It’s another scorching, summer day. Your friend, wiping off a bead of sweat, sighs and says, “Global warming!”

Not exactly. The temperature on any single day proves nothing. Hot days occurred in the past and hot days occur today. Experiencing just a single hot day does not tell us if it is a normal hot day or a hotter than normal hot day. This is the issue that James Hansen, a notable climate researcher, and his colleagues set out to address in their recent paper.

The authors analyzed global temperature data from 1951 to 2010. They focused on summer months and grouped the measurements by decade. For each decade they calculated the average (mean) and a measure of how much individual measurements varied from the average (standard deviation). They then plotted the relative frequency of occurrence for each temperature.

To create the plot, the authors used the mean and standard deviation of a reference period from 1951 to 1980. The horizontal axis indicates the number of reference standard deviations away from the reference mean (for example, 0 is exactly at the reference mean, 4 is 4 standard deviations above the reference mean, and -1 is one standard deviation below the reference mean).

To give an idea of what standard deviation means, for a bell-shaped curve like the black one, there is over a 30% chance of experiencing a temperature more than 1 standard deviation from the mean, less than 5% for temperatures beyond 2 standard deviations, and less than 0.3% for temperatures beyond 3 standard deviations.

What the plot shows is that as the decades advance, the mean temperature, which is near the peak of each curve, gets larger (temperatures are hotter). As decades advance, the standard deviation, related to how fat the curves are) gets larger as well (temperature is also more variable). Cold days have only reduced slightly in frequency, but hot days have gotten much more common. For example, looking at values three standard deviations away from the reference mean (a cutoff for extreme hot days), a temperature that for 1951-1960 had close to 0% chance of occurrence had about a 6% chance of occurrence in between 2001 and 2011.

This work shows, in clear and explicit terms, that in the aggregate, our hot days are getting hotter. Moreover, temperature has not only increased, but also become more variable, leading to much more frequent, excessively hot days with no real change in the number of cold days.

While the conclusion is obvious -significant action is needed to stall this trend- this, as we know all too well, is much easier said than done.