View Full Version : Reality of Hockey Stick Graph

Gary Severson
08-16-2011, 05:27 PM
Fallacy of critics of hockey stick evidence for MMGW.


Greg Burnham
08-16-2011, 06:10 PM
[The author of this article believes in MMGW. That's correct, he believes that CO2 is contributing to global warming and he believes that humans are responsible for it. Still, he admits the "Hockey Stick" is entirely flawed. -- Greg]


A prime piece of evidence linking human activity to climate change turns out to be an artifact of poor mathematics.


Progress in science is sometimes made by great discoveries. But science also advances when we learn that something we believed to be true isnt. When solving a jigsaw puzzle, the solution can sometimes be stymied by the fact that a wrong piece has been wedged in a key place.

In the scientific and political debate over global warming, the latest wrong piece may be the hockey stick, the famous plot (shown below), published by University of Massachusetts geoscientist Michael Mann and colleagues. This plot purports to show that we are now experiencing the warmest climate in a millennium, and that the earth, after remaining cool for centuries during the medieval era, suddenly began to heat up about 100 years ago--just at the time that the burning of coal and oil led to an increase in atmospheric levels of carbon dioxide.

I talked about this at length in my December 2003 column. Unfortunately, discussion of this plot has been so polluted by political and activist frenzy that it is hard to dig into it to reach the science. My earlier column was largely a plea to let science proceed unmolested. Unfortunately, the very importance of the issue has made careful science difficult to pursue.

But now a shock: Canadian scientists Stephen McIntyre and Ross McKitrick have uncovered a fundamental mathematical flaw in the computer program that was used to produce the hockey stick. In his original publications of the stick, Mann purported to use a standard method known as principal component analysis, or PCA, to find the dominant features in a set of more than 70 different climate records.

But it wasnt so. McIntyre and McKitrick obtained part of the program that Mann used, and they found serious problems. Not only does the program not do conventional PCA, but it handles data normalization in a way that can only be described as mistaken.

Now comes the real shocker. This improper normalization procedure tends to emphasize any data that do have the hockey stick shape, and to suppress all data that do not. To demonstrate this effect, McIntyre and McKitrick created some meaningless test data that had, on average, no trends. This method of generating random data is called Monte Carlo analysis, after the famous casino, and it is widely used in statistical analysis to test procedures. When McIntyre and McKitrick fed these random data into the Mann procedure, out popped a hockey stick shape!

That discovery hit me like a bombshell, and I suspect it is having the same effect on many others. Suddenly the hockey stick, the poster-child of the global warming community, turns out to be an artifact of poor mathematics. How could it happen? What is going on? Let me digress into a short technical discussion of how this incredible error took place.

In PCA and similar techniques, each of the (in this case, typically 70) different data sets have their averages subtracted (so they have a mean of zero), and then are multiplied by a number to make their average variation around that mean to be equal to one; in technical jargon, we say that each data set is normalized to zero mean and unit variance. In standard PCA, each data set is normalized over its complete data period; for key climate data sets that Mann used to create his hockey stick graph, this was the interval 1400-1980. But the computer program Mann used did not do that. Instead, it forced each data set to have zero mean for the time period 1902-1980, and to match the historical records for this interval. This is the time when the historical temperature is well known, so this procedure does guarantee the most accurate temperature scale. But it completely screws up PCA. PCA is mostly concerned with the data sets that have high variance, and the Mann normalization procedure tends to give very high variance to any data set with a hockey stick shape. (Such data sets have zero mean only over the 1902-1980 period, not over the longer 1400-1980 period.)

The net result: the principal component will have a hockey stick shape even if most of the data do not.

