The Clarke ref is the first [cite](http://yly-mac.gps.caltech.edu/AGU/AGU_2008/Zz_Others/Li_agu08/Clarke2007.pdf) at the top of this thread. He uses the basic wave equation, his Eq(4.6) and Eq(4.8)
$ f''(t) + \omega ^2 f(t) = 0 , \ \omega \approx 2\pi/4.25 yr$
which gives K=2.2
I will also have to look at this Clarke ref:
A. J. Clarke, “Analytical theory for the quasi-steady and low-frequency equatorial ocean response to wind forcing: The ‘tilt’ and ‘warm water volume’ modes,” Journal of Physical Oceanography, vol. 40, no. 1, pp. 121–137, 2010.
The best antidote for overfitting is to use parameters that have physical significance and are out-of-the-box based on other evidence. Doing a sensitivity analysis around these points might be useful as well.
I have bothered Nick Stokes on his blog before. He is obviously a very experienced hydrodynamics researcher with skills at numerical modeling and statistics. He is a member here, but I don't think he reads it routinely. Like I said, I place comments on his blog, but usually only get feedback from naysayers. A frequent nemesis of mine is Pekka Pirrila. This is what he said after a comment I posted to Nick's blog
> "The paper of Clarke et al is looking at the mechanisms of ENSO and makes conclusions at the level their research can support referring to approx. 2 pi / 4.25 yr as a reasonable interannual frequency, and stating also that "The above idealized model errs in several respects". They present justification for their approach, but consider many details only illustrative. A very different style than what I have seen from you."
The Eureqa suggestion is intriguing. I have so many tricks up my sleeve as to how to use it properly might warrant a page.
The averager or smoother is interchangeable. Nick Stokes actually has a recent post on his blog pertaining to the challenges of getting a derivative off of a noisy function. One thing he finds is that smoothing is commutative with differentiation -- i.e. one can filter and then differentiate or differentiate and then filter. But some filtering is required otherwise the data is buried in seasonal noise. To bring it full circle, I suggested that this is one application that could benefit from his ideas with regards to a second derivative. I don't recall seeing him reply though.
I can appreciate that he may think that what I am trying to do is trivial in comparison to the compute-heavy 3-D finite element fluid modeling he has probably done over the years. If he is carrying that baggage I can understand. As I said, I am only interested in the first-order effects and don't carry any of that baggage.