The hook-shaped instrument in this case, though, is the 1998 climate reconstruction graph calculated by University of Virginia environmental science professor Michael Mann and colleagues.

The graph, featured in the 2001 Intergovernmental Panel on Climate Change report, shows a relatively flat average global temperature for the past 600 years or so, followed by a swiftly climbing trend line beginning about 1900 and continuing until the present day. It has come to be known as the hockey stick because that is what it resembles - although if the hockey stick is right, the ice is melting.

The take-home message from Mann and colleagues - their data set is commonly called MBH98, for Mann and co-authors Bradley and Hughes - is the 20th century has been the warmest of the last thousand years or so. Furthermore, the upward trend has been strongest in the latter half of the 20th century, supporting the contention that global warming is real, gathering strength and very likely caused by human activities.

For every action there is an opposite reaction. Two Canadian investigators - minerals expert Steven McIntyre and University of Guelph economist Ross McKitrick - examined the methodology used by Mann and declared it incorrect. The hockey-stick analogy is wrong, they said, arguing the Mann group's calculations generate a hockey-stick shape no matter what data they use.

The McIntyre-McKitrick results, or MM05 on your scorecard, have been seized by climate skeptics to try to discredit one of the fundamental conclusions of the IPCC report: the globe is warming unusually as a result of human activity.

So, who is correct? Hard to tell. This is a case where two research groups take the same data, apply more or less the same methods and come up with two sharply differing results. This can be somewhat disconcerting for anyone who thought math was supposed to provide only one right answer.

Journalists are not the sort one ordinarily would turn to for an explanation of statistics. Most people who become journalists do so because it does not require calculus. Even the august Wall Street Journal's story on the controversy merely allowed it was a complex technical issue and let it go at that.

On the other hand, both sides of the controversy seem to recognize this numbers gap. RealClimate.org has put out a "Dummies Guide" to the issue, and McIntyre and McKitrick's ClimateAudit.org site has compiled a more-or-less plain language "backgrounder" for their work.

Climate reconstructions for the period prior to about 1850 (there were few thermometer records kept before this) are done using what are called climate proxies: tree rings, ice cores, sediments and other physical information that retain some information about the weather of the time. Trees, for instance, grow faster in warmer temperatures and with more rainfall, so by looking at fossil tree rings, you can infer what the climate conditions were.

Most trees also grow faster when they are young, however, and slower as they age, so the records are subtle. You have to make assumptions about how fast the tree would have grown anyway, given its innate vitality. Furthermore, tree rings do not reveal what climatologists call low-frequency changes - long, slow temperature trends. Sediment records are better at extracting these.

Still, these subtle records are the only ones available. Scientists need experience, ingenuity and mathematical tools to gain insight into past climate and current trends. The trick - even with mathematics - is to make decisions about how you are going handle things. Different decisions lead to different results.

After climatologists gather all the data, they apply certain statistical tools. That is what lies at the heart of the MBH98 vs. MM05 controversy - a method dauntingly named "Principal Component Analysis." This is a statistical way of handling complex and noisy data to not only extract essential and meaningful information, but also make it easier to handle mathematically.

It works by first subtracting the mean from each data range. Then you take the remainder and do it again, and then again, until the differences no longer yield statistically significant answers. To figure this out, you have to calculate covariance matrices and eigenvalues ... but let's not go there.

The standard method of normalizing is to take the mean of the entire data set -- in this case from about 1400 to 1980. But Mann et al. did not do this. Instead, they normalized their data using only the mean of the 1900 to 1980 period.

McIntyre-McKitrick reproduced the data set by normalizing over the mean of most - but not all - of the data set. They removed some tree ring data they considered unreliable as temperature proxies.

So, the two groups made different decisions about techniques to interpret the same data. McIntyre and McKitrick argue their normalization is more standard, but statistical methodologies do allow different approaches - if there is a good reason for the change. Mann's group argues it did have good reasons for the strategy.

"MBH98 were particularly interested in whether the tree ring data showed significant differences from the 20th century calibration period, and therefore normalized the data so that the mean over this period was zero," RealClimate's guide for dummies said.

On this point, some statisticians agree with Mann, but some do not. It depends on what you want to know.

The statistical significance of the PCA iterations is also a point of contention. The Mann group found that, in its construction, two PCA components well explained the data, and further iterations were not statistically significant. In their analysis of the MM05 reconstruction, they found it necessary to include 4 or 5 PCA components as statistically significant.

Quite technical, but in simpler terms, when these later components are included in the MM05 reconstruction, the result closely resembles the Mann hockey stick.

"If they were to follow through on their approach and arguments, they would use four or five PCAs," Caspar Amman, a paleoclimatologist at National Center for Atmospheric Research told UPI's Climate, "and that gets the same construction as Mann."

The MM05 backgrounders noted, however, "We provide compelling evidence that the early portion of Mann's own reconstruction fails an important and standard statistical verification test, as well as other tests."

Whichever graph you prefer, the controversy does not undermine the fact of global warming, and McIntyre and McKitrick explicitly say as much in their backgrounder. "Does your work disprove global warming?" they asked in their paper.

"We have not made such a claim," they responded to themselves. "There is considerable evidence that in many locations the late 20th century was generally warmer than the mid-19th century." The question then is whether the mid-19th century was anomalously cool.

Despite the visual drama of the hockey stick, the IPCC did not reach either its scientific or policy conclusions based on it. The IPCC pronounced global warming a major issue in 1995 - three years before the Mann hockey stick appeared.

Climate is a weekly series examining the potential human impact on global climate change, by environmental reporter Dan Whipple.

All rights reserved. Copyright 2004 by United Press International. Sections of the information displayed on this page (dispatches, photographs, logos) are protected by intellectual property rights owned by United Press International. As a consequence, you may not copy, reproduce, modify, transmit, publish, display or in any way commercially exploit any of the content of this section without the prior written consent of by United Press International.

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