Actually you gave me a fun idea, Graham! In a sandpile when the sand is at the [critical angle of repose](http://en.wikipedia.org/wiki/Angle_of_repose), as steep as possible, small landslides occur... and at least in theoretical models, these landslides are roughly scale-invariant: there are small ones and big ones and bigger ones, with the frequency of a landslide of size $x$ being $\propto x^{-p}$ for some power $p$. Under some conditions sand naturally organizes itself into dunes that are near the critical angle of repose: this is called [self-organized criticality](http://en.wikipedia.org/wiki/Self-organized_criticality). The idea is that this system naturally has a second-order phase transition as some sort of attractor.

Maybe Pacific warm water that's just about ready to slosh back east is a bit like a sandpile at its critical angle of repose! If so, there might be a second-order phase transition here.

I feel this idea is a overly naive, but it might have some merit, or lead to some better ideas.