October 26, 2004 

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

By Richard Muller
October 15, 2004

Progress in science is sometimes made by great discoveries. But science
also advances when we learn that something we believed to be true isn't.
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 wasn't 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, you'll 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 McKitrick's only failure
was in not convincing Nature that the paper was important enough to

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 doesn't 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.
                            *  *  *

Richard A. Muller, a 1982 MacArthur Fellow, is a physics professor at the
University of California, Berkeley, where he teaches a course called
"Physics for Future Presidents." Since 1972, he has been a Jason
consultant on U.S. national security.

Outgoing mail is certified Virus Free.
Checked by AVG anti-virus system (
Version: 6.0.778 / Virus Database: 525 - Release Date: 10/15/04

Incoming mail is certified Virus Free.
Checked by AVG anti-virus system (http://www.grisoft.com).
Version: 6.0.782 / Virus Database: 528 - Release Date: 10/22/2004