Here is a type of diagram which I often do on tree ring data. I’ve never seen anything like this in the tree ring literature, but some of you may be interested.
The top panel simply plots the cumulative growth of each tree in a network on a time scale. The slope of the plot for each tree indicates its growth rate. It’s a pretty simple and obvious thing to do, so you’d think that people would do it all the time, but they don’t. There are a lot of datapoints plotted here – 18,851.
The middle panel is the Tornetrask RCS ring width "chronology" (my calculation which is pretty close to the figure in Briffa et al, NATO 1996), which is essentially the mean growth after removing the "age-related" trend. In RCS standardization, the negative exponential model is fitted to all the measurements, rather than to each core individually. In "conservative" standardization, a negative exponential model, or as a default a stright or negative-sloping straight line) is fitted to each individual tree. The bottom panel shows the implied amount of "adjustment" from the age-adjustment – negative values "gross up" the site chronology, rather than the opposite. (Maybe I should reverse this in future presentations). I think that there are all kinds of interesting statistical issues involved in these "standardization" processes, which, as far as I can tell, have never been considered by real statisticians. Cook is by far the best of the dendrochronologists at statistics, but the whole field needs housekeeping. I’ve been working on this from time to time and have some interesting results, but obviously have some other irons in the fire.
I’m showing this graphic because of the recent interest in my Tornetrask post and it illustrates some thoughts that I may not have articulated, but influence my views on some of these matters. [Note: the graphic below and a few comments have been updated on Mar. 20, 2005. In doing this graphic before for web-version, I didn't remove NA data. You see the effect of a long NA patch in a core in the 12th century which is perfectly level. I'll post a bit about NA in these records in connection with Polar Urals where it is pervasive. The plotting function didn't plot values after an NA value. The update does - that's why it's a little denser in this version.]
Just looking at the top panel, I find the relative linearity of growth in many cores to be quite striking. Obviously some cores have a juvenile growth spurt – this is an effect that is allowed for by the negative exponential models. But a lot of cores don’t seem to have much of a juvenile effect. For example, look at the "alpha" trees in the first millennium: they start off as fast-growers and keep growing fast until they die. The modern "alpha" trees are also fast growers from the start( I mis-described one tree in the prior version.)
Secondly, the recruitment of new trees is obviously not homogeneous. There are some big gaps, e.g. the 16th century and from the late 18th century on. Impressionistically, periods of long-term high RW "chronologies" seem to be somewhat biased to periods of low recruitment and vice versa. It makes one wonder about whether the negative exponentials are really modeling this the right way.
You can see that the age-adjustment factor has been increasing in the past 150 years and is presently at the highest level in the entire record (because of the lack of young trees sampled.) The contribution of the "alpha" tree to the 20th century chronology will be remarkably high because its modern growth is high relative to its age.
FIGURE 1. Tornetrask. Top panel – Cumulative ring width by individual core; middle – RCS "chronology" (smoothed); bottom; the implied age adjustment in the RCS chronology. [Amended Mar. 29, 2005]
The diagram for the Tasmania site, also beloved of multiproxy studies, has some quite spectacular aspects to it – I’ll try to tidy it up and post it up in a week or two.