Archive for the ‘nonlinear trend’ Category


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.