Climate Change and Extreme Heat

This summer, parts of the USA, Europe, China, and South America have sweltered through extreme heat, sometimes referred to as “heat wave” conditions, although there’s no universal agreement on exactly what a heat wave is and no agreed-upon measure of the severity of extreme heat.

With such imprecision and ambiguity, naturally there is considerable confusion about the impact climate change (a.k.a. global warming) has on extreme heat. Too many people adopt the naive premise that the only effect of climate change is to make each heat wave a couple degrees hotter. The truth of the matter is that because extreme heat is extreme, it is by definition rare, and that is exactly the case in which a small change in the mean value — the result of global warming — can bring about a large change in the number and extremity of extremes. Everyone understands that rare events (like heat waves) are made hotter (on average), but few appreciate how profoundly they are made more common.

This is sometimes illustrated by a graph like this one, of the “probability density” of temperature

The area shaded pink indicates extreme heat, while the area shaded light blue indicates extreme cold. In point of fact, it is the rarity of these events which defines them as extreme; we generally determine these extreme limits by observation, in order to prepare for extreme heat events based on how likely they are to occur and how severe they will be.

I’ve chosen to define “extreme” as being more than 2 “standard deviations” above or below the mean, which for a normal probability distribution means a 2.3% chance of extreme heat and the same chance of extreme cold. Climate change (global warming) is changing the odds, in particular changing the mean value; when we change it by a fraction of a standard deviation, it has its strongest impact on the extremes of the distribution.

The probability density function has been shifted to the right; a modest increase due to global warming. But as a result, the area in the “extreme heat” region has nearly tripled, while the area in the “extreme cold” region is reduced to less than a third of its former value. Here’s another version (a bit more schematic) of the same graph:

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When considered carefully, the principle is sound: small changes in the mean can bring about relatively large changes in the likelihood of extremes, when the distribution itself shifts but doesn’t change its shape. This seems to be the case, at least approximately, in the real world.

To see what real-world probability distributions actually look like, I acquired daily temperature data for the state of Arizona, which I got from the ERA5 reanalysis data set over the geographical range 109 to 115 °W longitude, 31 to 37 °N latitude. That’s not exactly the same as the state of Arizona, but is very close, and will certainly reveal how extreme heat in that region has changed over the years.

Then I divided the data into two intervals, before and after the year 2000, and estimated the probability density of daily summer high temperature for each. I did so by a histogram, as well as a kernel density estimator to give a “smooth” estimate, and here’s the probability density for the pre-2000 interval:

In this case, for this region, a good threshold temperature to define “extreme heat” is 100°F or hotter; days reaching that temperature can be called extreme. Note that this is the average for the entire state, and goes to show just how hot it is in general; until the state-wide average gets to 100°F we can’t really call it extreme. Prior to the year 2000, there were — on average — 3.2 extreme days per year, reaching 100°F or hotter.

Here, in red, I’ve added the estimated probability density for the years since 2000:

As in the schematic diagrams at the beginning of this post, a modest increase in the mean has brought with it a sizeable increase in extreme heat and decrease in extreme cold. Since 2000 Arizona has, on average, reached 100°F 6.8 days per year. That’s twice as often as before 2000, and the difference isn’t just a statistical fluke; it’s what is called “statistically significant.”

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I also counted the number of “extreme-heat days” (reaching 100°F or hotter) each year in this record (from 1950 to the present)

The solid line is a best-fit curve by quasi-Poisson regression (rather necessary to accommodate things, esp. the fact that the number of days per year can’t possibly be less than zero). It doesn’t mean the background level has actually followed this pattern, but it does suffice to show, statistically, that the number of extreme hot days is increasing over time. This analysis suggests it has risen from about 2 per year in 1950, to more like 8 per year now.

Don’t be too surprised that this year (2023) doesn’t have the most 100°F-days, despite the extreme heat this year. It’s simply because 2023 isn’t over yet, and these data only go to the end of July. All the 100°F-days in August (and there will be some) haven’t been counted yet for 2023, but when they are, it’s most likely to move into first place on the most-100°F-days list.

I also sought a measure of extreme heat which not only accounted for the number of days reaching a threshold, but how much it exceeds that value. One objective choice, a quantity I’ve found very useful, I call “extreme degree-days,” or XDD. It was given the same name but the different acronym “EDD” by Lobell et al. (2012, Nature Climate Change DOI, 10.1038/NCLIMATE1356) who related it to senescence of wheat when temperatures rise above 34°C (93.2°F) in India. When a day’s high temperature x exceeds a given threshold θ, we estimate the cost as C = x – θ extreme degree-days for that day. The total (XDD) for a given season/year is the sum of each day’s extreme degree-days.

Here’s the count of XDD (extreme degree-days), summed over the entire year, for a temperature threshold of 100°F, for the state of Arizona, for each year since 1950:

Once again, the solid line is a trend estimate by quasi-Poisson regression, and demonstrates (with statistical certainty) that the XDD values are trending upward, from about 1.4°F per year in 1950 to around 18°F per year now — a more than ten-fold increase in extreme degree-days.

And this graph, too, only includes data through the end of July for this year. Any XDD accrued in August (perhaps even September) will increase this year’s lead over its predecessors.

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The particular case of Arizona shows, without doubt, that a modest warming is directly linked with a big increase in extreme heat, doubling the number of extreme-heat days and increasing XDD (extreme degree-days) tenfold. Those who claim that the impact is “minimal” and or unimportant, are fooling themselves. I hope they don’t fool you, too.

The story in the city of Phoenix is even more troubling. Its hot extremes of daily high temperature show similar increase, but the hot extremes of the overnight low have risen even faster, far faster than the state as a whole. This is primarily due to the “urban heat island” effect, which makes it very difficult for urban areas to cool off at night. Unfortunately, lack of nighttime cooling is a major factor in the health impacts of extreme heat, making things far, far worse for the poor who can’t take refuge in air-conditioning.

Most Americans haven’t yet felt the heat like the desert southwest did this year. But their time is coming. As for the people of Arizona, your next heat wave might be years away, but before very long you’ll swelter through another angry summer, one even worse than this year.