Monday, August 6, 2012

Climate Dice Back in the Day

There's been much on blogs about "Climate Dice" and how humans are perhaps loading them. See the article by Andrew Revkin (New York Times) and more recently by Paul Krugman (New York Times) discussing the findings by James Hansen et al. on public perceptions of climate change, these links via Andrew Gelman. Basically, the data show that hotter extremes are becoming more likely.

Investigating the variability in climate, with analogies to random tosses of dice, has a long history, and not always considered in the correct way. C. F. Marvin, former chief of the US Weather Bureau, can be seen using such random methods in this article from Popular Science 1932 page 46.  Describing this methods a bit more, this newspaper article from 1931 begins with an especially lyrical view of his work :
Common dice, inventions of the ancients and purveyors of financial distress to unlucky moderns, have risen to a new dignity. After having been rolled in many places, ranging from the cobblestones of side streets to the green covered tables in palaces of chance, they are now being tossed with analytical earnestness by the hands of science.
In this new field the "galloping dominoes" are being used as a means of increasing man's working knowledge of the weather and its pranks. The greenback and silver involved when glassy eyed gamblers seek to get something for nothing are supplanted by graphs and slide rules in this new environment, where scientists seek the answer to the high sounding question, "Are meteorological sequences fortuitous?"
I think here one should read "random" for "fortuitous". The article's final question is the title of a paper by Marvin the appeared in December 1930 Monthly Weather Review (pdf). In that paper he uses such random methods to simulate graphs of precipitation and compares the results to actual records questioning "who could pick out the natural from the chance order"?

He does complicate things by confusing a sample and a population. He marvels at the fact that the products of the results on four tossed dice produces a histogram of measurements that is  sparse and skewed to the right, resembling a sample record of actual precipitation. Of course, this is a population of all the possible products and its sparseness will always be present. As he notes, there is no way to fill in between the products that can only be produced with four dice. This has no relation to the sampling variability and sparse histograms, of many shapes, that could result come from a skewed but continuous population of measurements. Of course, it was 1931!

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