Why a loaded die is like global warming

 by 21TonGiant

Extreme Heat Is Covering More of the Earth, a Study Says
[Via NYT > NYTimes.com Home]

The percentage of the earth’s land surface covered by extreme heat in the summer has soared in recent decades, from less than 1 percent in the years before 1980 to as much as 13 percent in recent years, according to a new scientific paper.

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I’ll explain in more detail below. The take home from this paper –  40 years ago, a twenty-sided climate die had 7 faces colored red for hot, 7 colored blue for cold  and 8 sides colored white for the average. Toss that die and the resulting temperature distribution could match the observed temperature distribution from 1951-1980 fairly well.

Now to match the data, the climate die needs to have 15 faces with red, 2 with blue and 3 with white.  In 50 years, all the die faces will be red. What was average or cold 50  years ago will be tales of legend in another 50. They simply will not occur.

We need to get started now.

A longer explanation

If you toss a die  six times and it comes up 6 every time you can be pretty certain it is loaded. Same with 100-year floods happening yearly. Or heat waves increasing from 1% of the Earth’s surface to 13%.

One of the things about extreme weather events – if they happen often enough, not only are they no longer extreme but we can see just what is likely causing them.

It now appears that many of the heat waves seen worldwide in the last decade would not have happened without global warming caused by humans.

According to the paper, these events are such outliers that they could not be caused by normal weather variation.  The chances of that are too small. They must have been caused by climate, not weather.

I’m going to do some simplifying here but hope to maintain the spirit of statistics.

A short primer on standard deviations. When we take the average of multiple events, , we need to take into account the extremes of the data. Simply, 1 & 100 along with 50 & 50 both have the same average but the extremes are very different.

The standard deviation is a measure of these extremes.  When you see something expressed  with ± , that usually is an indication of standard deviation. Without going into a lot of math, remember this: one standard deviation will contain about 68% of the data. There is about one in three chances that a specific data point will be outside the range of a single standard deviation.

Two standard deviations encompasses about 95% of the data. This is the threshold scientists have chosen as being statistically accurate. There is only a 5% chance that any specific data will reside outside the average ± 2 standard deviations.

What about 3 standard deviations? That means that 99.7% of all the data can be included and only 0.3% will be outside it. There is only a 1 in 370 chance that any particular data point examined that should be included in the data set is outside of it. 

So, normally when looking at the set of data examining heat, we would have a global average with some variation defined by the standard deviation. Say we take an average of all the temperatures globally over a 30 yeat periofd and create an average.

Now, if we look at specific heat events at specific times, they will vary  from this mean. In a normal curve, 67% of them will be within 1 standard deviation, 95% within two standard deviations and 99.7% within 3 standard deviations of the average.

A “once in a century” event is one expected to have a 1% chance of happening in any one year. It would be between a two and a three standard deviation event (actually 2.5). An event that would be outside three standard deviations would be a ‘once in every 3.7 centuries.’

A problem with looking at a specific heat event is whether it lies so far outside the expected standard deviations as to be truly different. It might just be normal variation, just something that happens infrequently.

What happens, though, when that ‘once every 370 years’ event happens 4 times in a decade? Or the ‘once in a century’ happens every year?

Just as a die  that came up 6 six times in a row  is indicative of something wrong, so is having a lot of events at 3 standard deviations or higher occuring regularly.

This paper looked at global temperatures from 1951-1980, creating an average and standard deviations. They then looked at specific events (summer months in specific years) and found many more extreme events happening in recent times.

The number of events 3 or more standard deviations above the mean has increased substantially. We would expect from statistics that only about 0.15% of the land data points to be hotter than 3 standard deviations in any given year.

In 1955, there was essentally no areas on Earth where the temperatures were three standard deviations away from the average. Same in 1965 and 1975. Not too unexpected as they are parts of the years used to establish the average.

In 2000, 5% of the world has summer temperatures greater than 3 standard deviations. In 2010, 13% the globe was hotter than 3 standard deviations. In 2011, it was 8%.

One hundred times more of the globe was hit with temperatures 3 standard deviations above the mean during the summer months in the last decade than would be expected.

They also looked at the actual distribution of temperatures. If nothing had chanced since the 1951-1980 average, we would expect to see just as many colder temperature extremes as higher. That is because a new extreme would have just as much chance of being lower as being higher since the extremes were determined by chance.

But, in the decades following 1991, there has been a strong shift of both the extremes and the average to a higher temperature – about 1 whole standard deviation. What this means is that what would have been a 3 standard deviation heating event in the 50s is now only a 2 standard deviation event.

This is really horrifying to think about. What had been an event that happens once in 15,787 years – a 4 standard deviation event –  now happens every 370.

Events that used to be 1 in 20 are now 1 in 3. The chance of two 1 in 20 events happening in successive years had been 1 in 400 – not likely at all that anyone would see two of them.

Two 1 in 3 events – they would happen about once a decade. 

So, think of the worse drought seen in the last 400 years. Now think of that happening once a decade!

These statistical methods allow the researchers to determine that the extreme summer temperatures in Texas in 2011, Moscow in 2010 and France in 2003 almost certainly would not have happened without humans loading the climate dice.

And now to really freak you out. If things continue as usual over the next 50 years, the distributions will continue to shift so that, what had been once in every 370 year events will be the norm. That is the Texas drought in 2010 will be what anyone living then will expect.

The climate die will be only red.