March Madness

The National Climate Data Center has updated their temperature data for individual states and for USA48 (a.k.a. the conterminous United States, a.k.a. the “lower 48”). The headlines are that this March was the hottest March on record nationally, and this year’s 1st quarter (January through March) was likewise the hottest on record. Much of the central U.S. was as much as 15 deg.F hotter than average this March:

If we just plot monthly temperature anomaly for USA48, we find that March 2012 was not the most extreme on record:

It was, however, the 2nd-most extreme on record, and the top two highest anomalies have occurred since the year 2006. Is this because of global warming? Is it because average temperatures have risen? Or — can it be a sign of a change in the nature of extreme weather itself? Let’s take a look.

The first thing to note is that different months exhibit different variance for their average temperatures. This can be seen in a boxplot of monthly anomalies:

It is also evident if we simply compute, and plot, the standard deviation of monthly anomalies for each month separately:

Winter/early Spring months tend to show greater variation than summer months. In fact the standard deviation of February anomaly is almost 3 times as large as that for July. So, when monthly anomalies reach extreme values we can expect it to happen during January, February, and/or March, i.e., the 1st quarter of the year.

We can compensate for the unequal variance of different months by computing standardized anomalies. In fact we can call these “monthly” standardized anomalies, because we’ll divide each monthly value by the standard deviation for that same month. When we do so, suddenly this last March is not so extreme:

By this measure, March 2012 is now 3rd all-time highest, 2nd-highest occurred in 1998, and the highest standardized anomaly occurred in 1963. This casts doubt on the idea that extreme behavior itself has fundamentally changed.

We still note that there is a high frequency of extreme values — even for standardized anomalies — since 1998. If it’s not due to a change in the nature of extremes, could it simply be due to a change in the average temperature over time? Let’s compute residuals as the difference between each monthly value and the smoothed value shown (as the red line) in the 2nd graph (of raw anomalies). Then let’s compute standardized residuals by dividing each monthly residual by the standard deviation for that same month. That gives us this:

Now that we’ve compensated for the change in average value (due to global warming) and the month-dependent variance, we see that although March 2012 was unusually hot, it wasn’t out of line with other extreme values. As a matter of fact its standardized residual anomaly was only 11th-highest on record. That’s high, but not indicative of a change in the nature of extremes as compared to the time-dependent mean value. Nor is there obvious evidence that recent data show more extremes than previous decades.

In fact when we compensate for the change in average value and the month-dependent variance, the resultant standardized residual anomalies appear to follow the normal distribution:

If we apply the Shapiro-Wilk test to these values, there’s no evidence at all of any departure from the normal distribution (p-value 0.427). Furthermore, the most recent (March 2012) standardized anomaly is only a once-in-about-13-years event.

What does it all mean? My opinions are:

1: The extraordinary record-breaking heat in March 2012 is due to two factors. The first is ordinary variation in weather, the kind that has produced extreme heat in the past. The second is an increase in the mean value of temperature, caused by global warming. So: yes, global warming was a contributing factor to the record-breaking March heat.

2: I see no sign that global warming has changed the shape of the distribution of temperature variation in the lower 48 states of the U.S., only that it has caused a change in the mean value.

3: The kind of extraordinary heat we have just witnessed is no longer a once-in-a-century-or-two kind of event. It’s now about a once-in-a-decade event. As average temperature continues to rise, it’ll become even more common.

Many would like to blame the record heat on ordinary weather variation, in particular on “blocking events” which often lead to sustained extreme heat. Certainly that was a factor — without that kind of weather variation we wouldn’t have had extreme heat this March. But without global warming, it wouldn’t have been as hot as it was. And it won’t be too long before it gets even hotter.

UPDATE

I compared the standardized residual anomalies for various episodes, including: pre-1960 vs post-1960, pre-1975 vs post-1975, and pre-2000 vs post-2000. In all three cases, the Kolmogorov-Smirnov test indicates that there’s no difference in the distributions before and after. So it really does seem that the change in mean value is the only detectable change in monthly average temperature for USA48. The distribution remained the same except that its average value has been creeping higher.

This is just one reagion, it could be different for other areas of the globe.