People requested that I look at the relationship between the change in mean temperature and the change in the frequency of extreme heat, not using temperature at the 850 hPa level (about 1.5 km altitude), not using a reanalysis data set which doesn’t incorporate any actual temperature measurements, not using anomaly data, and not restricting analysis to Dec-Jan-Feb (winter months in the northern hemisphere).
Let’s try to do this right. Let’s use actual temperature data from actual thermometers. Let’s look at temperature at earth’s surface, where we actually live. Let’s use temperature rather than temperature anomaly, since that’s what actally defines what a region would experience as extreme heat. Since I’ll be looking at northern hemisphere locations, let’s use data from Jun-Jul-Aug, actual summer months.
I acquired daily temperature data from ECA&D (European Climate Assessment & Dataset). I then isolated the data from June, July, and August. In order for a year to be included, it had to have data for at least 85 of the 92 summer-month days. In order for a station to be included, it had to have data for at least 100 years since 1900, including at least one year in the 2010’s. That left 167 locations (mostly in Europe, entirely in the northern hemisphere) with sufficient data to be included.
For each year, I tallied the number of hot days. “Hot” is defined relative to what was normal for that location prior to 1980. The cutoff limit was chosen as the 97.5th percentile, which for a normal distribution corresponds to 1.96 standard deviations above the mean (but no normal-distribution assumptions are involved in the actual analysis).
I then compared mean summertime daily temperature for the first 30 years of data, to that for the last 30 years of data, and compared the number of hot days for the same time spans.
The result? Here’s a graph of the change in mean temperature between those two 30-year periods; red circles mark locations where the temperature increased, blue circles where it decreased, and the size of the circle indicates how much the temperature changed:
Here’s a graph of the change in the total number of hot days during the 30-year time span, red circles for locations where there were more hot days, blue circles for locations with fewer hot days, and the size of the cirlce indicating how much the number changed:
Comparison of these graphs reveals that the pattern of changes in the number of hot days is quite similar to the pattern of changes in mean temperature. Yes, the increase in extreme heat is strongly correlated with the increase in mean temperature.
This strongly and unambiguously contradicts the idea that “The pattern of the change in extreme warm daily temperature probabilities looks nothing like the mean warming pattern.” For the few locations I’ve examined, the same contradiction is found if, instead of doing it right, you mimic Sardeshmukh’s procedure and use reanalysis data at the 850 hPa level, using temperature anomaly rather than temperature, restricted to Dec-Jan-Feb, but use a different reanalysis data set (from ECMWF). The same contradiction is also found if you use Dec-Jan-Feb reanalysis data for temperature at the surface (T2m) rather than the 850 hPa level.
All of which argues that IF the results of Sardeshmukh et al. are correct for the data set they used, then there just might be quite a problem with that data set because it’s contradicted by other reanalysis data, surface temperature data from reanalysis, data from summer months for the northern hemisphere, and of course, actual thermometer data.
If the sole purpose of Sardeshmukh et al. is to demonstrate that changes in the probability of extremes depends on changes in the probability distribution’s shape as well as its mean and standard deviation, then their work is rather trivial. If, however, their purpose is to suggest that this phenomenon is presently happening on actual planet Earth, then they seriously need to reconsider.