Feb
28
2009

Hey, Candace! Looks like you were right!

The hounds of spring are on winter’s traces: It appears that winter and summer temperatures are yoked together.  (This photo is for you, Thor.  I'm a cat person myself. Title explained here.)
The hounds of spring are on winter’s traces: It appears that winter and summer temperatures are yoked together. (This photo is for you, Thor. I'm a cat person myself. Title explained here.)Courtesy sbpoet

Last week, Candace asked whether there’s a connection between winter temperatures and summer temperatures. She noted that the winter of 2007-08 was pretty cold by recent standards, and the following summer was cool as well. Is there something going on here?

Liza searched the Web but couldn’t find anything definitive. I (after pooh-poohing the idea that this has been a warm winter – if you want to pay my heating bill, you’re welcome to it!) decided to crunch the numbers.

First, I went to this site. It records monthly average temperatures going back to December 1978.

Actually, it records temperature anomalies – whether the observed temperature in a given month is higher or lower than the average. They use the 20 years of 1979-1998 as their baseline. A reading of 1.00 means the temperature was 1 degree Centigrade (1.8 °F) warmer than expected. (One degree may not sound like much, until you realize it means 1 degree of every minute of every hour of every day. It quickly adds up to a lot of heat.) A reading of -1.00 means it was 1 degree cooler.

Using temperature anomalies is good for this exercise, as it removes the effects of global warming. Because global temperatures rose during the period under study, a “warm” winter in the late ‘70s might be considered only “average” today. In fact, that’s exactly what happened last winter. It was almost perfectly average by historical standards, but because recent winters have been so much warmer, it felt cold to us.

Getting back to Candace’s question: does a warm winter predict a warm summer? To answer this question, we have to calculate my all-time favorite statistical formula, the coefficient of correlation!

It sounds like a mouthful, but it’s a pretty easy concept to grasp. The coefficient of correlation measures how tightly two sets of numbers go together. For example, if you surveyed 100 people, and asked each one what year they were born, and how old they were, you would find that every single person born in 1990 was the exact same age. The first number (year of birth) and the second number (age) are linked together 100%.

OTOH, if you asked those people for the last digit in their telephone number, you would find no relationship whatsoever. A person born in 1990 is just as likely to have a phone number ending in 9 as ending in any other number, and the same goes for people born in every year.

Calculating the coefficient of correlation (or “coco,” as I affectionately call her), requires wading through a truly horrific battery of equations all to arrive at a number between 0 and 1. A coefficient of 1 means the two sets of numbers are perfectly synched together; a coefficient of 0 means there is no connection whatsoever.

So, I went back to the temperature data. First, I defined “winter” the same way the weather bureau does: December, January and February, the three coldest months of the year. (None of that solstice-equinox nonsense here!) I defined “summer” as the three warmest months: June, July and August, again following weather bureau standards. Using the Northern Hemisphere Land figures (sorry, they didn’t have anything Minnesota-specific), I came up with an average anomaly for every winter and every summer. I crammed the numbers into the formula, turned the crank, and came up with a coefficient of…

(drum roll, please)

0.71

OK, now what does that mean?

Well, in general, a score below 0.30 is considered inconclusive. It’s too close to zero—the “relationship” could just be random. A score between 0.30 and 0.50 is generally considered moderate—there’s a connection there, but it’s somewhat weak. A score over 0.50 is generally considered strong—there’s definitely something important going on there.

(This is especially true in highly complex systems, like weather, where a lot of different factors can affect your results. In a very simple system, you’d probably want a result much closer to 1.)

It all boils down to this: we can be more than 99% certain that, yes, there is a connection between a warm winter and a warm summer, or a cold winter and a cool summer. How much of a connection? For that, we need another figure, the coefficient of determination.

This one is much easier. Just square the coefficient of correlation. 0.71 squared yields 0.5041. That means 50% of the variability in summer temperatures is determined by the winter temperatures.

And “variability” is the key. Like I said, weather is an extremely complex system. Lots of things can affect the temperature for a day, a week, even a season. The fact that this winter is warmer than last winter does not guarantee that this coming summer will be warmer than last summer. (For example, the winter of 2003-04 was one of the warmest on record, but the following summer was one of the coolest in the study period.)

What this number does mean is, that of all the factors that will affect next summer’s temperatures, half of them seem to be connected to winter temperatures. And this winter was warmer than last winter.

Just for fun, I also ran the calculations the other way, to see if a warm summer predicts a warm winter. The coefficient of correlation was 0.54, and the coefficient of determination was 0.29. So, again, there is a connection, but it seems to b a good deal weaker.

A word of caution: one thing statisticians like to say is “correlation is not causation.” Partly because it’s fun to say, but mostly because it’s true. Just because two things are correlated does not mean one causes the other. We have not proven that warm winters cause warm summers. It could be that winter temps and summer temps are both boosted by some other factor – El Nino, perhaps. All we can say is that there is some sort of connection going on, and that it probably wouldn’t hurt to lay in some tanning cream now.

Your Comments, Thoughts, Questions, Ideas

Candace's picture
Candace says:

=)

posted on Wed, 03/11/2009 - 10:41pm
`DO's picture
`DO says:

You have noted co-variance but not causality. Warm summers could cause warm winters -- or it could be due to some other factor entirely. Interesting piece of work tho.

posted on Fri, 03/13/2009 - 4:55pm
Gene's picture
Gene says:

The last paragraph specifically addresses causality, or lack of same. The penultimate paragraph specifically addresses the summer-winter link, or weakness thereof.

posted on Fri, 03/13/2009 - 7:20pm
teedy's picture
teedy says:

those are cute dogs

posted on Mon, 03/30/2009 - 9:51am
Anonymous's picture
Anonymous says:

i feel bad for those dogs i would hate to live my life as a dog model. espically having all those people stare at you and you know some people say nasty stuff about you.

posted on Mon, 03/30/2009 - 11:13am
Liza's picture
Liza says:

I don't think those dogs are "dog models" in any formal sense. I think they belong to the person, sbpoet, who posted the photo on Flickr.

posted on Mon, 03/30/2009 - 1:48pm
Gene's picture
Gene says:

If people do say nasty stuff, I suspect the dogs remain blissfully unaware. ;-)

posted on Mon, 03/30/2009 - 5:38pm
Pan's picture
Pan says:

Ehhh, dogs are awesome, but cats are way better, I can't say I care much about the dogs. Really dogs can be cute but then again they are balls of fur who chase cars and oh they are just weirdos!

posted on Mon, 03/30/2009 - 1:04pm
Anonymous's picture
Anonymous says:

so cute!

posted on Mon, 03/30/2009 - 1:42pm
Gene's picture
Gene says:

The figures for winter 2008-2009 are in. It was the third-warmest winter in the recording period. Plugging the numbers into the formula, the summer-temps-affect-winter-temps link is slightly stronger -- coefficient of correlation is now 0.54, and the coefficient of determination is 0.32. That is still much weaker than going to other way: winter-temps-affect-summer-temps.

It will be interesting to keep an eye on summer temps this year and see what happens.

posted on Thu, 04/23/2009 - 11:02am

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