Right now I feel Graham is way ahead of me; I need to slowly catch up by writing blog articles explaining his work. That's my main way to understand things.

However, I think it would be good to talk about what to do next. Dara O Shayda is now offering us a lot of computer power, data storage, and his own abilities. Daniel Mahler is now starting to produce interesting visualizations of what look like "empirical orthogonal functions" for the Earth's climate. WebHubTel is working on simple physical models of El Niños. I'm having trouble keeping up with what they're doing! It would be nice if we could agree on some goals and then work toward those goals... leaving room for different people to do what they enjoy, of course.

Here are some rough ideas:

1) It should be possible to simplify Ludescher _et al_'s prediction algorithm while having it work just as well, or almost as well.

a) Graham has already found at least one example: replace correlations by covariances! Covariances are logically simpler, but they work about equally well:

b) Another possibility is this. Ludescher _et al_ work with * quantities $C_{i,j}^t(\tau)$ that say how air temperatures at times $t$ at locations $i$ _*outside*_ the El Niño basin are correlated to air temperatures a time $\tau$ earlier _*inside*_ the El Niño basin, and also

* quantities $C_{i,j}^t(-\tau)$ that say how air temperatures at times $t$ at locations $i$ _*inside*_ the El Niño basin are correlated to air temperatures a time $\tau$ earlier _*outside*_ the El Niño basin.

These are logically quite distinct, and we might hope that one is more important than another for El Niño prediction. We can find out.

c) Ludescher _et al_ define their link strengths $S_{i,j}$ in terms of $C_{i,j}^t(\tau)$ and $C_{i,j}^t(-\tau)$ where $\tau$ ranges from 0 to 200 days. Do we really need this, or would some specific choice of $\tau$ work almost as well?

Etcetera. The point of this sub-project is to better understand what really matters.

However, I think it would be good to talk about what to do next. Dara O Shayda is now offering us a lot of computer power, data storage, and his own abilities. Daniel Mahler is now starting to produce interesting visualizations of what look like "empirical orthogonal functions" for the Earth's climate. WebHubTel is working on simple physical models of El Niños. I'm having trouble keeping up with what they're doing! It would be nice if we could agree on some goals and then work toward those goals... leaving room for different people to do what they enjoy, of course.

Here are some rough ideas:

1) It should be possible to simplify Ludescher _et al_'s prediction algorithm while having it work just as well, or almost as well.

a) Graham has already found at least one example: replace correlations by covariances! Covariances are logically simpler, but they work about equally well:

b) Another possibility is this. Ludescher _et al_ work with * quantities $C_{i,j}^t(\tau)$ that say how air temperatures at times $t$ at locations $i$ _*outside*_ the El Niño basin are correlated to air temperatures a time $\tau$ earlier _*inside*_ the El Niño basin, and also

* quantities $C_{i,j}^t(-\tau)$ that say how air temperatures at times $t$ at locations $i$ _*inside*_ the El Niño basin are correlated to air temperatures a time $\tau$ earlier _*outside*_ the El Niño basin.

These are logically quite distinct, and we might hope that one is more important than another for El Niño prediction. We can find out.

c) Ludescher _et al_ define their link strengths $S_{i,j}$ in terms of $C_{i,j}^t(\tau)$ and $C_{i,j}^t(-\tau)$ where $\tau$ ranges from 0 to 200 days. Do we really need this, or would some specific choice of $\tau$ work almost as well?

Etcetera. The point of this sub-project is to better understand what really matters.