In the first post on Kaufman et al, I observed that, like other Team multiproxy studies, its HS-ness is contributed by only a few series. As shown below, a composite of 19 out of 23 Kaufman proxies does not yield an “unprecedented” late 20th century (tho it yields an elevated late 20th century.) A composite consisting only of ice cores shows nothing unusual about the 20th century. However, four proxies ( 1: Blue Lake (Alaska) varves, 4: Iceberg Lake (Alaska) varves, 9: Big Round Lake (Baffin Island) varves and 22: Briffa’s Yamal tree ring chronology) have a very pronounced HS and in the Kaufman CPS, these 4 series are the “active ingredients” in the Kaufman HS.
Figure 1. Left – composite of 19 Kaufman proxies; right – composite of 4 Kaufman proxies. (The three Finnish sediments are used in native orientation, rather than the Kaufman orientation, which is inverted from the original orientation e.g. the Tiljander series discussed in the previous post.)
Briffa’s Yamal series is almost as notorious at CA as Graybill’s bristlecone pines and the consistent Team selection of this series rather than the nearby Polar Urals series has been noted unfavorably on many occasions.
Rather than dealing further with the tired Yamal series one more time, today I want to discuss one of the new “ingredients” – Loso’s Iceberg Lake reconstruction, which, in Kaufman’s rendering, also has a notable HS shape – in this case, limited to the last 4 decades of the 20th century.
Loso’s original article was in the form of an actual temperature reconstruction. Here is the Loso reconstruction (decadally averaged) in the original units – left scale – and as re-scaled by Kaufman into SD Units. Note the impact of changing from deg C to SD Units. Variation in the original reconstruction was very small – the step change in the 1960s was a couple of tenths of a degree. But in Kaufman’s SD Units, this small step change becomes a step change of 4 sigma – one which, together with Yamal and a couple of others, ends up having an impact on the overall reconstruction. (Kaufman’s Yamal version closes the 20th century at an astonishing 7-sigmas. )
While Kaufman’s re-scaling obviously warrants attention, I’d prefer that readers not dwell on this step at this time, as there are some very interesting aspects to the Loso data that shed light on the properties of varve thicknesses as a temperature proxy. Here is the underlying Loso varve “chronology” (using this term as in tree ring networks), plotted from original data. A couple of points here. First, the varve chronology doesn’t look much like a plot of temperature data – it’s far too spiky; the distribution is clearly not a normal distribution and visually looks like it is a fat-tailed distribution (which proves true). Secondly, there seems to be a step change in 1958, with an actual discontinuity in the original data in 1957. One wonders whether there is some sort of inhomogeneity. Also worrying is what seems to be a sort of “divergence problem”: the trends since the 1960s seems to be down, even though temperatures have been going up, with the HS-ness of the series perhaps resulting from some sort of 1957 inhomogeneity. I looked at data from individual cores to assess this troubling visual appearance.
Given the visual appearance of a non-normal distribution, I did a qqnorm plot of all the varve width data (left panel) and, on the right, a similar plot for the logged varve widths. (Loso’s temperature reconstruction is log-transform of his varve width chronology.) As you can see, the original varve widths are remarkably fat-tailed; indeed, even the log-transformed varve widths are far from normal and remain fat-tailed. This creates major complications for simplistic efforts to average a few measurements in making a varve chronology or to “standardize” data as we shall see below. The combination of wildly non-normal fat tails and probable inhomogeneity makes this a very problematic raw material for construction of a temperature index, as I’ll further show below.
One advantage of mineral exploration experience is that one understands the importance of examining individual cores. Fortunately, Loso provided some raw information on this. The modern portion of the Loso reconstruction is calculated from only 1-3 cores (A,K,M), shown below over the period 1000-2000 in both linear and log scales. Core M has a discontinuity of nearly 400 years – I haven;t examined the cross-dating of this core, but I wonder how they established this discontinuity which seems troublingly long. You can see that Core A and Core K have very different contributions to HS-ness: Core K shows no modern HS-ness. The entire HS-ness of the Loso reconstruction, one of the two largest contributors to the Kaufman HS, comes entirely from Loso Core A, where there seems to be an inhomogeneity around 1957.
I noted above that it was not easy to make an average when confronted with wild distributions such as the one observed here. Loso attempted to mitigate the wild non-normality by the expedient of simply deleting some of the larger excursions in his calculation of the chronology average. (In 1957, all three values were deleted and that’s why there is no value for that year.) This is explained as follows:
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.
I examined the calculation of the “average” varve thickness from 1860 to 2000 and identified excluded varves (by figuring out which varves, if any, were excluded in order to yield the reported average as opposed to the average using all the varves.) In the figure below, I’ve plotted varve widths for the 3 cores from 1860-2000 in both linear and log scales, marking the excluded varves in red. Loso says that “sediment structure” rather than thickness was the basis for exclusion, but one can’t help but wonder how solid this classification really is. Regardless, the high values in Core A clearly result from some sort of inhomogeneity in the Core A data starting around 1957-8 – and seemingly settling down in more recent values. If this data was revisited in a few years, I wonder whether it would have reverted back to a more average value.
The construction of a sediment “chronology” has much in common with a tree ring chronology. Indeed, it looks quite a bit harder to me that for tree rings, since there seems to be considerably more inhomogeneity between cores and local sedimentation conditions having a substantial impact. The number of cores used in the varve chronology (1 to 3) are FAR less than minimums required for construction of a tree ring chronology under far less trying circumstances. To my knowledge, this is not confronted by the varvochronologists.
After excluding a few series, Loso constructed a chronology by averaging the remaining values. This is done at the native value stage (pre-logging.) Since non-excluded outliers from the extreme fat-tailed distribution are not “cut” (a precaution common in mining exploration to mitigate “nugget” effect), even after averaging with 1-2 other values, such outliers can still have a dramatic impact on a chronology. The Loso chronology is still fat-tailed. Loso’s temperature reconstruction is a re-scaling of the log of the varve chronology.
This partly mitigates the non-normality, but, at first glance, this seems both a step too late and, given the non-normality of the logged varve widths, not necessarily an adequate precaution. I haven’t pondered all the issues of how to deal with such refractory raw ingredients, but it would be worth examining the effect of a non-parametric standardization of the actual distribution to a normal distribution (with a relative low ceiling – maybe 2 sigma – on the contribution of any one varve.)
This would still not mitigate the apparent inhomogeneity of Core A. Here one would welcome a far more expansive exposition by Loso than the one actually provided. One would also welcome the adoption by varvochronologists of some of the precautions developed by dendros over the years – which Loso’s chronology doesn’t meet.
As matters stand, the second ingredient to the Kaufman Hockey Stick (after the Yamal substitution) is the Loso Iceberg Lake varvochronology – where, unfortunately, there is evidence that the HS-ness of this series is a result of an inhomogeneity in Core A (one not shared by Core K).