> Unfortunately El Nino doesn’t look very scale invariant.

Right.

For those who don't know what Nad and I are talking about: in a 2nd-order phase transition (like the point where the difference between the liquid and gas phases of water ceases to exist), a physical system becomes scale-invariant. This is reflected in the fact that its 2-point functions obey a power law. Physicists love to think about the situations, mainly because the math is tractable.

I _don't_ expect that the sea surface temperature becomes scale-invariant at the onset of El Niño, or that the 2-point functions of the sea surface temperature obeys a power law. I merely expect that the 2-point function decays more slowly at the onset of El Niño than at other times. I would like us to take a look and see if this is true. I'll propose a specific programming challenge for this.

I wrote:

> Okay, seasonally adjusted temperature seems a much clearer term for “actual temperature at some location and some day value minus the average over years of the temperature at that location on that day of the year.”

> I think their description is better.

Misunderstanding. I meant "seasonally adjusted temperature" is much clearer than what Graham had initially proposed: "temperature anomaly". Obviously “actual temperature at some location and some day value minus the average over years of the temperature at that location on that day of the year" is even clearer, but it's too long to say over and over. We need a shorter term, which we will precisely define at the beginning of any article about this stuff.

Yes. I agree that subtleties arise in situations where we have two concepts of mean (like mean over years and mean over days in the year), or one concept of mean that no longer obeys $\langle \langle X \rangle Y \rangle = \langle X \rangle \langle Y \rangle$ (like "mean over the last 365 days"). In any work we do, we'll have to be careful about these issues. You are right about that.
$$\langle (A - \langle A \rangle ) (B - \langle B \rangle ) \rangle = \langle A B \rangle - \langle A \rangle \langle B \rangle$$
$$\langle \langle X \rangle Y \rangle = \langle X \rangle \langle Y \rangle$$