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.


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.

23 responses to “March Madness

  1. How much, if any of the greater variability for the colder months comes from the fact that they have experienced a higher trend?

  2. flakmeister1

    It gets better…. NOAA also declared the April-11 to Mar-12 12 month period, the warmest on record….

    Just move along folks, nothing to see here…

  3. This is interesting. I just recently read “Extremely Hot” by Stefan Rahmstorf and Dim Coumou at They argue that a static variability shouldn’t be assumed as temperatures increase. More examples of analyses such as yours, in a variety of locations, could show that the data don’t obviously violate that assumption. If so, it should make assessment of future implications somewhat simpler. Good news, for various managers who are trying to plan for decades in advance.

  4. This is a very good, succint statement of what climate scientists have long suspected. I’m bookmarking this one for future reference. Thanks.

  5. Form a similar thread over at RealClimate: Put another way; if it’s 30 or 40 degrees warmer than normal in March that’s pretty damn warm for that time of year….were it 30 or 40 degrees warmer than normal in August….that’s hell or high water country…

  6. See the UPDATE for results of direct comparison of the distributions before and after various times.

  7. A measured and reserved analysis, somehow I feel the media would prefer more hype. The weather in the UK has also broken records, the serious press has not over hyped the link and the more excitable media has a tendency to dismiss AGW and avoids mentioning it.

  8. Hansen et al cover this question globally (for summers) and suggest that the distribution is broadening as well as shifting up:

    Click to access 20111110_NewClimateDice.pdf

  9. it seems that February is the cruellest month (apologies TS Eliot)

  10. 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

    This level of concepual understanding is completely lost on the folks at WUWT. One of Anthony Watts’s favorite things to do is parade around the latest study on some extreme event (like this, the Russian heat wave, …) that explains the particular weather feature responsible and claim that this shows it has nothing to do with global warming. The fact that it is always possible to blame an extreme event on a particularly extreme weather pattern guarantees that he will always be able to play this game and guarantees that his minions will always get to hear what they want to hear.

  11. There is some evidence that blocking patterns are increasing in duration because of climate change (Arctic Amplification to be specific), so this explanation is not necessarily inconsistent with the rest of your analysis.

    Click to access Francis_Vavrus_2012GL051000_pub.pdf

    It’d be interesting to redo your analysis including only the approximate area (states) to the southeast of that “interesting” March jet stream pattern.

    Great post, thanks.

  12. Horatio Algeranon

    RE Update:

    If you are not seeing any difference between “before” and “after,” perhaps you need to do the “Smirnov test” a few more times.


    [Response: Truly, funny!]

    • Yes, but the Smirnov test often leads to duplicated data–rarely, to duplicated results.

      • In the most extreme applications of the Smirnov test can lead to duplicated results. From experience I can tell you that extreme applications of Smirnov will lead to seeing the same thing twice!

      • Jmsully,
        I personally know of instances where extreme applications of the Smirnov test have led not just to duplication of results, but to reproduction!

      • Horatio Algeranon

        Well, since the conversation (or at least “bridge to the alligator swamp” offshoot of it) has now clearly turned to highly arcane technical matters, Horatio would just add that for doubling, cycles, random walks, etc, Smirnov ain’t worth Jack, (just Horatio’s humble opinion)

    • In absinth of any better method, I guess.

      • The likelihood of unplanned reproduction is increased if your method of prevention is based on unreliable extrapolations of poorly-quantified cyclical patterns in historical data.
        [Can we all agree to refrain for making references to mathturbation???]

  13. Yes, but all of this data is contaminated by industrial levels of CO2. We should compare recent extremes to years when CO2 was at pre-industrial levels of arouned 280 ppm. And, all of this data is from a climate system subjected to increasing levels of CO2. There is not one data point from a equlibrium climate system. Doing statistics on an “out-of-control”, dynamic system means that the population being sampled is constantly changing. Thus, we have one data point from system1934 and one data point from system1963. These are fragments of weather PDFs that belong to different weather systems with different levels of greenhouse gases (i.e., energy). Plotting them together is a little like plotting the weights of different kinds of fruit togther.

    What is the variability of the weather system under equlibrium conditions? Events like the MWP and the LIA suggest that it is larger than hinted at above. However, pushing the system by adding greenhouse gases changes the shape of the PDF. And, just as we often underestimate preindustrial variablity of weather, we also underestimate how much changing levels of CO2 distort the PDF for various weather events.

    All weather and climate events (at a given time) are parts of the same weather and climate system, and are driven by the same energy. Energy from AGW is in the system and affects all weather. All weather is affected by all the energy in the system. Increasing CO2 increases the energy in the system, which affects all the weather. As long as CO2 is increasing, the concept of “ordinary” weather is silly.

    [Response: Frankly, your comment makes no sense to me. The plain fact is that the distribution of deviations from the mean is normal, and has remained unchanged throughout the time span of observation — only the mean itself has changed.]

  14. Tamino,

    If as Hansen believes the distribution is broadening and yet your analysis suggests that it is not, at least in any statistically significant way in the lower 48, might this be an example of the law of large numbers, where the reason why there is no detectable broadening in the lower 48 is related to only 1.5% of the globe being the subject of your analysis?

    [Response: Perhaps, but I think it’s more likely that the disagreement isn’t because of larger numbers, but due to the fact that different regions are behaving differently.]

    Also, Douglas mentions how Arctic Amplification is presumably resulting in more blocking. The jet stream slows (related to the lengthening of the residence time of water vapor in the atmosphere that came up in an earlier discussion here, I believe), so that whether pattterns stall, and likewise, Rossby waves become more high amplitude, resulting in the deeper incursions of warm air in the north at the peaks and deeper incursions of cold air in the south at the troughs. This presumably leads to the greater global variability that Hansen claims to see.

  15. > Increasing CO2 increases the energy in the system
    But where? I think the naive idea is that climate change will put more heat into the cold side of a heat engine. But isn’t it more like putting the excess heat around the hot side of the heat engine? Less rather than more storm strength is the example I think from Isaac Held some time ago hereabouts.