Is temperature variance changing?

People in agriculture often talk about “weather getting more variable.” It’s usually hard to know exactly what they mean – sometimes they are talking about precipitation becoming less frequent and more intense, and sometimes they're talking about hot extremes becoming more frequent. But it’s well known that what was considered “extreme” historically can become more frequent just by shifting the mean of the weather distribution, without any change in variance. The IPCC SREX figure below shows that clearly in the first panel.

We care about variance, though, not just because of its ability to increase the occurrence of historical hot extremes. If variance is increasing, this would mean more uncertainty faced each year by farmers and markets about what the growing season weather will be. Note that we are talking here strictly about weather variance. The variance in production can increase just from a shift in the distribution towards less favorable temperatures, as we showed in a recent study led by Dan Urban.

The question of whether variance per se has been changing (or is projected to change) has received much less attention than whether extremes are becoming more common. This is partly because changes in variance are harder to measure than shifts in means or increases in extreme events. But an interesting analysis by Donat and Alexander in GRL sheds some light directly on the variance question. They looked at the distribution of daily temperature anomalies for two 30-year time periods: 1951-1980 and 1981-2010. The figure below from their paper maps the change between the two time periods for three parameters of the distribution (mean, variance, and skewness), both for minimum (left) and maximum (right) temperature.

Two things seem new to me here. (Certainly the shifts in mean are not new, but it’s interesting to note that the shifts are about equal for minimum and maximum temperature.) First, the variance changes are mixed around the world, and not statistically significant in most places (the significant areas at 10% are shown with hatching). The authors also say that the variance changes depend a lot on what criteria they use to exclude grid cells without enough data.

The second interesting thing is that the skewness has increased in most parts, much more uniformly than the changes in variance. Just to be clear, we are talking about skewness in the statistical sense, not in the way it is sometimes used to mean “distorted” or “biased”. An increase in skewness means that the distribution is now less left-skewed or more right-skewed than before, which would mean that for a given average, there is a higher chance of having warm anomalies and a lower chance of having cool anomalies (see bottom panel of ipcc figure above).  

It’s hard to know what exactly is driving the skewness, but I suspect their paper will spur some more focus on this issue. Maybe it has to do with the shift in rainfall distribution toward heavier events, with less rainfall during moderate events. For now it seems safe to say that temperatures are not clearly becoming more variable for most parts of the world, but they seem to be slightly more skewed toward hotness.