Open Mind

Change Points

April 8, 2007 · 26 Comments

In my last post, I showed temperature time series for the five Swiss stations which report data to the European Climate Assessment and Dataset Network (ECA). A reader, Kelly O’Day, commented that he (she?) had applied “change point analysis” to the data, in order to determine the times when significant changes in the mean value may have occurred. The change point analysis appears to be based on a statistical test called CUSUM (for CUmulative SUMs). The results are fascinating, especially in indicating that all five Swiss stations show a significant change around 1988.

There’s a variant of this test called SCUSUM (for Scaled CUmulative SUMs), which accomplishes the same thing but with a different scaling for statistical analysis; it’s described (in the context of looking for period changes in variable stars) in this paper. I decided to apply SCUSUM analysis to the data myself. First I transformed raw temperature (daily mean temperature from ECA) to temperature anomaly by subtracting the seasonal pattern from the data. Then I ran the SCUSUM analysis to determine when changes may have occurred.

The SCUSUM test amounts to a scaled comparison of average values before and after each moment of time. This generates a measure for each moment, and the time at which this measure is greatest (in absolute value) indicates the moment at which the before and after averages show the most statistically significant difference. Whether the difference is “significant” or not depends on the number of data points (see the aforementioned paper about that), but when there’s lots of data (as in these temperature time series) we can reliably say that values above 4 are significant, so that the average value before the “change point” really is different from that after.


All five stations show the same moment of maximum SCUSUM value, and all five are statistically significant. So we can say reliably that the average temperature in Switzerland before 1987.6 is different from that after 1987.6. In fact, 1987.6 appears to be a “change point” for Swiss temperature, at all five ECA stations.

The other peaks in the SCUSUM graph do not necessarily indicate such change points. In order to determine others, we should separate the data at the known change point — 1987.6 — and re-run the SCUSUM analysis on each part separately. Now we start to get different results for different stations. For Basel, e.g., we find no significant change point in either section. But for other stations, we find multiple change points; these are listed in this table (the arrow indicates the “primary” change point):

Basel Geneve Lugano Saentis Zuerich
1920.0 1920.0 1920.0 1920.0
1942.2 1942.2 1939.2 1942.2
1962.1 1952.6 1952.7
==> 1987.6 1987.6 1987.6 1987.6 1987.6

It should be emphasized that although SCUSUM (and CUSUM) identify changes in the average value, this doesn’t mean that the changes are sudden; they could be, but they could be smooth as well. It also doesn’t mean that no other changes have occured, but these are the ones that can be verified as statistically significant.

Kelly O’Day found very similar results, but not exactly the same:

Basel Geneve Lugano Saentis Zuerich
1920 1919 1920
1943 1940 1943
1962 1951
==> 1988 1988 1988 1988 1988

The differences are due to two factors: 1. I’ve used the daily data (with the seasonal trend subtracted), while O’Day used 1-year averages to remove the seasonal trend; 2. O’Day’s analysis is based on CUSUM while I’m using SCUSUM. Despite these differences, the results are remarkably similar.

We can calculate the average temperature anomaly during each time period, and plot the approximate temperature anomaly as a step-function of time:


The graph is rather crowded, so I’ll magnify the temperature axis to make the changes easier to see:


Another way to characterize the temperature changes is by fitting a polynomial to the data; this graph superimposes a 6th-degree polynomial fit of the temperature anomaly:


Any way we characterize it, Lugano shows quite a complex change of temperature over the last century. But the fastest change, and the highest temperatures, have been witnessed during the modern global warming era (1975 to the present). This much is certain: Lugano, and in fact all of Switzerland, is getting hotter.

Categories: Global Warming · climate change

26 responses so far ↓

  • Eli Rabett // April 8, 2007 at 5:21 am

    Interestingly these do not correlate very well with change over to the automatic stations which occured in the 1978-1882 time frames (went looking for Geneva yesterday).

    [Response: I guess the change brought about by automation was less than the changes induced by nature. It’s also possible that the Swiss, by carefully maintaining parallel records during transition periods, have eliminated most of the change due to automation. They are, after all, sticklers for precision.]

