The majority of Kaufman’s varvochronology proxies are various functions of varve thickness – which, if anything, seem more problematic than sediment BSi.
While Kaufman’s offering memorandum to NSF promised consistency, the handling of varve thicknesses in the various selections seems to be anything but. Kaufman et al 2009 gives no hint of the varied functional forms used to create varve thickness proxies. While none is quite exotic as the Hallet Lake cube root of the product of BSi and flux_all, there is an intriguing variety of forms.
1- the Blue Lake temperature reconstruction is a linear function of logged varve thickness (unadjusted for density). “Turbidites” are a problem in these records and they state (Bird et al 2009):
Twenty-one anomalously thick layers, ranging from 1.1 to 18.14 cm thick were also identified in the cores (Fig. 4). Based on sedimentological characteristics (i.e. presence of graded bedding) the layers were identified as turbidites and excluded from the thickness record and varve chronology.
There isn’t any mention of tephra, though tephra are an important feature of some lake sediments. Cross-dating is via Cs137, Pb210 and C14 (per NSF abstract.)
4. Loso’s Iceberg Lake varves are linear in varve thickness (no logging), also unadjusted for density. They removed 82 varve measurements; they combined the remaining varve measurements. (As noted in the Loso post, there is considerable evidence of a 1957 inhomogeneity not adjusted for.) Loso:
Scattered among the other well-dated sections are isolated strata that record episodic density flows (turbidites), resuspension of lacustrine sediment by seismic shaking and/or shoreline-lowering events, and dumping of ice-rafted debris. The case for excluding such deposits from climatologically-oriented varve records has been made elsewhere (Hardy et al., 1996), and we accordingly removed measurements of 82 individual laminae from these other sections. Those removed (mostly turbidites) include many of the thickest laminae, but sediment structure (not thickness) was in all cases the defining criterion for exclusion from the master chronology.
Again, no mention of tephra. No mention of Cs137, Pb210 or C14 cross-dating.
Note: Cascade Lake, Alaska, another Kaufman student site, was not used. Kathan stated:
The cores are composed of rhythmically laminated mud, with an average lamination thickness of 0.4 cm; these laminations do not represent annual sedimentation (e.g. varves).
Kathan observed the presence of tephra and used a couple of known tephra for her age-depth relationship.
6. Lake C2, Ellesmere Island. This is an old 1996 data set (not collected in the ARCUS2K program) for which there is no archive (Bradley of MBH was a co-author; Bradley assured the House Energy and Commerce Committee that he had archived all his data, but I guess that he forgot about Lake C2.) [Update: sept 23 3.20 pm: Scott Lamoureux of Queen's University near Toronto has just emailed me the C2 annual data, noting that it had originally been archived with NCDC and been inadvertently removed at some point, a situation he is now redressing. I've posted the data up at CA/data/kaufman/C2_annual.dat.] They made a varvochronology explicitly borrowing from tree ring methods by first “standardizing” the data against their “expected” values, which, in this case, appear to be by dividing the varve width by the linear trend. Bradley observes that one trend goes up and one goes down – an inconsistency that didn’t seem to bother anyone at the time, nor seemingly Kaufman in its present iteration. (Without original data, it is of course impossible to determine exactly what they did.) No mention of Cs137, Pb210 or C14 cross-dating. (Lamoureux and Bradley 1996; Hardy et al 1996)
A major turbidite was mentioned in 1957 (the same year as a major turbidite in Iceberg Lake above, presumably a coincidence.) Lamoureux and Bradley 1996 mention both a filtered and unfiltered version – in the filtered version, identified turbidites are replaced by the series mean. This data set is pretty much inaccessible to any any analysis.
8 – Lower Murray Lake, Ellesmere. This is a new record from Bradley’s program. The varve chronology is archived, but not the varve measurements. The caption to Besonen et al 2008 Figure 7 states: “13 turbidites were replaced with the period average thickness” in one version of the top panel. It looks like the version after adjustment is what is archived. This article also posits that a “clearly erosive” 1990 turbidite event cleanly erased the previous 20 years from the lake:
the prominent turbidite event recorded in the 1990 varve was clearly erosive. Thus, assuming the 137Cs peak in sample 3 represents ~1963, if we take the centre of the 0.5 cm zone as 1963, it suggests that the varves from ~1970 to 1989 inclusive were eroded by the 1990 turbidite.
As far as I can tell, no other erosive turbidite events are accounted for in any other Kaufman series – surprising that one only occurs at this site. In this case, density values are calculated yielding a mass_flux estimate. Kaufman uses the log(mass_flux) in his composite.
C14 cross-dating carried on 2 samples (due to unavailability.) Dates were older/much older than the presumed varve date. Limited Cs137 and Pb210 dating was carried out due to “cost constraints” (notwithstanding the commitment to NSF to do this work):
Owing to cost constraints, only the top 2.5cm (five samples) of sediment were analysed.
The Cs137 peak was unexpectedly high in the sample leading to the hypothesis of an erosive 1990 turbidite (as opposed to core loss at the top, the possibility of which seems at least possible but which was not discussed – the team being content with the erosive turbidite theory.)
9 – Big Round Lake, Baffin Island. This varve thickness record goes back only to 980AD, prior to which the sediment lacked a varve structure. Sand thicknesses (if present) are reported for each varve layer and the residual is used by Kaufman. A linear function is used.Thomas and Briner 2009 url Cross-dating here was done by 239+240Pu; no 137Cs or 14C measurements are reported (and none were carried out for some reason, a point confirmed by the authors.)
10 – Donard Lake, Baffin Island. This is the last North American varve thickness series in Kaufman 2009. This is an older series (2001) predating the ARCUS2K program. Moore et al 2001 does not discuss the handling of turbidites. No radiogenic cross-dating is reported.
The need for some sort of handling of non-normality is shown by the following diagram showing a histogram of the Loso varves (truncated at 60 mm for visibility here, though there are a number of thicker varves) together with the best fit under several different distributions. As you can see, the distribution is far from normal. The log transformation, that is semi-popular among varvochronologists, doesn’t really do the trick either. An inverse gamma distribution fits better than log-normal (I looked at this because the fat-tailed Levy distribution is a special case of an inverse gamma distribution.)
Taking a simple average from this sorts of weird distributions (as is done in most of these recons) doesn’t seem like a very diligent way of handling the non-normality. While the functional form of the Hallet Lake BSi flux series is not very attractive, one can sense the underlying motive for trying to do something to coerce the data into a comparison with temperature.
I presume that varve distributions for the other sites (with far more incomplete archives than Loso) have similarly problematic distributions and this is one of the reasons for the quirky handling. All in all, we see at least 4 distinct methods (before turbidite adjustment): linear; log of varve thickness; log of varve mass flux; detrended linear. I suspect that there are further differentiae beneath the surface.
As to the question – to log or not to log – my guess (as of today) is that, if these series are to be used, it would make more sense to do a sort of non-parametric mapping of the distribution (handling nugget effects severely) onto a normal distribution – prior to doing any correlations or reconstructions. Of course, there’s another possibility – these things aren’t temperature proxies and shouldn’t be used in major reconstructions – a possibility that we shall examine more as we get a better understanding of varvochronology.