**The average trend is a cooling one**

The American prophets of the climate apocalypse are telling us that Rick Perry is witnessing a frying death of his state of Texas that is suffering from global warming: the theory of anthropogenic climate change exactly predicts a higher number of TX arsons in 2011, too. They have used the warm Texan summer days of 2011 as another argument.

So I decided to look how the temperature trends look like in the capital of Texas, Austin, since the beginning of the records available to Mathematica. And I wanted to know the trends for each of the 366 days of the (leap) year. First, I imported the data by this command:

austindata = WeatherData["Austin", "MeanTemperature", {{1900, 1, 1}, {2011, 12, 31}, "Day"}]All other operations I did are self-evident to the readers with some knowledge of statistics so I don't need to include the source code in Mathematica.

It turns out that the command above produces 25,965 daily temperature readings that start on April 1st, 1938: Austin provides us with a longer record than e.g. Dallas, Houston, and others which is why I chose it. This number of days is equivalent to 71.1 years which is about what you would expect because 2 years of data – somewhere between 1971 and 1973 or so (which is almost exactly in the middle of the interval 1938-2011, so the gap won't detectably affect the trends) – are missing.

For each of the 366 possible {month,day} combinations in a year, I computed the slope – cooling or warming trend – out of all the available data i.e. all the available years. The trends for February 29th is only computed from the leap years but that's enough, anyway. What are the results?

*The temperature trend in °C per century for each of the 366 possible dates. Click to zoom in.*

You see a pretty chaotic curve which may be something in between red noise and white noise. The possible trends reduced to particular {month,day} combinations go from –9.6 °C per century for December 25th to +10.3 °C per century for February 21st. Yes, the Christmas Days in Austin since 1938 have been cooling with the trend of almost 10 °C and the city hasn't died because of that. It's likely that nobody has even noticed that the Christmas Days in Austin got about 7 °C cooler since the late 1930s even though statistics clearly shows it's the case. Similar comments with the opposite sign hold for February 21st.

You may want to see the possible trends for the 366 days in terms of a histogram:

*On the y-axis, I depicted the number of dates (the total number is 366) for which the Austin temperature trend in °C per century (on the x-axis) belonged to particular bins.*

It is hard to overlook that the center of the bell curve is shifted to the left. And indeed, if you compute the average and standard deviation (or root mean square) of the 366 calculated trends, you will get

trend = –0.23 °C ± 2.30 °C per centuryIn other words, the average temperature trend in Austin since 1938 has been a cooling one, but a very small one, by less than a quarter of a Celsius degree per century. 214 out of 366 days i.e. 58% – a minor but detectable majority – report a cooling trend.

However, different days in the year experienced very different trends. The standard deviation is 2.3 °C per century, a full order of magnitude higher than the mean value: note that this is a pretty typical distribution of trends you encounter whenever you deal with many different trends associated with particular places or particular days of the year: we found an almost identical root mean square in the case of the distribution of trends at the HadCRUT3 stations (which offer 77 years of data in average, which is also similar to Austin in Mathematica). If I remember well, the standard deviation was also about 2.3 °C so some readers will surely start to call it a universal law.

Let me emphasize that the origin of this width of the statistical distribution is clearly natural: these are natural location-dependent and time-dependent variations that Nature can't ever eliminate and that have existed on Earth for billions of years. Many champions of the panic try to emphasize that we must distinguish the climate and the weather. Indeed, they refer to different pieces of the information about the atmosphere. However, what those folks generally misunderstand is that the changing weather is far more important than the climate change.

And the distribution is getting thin slightly more slowly than the normal distribution (but the deviation from the Gaussian shape isn't too large) because you may see trends as large as ±10 °C per century which corresponds to a "four-sigma effect" (note that 10 °C is greater than 4 × 2.3 °C) which is somewhat unlikely to occur even if you have 366 datapoints to check (only three-sigma effects are likely to occur for 300 datapoints by chance).

The average cooling trend would be more substantial if we had the (mostly warm) data from the bulk of the 1930s and not just the daily data since 1938. At any rate, there has been no warming in Austin, Texas, since 1938, and the same conclusion almost certainly holds for a big majority of the weather stations in Texas.

**Bonus: Christmas Day in Austin**

If you're interested in the Christmas Day – December 25th – in Austin, this is the graph you look for:

*December 25th temperatures in Texas, 1938-2010*

The dip near the 44th year seems to be real (–9.28 °C on December 25th, 1983: chronicles show that this big freeze isn't a bug of Stephen Wolfram); I have just omitted the missing days from the years 1971, 1972 from the dataset. You may see that a natural interpolation of the data sees the temperature for this day decrease from about 15 °C in the late 1930s to 7 °C in recent years. Such temperature changes for a given day are completely normal and I guess that 80-year-old inhabitants of Austin haven't even noticed that the Christmas Day has been changing in this way.

The idea that temperature trends for a particular day and place accumulating something like 1 °C in a century are dangerous is totally preposterous. Even trends comparable to ±10 °C per century are relatively common as we have seen.

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