  • nanny_govt_sucks // April 8, 2007 at 5:31 pm

    So something changed in 1987, causing all temps in Switzerland to jump up about a degree, and you’re sure that the change had to do with climate?

    Is it possible that temp measurements throughout Switzerland were standardized or some new method was adopted at that point in time?

    [Response: Eli Rabett has investigated this in some detail (more than I did), and identified many of the changes in procedure for Swiss temperature measurements. This includes the station move in Geneva in 1962, the switch to automated measurements in 1978-1982, and the use of overlapping measurements for over 30 years (in Geneva at least, from 1962 to 1995) in order to establish the relationship between one set of records and another. We’ve both mentioned the Swiss reputation for precision. Most recently, Eli has commented that the “change points” identified by my SCUSUM analysis and Kelly O’Day’s change point analysis, do not coincide with any of the instrumental or procedural changes.

    Of course it’s *possible* that some other change occured, which is not documented in any of the datasets, which somehow affected all five stations by about the same amount, in the same direction, at the same time. And it’s possible that monkeys will fly out of my arse.

    I think this is the third time you’ve asked essentially the same question. You’re trying awfully hard to imply that the evidence which came from thermometers, standardized by well-documented procedures, by a nation known as sticklers for precision, doesn’t indicate what the temperature is. If you want to suggest that it’s due to some procedural or instrumental change, then let’s hear your evidence.

    Do you think it’s *possible* that Switzerland has been getting hotter?]

  • Kelly O'Day // April 8, 2007 at 9:26 pm


    Thanks for following up on my change point analysis. It helps to see that you got comparable results with the daily data and SCUSUM technique.

    BTW, it’s Mr. Kelly O’Day.

    I’m working on other cities and countries to see if similar patterns emerge. So far, I have found the exact same pattern in Paris, with a change point in 1988.

    I’ll post the results on my site soon.


  • inel // April 8, 2007 at 11:34 pm


    Looking at this from another angle …

    In Switzerland last autumn (fall) press releases—public information documents in this case rather than marketing hype—from MeteoSwiss highlighted the record temperatures of autumn 2006, and quoted autumn (September through November) 1987 as the date of the previous autumnal record temperatures for Switzerland. In other words, the temperature change in the latter half of 1987 was significant enough for MeteoSwiss climatologists to refer back to it in their own announcements nine years later (hardly likely if MeteoSwiss had changed any measurement processes or devices themselves without correcting for such changes). Here is the press release in plain French, German, and Italian.

    If you have ever worked in a technical capacity with Swiss engineers and scientists, or even sat on any train departing from any station in Switzerland as soon as the second hand reaches the top tick (for 12) on the large Swiss railway clock, you would soon learn that Swiss precision is not an attribute you do well to question—unless you can be more precise than the Swiss themselves ;-)

  • inel // April 8, 2007 at 11:37 pm

    tamino, I am so imprecise, I messed up my ’strong’ closure before “In other words …” sorry

    [Response: Fixed!]

  • inel // April 9, 2007 at 10:23 am

    Merci beaucoup, tamino. You might find it interesting to note a statement from Dr. Stephan Bader of MeteoSwiss which corroborates your change point analysis.

    [Interesting comments from Dr. Bader. It seems quite certain that yes, late in 1987, Switzerland got a good bit hotter.

    Credit where it’s due: it was Kelly O’Day who first did the change point analysis, and got very interesting results. I was just repeating his analysis with a slightly different method.]

  • nanny_govt_sucks // April 9, 2007 at 5:24 pm

    Do you think it’s *possible* that Switzerland has been getting hotter?

    I think that if the temp measurements reflect reality and not some measurement/third variable artifact, then it is only fair to say that Switzerland got “hotter” around 1987, and there’s little that can be said of any significant trend before or after that time.

  • Hank Roberts // April 9, 2007 at 6:58 pm

    Er, why? For this one statistic, yes, that’s what it does.

