4. RECONSTRUCTIONS AND EXPLORATION OF PRINCIPAL COMPONENT METHODOLOGIES

Mann et al. (2005) identify two major methods of climate reconstruction, which they describe respectively as climate field reconstruction (CFR) methods and what they describe as simple climate-plus-scale (CPS) methods. CFR methods are claimed to "assimilate proxy records into a reconstruction of underlying patterns of past climate change" and among papers identified as using these methods are MBH 98, Evans et al. (2002), Luterbacher et al. (2002), Rutherford et al. (2005) and Zhang et al. (2004). In contrast CPS methods are said to "composite a number of proxy series and scales the resulting composite against a target (e.g. Northern Hemisphere temperature) instrumental series." Examples of papers using the CPS methods include Jones et al. (1998), Crowley and Lowery (2000), Briffa et al. (2001), Esper et al. (2002), Mann and Jones (2003) and Crowley et al. (2003). Although the language describing both of these methods seems somewhat obscure, it would appear that CFR methods are just principal component methods as describe earlier and in the appendix and that CPS methods are just simple averaging of climate proxies and then scaling them to actual temperature records.

The key issue in dispute is the CFR methodology as used in MBH98 and MBH99. The description of the work in MBH98 is both somewhat obscure and as others have noted incomplete. The essence of the discussion is as follows. Principal component methods are normally structured so that each of the data time series (proxy data series) are centered on their respective means and appropriately scaled. The first principal component attempts to discover the composite series that explains the maximum amount of variance. The second principal component is another composite series that is uncorrelated with the first and that seeks to explain as much of the remaining variance as possible. The third, fourth and so on follow in a similar way. In MBH98/99 the authors make a simple seemingly innocuous and somewhat obscure calibration assumption. Because the instrumental temperature records are only available for a limited window, they use instrumental temperature data from 1902-1995 to calibrate the proxy data set. This would seem reasonable except for the fact that temperatures were rising during this period. So that centering on this period has the effect of making the mean value for any proxy series exhibiting the same increasing trend to be decentered low. Because the proxy series exhibiting the rising trend are decentered, their calculated variance will be larger than their normal variance when calculated based on centered data, and hence they will tend to be selected preferentially as the first principal component. (In fact the effect of this can clearly be seen RPC no. 1 in Figure 5 in MBH98.). Thus, in effect, any proxy series that exhibits a rising trend in the calibration period will be preferentially added to the first principal component.

The centering of the proxy series is a critical factor in using principal components methodology properly. It is not clear that Dr. Mann and his associates even realized that

'CFR methods are essentially the methodology that was used in MBH98 and MBH99. However, the methods in MBH98 and MBH99 were not formally called CFR methods, the climate field reconstruction phrase being coined only later.

their methodology was faulty at the time of writing the MBH paper. The net effect of the decentering is to preferentially choose the so-called hockey stick shapes. While this error would have been less critical had the paper been overlooked like many academic papers are, the fact that their paper fit some policy agendas has greatly enhanced their paper's visibility. Specifically, global warming and its potentially negative consequences have been central concerns of both governments and individuals. The 'hockey stick' reconstruction of temperature graphic dramatically illustrated the global warming issue and was adopted by the IPCC and many governments as the poster graphic. The graphics' prominence together with the fact that it is based on incorrect use of PCA puts Dr. Mann and his co-authors in a difficult face-saving position. We have been to Michael Mann's University of Virginia website and downloaded the materials there. Unfortunately, we did not find adequate material to reproduce the MBH98 materials.

We have been able to reproduce the results of McIntyre and McKitrick (2005b). While at first the McIntyre code was specific to the file structure of his computer, with his assistance we were able to run the code on our own machines and reproduce and extend some of his results. In Figure 4.1, the top panel displays PC1 simulated using the MBH98 methodology from stationary trendless red noise. The bottom panel displays the MBH98 Northern Hemisphere temperature index reconstruction.

Figure 4.1: Reproduced version of Figure 1 in McIntyre and McKitrick (2005b). Top panel is PC1 simulated using MBH 98 methodology from stationary trendless red noise. Bottom panel is the MBH98 Northern Hemisphere temperature index

reconstruction.

Discussion: The similarity in shapes is obvious. As mentioned earlier, red noise exhibits a correlation structure, which, although it is a stationary process, to will depart from the zero mean for minor sojourns. However, the top panel clearly exhibits the hockey stick behavior induced by the MBH98 methodology.

Figure 4.2: This is our recomputation of the Figure 2 in McIntyre and McKitrick (2005b). The lower panel is what MM05b call the 'Hockey Stick Index' for PC1s. For 10,000 simulated PC1s, the histogram shows the distribution of the difference between the 1902-1980 mean and the 1400-1980 mean divided by the 1400-1980 standard deviation using the MBH98 data transformation. The top histogram is based on the centered PCA computation.

Discussion: Figure 4.2 is our recomputation of the Figure 2 in McIntyre and McKitrick (2005b). The lower panel is what MM05b call the 'Hockey Stick Index' for PC1s. For 10,000 simulated PC1s, the histogram shows the distribution of the difference between the 1902-1980 mean and the 1400-1980 mean divided by the 1400-1980 standard deviation using the MBH98 data transformation. The top histogram is based on the centered PCA computation. Although our result is not identical to Figure 2 in MM05b, it reproduces the essential features of MM05b. In particular, the MBH98 methodology (and follow-on studies that use the MBH98 methodology) show a marked preference for 'hockey stick" shapes. The negative values between −2 and -1 indicate the 1902-1980 mean is lower hence the blade of the hockey stick is turned down, while the positive values between 1 and 2 in the bottom panel indicate the hockey stick blade is turned up.

Figure 4.3: This is a recomputation of Figure 3 from MM05b. The North American Tree Network PC1 is a proxy featured prominently in MBH98. It is a PCA reconstruction of a series of tree ring proxies using the MBH98 methodology. The upper panel is the PCA reconstruction using the MBH98 data transformation. The lower panel is the reconstruction using the centered PCA methodology.

Discussion: In addition to the hockey stick shape of the upper panel it is worth noting that the lower panel exhibits considerably more variability. As mentioned in earlier discussions, PCA seeks to identify the largest contributor to the variance. It is not inherently a smoothing mechanism. The MBH98 offset of the mean value creates an 'artificially large deviation' from the desired mean value of zero.