How Extreme is Extreme Weather?

Lubos Motl has a post on his blog The Reference Frame that puts the recent extreme heat in Russia into perspective:

July 2010 was unusually warm in Western Russia - and Moscow. It actually turns out that a bigger portion of Russia was below the normal temperature than the portion of Russia above it. But that can't change the fact that Moscow et al. was really warm.

I picked Mathematica and used the WeatherData function to find out that the average July 2010 temperature in Moscow was 3.5 standard deviations above the mean temperatures for July 2010 - that can be extracted from the record available via Wolfram's software. By a standard deviation, I mean the root mean square of the differences of July temperatures in the past from their overall average.

Now, how likely it is for a quantity to be more than 3.5 sigma separated from the mean? It's useful to memorize the following table of the odds:

greater than 1.0 sigma: 1 in 3
greater than 1.5 sigma: 1 in 7.5
greater than 2.0 sigma: 1 in 22
greater than 2.5 sigma: 1 in 81
greater than 3.0 sigma: 1 in 370
greater than 3.5 sigma: 1 in 2150
greater than 4.0 sigma: 1 in 15,800
greater than 4.5 sigma: 1 in 147,000
greater than 5.0 sigma: 1 in 1.74 million

Great. So the odds that a normally distributed quantity deviates at least by 3.5 sigma from the mean is something like 1 in 2,000. In the article that Pielke refers to, they clearly used a 4-sigma deviation so that the odds are 1 in 15,000. But that doesn't really change the qualitative story.

Now, is it shocking that Moscow has experienced temperatures that are expected once in 2,000 or 15,000 years? Well, if Moscow were the only city that matters, if July were the only month in the year, and if the temperature were the only quantity that can excite us and that can drive the climate alarmism, the answer would be that it would be relatively unusual. It would be as unusual as living in the year when the Son of God was born, among other things. ;-)

That wouldn't be impossible but it would be somewhat exciting.

But Moscow is not the only city, July is not the only month, and temperature is not the only quantity that can be interesting or that can look like a sign from the heavens to some sensitive individuals. How many independent quantities similar to "average July temperature around Moscow" does the world's atmosphere (and ocean) produce every year?

Well, it's many thousands. The population of Moscow (including its largely integrated vicinity) is about 11 million people - the most populous city of Europe - which is still just 1/600 of the world's population. So it's OK to assume that there are "600 places in the world similar to Moscow". And we generously ignore the ocean where almost no one lives but that can also experience extreme weather.

Besides 600 places in the world, there are 12 months in a year and roughly 5 major quantities - temperature, pressure, wind speed, precipitation, and cloudiness - that we could find as interesting as the temperature. All these parameters are pretty much independent. So how many quantities are there that can be potentially as interesting as July temperatures in Moscow? It is

600 x 12 x 5 = 36,000 a year.

So even if you generously say that the Moscow temperature was not 3.5 but 4 sigma above the mean - the odds are 1 in 15,000 - it means that in average, two such "impossibly rare" events should occur somewhere in the world every year! It is actually unlikely ("less likely than yes") that no such event will occur during a given one year.

These are all back-of-the-envelope numbers but they give a very good estimate. People need to be more numerate. Using basic math and a bit of statistics is an excellent way to find your way through today's world.

Just like our ancestors wouldn't have wandered out onto the East Africa plain without a weapon, people today shouldn't read "facts" and reports without a little number sense and an ability to do back-of-the-envelope estimating. Otherwise, you will be bamboozled by those who want to sell you something that you probably don't need.

Diverting big tax dollars into fighting "global warming" is just such a boondoggle in my mind. The fact that IPCC models have over-estimated "global warming" and are getting worse doesn't get the same attention as a heat wave in Russia. As Lubos Motl points out, the same time the Moscow area was experiencing extreme heat, the average over Russia was quite normal. He doesn't mention that during the same time extreme cold was being experienced in South America and Australia and that the ice sheet around Antarctica is at a

I use the following measurement of global sea ice as my "thermometer". I sure don't see any "runaway" global warming in this graph from the University of Illinois Polar Research Group.

Click to Enlarge
Eyeballing this measurement of how ice extent deviates from a 30 year average shows that there is no trend. There is no runaway global warming that is melting the ice at the poles. The global warming alarmists tell us that the effects of global warming will be worse at the higher latitudes. If so, you would expect sea ice to be the "canary in the coal mine" to alert us of the danger. Well, this canary isn't singing.