially confounded by the effect (trend) caused by changing tree age/size (size actually being the better predictor of the two, but age being the one that workers typically try to remove; the two will typically be highly correlated, but not identical). That size-induced trend is noise, to be removed. Given that all that one has, data-wise, is the end result of the growth process from some number of trees at a site (i.e. a set of series of ring measurements), how exactly should one remove that “trend noise” effectively?
This situation immediately suggests the time-weary, go-to scientific method–controlled experimentation–to get a quantitative approximation of this age/size effect. Reader “kch” asked about the problems with doing that, and I responded there. The bottom line is that it can’t really be done, for practical/financial reasons. However, the question leads me into an essay on scientific practice. For some, these points will be obvious and uninformative, but not for others; I’m not trying to talk down to anybody here.
We can usefully classify all experiments into three fundamentally different types: (1) controlled, manipulative experiments on real-world objects, (2) observational or “natural” experiments on real objects, and (3) model experiments on simulated objects. Each, without question, has its very important place in science generally, and the use of each depends on the nature of the question at hand.
Focusing here on the second type only, a “natural” experiment is one in which one attempts to collect data in such a way that an approximation of a controlled, manipulative experiment is achieved. Depending on the complexity of the topic under study, this may not be easy, but for the tree ring detrending problem, the application is appropriate and pretty straightforward. It has been around since (at least) 1936 in a relatively obscure work by a man named Erlandsson* in Sweden, and currently goes under the acronym of RCS (Regional Curve Standardization). The fundamental idea is very simple: if you sample enough trees of enough different sizes, you will be able to estimate the size effect, and hence, remove it. This estimate is termed the “Regional Curve” (RC); it is then removed by either ratios or differences, from each individual tree core. [The term “regional” is a misnomer when RCS is applied to a single site, which it can be if desired. It can also be applied at some larger, regional scale].
So, that’s a very useful application of the natural experiment concept indeed. The problems arise in the actual implementation, not the concept itself, which I will go through briefly.
First and most importantly, it is essential that for all time periods of interest (back 200 years, back 1000 years, whatever) that one has a good mixture of tree sizes in the sample at all times. This is in fact an enormous problem with existing data sets, and it ties directly to field sampling issues, which have historical roots.
Second, the procedure works best when there are little or no inherent growth rate differences between trees, as can arise due to either genetic or micro-site (especially, soil) differences between the individual trees used to create the RC. Genetic variation between taxa is controlled for, essentially always, by creating a separate RC for each taxon (typically, taxon = species), but potential intra-taxon variation is not controlled for directly. Indirectly however, it is controlled for if one creates a separate RC for each site, and my strong opinion is that this is therefore the best way to proceed. Any remaining, intra-site, intra-taxon variation, due to either genetics or micro-environment, then constitutes the random variation (noise), and its presence is why a number of trees at any given site are always sampled.
This procedure does not guarantee that all trees of a taxon at a site will have identical inherent growth rates. However: (1) one has at least reduced the variance as much as one confidently can, and (2) it is entirely reasonable, biologically, to assume that strong genetic biases in individual trees are minimized, given that many species, especially among the conifers so commonly used in dendroclimatology, are wind-pollinated outcrossers (i.e. not highly inbred). That tends to equalize things, genetically, about as well as can be. Here also is just where the observational skills of field samplers come into play: if there is reason to believe a particular tree is favored/unfavored by its micro-site conditions, and will therefore impart a bias, then don’t sample it. Good field workers have a lot of skill in making just such judgments in order to reduce such sources of noise. And, as always, one should sample as many trees as feasible, to reduce the sampling error, assuming one has first taken care to minimize potential biases.
Getting back to the first issue, which is likely the more serious one, the problem is that field samplers very frequently sample the oldest trees at a site at the expense of younger/smaller trees, in attempting to carry the chronology as far back in time as the oldest trees will allow. I call this a “historical root” because the practice originated before the RCS method, with its requirements, was described/developed. Such trees should indeed be sampled, but this has to be accompanied by an equal sampling of trees of all other ages/sizes in the stand, right down to saplings. [This reality will rule out sites that are relatively even-sized, arising from a regeneration pulse sometime in the past, but there are plenty of continuously regenerating, multi-sized stands in the world to sample].
Additionally, it is also necessary to truncate the sample for the older/larger trees, meaning, one must exclude from the data set the later (outer-most) rings of the the older trees. The reason is that, as you proceed back in time, the number of cambially late (i.e. outer-most) rings in the sample decreases, necessarily. If you include them, you will bias the resulting RC whenever there is a long term environmental trend. This is in fact one of the three fundamental roots of the problem with the use of the RCS method. The other two are (1) the purely geometric component of ring width is never removed, and (2) even if you do remove that effect, if there is in fact little or no biological age/size effect, then no further detrending is needed, at all.
In the latter case, performing RCS detrending in the presence of a true environmental trend will thereby under-estimate that trend. But existing analytical methods cannot, by themselves, tell you whether there is or is not a true age/size effect in the data, which in turn means that you cannot really say anything at all about the magnitude of the environmental trend, and any attempt to do so is unwarranted. Don’t waffle on about “reasonable approximations” or use similarly vague and useless phrases, and don’t justify it because everybody else uses the same techniques. The simple fact is that you don’t know what the analyzed data actually inform you of, neither as a central point estimate, nor as a confidence interval thereof.
Ask any questions or make any comments you may have.
*Erlandsson S (1936) Dendrochronological studies. Geochronology Institute Report 23, University of Upsala, 1–119.