I discussed Fisher’s Greenland dO!8 proxy yesterday and thought that it would be interesting to discuss its particular function in hockey stick manufacture in Jones et al 1998. Each hockey stick is, after all, made by a master craftsman. The Greenland dO18 is one of only 10 series in Jones et al 1998. Let’s see if we can figure out exactly what its particular function in making a good hockey stick and why it was chosen.
One important technique in making hockey sticks is the splice. This can occur in many different forms. Most people have been distracted by petty issues like splicing instrumental and proxy records and failed to appreciate the artistic splicing that occurs between short and long series, which are integral to one style of hockey stick manufacture as practiced by one group of artisans.
To illustrate this, I’ve selected the Greenland dO18 series (available in the MWP) and 2 shorter series from Jones et al 1998. This is in about the right proportion to the 10 series used in the original, where there are only 3 series are available at the start of the 11th century and only 4 prior to 1400. The other 2 series (Kameda melt, also from Greenland and the Jacoby NH reconstruction) obviously have a very different appearance from the Greenland dO18. It takes a discerning eye to "understand" that all 3 series are a temperature "signal" plus white noise, despite their differing appearance. (If you are not a member of the Hockey Team, you will not understand this. I am not one of the elect who can recognize the common signal in all 3 series.)
But you can see one big difference: the long MWP has no centennial variation and just looks like noise on a centennial scale, while the two short series have a lot of centennial variation and much more autocorrelation.
Following Jones, all series are standardized on the 1901-1950 intervals. Trenberth 1984 pointed out within climate literature the well-known statistical point that means and standard deviations calculated on short segments of autocorrelated series may not be very accurate and the longest possible record should be used. However, this is contrary to usual Hockey Team short-segment standardization and was not done here either. You can see that, when one series has little centennial fluctuation and the others do, their relative appearance will differ quite remarkably depending on which 50-year period was used for standardization.
Figure 1. Three of 10 Jones et al 1998 series. Red – smoothed with 21 -year gaussian filter.
I’ve been able to replicate the general appearance of Jones’ results using a full data set, but not exactly. In the figure below, I’ve applied the Jones’ method as best as I can to a data set consisting of only the above 3 series, hoping that this can isolate important aspects of form and function. I’ve done this in two steps. The middle panel shows the simple average of the 3 series, which already captures some of the main features of the Jones hockey stick, but with an extremely noisy MWP.
The bottom panel shows the effect of a "variance stabilization" method (copyright Hockey Team) on this 3-series network as presented by noted statisticians Briffa and Osborn in the noted statistical journal Dendrochronologia. This seminal article has been applied by other hockey players, but has been sadly neglected by applied statisticians and workers in other disciplines.
If you have a network of white noise, the variance of the mean is 1/sqrt(N). So in the early portion of this network with only 1 series (or 3 of 10 in the full network), the variance in the MWP blows up. Briffa and Osborn calculate the average interseries correlation- which is about 0.15 or so at best – and use this to calculate the "effective" number of series relative to the "effective" number of series when there is a full network. In this small subset, the "effective" number of series in the last portion is a shade under 3 (interseries correlation of 0.17) and is only 1 "effective" series in the first portion. So following this procedure, the variance of the portion of the network with only 1 series is reduced to reflect the "effective" number of series. I’ve figured out the main steps, but haven’t got this step exactly. I’ve asked Jones for code and exact data so that I could exactly replicate his results, but guess what – he refused.
What is rather pretty about showing this with only 3 series is how it lays bare rather nicely a couple of the key components of the Jones hockey stick and how it achieves a rather good emulation all by themselves. You can directly see how the Greenland dO18 series carries into the MWP portion of the shaft – which is noisy and featureless; while the Jacoby NH series with its extreme lack of high-frequency character imprints the second half.
Figure 2. Top – archived version. Middle – 3 series version pre-stabilization. Bottom – 3-series version, post-stabilization.
I’ve posted on the other two Jones et al 11th century proxies – Briffa’ s Polar Urals and Tornetrask series -at length here – look at the Jones et al 1998 Category on the right. There’s nothing presented here that doesn’t apply to them. If anything, they have their only little tweaks to "improve" the hockey stick – little "adjustments" showing the handwork of master artisans. A connoisseur should be able to identify a Jones-type series by its craftsmanship, which differs from Mannian craftsmanship: a long featureless MWP; centennial variation initiating in the LIA; modern values squeaking out a bit higher than the MWP.
In fact, we get the key elements from only two series – the Greenland series and the Jacoby series. as shown below:
Figure 2. Top – archived version. Middle – 2 series version pre-stabilization. Bottom – 2-series version, post-stabilization.
Of course, just showing the proxies by themselves leaves the hockey stick unfinished. Indeed, if one looks at the proxy portion of the Jones HS by itself, it’s possible that someone might say: so what. So the master craftsman then puts the instrumental record in a bold flourish and voila, ready to go out on the rink.