From the ABC 7 Weather team

Black swans, gaussian curves and mild weather: A math explainer

April 20, 2011 - 03:47 PM
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The results from our recent poll show a Guassian distribution. Join me on a quick journey through the curvy world of probabilities, and what they mean in our warming climate.

OK, I hope the title got your attention. Allow me to take you on a quick journey through the curvy world of probabilities and what they mean in our warming climate. Our recent poll asked what temperature you think of when you hear the word “mild” in the forecast. Here were the results:


Now I’ll rotate that image 90 degrees counterclockwise:


Notice how the highest number of responses falls right in the center? We chose a range of “mild” to be from 50 to 75 degrees, and most of your answers fell right in the middle around 65 degrees. What if we had created more categories and made the temperature ranges only 2 rather than 5 degrees? The result probably would look something like this:


National Curve Bank

In mathematics, that’s called a Gaussian or “normal” distribution. Make enough measurements or ask enough people about some variable, as we did with the poll, and you get a range of results with the highest probability centered in the middle.

If I had chosen the “mild” range to be 20 to 65 degrees, the curve would have peaked far to the right. Not many of us feel that 20 degrees is mild. So, I selected a range that I thought would illustrate this normal distribution. Here’s a great video showing how this phenomenon happens and how you can try it at home:

As you can see from the poll, some of you are tough and consider 50 degrees to be mild. (I’m sure if we asked some Inuit people what “mild” was, they might’ve answered 30 degrees.) But only 4 to 7 percent of you think “mild” is in the 70s. These extreme left and right edges of the curve are what some mathematicians and statisticians call “black swans,” meaning the probabilities there are so far out they’re almost not foreseeable at all.

I hope you’re still with me. Let’s finish with what this distribution means for record high temperatures. Take a look at these new “normal” temperatures from the National Atmospheric and Oceanic Administration:


Let’s not argue whether it’s due to natural or human activities, but maybe we can agree that in the long term the average global temperature is rising? Take a look:


Yes, these are “government” sources but bear with me. I know these scientists. They are honest and have no agenda. It's true that there are long-term natural variations that we still need a better understanding of as to why there was little global temperature change from 1945 through 1980. But we are sure in a warming phase now.

So what’s the big deal if we are shifting from the previous climate norms shown above to a new climate where the mean (remember the 65 degrees on our poll) is 5 degrees higher?

Well, the probability of record heat becomes higher. The probability of more continuous 90-degree days becomes higher. The “normal” curve moves a bit (or a lot) to the right, and the “black swan” extremes become a bit more likely. In a warmer world, should we expect the “once in a 100 year” heat waves to become more probable? Or should I worry about not having enough wood for heating in the coming years? Which is more probable?

We might just have to post another poll asking this.

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