    Are you saying it precludes finding a trend on either side of that point in time by any means at all?

    If so, why?

  • tamino // April 9, 2007 at 8:53 pm

    Finding trends post-1987.6 will naturally be very difficult, because there’s just under 20 years of data — which is not very much for finding temperature trends with statistical significance. That’s probably why four of the five stations show no statistically significant trend (yet) after that time.

    But Lugano shows such a strong trend since 1987.6 that it’s statistically significant: linear regression indicates a warming at 4.8 deg.C/century (about 2.5 times the global average).

    In spite of that, it’s quite possible for individual sites to show “step changes” even as the globe as a whole warms more smoothly. I’ve studied a lot of temperature time series, and one of the phenomena I’ve noticed is that many locations show step changes, but it happens to different places at different times. The accumulation over time of many step changes in small areas leads to a much more steady rise in the global average temperature.

    ECA provides more than just daily mean temperature; they also supply max and min temperatures, cloud cover, humidity, precipitation, snow depth, and total hours of sunshine. Perhaps I’ll do a post about the other climate data for a Swiss location (Lugano seems like an interesting case).

  • inel // April 9, 2007 at 10:39 pm

    Hello ngs,

    I appreciate you have been studying and working on climate change for a long time—far longer than I—and your skepticism is thoroughly consistent. Healthy skepticism is good, as it demonstrates a curious mind and a desire to get to the heart of an issue. Still, I cannot figure out why you persist.

    Is your name the clue: are you scared the U.S. Government may actually do something that affects your standard of living one day?

    Are you keen to achieve one or more of these goals:

    to disprove climate change?
    to disprove anthropogenic contributions to climate change?
    to discredit climate scientists?
    to keep the debate going in order to prevent action being taken to combat climate change?

    I am honestly intrigued.

  • Dano // April 10, 2007 at 2:32 am

    The facts don’t fit na_gs’ beliefs, so they must be wrong.

    Simple, yet complex.



  • Steve Bloom // April 10, 2007 at 6:21 am

    I can’t help but note the vast irony arising from the contrast between these two posts and the casually fraudulent treatment temp records get on the CO2 Science site.

    I seem to recall that Nanny rather defended CO2 Science on that point, and even went so far as to defend the egregious
    “no global warming since 1998″ load of crap. Since as of the March data 2007 remains on track to set a new global record, we may soon have an opportunity to see how such folks (including Lindzen and Carter) accept their comeuppance.

  • inel // April 10, 2007 at 8:38 am

    Dear Dano,

    Thanks for your assessment. I would like to hear directly from ngs too.

  • Adam // April 10, 2007 at 9:21 am

    It may be coincidence but I Lugano is the only station on the southern side of the Alps, all the others being to the North.

  • Hank Roberts // April 10, 2007 at 2:11 pm

    Don’t ’step changes’ show up in all sorts of measures? I recall ‘growth spurts’ in youngsters used to be thought an illusion, because all the data were averages. Then pediatricians had parents measure kids every single day, and lo, it happens just as the parents had been claiming.

    [Response: I’ve used the same analogy myself. Individual children often show step changes in height, but the average for an entire class (or age group) shows much smoother increase.

    However, I’ve seen enough temperature time series to know that both step changes, and steady rise, are fairly common at individual locations.]

  • inel // April 10, 2007 at 2:25 pm

    Adam and tamino,

    It is definitely worth assessing climate north and south of the Alps separately, just as MeteoSwiss meteorologists do. Lugano would be a good choice. Another interesting Swiss site is Jungfraujoch

  • Adam // April 10, 2007 at 4:05 pm

    There are three basic areas to Switzerland (though this is simplifying things a bit). There’s the northern lowlands (represented by Zuerich & Basel), the northern side of the Alps (respresented aby Geneva and Saentis and would include Jungfraujoch) and the southern side of the Alps (represented by Lugano). This last region only includes Ticino in Switzerland so Lugano is probably a good respresentation.

    There are many stations in Switzerland especially in the northern side of the Alps as many ski resorts have weather stations and they do a lot of avalanche research.

