2018 is shaping up to be one of the warmest years on record. With heatwaves currently sweeping through much of the world, it is worth taking a look at just how extraordinary the rise in global temperatures has been.
Here is a picture, courtesy of NASA, of the rise in global surface temperatures:
The plot shows anomalies in global temperatures relative to the average temperature in 1951-1980. Since 1880, the temperature has gone up by 1.2 degrees Celsius.
Here is what is even more remarkable. In this short period of time, we have seen nineteen record-high temperatures, with most of the records taking place after 1980 (shown in green in the plot).
It sure looks like the Earth is getting warmer. But maybe the Earth is just suffering from some bad luck? How likely is it that a pattern like this would arise just by chance?
It is easy enough to answer this question by using a technique called the bootstrap. Let me spare you the geeky details, except to say that the bootstrap simulates alternative histories. Using the observed temperatures, we can simulate an alternative history of temperatures—under some assumptions—and calculate the number of record-high temperatures. We can then compare the actual number of record-high temperatures to the simulated results.
Here is what you get if you do so:
None of the simulations even get close to the nineteen record highs. In other words, nineteen record highs would be extremely unlikely to happen by chance alone.
The simulation above assumes that the global temperature in one year is independent of the temperature in nearby years. In reality, that is not the case, for a variety of reasons including El Niño.
It is easy enough to account for this. (I use a simple technique called a moving block bootstrap.) If we assume that temperatures are dependent in blocks of ten years, we get the following:
Only 0.4% of the simulations give results that are more extreme than what we observe in reality. Again, strong evidence against "just bad luck."
We can be more systematic and repeat the same calculation for a variety of assumptions on how temperatures depend over time:
Even if temperatures were very persistent, that many record-high temperatures would still be unlikely.
Just some graphs to ponder.
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Jupyter notebook with Python code that was used to obtain the plots can be found here.