McIntyre and McKitrick sent their detailed analysis to Nature magazine for publication, and it was extensively refereed. But their paper was finally rejected. In frustration, McIntyre and McKitrick put the entire record of their submission and the referee reports on a Web page for all to see. If you look, youll see that McIntyre and McKitrick have found numerous other problems with the Mann analysis. I emphasize the bug in their PCA program simply because it is so blatant and so easy to understand. Apparently, Mann and his colleagues never tested their program with the standard Monte Carlo approach, or they would have discovered the error themselves. Other and different criticisms of the hockey stick are emerging (see, for example, the paper by Hans von Storch and colleagues in the September 30 issue of Science).

Some people may complain that McIntyre and McKitrick did not publish their results in a refereed journal. That is true--but not for lack of trying. Moreover, the paper was refereed--and even better, the referee reports are there for us to read. McIntyre and McKitricks only failure was in not convincing Nature that the paper was important enough to publish.

How does this bombshell affect what we think about global warming?

It certainly does not negate the threat of a long-term global temperature increase. In fact, McIntyre and McKitrick are careful to point out that it is hard to draw conclusions from these data, even with their corrections. Did medieval global warming take place? Last month the consensus was that it did not; now the correct answer is that nobody really knows. Uncovering errors in the Mann analysis doesnt settle the debate; it just reopens it. We now know less about the history of climate, and its natural fluctuations over century-scale time frames, than we thought we knew.

If you are concerned about global warming (as I am) and think that human-created carbon dioxide may contribute (as I do), then you still should agree that we are much better off having broken the hockey stick. Misinformation can do real harm, because it distorts predictions. Suppose, for example, that future measurements in the years 2005-2015 show a clear and distinct global cooling trend. (It could happen.) If we mistakenly took the hockey stick seriously--that is, if we believed that natural fluctuations in climate are small--then we might conclude (mistakenly) that the cooling could not be just a random fluctuation on top of a long-term warming trend, since according to the hockey stick, such fluctuations are negligible. And that might lead in turn to the mistaken conclusion that global warming predictions are a lot of hooey. If, on the other hand, we reject the hockey stick, and recognize that natural fluctuations can be large, then we will not be misled by a few years of random cooling.

A phony hockey stick is more dangerous than a broken one--if we know it is broken. It is our responsibility as scientists to look at the data in an unbiased way, and draw whatever conclusions follow. When we discover a mistake, we admit it, learn from it, and perhaps discover once again the value of caution.

Gary Severson
08-16-2011, 06:45 PM
Greg, when did Muller write this piece? My post below from the art. in my 1st post from above may clear up Muller unless Muller was writing this after this 2004 art.

MYTH #4: Errors in the "Hockey Stick" undermine the conclusion that late 20th century hemispheric warmth is anomalous.

