The recent heat dome of June 2021 roasted much of Western and Central Canada with record breaking temperatures. Sea life was cooked in the oceans. Wildfires continue to rage across the countryside. This suggests the statistical question: How extreme were these extremes?

Climate statistics and modelling is an immensely complicated endeavour with many specialists among our SSC members. Instead of a grand climate model, I considered a much simpler question: How likely would a 37°C high temperature be in the city of Edmonton based on the 20th-century data? Environment Canada collects data across the country including daily high and low temperatures. One weather station in downtown Edmonton has temperature measurements from 1938 to 2000. If we consider the maximal June temperature over these years, we get an average of

$$ \mathrm{mean}_{y = 1938,\ldots,2000}\left[ \max_{d = 1,\ldots,30} \{\text{high temp}\}_{y,d} \right] = 28.8C$$

with the standard deviation of 2.3 and a very normal looking distribution based on standard goodness-of-fit tests (Kolmogorov-Smirnov, Shapiro-Wilk, Anderson-Darling, etc.). The 37°C high temperature is 3.57 standard deviations above the mean. Over an entire century of Junes, the probability of seeing such a high temperature is 1.8% using the normal distribution, which suggests this was more extreme than what we would reasonably expect to see in the 20th century. Using the generalized extreme value (GEV) distribution, we see a similar tail probability of 2.9%.

Taking the same approach for the maximal nightly low temperature—i.e., the hottest night in June—we have an average of

$$ \mathrm{mean}_{y = 1938,\ldots,2000}\left[ \max_{d = 1,\ldots,30} \{\text{low temp}\}_{y,d} \right] = 14.9C,$$

a standard deviation of 1.6, and another normal looking distribution. Our hottest night dropped down to only 23°C this past June, which is 5.06 standard deviations above the mean. The probability of seeing such a hot night in at least one of 100 years is 0.002%. The GEV distribution gives a similarly tiny tail probability of 0.044%. Thus, we can conclude that the June heat dome was, in fact, a significant outlier for the city of Edmonton and based on news coverage, much worse for other locales.