The Probability of Global Warming

Forbes magazine has become a real dreg of climate change denialism, bringing in paid shills to write up the standard nonsense put out by the fossil fuel industry. Which means I have to spend a lot of time reading it. The reward is they will, on occasion, bring in someone to write about the science. These articles are frequently written by noted climate scientists and can be excellent sources of information.

Today, I read one that really caught my attention - The End of the Partisan Divide Over Climate Change. The article was hopeful and that part was nice. The author, Tom Zeller Jr., wrote about how polls show even Republicans are starting to agree CO2 needs to be regulated as a pollutant. But, that wasn't the part I found most interesting. It was the last paragraph that really got my attention. Referring to the fact that 2014 was the hottest year ever recorded, he said:

After all, a record-setting year every now and again is no big deal. Anomalies happen. But the fact is that all 15 years since the year 2000 have been among the top 20 warmest years ever recorded. The odds of this happening randomly, or as a part of natural variability? About 1.5 quadrillion to one.

This is a very different way to look at it and is very persuasive. If correct, these figures show there can be no doubt about the reality of global warming. That figure is devastating to any claim global warming is not real.

The calculations were performed by a team of university statisticians and I am confident in their accuracy.  But, let's look at the figures for ourselves and see if we get something close to the same number.

The way to imagine this is to suppose we have a bag filled with tokens numbered from 1 to 135. That is the number of years in the recorded temperature record. Number 1 would be for the hottest year on record, number 2 for the second hottest and so on. Now, we are going to reach into the bag and blindly draw out a token for the year 2014. The chances of that token being between 1 and 20 (inclusive) is 20/135 = .148148. That is a 14.81% chance, or one chance in 6.75 tries. Now, we do it again for 2013, but we took out a token already and we know the token was in the top 20 (that is the situation we are calculating the odds for), so there are only 134 tokens remaining and 19 of the top 20. The odds of 2013 being randomly one of those top 19 years is 19/134 = .141791. That is a 14.18% chance, or 1 chance in 7.05 tries. We can continue this process for all fifteen years since 2000 and the odds would be 18/133 for 2012; 17/132 for 2011, 16/131 for 2010, etc.

Those are the odds for each year individually. But, we want to know the odds for all of them at once. To get that figure we multiply the individual probabilities together. For the fifteen years in question, that would be (20/135) * (19/134) * (18/133) * (17/132) * ......

When I do that, I get 5.0409 x 10^(-16). That is percentage of .00000000000000504%, or one chance in 1,983,770,000,000,000.

Or 1 chance in about 2 quadrillion tries, very close to what the article quoted.

In other words, there is positively no way it could be a random occurrence. Global warming is most definitely real.

I never doubted the professors were right, I just wanted to make sure no one else did, either.