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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Open Mind 
Please look at the PNW when you have time. I think things have heated up quite a bit over the time frame you are using. I think the PNW started out cooler and more survivable than many areas of the planet, but the changes in baseline temp, precipitation, etc. have created a lot of heat-stressed forest and grassland that can really burn when a spark ignites somewhere.
Great to have you posting again.
Cheers
Mike
Glad to see you back writing again.
I get that you are focused on extreme heat events for your recent analyses, but I think it might also be interesting to look at the evolution over time of daily low temperatures at various seasons (and locations). Does the probability distribution of daily lows shift similarly to daily highs? More? Less? Perhaps your analysis showing similar pdfs at early and later times implies the answer. But it would still be interesting to see the analysis. Some other analyses have shown that daily lows have increased more than daily highs, at least in some locations.
It’s possible to do without the assumption of Normality by using a Mann-Whitney test or its more modern version, the Wilcoxon–Mann–Whitney test or its modification, theFligner–Policello test.
These are available in the robustrank package in R, and written up by that package’s author and a colleague, at
Fong, Youyi, and Ying Huang. “Modified wilcoxon–mann–whitney test and power against strong null.” The American Statistician 73, no. 1 (2019): 43-49.
A very quick view of where average summer temperatures are rising most sharply in the NH can be see using the maps on the GISTEMP web page. The map for July & for August averaged for 2010-20 (with 1950-80 anomaly base) shows south-central France as the western end of a hot-spot stretching across Southern Europe while N’Orleans has, if anything, got away with less-than-average AGW. The two maps also suggest that the NWP regions of the USA (where this issue kicked-off) are more susceptible to high temperature in August rather than July.
disregard my pnw review request, you just did that. Apparently, my specific aging process involves advancing tremors, loss of balance, occasional disorientation and some memory loss. Docs tell it does not look like Parkinsons, so that’s good I guess.
I may eventually fail to remember how to turn on the computer and I plan to post less after that happens. I plan to spend more time on the floor then and let the dogs and grandkids and great grandkids crawl all over me.
Cheers
Mike
Dear Tamino,
My apologies if this kind of request is impinging excessively on your time. Feel free to ignore me.
That said, would it be possible for you to run a quick similar analysis
to the average Summer temperatures in mainland Portugal?
Mainland Portugal lies roughly between Lat: 42N to 37N and Long: 6W to 9W.
Whilst the Iberian Peninsula as a whole is, for sure, very susceptible to extreme heat, and drought with tendency for desertification and expansion across the Mediterranean of Sahara’s northern boundary – (not at all dissimilar to what is happening in the North American Southwest states) I wonder if the extensive portuguese Atlantic coast is having/will have some mitigating influence on these extreme events – particularly when the “north Atlantic cold blob” is not that far off our coast, and, at any rate, Portuguese climate is strongly influenced by the warm Gulf Stream which has been weakening in the past few decades.