Saturday, February 23, 2013

An Interesting Puzzler

Eli's attention has been drawn to a new paper in Climate of the Past, Multi-periodic climate dynamics: spectral analysis of long-term instrumental and proxy temperature records by H.-L. Lüdecke, A. Hempelmann, and C. O. Weiss. 

The paper itself looks at eight long term (back to 1757) instrumental temperature records in central Europe from Prague, Hohenpeißenberg, Kremsmuenster, Vienna, Paris and Munich.  They find that these records overlap well, and may be decomposed using Fourier analysis.  The data and the  decomposition show no long term temperature anomaly trends. 

Eli is in the habit of inspecting the carrots, so he went over to the BEST database and took a look at the temperature trends in Europe and Austria, as representative of the area studied in Luedecke, et al. for the same period compared to the Fourier fit.

Quite a difference.

The puzzler is why, what is the root cause of this difference.  The answer has some interesting implications for some of the Rabetts favorite things.


Rattus Norvegicus said...

I seem to recall that Ludecke is associated with EIKE. That might explain something...

Anonymous said...

Lüdecke is an "Advisory Board" member of EIKE.

The reviewers' notes prior to publication of this paper are interesting (and so is the Editors' comment).

EliRabett said...

Well that may have influenced how happy they were with their answer, but it is not the answer:)

Anonymous said...

little ice age ended approximately in 1590 and then again in the 1930s. and probably also in 2160. this cycle explains why River Thames should freeze in 2046:

Anonymous said...

The bunnies might find an answer here:

German speaking bunnies will enjoy Georg Hoffmann's post at primaklima:


Nick Stokes said...

I think the reason for the discrepancy is that the blue Ludecke curve is derived by retaining just the first six Fourier components. Now six components can account for about six wiggles, and if there are more than that in the data, they will produce spurious excursions.

I notice that in Fig 1 where they list the DFT components, they stop soon after the first six. But they don't seem to be tapering rapidly. I think this truncation is the issue.

Incidentally, I couldn't find the final version of the paper asserting that there were no long term trends. They certainly shouldn't say that, because the DFT assumes periodicity. It can't predict a long term trend. If there is one, DFT will say it is a sawtooth wave.

Anonymous said...

The problem seems to occur because the two datasets don't seem to match from 1750 to 1900.

Anonymous said...

yes, the data is different, especially from 1750-1800

toto said...

"Now six components can account for about six wiggles,"

Once again showing by high mass/volume ratio, I'm not getting this.

E.g. if you had a perfect sinusoid at one single frequency, couldn't you perfectly capture an arbitrarily long series (with arbitrarily many wiggles) with just one Fourier component?

chris said...

The Ludecke analysis is rubbish - the "projection of future NH temperatures mainly due to the ~ 65-yr periodicity" is the sort of tosh that no competent scientist would perpetrate, but which seems to be allowed in the nether regions of climate science, perhaps because editors are a little wary of calling a shovel a shovel in a rather contentious field.

I'm curious to know the siting of these temperature instruments in Prague, Vienna, Paris, Munich etc. Otherwise it seems somewhat dubious to use only the Kremsmunster data from the large set of temperature series that constitute the HISTALB Greater Alpine Series (GAR) of Auer et al. (2007) [Int. J. Climatology 27, 17-46]. Auer’s composite GAR temperature series (see Figure 12 of Auer et al (2007) ) looks pretty close Eli’s composite of the Best Europe/Austria series.

…oh well. Take any old time series. Fourier transfrom it to pull out the frequency components and their amplitudes. Select the dominant frequency components and reconstruct a smoothed time series from these. You’re going to get something that matches your original series, irrespective of whether the system has intrinsic periodicity or not. What have you learned? Not much.

chris said...

toto, yes, with one Fourier component (a frequency and it amplitude) you can construct an arbitrarily long series, with many wiggles. However it depends how you define a "wiggle"! Ludecke's time series (1760-2000) encompasses only half a cycle (half a wiggle) of their lowest frequency component, and so it is the substructure of this lowest frequency component that requires the other higher frequency components.

In essence if Ludecke were truly to believe in their analysis they might project their constructed time series back several cycles (e.g. back 750 years say), and forwards by some amount and one would then have a regular series with some interesting fine structure (lots and lots of wiggles!) from which one might deduce a reconstruction of past temperatures (e.g. back as far as one wished), and a projection of temperatures far into the future. What would it mean with respect to true temperature variation in the past and future? Nothing very much...

Nick Stokes said...

Yes, that was a loose comment - I meant 6 independent (non-periodic) wiggles. And even that is hard to make precise. But the point remains - if you force a fixed number of orthogonal functions to fit something they can't, they respond with spurious excursions. This is well-known with the Gibbs effect, when you try to fit to a discontinuous function.

Anonymous said...

Fourier analysis is an excellent way of describing an observation.

It has, however, no predictive power whatsoever unless cyclic phenomena are the only influence. It's descriptive, not prescriptive, and simply does not apply outside the observation interval in the presence of non-cyclic changes. As Tamino has noted, this is more properly termed "mathurbation"...

Describing observations is fine and dandy. Predictions, however, really require an understanding of physics, of causal relationships, not just low-fidelity (as in only six components) descriptions.

Sad, really. If the authors actually (and/or honestly) understood their tools, they would not make predictions outside their data without a physical basis. The physical basis that will shape the future evolution of the climate, dependent upon emissions and forcings rather than simple descriptions of what went before.


John Mashey said...

They referenced Scafetta, so they should know it can all be ascribed to the planets, as one can see by watching this talk for the EPA, or flipping through the 76-page slide deck (or an hour talk) to p.62. Immersion in this material could be useful in preparation for reading Lüdecke, et al.

Anonymous said...

-- by Horatio Algeranon

The cycles will continue
On that we can depend
But not in climate data
But nonsense without end

Anonymous said...

I think what Lüdecke et al meant to say was "for entertainment purposes we include a Fourier transformation"...

Bernard J.

Anonymous said...

Hooray for Fourier

-- by Horatio Algeranon

Elementary, my dear Wattson
The math of Fourier
A math decomposition
Of temperature in a way

That makes it look like cycles
Are governing the day
Instead of greenhouse gases
Hooray for Fourier!

Captain Pithart said...

Lüdecke is not only on the advisory board. He is a central part of EIKE, and one of their "press secretaries". However, unlike some of the other prominent members (eg. Limburg), he actually accepts some of the basic physics.