Understanding odds and climate statistics

2012 July 11
by Colin

The NCDC and Jeff Masters have gotten a lot of press in both major media and the blogosphere with this Washington Post snippet from earlier this week:

The National Climatic Data Center has just released its “State of the Climate” report for June 2012. The last 12-month period on the mainland United States, it notes, were the warmest on record. What’s notable, however, is that every single one of the last 13 months were in the top third for their historical distribution–i.e., April 2012 was in the top third for warmest Aprils, etc.

“The odds of this occurring randomly,” notes NCDC, “is 1 in 1,594,323.”

Meteorologist Jeff Masters puts it this way: “These are ridiculously long odds, and it is highly unlikely that the extremity of the heat during the past 13 months could have occurred without a warming climate.”

Sounds like a pretty long bet; anyone want to take it? Apparently Steven Goddard does…

Now I am going to apply the same math to the ice age scare of the 1970s. In 1974, the CIA reported that Eastern Canada had been below normal for 19 months in a row.

The odds of being below normal are one out of two. So if we raise two to the nineteenth power, we can conclude that the global cooling of the 1970s was a one in 524,288 event, colder than the last three or four ice ages! No wonder Hansen had to erase it!

This is incorrect. The odds of 19 statistically independent 50/50 events (such as a coinflip) coming up in a row is 524,288 ( 1 / 2^(19) ).

However, like an elite baseball player such as Albert Pujols performing above league average, a train of XX months in an integrated system like the climate is not statistically independent. Having multiple warm (or cold) months in a row implies an atmospheric setup conducive to warm or cold. This shows that months are correlated with their neighbors (being mostly strongly tied to those months immediately preceding and following them) and therefore the odds aren’t 50/50.

In addition, the NCDC argued that it was a 13 month period that was “this warm,” which meant that it was a 13 month running period which had temperatures YY degrees above some baseline. This is fundamentally different from saying “it was 13 months above average” which, it also was, but it’s obviously more likely to get 13 months above-average from a statistical standpoint because not every string of 13 months of above-average temperatures can be the warmest string of 13 months in a row (example, not every 20+ game hitting streak can be DiMaggio’s 56 game hitting streak).

This also raises issues with the NCDC/Masters number as well. The 1-in-1.6 million figure appears to have arisen from estimating the odds of piling 13 month chunks in a row with this degree of heat (assuming each month has a 1-in-3 shot of reaching that benchmark, which seems arbitrary), and then extrapolating forward ( (1.6 million / 13 months) -~ 2012 AD ) to get the projected 124,652 AD date that Masters uses. This also suffers from the same fundamental flaw the Goddard analysis did (although not as significant because of the magnitude vs. sign effect noted above).

The recent heat wave likely remains unprecedented in the North American historical record, however, bad statistics have certainly not endeared those on either side of the AGW debate to educated readers.

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