This statement embraces at least two distinct falsehoods. The first falsehood holds that the “Hockey Stick” is the result of one analysis or the analysis of one group of researchers (i.e., that of Mann et al, 1998 and Mann et al, 1999). However, as discussed in the response to Myth #1 (http://www.realclimate.org/index.php/archives/2004/12/myths-vs-fact-regarding-the-hockey-stick/#myth1) above, the basic conclusions of Mann et al (1998,1999) are affirmed in multiple independent studies. Thus, even if there were errors in the Mann et al (1998) reconstruction, numerous other studies independently support the conclusion of anomalous late 20th century hemispheric-scale warmth.
The second falsehood holds that there are errors in the Mann et al (1998, 1999) analyses, and that these putative errors compromise the “hockey stick” shape of hemispheric surface temperature reconstructions. Such claims seem to be based in part on the misunderstanding or misrepresentation by some individuals of a corrigendum (http://holocene.meteo.psu.edu/shared/articles/MBH98-corrigendum04.pdf) that was published by Mann and colleagues in Nature. This corrigendum simply corrected the descriptions of supplementary information that accompanied the Mann et al article detailing precisely what data were used. As clearly stated in the corrigendum, these corrections have no influence at all on the actual analysis or any of the results shown in Mann et al (1998). Claims that the corrigendum reflects any errors at all in the Mann et al (1998) reconstruction are entirely false.
False claims of the existence of errors in the Mann et al (1998) reconstruction can also be traced to spurious allegations made by two individuals, McIntyre and McKitrick (McIntyre works in the mining industry (http://www.exxonsecrets.org/html/personfactsheet.php?id=1007), while McKitrick is an economist (http://www.environmentaldefense.org/article.cfm?contentid=3804&CFID=21084385&CFTOKEN=29888831)). The false claims were first made in an article (McIntyre and McKitrick, 2003) published in a non-scientific (social science) journal “Energy and Environment” and later, in a separate “Communications Arising” comment that was rejected by Nature based on negative appraisals by reviewers and editor [as a side note, we find it peculiar that the authors have argued elsewhere that their submission was rejected due to 'lack of space'. Nature makes their policy on such submissions (http://www.nature.com/nature/submit/gta/index.html#7) quite clear: "The Brief Communications editor will decide how to proceed on the basis of whether the central conclusion of the earlier paper is brought into question; of the length of time since the original publication; and of whether a comment or exchange of views is likely to seem of interest to nonspecialist readers. Because Nature receives so many comments, those that do not meet these criteria are referred to the specialist literature." Since Nature chose to send the comment out for review in the first place, the "time since the original publication" was clearly not deemed a problematic factor. One is logically left to conclude that the grounds for rejection were the deficiencies in the authors' arguments explicitly noted by the reviewers]. The rejected criticism has nonetheless been posted on the internet by the authors, and promoted in certain other non-peer-reviewed venues (see this nice discussion (http://web.archive.org/web/20041021080002/davidappell.com/archives/00000427.htm) by science journalist David Appell (http://davidappell.com/) of a scurrilous parroting of their claims by Richard Muller in an on-line opinion piece).
The claims of McIntyre and McKitrick, which hold that the “Hockey-Stick” shape of the MBH98 reconstruction is an artifact of the use of series with infilled data and the convention by which certain networks of proxy data were represented in a Principal Components Analysis (“PCA”) (http://www.realclimate.org/index.php?p=26), are readily seen to be false (http://www.realclimate.org/index.php?p=8) , as detailed in a response by Mann and colleagues to their rejected Nature criticism (http://www.realclimate.org/index.php?p=8) demonstrating that (1) the Mann et al (1998) reconstruction is robust with respect to the elimination of any data that were infilled in the original analysis, (2) the main features of the Mann et al (1998) reconstruction are entirely insensitive to whether or not proxy data networks are represented by PCA, (3) the putative ‘correction’ by McIntyre and McKitrick, which argues for anomalous 15th century warmth (in contradiction to all other known reconstructions), is an artifact of the censoring by the authors of key proxy data in the original Mann et al (1998) dataset, and finally, (4) Unlike the original Mann et al (1998) reconstruction, the so-called ‘correction’ by McIntyre and McKitrick fails statistical verification exercises, rendering it statistically meaningless and unworthy of discussion in the legitimate scientific literature.
The claims of McIntyre and McKitrick have now been further discredited (http://www.realclimate.org/index.php?p=10) in the peer-reviewed scientific literature, in a paper (http://www.realclimate.org/RuthetalJClim2004.pdf) to appear in the American Meteorological Society (http://www.ametsoc.org/) journal, “Journal of Climate (http://ams.allenpress.com/amsonline/?request=get-archive&issn=1520-0442)” by Rutherford and colleagues (2004) [and by yet another paper by an independent set of authors that is currently "under review" and thus cannot yet be cited--more on this soon!]. Rutherford et al (2004) demonstrate nearly identical results to those of MBH98, using the same proxy dataset as Mann et al (1998) but addressing the issues of infilled/missing data raised by Mcintyre and McKitrick, and using an alternative climate field reconstruction (CFR) (http://www.realclimate.org/index.php?p=29)methodology that does not represent any proxy data networks by PCA at all.

Greg Burnham
08-16-2011, 10:33 PM
It was published by the Massachusetts Institute of Technology on October 15, 2004 in Technology Review.