Mathematics

It was a mathematician, Joseph Fourier (1768-1830), who coined the term “greenhouse effect”. That this term, so commonly used today to describe human effects on the global climate, originated with a mathematician points to the insights that mathematics can offer into environmental problems. Three articles in the November 2010 issue of the Notices of the American Mathematical Society examine ways in which mathematics can contribute to understanding environmental and ecological issues.

Data about earthquakes indicates that there are thousands of small earthquakes that do no damage, and there are just a few very strong earthquakes that do a great deal of damage. A striking fact emerges from the data: Over a sufficiently long period of time, the sum of the “intensity” of all earthquakes of a given Richter scale magnitude is the same for any point on the Richter scale. So for example the total intensity of the 100,000 magnitude-3 quakes that occur over the course of a year is the same as the intensity of a single magnitude-8 trembler. Put another way, there is no preferred size or scale of earthquakes. This is an empirical fact that can be easily translated into mathematical terms, by noting that the data for earthquakes follows what is known as a power law. The author uses the example of earthquakes to formulate a hypothesis about “weatherquakes” extreme weather events like hurricanes and tornadoes. As in the case of earthquakes, he suggests, there is no preferred size or c of weatherquakes. That is, weatherquake phenomena also follow a power law. Taking the mathematics a few steps further, the author examines what would happen to the distribution of extreme weather events if the global climate heated up. The finding is worrisome: As temperatures rise, the most intense weatherquakes would increase in number.

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