Climate Audit

4 Comments have been submitted to GRL to date on McIntyre and McKitrick [2005]. We reported previously that the Wahl and Ammann comment was rejected (although this has not been acknowledged at the UCAR website.) A second comment has now been rejected. I think that there is a good chance that the other two Comments will be published together with our Replies. In our opinion, none of the criticisms have any bearing on our findings; in the two cases under consideration, we think that interesting issues were raised and that the comment and response will illuminate matters.

When Mann and others talk of supposed refutations of our findings as being in review, readers should bear in mind that the supposed refutations may not actually be refutations and may never see the light of day. In this case, the rejection of the Comment means that readers would not get to see our Reply. I think that our Reply may be of interest to readers so I’ve posted it up below.

Abstract: X [2005] appears to have misunderstood the points in McIntyre and McKitrick [2005a] (herein MM05-GRL) and his note does not overturn any of our conclusions. We showed that the principal component (PC) methodology of Mann et al. [1998] (MBH98) was severely biased, that it overweights problematic bristlecone pine series thereby incorrectly implying these are the dominant pattern in the NOAMER network, and that the MBH98 reconstruction lacked cross-validation skill in the controversial AD1400 step. X bypasses all these issues and instead tests the PC method on the irrelevant exercise of calculating an average tree ring chronology: a step that plays no role in the MBH98 method or in our critique thereof. Furthermore he fails to distinguish between identifying a distinctive pattern in a data set and establishing that a series has a significant relationship to climate.

1. Assessing the Impact of the MBH98 PC Method
X compares two PC methods, the MBH98 short segment standardization, reported in MM05(GRL), and a conventional centered calculation, but the comparison is not in the MBH98 context, which he made no attempt to emulate. X considered matrices re-combined from truncated PC decompositions under the following circumstances: a) both PC methods — MBH98 short-segment and conventional centered; b) two different truncations — 1 PC and 2 PCs. In each case, X calculated the vector of annual averages for each re-combination. He also calculated the vector of annual averages for the data set without PC decomposition and recombination. Under both PC methods, X reported that (1) the difference in annual averages between using 2 PCs and 1 PC was “quite significant”; (2) the contribution after the 2nd PC to the re-combined annual average was “negligible”; (3) if 2 PCs are used, the difference between the MBH98 short-centered method and a conventional method in annual average was “negligible”. X then concluded that our assertions “that the MBH results are fatally flawed by short-centering are groundless.”

With respect, X has proved nothing of the sort. At most, he has shown the biased PC method does not necessarily affect an averaging calculation that plays no role in the matters under dispute. He ignores the question of the impact of the biased PC method on actual MBH98 temperature index calculations and does not even mention our own detailed treatment of this matter in McIntyre and McKitrick [2005b], (herein MM05 (EE)). We did not take up the lengthy topic of how the PC methods affect actual calculations of the NH temperature index in MM05 (GRL), but specifically referred to MM05(EE), where we surveyed various permutations and combinations, sometimes yielding hockey stick shapes and sometimes not. We identified the critical factor in the non-robustness as being due to the impact of bristlecone pines under the various methods. Contrary to X’s implication, we did not carry out a NH temperature index calculation using only 1 PC from the North American network either in MM05 (GRL) or MM05 (EE). In our actual calculations, the fewest that we ever used for this network was 2 PCs, which, ironically, is the number advocated by X, notwithstanding the fact that we disagree with his justification for this number.

Irrespective of X’s assertion that the column means are relatively unaffected under biased PC methods, it is obviously not the case that the “same results” are obtained in all relevant situations, as X claimed. Notably, the PC1s are very different. Using the MBH98 method, the PC1 has a pronounced hockey stick shape and its weights are loaded on a small subset of bristlecone pines. The PC1 using a conventional centered algorithm does not have a hockey stick shape and the bristlecones are demoted to the PC4 and are not the dominant variance. While X also notes that a PC1 by definition summarizes the “major share” of variance, he then fails to acknowledge that it is materially different under the two methods.

