I decided to apply the method used in the post about the heat wave in the Pacific Northwest, to look at ERA5 data for daily high temperature, but for other regions. Having looked at a number of spots, let me show you what it looks like for two of them which represent very different recent history of extreme heat.

One is latitude 45°N, longitude 5°E, in France, not far from the city of Lyon (which is not far from the Swiss border). The other is just north of New Orleans, at latitude 30°N, longitude 90°W. We’ll start with France, and here’s the data for temperatures 90°F and hotter:

Right off the bat it “looks like” (there’s that phrase again) there have been more such days lately. I found the highest temperature for each year (excluding 2021, which isn’t over yet), and the trend (red line in the graph with pink shading for uncertainty range) is not only real (i.e. overwhelmingly statistically significant), it’s substantial, increasing by 6.4°F from 1950 to now.

To look for changes in the distribution, first I isolated the summer months (June, July, and August), then computed anomaly (the difference from the average value for the given time of year) in order to remove the seasonal cycle. Then I split the time span (1950 to now) into *three* segments: from 1950 to 1975, from 1975 to 2000, and from 2000 to now (this differs from the previous analysis, in which I only used two segments). Finally I estimated the pdf (probability density function) for each interval, both by constructing a histogram and by a smoothed estimate. Here they are, with interval 1 (1950 to 1975) in blue, interval 2 (1975 to 2000) in black, and interval 3 (2000 to now) in red:

Clearly the most recent time span (2000 to now) has far greater likelihood of extreme heat (which we get from very high temperature anomalies in summer). It also “looks like” the distribution got wider, making the excursion into extreme heat even more extreme.

All three time intervals have different distributions. But interestingly, if we offset each series by its own average, to get a distribution with the same *shape* but with average value zero, then the first two intervals show no significant evidence of a difference in their distributions. The real difference from time span 1 to time span 2, is the small increase in its mean value.

But the third interval has a pdf which is definitely of a different shape than the other two. In particular, its variance increased (the distribution got wider). More to the point at hand, the high-temerature end of the survival function tells us the likelihood of extreme heat during each span:

This region shows exactly the kind of temperature increase, not just of the average but of the extreme-heat region, which makes it vulnerable to never-before-seen heat waves.

Turning our attention to the western hemisphere, let’s look a bit north of New Orleans at latitude 30°N, longitude 90°W. Here’s the data for temperatures 92°F and hotter:

This time, the yearly high temperature series shows no significant trend:

Performing the same procedure as before to study possible changes in the distribution, I get this for this part of the USA (interval 1 in blue, interval 2 in black, interval 3 in red):

They all look similar, and when we use the Kolmogorov-Smirnov test, none of them shows any statistically significant sign of being different from the others. This overall picture, of a location *not* in danger of extreme heat because it has shown neither strong warming of its average nor widening of its profile, is confirmed by a close look at the high-temperature end of the distribution:

So far, all indication are that the change in a location’s susceptibility to extreme heat is dominated by the change in its summertime average temperature. I have not yet found a case where a shape change dominates, either to creates or to suppresses a significant change in extreme heat. It’s the change in average temperature (during summer, at least) which carries the day. But … I have a lot of locations yet to study.

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