The “Index of Leading Environmental Indicators 2005” of the Pacific Research Institute says the following:

“The “hockey-stick” graph, believed to be one of the leading indicators of global warming, is now being called “rubbish.” Scientists have shown that the graph’s underlying equation would generate the same result for any series of random numbers.

In another location, a Pacific Research writer says:

Scientists agree that global temperatures have risen about 0.6 degree Celsius over the past century. But the famous "hockey stick" graph claiming to prove that the past 25 years have been the warmest in the past 1,000 years cannot be taken seriously. Experts have shown that the computer algorithm used to generate the graph would produce similar results from any series of random numbers.

The “rubbish” claim is based on a quote from von Storch, although we obviously do not disagree with von Storch on this matter. Making the reasonable assumption that the last statement of each excerpt refers to our work, neither version is exactly what we said.

First, there is a difference between “similar results” as in the 2^nd excerpt and “the same result” in the 1^st excerpt. We obviously did not claim that you got the “same” result. Secondly, we did not show that the result held for “any series of random numbers”, but for red noise. Thirdly, we showed that the result held “nearly always” (over 99% of the time with red noise with the persistence properties of the North American tree ring network; less with AR1 red noise), rather than always. Ross has sent a note to Pacific Research Institute clarifying this.

The simulations reported in the GRL article pertained only to the principal components calculations for the North American tree ring. It showed that the method was extremely flawed through being biased towards selection of hockeysticks. The main point of the article was to demonstrate that like operations on red noise could yield spuriously high RE statistics and therefore that an RE statistic, without confirmation from other statistics such as R2, could not be relied upon to demonstrate recovery of a signal. Hence the term “spurious significance” in the title. This aspect of our presentation has gone essentially uncommented upon Mann et al. They have argued that we seek to “promote” the R2 statistic in preference to the RE statistic. We are taking no such position. We do hold that, if an actual temperature signal is being in the MBH98 15^th century reconstruction (which we doubt), then it will yield a significant R2 statistic as well as an RE statistic. Mann et al. withheld their (insignificant) R2 statistic in MBH98 and, in response to specific requests, have refused to produce this information or the digital version of the 15^th century step from which it could be calculated. Our own estimates is that it is approximately 0.0 under their methods and data.

For the purposes of the arguments presented in the GRL article, where we were merely seeking to demonstrate the existence of spurious RE statistics under red noise operations, we limited our comments to principal components methodology. In our EE article, we showed the non-robustness of the MBH98 reconstruction to the presence/absence of the hockey stick shaped bristlecone PC (under whatever guise). The EE article was an extension of our GRL findings to the full reconstruction. In working with the data, it is very clear to me that one (and especially two) hockey stick shaped series in a set of 22 proxies was sufficient to imprint a hockey stick shaped series on the 15^th century reconstruction under MBH98 methods.

It’s been recently argued in some posts here (John Hunter) that the impact of a hockey stick shaped PC1 would be negligible in a larger network. Hunter wondered what the result of reconstruction simulations would be. (Actually, he didn’t “wonder”; he demanded.)

The simulation of the MBH regression phase is complicated by some very distinct mysteries in the 15^th century component of Mann’s regression module. As I’ve posted here, the closeness of my emulation to the Mann reconstruction deteriorates significantly in the 15^th century. The early 15^th century component of the Mann reconstruction is essentially only a weighted average of the NOAMER PC1 and Gaspé series (this can be shown by examination of the archived RPC1 – see an earlier Replication posting on this). My emulation of Mann’s methods does not concentrate weights on these two series as heavily as the actual reconstruction. So there is still some aspect to the algorithm that enables increased weighting on hockey stick series that I’ve been unable to determine so far (and I’m really interested in seeing code to see how.)

I did small simulations (100) in which I mixed a hockey sticks from the PC1 simulations with 21 white noise series (making up 22 series as in the controversial 15^th century MBH98 step). The hockey stick index of the reconstructions was somewhat reduced from the hockey stick index of the PC1s (median – 63%), paralleling MBH where the hockey stick index of the final reconstruction is 67% of the NOAMER PC1. The 99% RE level is 0.50.

So back to Hunter’s question:

“how often do you think the reconstruction would also be hockey-stick shaped?". My tentative answer would be “hardly ever", but we won’t know for certain until Steve actually does the experiment.

In fact, the results are diametrically opposed to Hunter’s surmise. Whenever the PC1 had a hockey stick shape, the reconstruction did as well. So the reconstruction, like the PC1s, "nearly always" has a hockey stick shape.