relating back to the [discussion](http://forum.azimuthproject.org/discussion/1360/paper-ludescher-et-al-improved-el-nino-forecasting-by-cooperativity-detection/?Focus=13713#Comment_13713):



>>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.
>
>I was thinking about this idea and searched the forum to see if it came up before.
>The discussions of sloshing driving El Nino sound a lot like self organized criticality to me.
>That suggests one possible approach.
>
>Bialek, Nemenman & co as well as Sejnowski & Saremi have papers on measuring criticality in complex natural signals, particularly images and neural data
>by treating the pixel/signal intensities as the order parameter.
>This approach could be applied to the various gridded data sets like the NOAA surface tempreature, pressure, humidity ... data sets.
>It sounds like the they should be in a near critical state most of the time, and El Nino's should correspond to departures from criticality.
>
>I have seen a paper claiming that epilepsy attacks are departures from criticality
>I also think one that claims it for stock market crashes,
>but everything eventually get claimed to cause those.
>
>Link strength sounds like a partial indicator of criticality. Looking for criticality on the full data could be more promising.

I found the following older paper:

+ J S Andrade Jr, I Wainer, J M Filho, J E Moreira. [Self-organized criticality in the El Nino southern oscillation](http://scholar.google.com/citations?view_op=view_citation&hl=en&user=EwWccccAAAAJ&cstart=100&citation_for_view=EwWccccAAAAJ:HE397vMXCloC) Physica A: Statistical Mechanics and its Applications 215, 331--338 (1995). (The versions linked on Scholar are paywalled, but it is possible to find free versions on the internet.)

Following the citing and related papers on Scholar shows that scaling and criticality in climate is a lively cottage industry in its own right. One way this might be usable in El Nino prediction is to try and estimate the amout of energy built up in the system. This should primarily be a function of the water temperature differential across the the El Nino region and the sea level differential. If El Nino is really an SOC system the probability and likely size of the next event should be a function of the built up energy.

If El Nino is SOC, then there ought be mini/micro El Ninos happening on all space and time scales. These would be small backflows eastward from the warm pools. Is there a data set from which these would be detected easily? I know Paul has been looking into the details of the sloshing behavior. What data did you use to create your visualizations?

I should probably actually read the paper first :)