Naturally trendy?

This post has provoked various responses, both here and on other Internet sites. Some of these responses have been very valuable, but I believe that some of these are based on a misunderstanding. For instance, some seem to think that I am claiming that there is no auto correlation in the temperature record! For those who have this impression, I would urge to please read my post more carefully, because it is not my message. The same comments goes for those who think that I’m arguing that the temperature is iid, as this is definitely not what I say. It is extremely important to be able to understand the message before one can make a sensible response.

I will try to make a summary of my arguments and the same time address some of the comments. Planetary temperatures are governed by physics, and it is crucial that any hypotheses regarding their behaviour are both physically as well as statistically consistent. This does not mean that I’m dismissing statistics as a tool. Setting up such statistical tests is often a very delicate exercise, and I do question whether the ones in this case provide a credible answer.

Some of the response to my post on other Internet sites seem to completely dismiss the physics. Temperature increases involve changes in energy (temperature is a measure for the bulk kinetic energy of the moleclues), thus the first law of thermodynamics must come into consideration. ARIMA models are not based on physics, but GCMs are.

When ARIMA-type models are calibrated on empirical data to provide a null-distribution which is used to test the same data, then the design of the test is likely to be seriously flawed. To re-iterate, since the question is whether the observed trend is significant or not, we cannot derive a null-distribution using statistical models trained on the same data that contain the trend we want to assess. Hence, the use of GCMs, which both incorporates the physics, as well as not being prone to circular logic is the appropriate choice.

There seems to be a mix-up between ‘random walk’ and temperatures. Random walk typically concerns the displacement of a molecule, whereas the temperature is a measure of the average kinetic energy of the molecules. The molecules are free to move away, but the mean energy of the molecules is conserved, unless there is a source (first law of thermodynamics). [Of course, if the average temperature is increased, this affects the random walk as the molecules move faster (higher speed).]

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