Sunday, January 03, 2010

Warming trends in England from 1659

Because the Hadley Center has released the final temperatures in Central England for 2009, I decided to calculate a few things. Although I have also played with the monthly data, this text will be purely about the 1659-2009 annual data. It's 351 years in total.
A related link: The counterpart of this article for the world's second oldest weather station appears in the article Czech ClimateGate: Prague's Klementinum censored
The average of the 351 numbers is 9.217 °C. The Pythagorean average of the deviation of the annual data from this average is 0.659 °C. The global warming advocates like to emphasize the warming trend in the last 30 years. How does the warming trend in the last 30 years - and in all other 30-year periods since 1659 - look like in Central England?

Click to zoom in: the y-axis is the warming trend in °C per century, the x-axis is time from 1659-1688 to 1980-2009.

In the late 17th and early 18th century, there was clearly a much longer period when the 30-year trends were higher than the recent ones. There is nothing exceptional about the recent era. Because I don't want to waste time with the creation of confusing descriptions of the x-axis, let me list the ten 30-year intervals with the fastest warming trends:

1691 - 1720, 5.039 °C/century
1978 - 2007, 5.038 °C/century
1977 - 2006, 4.95 °C/century
1690 - 1719, 4.754 °C/century
1979 - 2008, 4.705 °C/century
1688 - 1717, 4.7 °C/century
1692 - 1721, 4.642 °C/century
1694 - 1723, 4.524 °C/century
1689 - 1718, 4.446 °C/century
1687 - 1716, 4.333 °C/century

You see, the early 18th century actually wins: even when you calculate the trends over the "sufficient" 30 years, the trend was faster than it is in the most recent 30 years. By the way, the most recent 1980-2009 tri-decade didn't get to the top 10 results at all; if you care, it was at the 13th place. ;-)

You can also see that the local trends are substantially faster than the global trends: that's because the global variations are reduced by the averaging over the globe. For the sake of completeness, these were the most intense 30-year cooling trends:

1727 - 1756, -3.962 °C/century
1863 - 1892, -3.956 °C/century
1729 - 1758, -3.723 °C/century
1728 - 1757, -3.719 °C/century
1726 - 1755, -3.649 °C/century
1862 - 1891, -3.413 °C/century
1666 - 1695, -3.315 °C/century
1730 - 1759, -3.203 °C/century
1861 - 1890, -3.021 °C/century
1865 - 1894, -2.952 °C/century

An obvious question is what happens if you consider 10-year, 15-year, or 50-year trends. With my Mathematica code, it's easy to find: you just change one number. ;-) As you may expect, if you use the 10-year or 15-year trends, the current era won't get anywhere close to the winners. For example, these are the 10-year trends:

There is nothing special whatsoever in the recent epoch. I won't even try to show you the list of winners because the recent decades would obviously be somewhere in the middle. The fastest warming trend extracted from 1 decade is by +18.6 °C per century in 1694-1703; the fastest cooling trend was by -23.9 °C per century in 1733-1742.

Yes, these are huge numbers and they're true. The superfast cooling is related to the excessively low temperatures recorded in England sometime in the early 1740s. Most people don't understand the "random walk" character of the temperatures: the shorter periods you consider, the faster trends you obtain: the trends approximately scale like 1/sqrt(time) - and in this case, the records were scaling even faster than that, as 1/time. Of course, none of these trends can be extrapolated to a century.

At the beginning, I chose the 30-year trend because it really had the highest chance to produce a recent "man-made" signal. It didn't. It's much more hopeless if you consider e.g. the 50-year warming trends:

Again, the recent era on the right side of the picture has no chance to compete with the late 17th and early 18th century: the 1960-2009 period with the +2.65 °C per century ends up outside the top ten. The winner is 1688-1737 with the trend +3.83 °C per century. The fastest cooling was in 1722-1771, by -1.69 °C per century. These 50-year trends can't quite be extrapolated to a century, either. But they're much closer to that than the 10-year or 15-year trends.

