## Earth Indicator: 3σ

August 7th, 2012 by Adam Voiland

Is that a three omicron? Nope. Three, rho? Strike two. Our latest Earth Indicator is three-sigma.

In Greek, sigma (σ) is the 18th letter of the alphabet. In statistics, it’s a symbol for standard deviation, a measure of how spread out a set of data points are from the average (which is often called the mean by statisticians). Data with a low standard deviation indicates that the data points are bunched up and close to the mean. A high standard deviation indicates the points are spread over a wide range of values.

In a standard bell curve, most data points (68 percent) fall within one standard deviation (1σ) of the mean (see the pink section in the graph below). The vast majority (95 percent, the combined pink and red sections of the graph) fall within two standard deviations (2σ). An even higher percentage (99.7 percent, the combined pink, red, and blue sections) fall within three standard deviations (3σ) of the mean. Just a tiny fraction of points are outliers that are more than three standard deviations from the mean. (See the parts of the graph with arrows pointing to 0.15%).

Now imagine that instead of generic data points on a generic bell curve the values are actually measurements of summer temperatures. That will give you a foundation for understanding the statistical analysis that James Hansen published this week in the Proceedings of the National Academy of Sciences.

One of his main findings: as seen in the graph above, is that the range of observed surface temperatures on Earth has shifted over time, meaning that rare 3-sigma temperature events (which represent times when temperatures are abnormally warm) have grown more frequent because of global warming.

Here’s how Hansen puts it:

We have shown that these “3-sigma” (3σ) events, where σ is the standard deviation — seasons more than three standard deviations removed from “normal” climate — are a consequence of the rapid global warming of the past 30 years. Combined with the well-established fact that the global warming is a result of increasing atmospheric CO2 and other greenhouse gases, it follows that the increasingly extreme climate anomalies are human-made.

Want to learn more? A press release is available here. And Hansen has also published a summary of his paper (pdf) and an accompanying Q & A (pdf) that offer more details.