    Thanks for the pointer inel, another one to look at is Pilatus ( whose name comes from the fact that it often has a cap of cloud on it. It overlooks Luzern.

  • inel // April 10, 2007 at 4:59 pm


    That’s funny—Pilatus is “One mountain … full of possibilities” in German and French. Sounds great! In English it is translated as “360° Switzerland on Lucerne’s doorstep” which sounds rather bland by comparison :-(


  • Dano // April 10, 2007 at 6:49 pm

    Hi inel,

    Never fear. Na_gs won’t come around for a few days. Then he’ll be back with the same tired ideological worldview that eschews nature and empirical evidence that don’t line up with his beliefs.

    There is a small but loud minority out there just like him. Almost identical.

    I’ve learned that they have very little play in policy decisions; knowing this saves one much time (and consternation wondering whether their small minority views will affect us all).



  • tamino // April 10, 2007 at 7:18 pm

    Although I’ve found ngs’s persistent questions disingenuous, I’ll point out that there are two results: 1. Some of us are a bit annoyed; 2. We’ve investigated the procedural history, and climatological variations, of Swiss temperature measurements in greater detail.

  • Adam // April 10, 2007 at 8:10 pm

    inel, I went up Pilatus (Europe’s/World’s steepest railway but it was cloudy so I couldn’t tell) in June and it was snowing at the top (it’s not *that* high). There were no 360 degrees then, more lots of possibilities (legends of Pontious Pilate, dragons and actual eerie mists). I think they probably think English speakers will only go up in good weather whereas the mainland-based visitors are less picky/discerning.

    Though touristified in a way that can be depressing, it’s still worth the journey up. There’s plenty of mountains to walk up to make up for it.

    Anyway, on a weather/climate basis it might be interesting to compare with the Rigi across the lake, a bit lower and generally sunnier. Only, of course, if someone had the time and inclination and access to the data.

  • inel // April 10, 2007 at 9:13 pm

    Dano, thanks for your comforting words. I am still curious as to why ngs and others like him persist with questions without offering their own answers. Hmmm …

    Adam, being Welsh I am proud of my dragon, and Google Earth shows Pilatus to be a good home for one ;-) Once upon a time, I was invited up in a hot air balloon over a field in Bubikon (long story) … which is midway between Säntis and Pilatus, if I had only known which peaks to look for.

  • Dano // April 11, 2007 at 1:44 am

    I am still curious as to why ngs and others like him persist with questions without offering their own answers.

    Inel, it is a facet of certain facts about human nature: they don’t want to find out the belief system that they have taken as their identity - their core, their center - is wrong. Therefore, they hand-wave and distract away.

    This is as predictable and as strong a fact of human nature as the sun rising in the east.



  • Adam // April 11, 2007 at 8:25 am

    inel, that sounds rather pleasant.

    Incidentally, something I forgot to mention earlier and it’s aimed generally rather than individually. I wouldn’t get too hung up on the Swiss stereotype of being sticklers for precision. They have built up a deserved reputation in many areas, but I’ve seen enough exceptions to the national stereotypes to pay little attention to them.

    However, the data we are looking at is likely to be very reliable due to those peculiar, multinational beasts, the meteorological observer and the meteorological archivist. In every country where I’ve had some contact I’ve found them to be the most pedantic (in a good way) people about the data. It makes sense because if you’re not, there’s no point going to the effort.

  • nanny_govt_sucks // April 21, 2007 at 12:04 am

    To all who question my motives or whatever, I ask you: Why does it matter? Either I’m right or I’m wrong, either my questions make no sense or they bring up new issues and uncover new facets of the science to explore. I’m interested in science and politics, if that helps you any. The GW issue is pretty solidly in both arenas, I would say, so I’m doubly interested. You can find out plenty about my political views at and in any of the writings of Harry Browne.

  • American libertarian views on climate change « inel // April 21, 2007 at 10:16 am

    […] for answering my questions in my comment #1001 up there by recommending Lew Rockwell and Harry […]

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