Predicting "record years" and climate change with easy mathS

Random events, like high or low temperatures, rainfall (or lack of it) per year, and overall crop production, are unpredictable. And yet, within a certain space of time, there are ways of predicting how often record-breaking weather will come around. Call it the easy math of climate change.

There are ways to tell when some records are going to be broken. Whenever engineers design a better swimsuit, the world is ready for new records at the Olympics. But some events, like weather, are dependent on so many variables that no one could predict exactly when a record year will strike. Statisticians can, however, predict how often a record year will strike over a particular span of time, and it takes some relatively simple calculation.

For the sake of simplicity, we'll estimate that whatever is being measured is a yearly occurrence – say, average temperature. Record keeping begins with the first year. The first year records are kept is always a ‘record-breaking' year. If someone were to look at the records being kept for anything, anywhere, at any time, yearly records kept for one year will have one ‘record-breaking year.'

Along comes year two. Either the second year is even more extraordinary than the first, and is another record-breaking year or it is less. If there are two possibilities, there is a ½ chance of another record year. So looking at a huge number of two-year records, people will find an average of one and a half record-breaking years per record. Half of the year two records will have exceeded the year one records, and half will not.

Year three can either be higher than both years before, lower than both years, or sandwiched between the years. Three possibilities yield a one-third chance of being a record-breaking year. So the number of total number of record breaking years for a three year stretch of time will be one (the first year), plus one-half (the second year), plus one-third (the third year). Look at a huge number of three-year records and you will find 1.83 record-breaking years per record.
Eagle-eyed readers will have spotted a pattern.

For three years, the way to calculate the number of ‘record breaking years) is this: 1 + ½ + 1/3.

For four, it would be this: 1 + ½ + 1/3 + ¼.

And so it goes. So for N years, the way to calculate the number of record-breaking years is:

1 + ½ + 1/3 + ¼ . . . . + 1/N

Some things to notice, as the number of years recorded increases, the number of ‘record breaking years' does not keep pace. This makes sense given what we know of records. It's relatively easy to beat the world's record if it's only been kept for three years. There will be roughly two record-breaking years in there, and one of them very well might be you. A record that's been kept for thirty years will have roughly four record-breaking years, even though it's six times longer. A record that's been kept for a hundred years should only have about five record-breaking years. Five hundred years should only yield seven record-breaking years.

All these calculations are dependent on each year being completely random. If it isn't, there is some outside force acting on it. This is one of the basic calculations that worry climate scientists. If a record of Canadian weather shows six record-high heat waves in the last forty years, when there should only be around four, while another record for Antarctica shows five when there should be around three, and all other records, everywhere, show an above-average number of record-breaking heat waves, then something is driving the temperature up. In a truly random world, there wouldn't be so many records being broken.

Top Image: Michael Martin

Via Prairie State and Utah.edu