Outline
Principal components analysis methodology edit
McIntyre and McKitrick's renewed criticism said there was a technical statistical error in MBH98 [61][97] relating to the principal component method used,[101] Peer reviewed studies by others found the issues raised by McIntyre and McKitrick were minor and did not affect the main conclusions of MBH.[61]
To overcome the problem that closely spaced networks with numerous tree-ring proxies in some areas could overwhelm widespread sparse proxy temperature records, the original MBH98 and MBH99 papers represented each dense network by using principal component analysis (PCA) to find the leading patterns of variation (PC1, PC2, PC3 etc.) ranked by the percentage of variation they explained. To establish how many significant principal components should be kept so that the patterns put together characterized the original dataset, they used an objective selection rule procedure which involved creating randomised surrogate datasets with the same characteristics and treating them with exactly the same conventions as the original data[131–136]. The MBH98 study put together temperature records of various lengths, including instrumental records from 1902 to 1980, and their convention centered data over this shared modern period.[huybers] The selection rule found two significant patterns for the North American tree ring network (NOAMER); PC1 emphasized high altitude tree ring data from the Western U.S. showing a cold interval followed by 20th century warming, PC2 emphasised lower elevation tree ring series showing less of a 20th century trend. The more traditional convention centering data over the whole period of the study would change the order of PCs and require more PCs to produce a valid result.[136–137] Studies found that the MBH results matched those from methods which did not include a PCA step.[RMO][WA][AW] Mann's subsequent reconstructions used the RegEM Climate Field Reconstruction technique incorporating all available individual proxy records instead of replacing groups of records with principal components;[306–307] the results were nearly identical. Rutherford et al.[1]
With the claim that centering over the modern period was "an unusual data transformation which strongly affects the resulting PCs", McIntyre and McKitrick centered NOAMER data over the whole 1400–1980 period and this changed the order of principal components so that the warming pattern of high altitude tree ring data was demoted from PC1 to PC4.[MM] Instead of recalculating the objective selection rule which increased the number of significant PCs from two to five, they only kept PC1 and PC2. This removed the significant 20th century warming pattern of PC4, discarding data that produced the "hockey stick" shape.[137, 306–307][WA] They said that "In the controversial 15th century period, the MBH98 method effectively selects only one species (bristlecone pine) into the critical North American PC1",[MM] but subsequent studies?? showed that the "hockey stick" shape remained with the correct selection rule, even when bristlecone pine proxies were removed.[WA]
The MMO5 paper said that the MBH98 (modern centering) "method, when tested on persistent red noise, nearly always produces a hockey stick shaped first principal component (PC1)", by picking out "series that randomly 'trend' up or down during the ending sub-segment of the series".[MM] Red noise for surrogate datasets should have the characteristics of natural variation, but the statistical method used by McIntyre and McKitrick produced noise based on 20th century warming trends which showed inflated long term swings, and overstated the tendency of the MBH98 method to produce hockey stick shapes.[139–140, 307] Tests by von Storch and Zorita using pseudoproxies and noise varying from red noise to white noise found that the MBH98 methodology caused only very small differences which were within the uncertainty range and had no significance for the final reconstruction.[2]
McIntyre and McKitrick also argued that "the MBH98 15th century reconstruction lacks statistical significance" on the basis of surrogate datasets using their red noise method. Other studies using appropriate red noise found that MBH98 passed the threshold for statistical skill, but the MMO5 reconstructions failed verification tests and their method had a data handling error.[huybers, WA] MM05 said that some of their red noise simulations "bore a quite remarkable similarity to the actual MBH98 temperature reconstruction", their code selected the 100 simulations with the highest "hockey stick index" from the 10,000 simulations they had carried out, and their illustrations were taken from this pre-selected 1%.