Finally, our generation teamed up with our parents, grandparents, and great grandparents can marginally win if we consider 100-year intervals:

But the warming trend in 1909-2008 (the fastest "modern" 100-year trend) was +0.87 °C per century. The warming trend in 1663-1762 was +0.86 °C per century which is not excessively different. ;-) The fastest cooling, 1718-1817, was by -0.59 °C per century. Note that there are no quotas: the positive and negative trends don't have to agree. In most cases, the maximum warming trends were faster than the fastest cooling trends. In some cases, namely the 10-year intervals, it was the other way around. Nothing should shock you here. They're pretty much random numbers.


The Central England data show nothing unusual about the evolution of current temperatures. And because there is really nothing special about Central England, it's reasonable to expect that no place in the world is experiencing anything unusual in the modern era, in comparison with other epochs since 1659.

And that's the memo.

P.S. A trivial Mathematica notebook is here: NB, PDF preview.


  1. I had been posting a plot of CET in news story discussions but was countered with two arguments. Firstly, "it's only one thermometer!!!" So I added a bunch more long-running sites. Second, that Grant Foster ("Tamino") had shown recent warming of CET to be pronounced compared to the former one. Being a chemist, I was not familiar with the smoothing function he used and my initial impression was wrong. He let me post a mistaken analysis and my rather quick admission of error. Once I studied up on smoothing functions I nailed it and...was moderated. Here is my result. (and this).

    "And because there is really nothing special about Central England, it's reasonable to expect that no place in the world is experiencing anything unusual in the modern era, in comparison with other epochs since 1659."

    A possible counterargument is that only the ~1750 update to Fahrenheit's scale (to use boiling water instead of horse or human body temperature) rendered thermometers reliable enough to give good absolute values. Yet even the original scale of 1724 should record variations well, which is what is important, but prior to that I think error bars may be rather large. I do think plots of the other long-running sites strongly supports your conclusion that there's nothing special about Central England though. Only three very long records show a shape faintly suggestive of AGW and one of them is already shown on my collection (St.Petersburg). The others are Uppsala and De Bilt, which are all nearly identical, but I didn't include since few have heard of them. They are plotted here. A few others exist that show odd trends (i.e. Paris has two linear trends that change over ~1850). None show a anything resembling a Hockey Stick with a very recent blade.

  2. Hi, Lubos (sorry about the accent, I have no idea how to make it).

    I have been following your blog with great interest for a few weeks. I have a couple of questions about your processing here -- a post that I find very interesting! Please consider I'm a medical biochemist, not a physicist.

    1. Some people say that non-gridded temps and gridded temps produce different results. Would gridding/not gridding affect yours? I have no idea of what gridding might be anyway (ok, setting the data on a spatial grid, whatever that is?)

    2. From what I've read it seems that weather/climate stuff is full of local nuances. Phenomena seem more local than global, or at least there's a lot of local variation. It seems to me, at any rate, that your inferring from central England to elsewhere might be abusive.

    Thanks in advance.

  3. Dear Baco,

    gridding is just a method to partially average the temperatures over a region so the gridded data get "slightly more global" than the local data.

    It's important to know that this is just a "compression" trick to reduce the amount of data. The relevant temperatures for anyone who is a "local object" is always the local temperature. And the relevant noise for everyone is the local noise, too.

    I assure you that you will get qualitatively identical results for almost any place in the world (except for a tiny portion of places where statistics guarantees that you will find unusual things - by chance - because statistics happens) as what you get in Central England. Just do it.

    The advantage of England is that there exist solid old thermometer data. But there is nothing special about England. I didn't have to be "lucky".

    All hypothetical trends get lost in the "weather noise".

    This noise gets reduced if someone computes global averages of the temperature - but this decrease is spurious. The averaging meant to reduce the noise is just a dirty trick to pretend that the noise is smaller than it is. The actual noise at any given place - which is what is relevant for anyone on the globe - is approximately as big as it is in England and you can never infer any "signal" out of this noise.

    As far as observable physics goes, recent unusual warming doesn't exist in England and it doesn't exist elsewhere, either.

