One excellent feature of the Alaskan varvochronologists is that (unlike, say, Bradley and his coterie) some of them show and archive their work. The Kaufman student MSc theses are good at this. So too is Michael Loso’s work on Iceberg Lake. Thus while one can raise an eyebrow at (and criticize) their statistical peregrinations, at least they provide enough material that one can at least analyse the data (Bradley’s 1996 C2 data remaining under security.) In an earlier post, I discussed Loso (2006). Today, I’ve got a few comments on Loso (2009), which I did not discuss in my earlier post. Loso (J Paleolim 2009) revisits Iceberg Lake varves with some interesting comments (without however satisfactorily resolving the fundamental inhomogeneity problems.) Like many paleoclimate articles, though the author is not a statistician, the topic is primarily statistical. And like most paleoclimate articles (also mainly statistical), there is no evidence that any reviewers were statisticians.
One of the fundamental inhomogeneities that plagued Loso (2006) was the changes in lake level, size and shape. Loso (2009) here revisited that problem, developing the scatter plot between the distance of the core from the nearest inlet (using geological information to derive this distance) and the varve thickness.
Loso Original Caption: Fig. 3 Relation between the distance separating the inlet stream and sampling site and average varve thickness. Each point (n = 42) represents the average varve thickness (mm) for a contiguous group of varves at one sampling site. For each point, distance from sampling site to nearest inlet (m) is based upon the position of the shoreline at the time the varves were deposited, taking into account the known history of shoreline variability. Contiguous period represented by each point ranges from 9 to 174 years (mean = 78.7 year; SD = 66.1 year). Solid line is a power-law curve fitted to show trend (y = 622.09 * x-0.66662), r2 = 0.84
Loso discusses this figure as follows:
Because of Iceberg Lake’s history of episodic changes in lake level (Loso et al. 2004), sediment accumulation rate at any given sampling site will vary not only as a function of bulk sediment input (controlled in part by climatic factors of interest), but also as an inverse function of lake size. This is because, when the lake shrinks, sediment inputs are deposited over a smaller surface area, and shoreline regression brings stream inlets closer to sampling sites in the lake bottom. To demonstrate this relationship, I analyzed the relation between distance to nearest stream inlet and average varve thickness during the period of well-dated shoreline occupations (1825–1998 AD, Fig. 3). To do this, all well-dated varve measurements (in this case including those excluded, on the basis of textural anomalies or other criteria, from the master chronology) were separated into contiguous groups so that each group represents deposition at a single sampling site during a single shoreline occupation. The average thickness of all measurements in a group are plotted against the distance from that sampling site to the nearest glacial stream inlet at the time of that particular shoreline occupation. The results (Fig. 3) show clearly that varve thickness, and hence sediment accumulation rate, increases in a nonlinear fashion as proximity to inlets shrinks.
[UPDATE Sep 23 11. 40 pm: No wonder this observation by Loso seemed so sensible. It was first hypothesized at Climate Audit two years ago!
The connection between inlet distance and varve thickness at Iceberg Lake was suggested by Willis Eschenbach at Climate Audit two years ago here:
My own feeling is that the dropping of the lake level in 1957 is the key to the greatly elevated values in recent times. It coincides exactly with the huge jump in the varve thickness in 1957. I think there are two reasons for this. One is that the distance from the inflow to the core sites is greatly reduced, which would make a permanent increase in the varve thickness.
This effect is obviously a MUCH stronger effect than the slight effect (if it even exists) between varve thickness and temperature. Indeed, the previous attempt to establish a relationship between varve thickness and temperature is obviously compromised (as discussed in our earlier post on this topic) by inhomogeneities in the lake. The measurement of the distance to the nearest inlet is probably not a measurement that would be available in most varvochronologies, but Loso doesn’t mind doing geology and seems to have done as reasonable job of estimating this value as one could expect under the circumstances.
So far so good (though it raises obvious concerns for the overall varvochronology project.) But having raised this important confounding factor, Loso is then faced with a non-trivial statistical problem of disentangling two factors in order to reconstruct temperature. And here Loso loses his way.
Loso’s remedy for the situation is merely to log-transform all the measurements:
The net effect of these shoreline changes is a heightened sensitivity to summer temperatures during warm periods that, when combined with the known non-linear relationships among stream discharge, suspended sediment concentration, and varve thickness (Gilbert 1975; Meade et al. 1990), contributes to the strong positive skew of the raw varve thickness measurements (Fig. 4a). … To compensate for this heightened sensitivity, which violates the goal of stationarity—a constant relationship over time between climate variable and proxy response—in proxy reconstruction (National Research Council 2006), I log-transform the raw measurements from the master varve chronology.
Yes, non-normality is a major problem with this data set. (Loso notes that a log-transformation still doesn’t get to normality, a point observed in my graphic yesterday showing the best fit of various distributions to Loso’s varve widths.) Loso’s adjustment also comes AFTER the taking of an average in the annual chronology – I’d be inclined to do so BEFORE making the chronology.
But that’s not the real issue – the real issue is that log-transformation does NOTHING to disentangle the fundamental non-stationarity identified by Loso. In order to deal with the confounding factors, Loso would have to use some sort of mixed effects model. And the trouble with that is that it would only work for the limited period in which Loso can reconstruct the nearest inlet distance.
It’s too bad that the senior paleoclimate community (Bradley etc.) are so enormously stubborn about statistical criticism. Instead of conceding and responding to Wegman’s criticism, it’s almost as though they’ve redoubled efforts to keep statistical outsiders away from the field. And thus we see relatively elementary defects repeated time after time, while industry leaders like Kaufman refuse to discuss such matters, in effect putting their fingers in their ears and saying “Nyah, nyah, I can’t hear you”. It’s bad enough for they themselves, but the worse side-effect is that it becomes very perilous for younger scientists to participate in such discussions.
Loso 2009 online here. Willis Eschenbach is acknowledged (h/t bender(: