My experience with Rahmstorf’s non-linear trend line

July 20, 2009

One of the original impetuses for me to start blogging was my experience with Stefan Rahmstorf concerning his 2007 paper “A Semi-Empirical Approach to Projecting Future Sea-Level Rise” (Science, 315, 2007).  I posted a several part critique on my old blogspot site, which I later ported over to this wordpress site. 

But this was only part of the story.  I  have decided to tell the rest of the story after reading “The Secret of the Rahmstorf ‘Non-Linear Trend Line’” at Steve McIntyre’s Climate Audit

Rahmstorf’s sea-level rise paper was based on plotting 120 years worth of sea -level rise rates vs each year’s corresponding global temperature.  Since both of these sets of data are quite noisy, Rahmstorf said ” Both temperature and sea-level curves were smoothed by computing nonlinear trend lines with an embedding period of 15 years.”

Rahmstorf referenced “New Tools for Analyzing Time Series Relationships and Trends” by Moore, et. al. (Eos, 86, 2005) for his nonlinear trend line smoothing technique.  This short paper refers to a variety of techniques for handling time series, including varieties of wavelet analysis and spectrum analysis.  The Moore paper invested several paragraphs on the use of Monte Carlo Single Spectrum Analysis for finding nonlinear trends in sea level and sea temperature, with the reader referred to a variety of  other papers to get the details. 

I waded hip deep into these papers  to get a handle on this new “nonlinear trend line” technique that led Rahmstorf to his startling projection of a huge sea level rise over this century.  I shouldn’t have wasted my time.  I found that I could essentially reproduce his results in an Excel spreadsheet by simply smoothing the original sea-level and temperature data with a 15 year FWHM Gaussian filter. 

Here is Rahmstorf’s sea-level rise rate vs. temperature after his nonlinear trend line smoothing and 5 year binning, followed by my sea-level rise rate vs. temperature after my 15 year FWHM Gaussian smoothing and 5 year binning, and finally, my version of the data without binning.

Rahmstorf's sea level rise vs T

Moriarty's sea level rise vs T binned

Moriarty's sea level rise vs T not binned

Rahmstorf binned his 120 data points into 24 bins containing 5 points each.   The binning was not needed to  remove noise that obfuscated his salient point – the data had already been smoothed through his non-linear trend line technique.     The binning could not be justified by claiming that it somehow made the plot of sea level rise rate vs temperature easier to read.  It actually reduced the amount of information to the reader by removing obvious real structure in the data.

I believe that Rahmstorf deliberately presented his data in a way calculated to deceive.  These are harsh words, and I say them with regret.

The only plausible reason that I can come up with for binning the 120 data points into 24 bins is because the resulting 24 points looked like they could conceivably be fit to a line without failing the laugh test.  Seeing the original 120 smoothed data points made it perfectly clear that there was not a linear relationship between the sea-level rise rate  and the temperature.  The full set of 120 data points also make it clear that when the temperature remains constant the sea level rise rate drops, in direct contradiction of one of Rahmstorf’s own working assumptions.

It turned out that Rahmstorf’s startling conclusion about extreme sea-level rise had nothing to do with any new sophisticated data analysis techniques for deriving nonlinear trend lines.  I got the same results as him using a simple spreadsheet.  Rather, his startling results came from his bogus interpretation.  Specifically, here are the three problems I identified:

1) The assumption that the time required to arrive at the new equilibrium is “on the order or millennia” is not borne out by the data. More…

2) Sea level rise rate vs. temperature is displayed in a way that erroneously implies that it is well fit to a line.  More…

3) Rahmstorf extrapolates out more than five times the measured temperature domain. More…

Rahmstorf’s code and peer review

In the midst of my wandering through a mathematical labyrinth to reproduce Rahmstorf’s results, before my simple excel spreadsheet approach, I asked Rahmstorf several questions via email.  Amazingly, he offered to send me his code, to which I happily accepted.  Here is what he said when he sent it (emphasis added by me):

From: Stefan Rahmstorf [mailto:rahmstorf@xxxxxxxxxxxx.xx]
Sent: Monday, August 20, 2007 13:20
To: Moriarty, Tom
Subject: Science paper

Dear Tom, see attached. Please report any issues you encounter, you are the first outside person to test this code.

Cheers, Stefan

Stefan Rahmstorf

So, the punchline is that although his data and results had been published a half a year before in the journal Science,  the highly regarded, unassailable, peer reviewed pinnacle of scientific research , I was “the first outside person to test his code.”

Again, I offer this harsh criticsm with regret, because Rahmstorf was, after all, kind enough to send me his code.


  1. Hi Tom, I can vouch for your assessment. Review of this paper is an ongoing project of mine too, and the post below, no so much to advertise it but let you know there is a lot more dirt to dig up on this issue of sea level projections http://landshape.org/enm/smooth-operator/.

    Considering the importance of it, it is astonishing that you were the first ‘outside’ person to show interest enough to request the code from him. One wonders who is ‘inside’ and ‘outside’.

  2. ‘Outside’ could mean that there were insiders who reviewed it, like the peer-reviewers.

  3. To be fair to Rahmstorf, it’s not his fault the peer reviewers had no interest in checking out his code. If all climate scientists were as willing to share their code as he, it would reduce much of the (justified) criticism of their approach that one finds on Steve McIntyre’s website. At least you can check out whether the results are reproducible and whether they stand up to analysis – without having to guess at what they’ve actually done.

  4. I don’t know Rahmstorf, but I do have a great deal or respect for the man to have provided his code to an email request. In my view, it shows that he, like a good scientists, puts his work out there for the rest of us to “throw bricks at it” – and thus to see if it “holds water”. Transparancy is so vital in science and yet has become so rare. By putting his work out for all to see, he will probably be critisized for one aspect or treament or another – but he will use his judgement, with all these imputs, to develop better code. Sounds pretty smart to me.

    As to who is “inside” and who is “outside”, my experience is that those on the “inside” are the members of the team that developed the code. “Outside” refers to anyone else…


  5. Excluding program code from peer review happens all the time, and not only in climate science. I have had the same experience with my own papers in the area of biochemistry.

    Who ever peer reviewed Excel, Origin, any of the commercial math and statistics packages?

  6. […] Sanity « My experience with Rahmstorf’s non-linear trend line Vancouver Underwater? July 23, 2009 First Boston, now Vancouver.  According to the Times […]

  7. Tom, I’ve done a post on this topic at Climate Audit here http://www.climateaudit.org/?p=6746. After allowing for autocorrelation in the residuals, there are only 3.34 degrees of freedom in the binned relationship (as opposed to the 24 used in Rahmstorf’s “significance” calculation.)

  8. […] quickly, early in this century. Later it will be too late to do much,’ says senior NASA scientist Stefan Rahmstorf in a recent article for the United Nations Office for the Co-ordination of Humanitarian […]

  9. I was not aware of your website until reading CA this morning. Good work. Have you notified Mr Rahmstorf and Science about this? I’ve seen him in interviews here in Germany. Be careful, he can be awfully spiteful to those who have non-consensus opinions. I’m looking forward to a reaction.

    “you are the first outside person to test this code.” Well, perhaps people have stopped listening to him?

  10. […] could be very closely reproduced using a much simpler smoothing technique (for example, see here and here).  I used a Gaussian filter with a blended polynomial fit at the […]

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