    Best wishes

  4. Thank you very much for your reply.

    I mentioned gridding apropos this.

    Allow me to check my understanding.

    Regarding the extrapolation from Central England, I understand you gave it a signal analysis approach; so you haven't found any (trend) signal amid the noise; and noise being about as much as anywhere else, so there will be no signal nowhere?

    And that moving averages and gridding would possibly or almost certainly create a (fake) signal where there is none?

    Sorry for asking, but these past weeks I have been dealing with stuff like this (weather related) which I never used before, so I need to check if I understand well.

    Thanks again.

  5. Dear Baco, thanks for your thought-provoking comments. ;-)

    Well, the signal - the "underlying CO2 warming trend in °C per century" - kind of "exists" everywhere. Except that it's much smaller than the local noise so you can't distinguish it locally.

    When you average over the stations, the signal in °C/century is unchanged but the noise goes down. If you have N independent quantities - e.g. stations' temperatures - with the same distribution, the width (error) of their average will be sqrt(N) times smaller than for each.

    With this averaging - a "conspiracy" requiring one to deal with very many stations at the same moment - it becomes easier to see the underlying "signal" because the noise decreases.

    I don't claim that you can actually distinguish the CO2 warming "signal" - because there's still too much "noise" (and predictable effects by other causes), even globally. But you surely get closer to this isolation if you average over many stations.

    At the same moment, it's clear that this averaging is artificial because no individual person, animal, or small ecosystem can ever "perceive" the temperatures at 10,000 stations worldwide. So it's really cheating.

    This relative decrease of noise is analogous to what happens when you replace a camera with small lenses by a bigger camera. The pictures can suddenly get sharper, smoother - and the noise calms down. It's because you collect a bigger number of photons, so the error (noise) of the number of photons that reach a given pixel on the CCD gets relatively smaller.


  6. I think I see your point.

    Firstly, you don't think that sliding averages (and other stuff like that, possibly) risks to create a signal out of noise. (Decades ago, a work of mine was snubbed at for this reason.)

    Then, averaging reduces noise. Makes sense, of course. (On this, it has just been occurring to me that the median is a better central tendency estimator than the mean, as it's less sensitive to extreme values).

    Thirdly, there's still too much noise (and measurement error) to see small effects.

    Finally, there's no such thing as an "average temperature" for real observers, but this seems a little from Schrodinger's Cat department, no? ;-)

    Thanks a lot!

  7. Dear Baco,

    concerning the first point, not at all! Sliding averages also create spuriously continuous time series which are then incorrectly interpreted as piece-wise trends. All these things must be carefully checked.

    The suppression of the noise - and the emergence of a trend - must never be an artifact of the methodology, e.g. averaging.

    Yes, there's still too much noise even after the most complete averaging.

    Concerning the last point, I am still saying the same thing. For an observer spatially located at X, only the behavior of the weather at X matters while the averages over the globe don't. There is no quantum mechanics involved here. Quite on the contrary, the global averages would only be relevant for a particular observer if there were telekinesis or other nonlocal processes.

    In fact, for most observers, the previous statement is relevant even when it comes to the temporal "position". The averaging over time - which also reduces noise - also hides that the observers are actually sustain much bigger variations.

    Each kind of process in Nature takes some characteristic time, and it is always wrong to substitute temperatures (and noise) calculated by averaging over *longer* periods than the characteristic time into these processes.

    For example, a plant may grow and collect a certain amount of heat in 3 months. So it's marginally OK to use 3-month averaged figures, and their noise, but it's wrong to use longer-time averages (than 3 months) simply because each plant of this type only grows for 3 months, and is capable to sustain the existing noise that occurs at this timescale.

    Best wishes

  8. Ah, now I see your point! Thank you.

    By the way, I suppose I can congratulate you on the SPPI blog having adopted this post of yours.

    Cheers from a snowless country.

  9. It is kind of amazing that the increasing part of the plots shows a different pattern that the decreasing sector.

  10. Nice demo dataset! I will see if I can make something out of this to show my students of R.

    Thank you for pointing it out.