"That was why I was asking you to include e^-r^2 in your wave-forms."
I don't have any spatial dependence in my analysis. I treat the oscillations as standing waves, with the spatial component assumed to separate out (of which I proceed to ignore for the moment).
This may or may not be correct but what I am looking for is physics-based heuristics -- remember that my goal is to be able to project the SOI for the CSALT model and also to help predict El Ninos, not necessarily reproduce the 3D dynamical flow. I am pragmatic in that regard -- simple physics and first-order approximations is my game.
This is the Mathieu differential equation I am dealing with
$ f''(t) + [a + q cos(\omega t)] f(t) = F(t) $
The perturbation is the *q* term on the LHS. If it wasn't for this, the result would be a sinusoid convolved with whatever the *F(t)* is, which is likely a sinusoidal forcing as well. As *q* gets bigger, the waveform starts to become more erratic and this is I am presuming represents the tide gauge fluctuations to first-order. This also leads to ENSO, as sloshing sea-level changes cause shoaling down into the thermocline, which can bring cold water to the surface.
That's the basic premise, no spatial coverage for now. I am trying to see how far I can carry this formulation, and based on the results of comment #23 , to me it looks very promising.
Cheers as always, because where else can we get this kind of discussion going?
"Have you commented on this somewhere?"
I really never said outright that I wasn't working the EOF approach, except on my blog --
I guess what I don't understand is how deconstructing one unknown into two or more unknowns makes the problem any easier. Some of the EOFs that I have seen are more complex than the original waveform. So we still have to understand the elements of the deconstruction to make predictions! Or am I missing something?
Yet perhaps that is what I am doing by adding a second mode in addition to the dominant tide gauge model. And from my assuming that these are standing waves, I sweep under the rug any spatial dependence, which means I don't have to officially call these EOFs.