"Math" Errors in Global "Science"

Some time ago, I reviewed how the "hockey stick" graph of Mr. Mann, which is the Rosetta Stone of Global Warming, had had been found wanting (a nice try, was how one put it).

Below, I have added part of a "Technology" web article (an MIT publication.) The MIT article concerns a "bombshell" and "incredible error" found by McIntyre and McKitrick. Mann's program would take random numbers having no trend and print out a hockey stick, supposedly

I was reminded of this older discussion, yes the errors have been known for years Mr. Gore, by the recent Ross McIntyre's blog recount of a NASA GISS' admission of of "mathematical error" regarding how temperatures have been misreported because of mathematical errors. Funny how errors always fall in the same direction. Also, the errors reporting bias toward warming seem to be computer errors, a scientist's equivalent of "the dog ate it."

As you may have read recently, since 1880, five of the ten warmest years in North America were in the 1920s and 1930s. The warmest recorded year was 1934.

Then, there is the IPCC warming bias errors
where the IPCC anonymous "scientists" forgot to use "real world" data:

The global average surface temperature trend in the 2007 SPM (see Figure SPM-3 top in HYPERLINK "http://www.ipcc.ch/SPM2feb07.pdf" the IPCC SPM) continues to show warming, but as has been summarized in

Pielke Sr., R.A., C. Davey, D. Niyogi, K. Hubbard, X. Lin, M. Cai, Y.-K. Lim, H. Li, J. Nielsen-Gammon, K. Gallo, R. Hale, R. Mahmood, S. Foster, J. Steinweg-Woods, R. Boyles, S. Fall, R.T. McNider, and P. Blanken, 2007: HYPERLINK "http://climatesci.colorado.edu/publications/R-321.pdf" Unresolved issues with the assessment of multi-decadal global land surface temperature trends. J. Geophys. Res. in press,
there is a significant warm bias in the construction of a global average surface temperature trend.

What these observations mean is that the statement in the IPCC SPM that there is a positive radiative forcing of 1.6 [0.6 to 2.4] Watts per meter squared in 2005 (when this was not true based on real data) is a particularly egregious error.

Rather than relying solely on model based estimates to calculate a global radiative forcing, the authors of the IPCC Report should have also used real world data for the assessment of the net radiative forcing.

A claim that a time period of several years is too short to assess the radiative heating is spurious as long as the sampling of the ocean heat content is sufficiently dense. As discussed in

Pielke Sr., R.A., 2003: HYPERLINK "http://blue.atmos.colostate.edu/publications/pdf/R-247.pdf" Heat storage within the Earth system. Bull. Amer. Meteor. Soc., 84, 331-335,

“A snapshot at any time documents the accumulated heat content and its change since the last assessment. Unlike temperature, at some specific level of the ocean, land, or the atmosphere, in which there is a time lag in its response to radiative forcing, there are no time lags associated with heat changes.”

The IPCC finding that the total 2005 net anthropogenic radiative forcing has a best estimate of +1.6 Watts per meter squared and that the total 2005 net radiative forcing has a best estimate of +1.72 Watts per meter squared is inconsistent with the observed changes in upper ocean heat content.

The omission of a discussion of the conflict between real world observations and the model estimates of radiative forcing is a serious error in the IPCC SPM.

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

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....