2. Necessary versus Sufficient Conditions for Significance in PC Calculations
X appears to equate a tree ring series having a distinct pattern in a PC decomposition with it being a valid temperature proxy. He partitions the North American data set into two groups, the bristlecone pines discussed in Graybill and Idso [1993] and all the others. The Graybill-Idso series indeed have a substantially different growth pattern than the rest of the North American tree ring data set, but Graybill and Idso themselves (and others) deny that this pattern is temperature-driven. Indeed, that is one of the principal grounds of our critique of MBH98″¢’‚¬?that data widely regarded as a nonclimate proxy receive the dominant weighting in the final results. We elaborated this point in MM05(EE), and pointed our GRL readers to that discussion (see para. 13). Merely because a shape term is “different” is not sufficient grounds to conclude that it is a “proxy derived temperature history”. The latter claim has to be established on other grounds. But the available literature, which we survey in MM05(EE), shows these series are singularly unsuited as climate proxies.

At the risk of appearing didactic, we can illustrate the difference between a series having a “distinct shape term” and it being a valid temperature proxy through a simple but vivid counterexample. In the North American AD1400 tree ring network (consisting of 70 chronologies), we substituted 15 weekly technology stock price series sampled over 581 weeks prior to the market peak in April 2000 for the 15 bristlecone series that were top-weighted in the MBH98 PC1. PC calculations on the new network, combining tree ring chronologies and technology stock prices, show that, under both short-segment and centered PC methods, the inclusion of the technology stocks resulted in a “distinct shape term” requiring a separate PC to represent. Indeed, under the MBH98 method, the “shape term” from the technology stocks manifested itself in the PC1.

X uses informal criteria to decide if a “shape term” is different. A more formal method for deciding the number of PCs to retain is Preisendorfer’s Rule N [Preisendorfer, 1988; Overland and Preisendorfer, 1982]. But neither Rule N nor informal identification of a “distinct shape term” is a sufficient condition for significance, merely a necessary one. Passing a Preisendorfer Rule N test would obviously not qualify the technology stocks as climate proxies. The same argument applies to the bristlecone pine series. In terms of X’s argument, the appearance of a distinct “shape term” due to the bristlecone series may in fact identify outliers and imply that the underlying series contributing to the “shape term” ought to be excluded altogether from the data, if they are known on a priori grounds to be invalid for the purpose of the study.

3. Other Issues
X asserts that the first step in MBH98 principal components calculations was to standardize on the 1902-1980 period. He implies that this information came from MBH98 itself, but the original article states only that “conventional” methods were used. His source for this information was our article, but X fails to attribute the observation to us.

X suggests that the small size of the standard deviations of our simulated PC1s is somehow relevant. The standard deviations of our simulated PC1s are quite comparable to the standard deviations of the MBH98 NOAMER PC1. In actual MBH98 procedures (not discussed in X), tree ring PCs are standardized a second time on the 1902-1980 interval. Thus, the multiplication by a factor of 50 complained about by X is inherent in MBH98 methods and his complaint should be directed at them. But since the series then enter into a regression calculation, the matter is moot since changes in scale simply result in changes in regression coefficients.

REFERENCES
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Graybill, D. A., and S. B. Idso (1993), Detecting the aerial fertilization effect of atmospheric CO2 enrichment in tree-ring chronologies, Global Biogeochem. Cycles, 7, 81– 95.
Mann, M.E., R.S. Bradley and M.K. Hughes (1998), Global-scale temperature patterns and climate forcing over the past six centuries, Nature, 392, 779-787.
Mann, M.E., R.S. Bradley and M.K. Hughes (1999), Northern Hemisphere temperatures during the past millennium: Inferences, Uncertainties, and Limitations, Geophys. Res. Let., 26, 759-762.
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McIntyre, S. and R. McKitrick (2005b), The M&M Critique of the MBH98 Northern Hemisphere Climate Index: Update and Implications, Energy and Environment 16, 69-99..
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Preisendorfer, R., (1988), Principal component analysis in meteorology and oceanography. Elsevier Science.
X, (2005), Comment on “Hockey sticks, principal components and spurious significance” by S. McIntyre and R. McKitrick, Geophys. Res. Let., 32, XXXX, doi: XXXXXXXXXX.