What is a Bell Curve and Standard Deviation?
Sigma (σ) is a letter of the Greek alphabet. It is used in statistics to represent
standard deviation. It essentially describes how much data is spread out from the average, or mean. A plot of a normal distribution of data typically yields the familiar bell curve. Here are six examples of normal distributions with different standard deviations. Low standard deviation, in blue, says the data points are bunched up and close to the mean. High standard deviation, in yellow, says the data is more spread over a wider range.
Click image for source.
In a standard bell curve, 68% of the data points fall within one standard deviation (1σ) of the mean. While 95% are within two standard deviations (2σ). Three standard deviations (3σ) of the mean will contain 99.7% of the data. Very few points will lie beyond 3σ. Those are the characters that make up the extreme right wing and left wing fringe. The scientists reporting the finding of the Higgs Boson spoke of data within 3σ and how certain they were of it.
How is Temperature Related?
Now, substitute temperature variations from the mean, or anomalies, into a plot. The graph on the left shows how frequently summer temperature anomalies occurred in the 30-year base period 1951-1980, a time of stable global climate. The standard deviation σ was 0.6°C (1.1°F) in 1951-1980. Or, 68% of the variations measured were within 0.6˚C of the mean. By the next decade of 1981-1991, the peak of values shifted toward the right indicating warmer temperature anomalies. Each successive decade has shifted the curve more to the warmer end of the curve. In addition, there are many more temperature anomalies beyond the 3σ tail at the right end of the graph. And, the curve is more spread out indicating larger standard deviation of temperature anomalies.
The surface temperatures have increase over the recent 3 decades. And, the number of extreme high heat events beyond 3σ has increased.
As stated by Hansen...
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.
Below is an animation of the data presented by Hansen and his colleagues.
Q&A with James Hansen
Hansen supplied a number of answers and explanations which you can
access at this link. The link is to a 4 page pdf titled
Q&A of The New Climate Dice. He addresses several questions, in particular, how the coming years are going to be like rolling a loaded dice for extremes of high temperature anomalies. They are going to be more frequent and more severe. There will still be the occasional colder than normal year. But, hotter than normal will be more frequent and worse. Not a good prospect.
Some questions he considers are...
1. What is the most important finding of the paper?
2. Why is such an anomaly important? Isn't it just a few degrees warmer than average?
3. Didn't 3-sigma events occur in the past?
4. So you can use your old metaphor of "loaded" climate dice to describe the situation?
5. Why are you also introducing the "bell curve?" Isn't that too esoteric for the public?
6. How is the "bell curve" related to "loaded climate dice?"
7. You note that the bell curve has become "squashed". Is that important?
8. How do you know that the bell curve will continue to shift to the right?
9. What are consequences of the increasing extremes?
10. Are we necessarily going to see more and more extreme climate? Gloom and doom?
11. Could we just redefine what is normal climate, obtaining a new symmetric bell curve?
12. Did you write this paper and your 1988 paper because of the extreme droughts?
13. Are there other effects that should be noticeable, besides the climate extremes?
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