## Tuesday, December 20, 2005

### Temperatures' autocorrelation

Imagine that the Church would start to control the whole society once again. A new minister of science and propaganda would be introduced to his office. His name would not quite be Benedict but rather Benestad. How would they use scientific language to argue that the Bible in general and Genesis in particular literally describes the creation? They would argue that Genesis predicts water, grass, animals, the Sun, the Earth, and several other entities, and the prediction is physically sound. If anyone tried to focus on a possible discrepancy or a detail, Benestad would say that the heretics were pitching statistics against solid science.

The choice of the name "Benestad" will be explained later.

Do you think that the previous sentences are merely a fairy-tale? You may be wrong. First, we need to look at one scientific topic.

Cohn and Lins

Last month, we discussed the critical exponents that appear in the autocorrelation of the temperature measured at some place XY as a function of time.

Cohn and Lins have just published a paper in Geophysical Research Letters whose main point is completely obvious: the argue that because of long-term persistence (LTP), it is often difficult to distinguish "natural trends" based on "natural inertia" from "additional trends" that are caused by new factors. This fact makes it hard to calculate the statistical significance of the results.

Steve McIntyre discusses this topic in his characteristic, highly detailed and technical manner and he refers not only to a 2002 article by Pelletier but also to a text by Rasmus Benestad who does not like the paper of Cohn and Lins because it could be "misused by the septics". What does Rasmus Benestad have to say about the scaling laws of the autocorrelation?
• There is no information encoded in the statistics of the temperature averaged over different time scales, and people should not look at it.
• Cohn and Lins and whoever tries to study statistical properties of the autocorrelation is "pitching statistics against physics".
• Even if there were some information in the statistics, global climate models should not be tested whether they agree with the observed behavior.
• Global climate models are the holy principle of physics because they predict global warming, exactly what is seen in the real world, and therefore we must trust them.
• Global warming is also real, especially because it is predicted by the global climate models.
• Even if someone tried to test these models and if he found a disagreement (which seems to be the case), one should believe the models and not the observations because the models are governed by the "laws of physics" while the observed power laws are "just some statistics".
• "Statistics does not usually incorporate physically-based information, but derives an answer from a set of given assumptions and mathematical logic."
• Finally, Benestad claims that chaotic behavior cannot be found at scales longer than the length scale of a molecule.

The similarity with our Catholic thought experiment is breathtaking. The essence of science is very different from what Mr. Benestad is imagining:

• Observed data evaluated using statistical methods represent a completely essential part of the scientific research of any complex enough system and virtually all other systems.
• When we want to improve our understanding of a physical situation, it is absolutely necessary to try to compare our models with increasingly difficult sets of observed phenomena, datasets, and their statistical and other properties.
• The scaling laws are among the sharpest and scientifically most well-defined features of the physical systems that exhibit chaotic behavior.
• The weather and the climate exhibit chaotic behavior which is why the research of the scaling laws is relevant in this field.
• It is a complete nonsense that stochastic behavior only appears at the length scale of the molecules or shorter. It is enough to magnify the "water molecules" and the "seeds of dust" in order to see make the relevance of mathematics of the Brownian motion at longer distance scales relevant.
• The weather at many scales is analogous to such a magnified Brownian motion experiment.
• If a model is found to disagree with the observed long-term persistance and/or the observed autocorrelation laws at long time scales and if the statistical ensembles are large enough to allow us to make conclusions, then the model is falsified. It fails to be a credible model for predictions at these time scales.
• If 38 models are found to disagree with the observed features of the data, then all of them are falsified, and the number 38 does not make the degree of the falsification any weaker.
• If these models are as complicated as the Rube Goldberg machines, it does not make them "scientifically correct". Models can only become credible if they correctly describe and/or predict a large number of observables. This number must be greater than number of parameters that the model depends upon.
• While it is true that the classical behavior typically emerges at long distance scales and long time scales, it is not true that the effective long-scale theory is governed by the same physical laws that we would naively derive "microscopically" by ignoring the "quantum" and "chaotic" effects.
• For example, the critical exponents may be very different than the naive, classical exponents. Also, the parameters are renormalized, their signs may often change, and new effects are generated.
• Also, it is not true that the first ideas we have are the correct ones, even at macroscopic distances. Continental drift was also thought to be physically impossible, and testing our models against reality is completely necessary.

I claim that Rasmus Benestad misunderstands every single point listed above. His approach to the climate is exactly as unscientific as the approach of the fundamentalist Christians. He already knows the "truth" - based on very naive models of reality and on his misunderstandings of critical behavior described above - and he won't allow anyone to change a single letter about it by making comparisons with the "dirty statistics", i.e. with the observations of reality.

What's even more troublesome is that Rasmus Benestad is the kind of people that our society is hiring to study the climate. We're not yet in a scientific age because if our age were scientific, religious fanatics like this one would have to do completely different things than science.