Jim, Thanks for that note summary. I agree that the Kim paper is a tough slog, with a perhaps too facile "just so" narrative, but I have learned that this is quite typical for climate science papers.
Yet the authors did somehow pull this biennial odd/even periodicity out of the muck, which is what intrigued me since I am seeing this effect as well.
Part of what sets my approach apart is that I am not using any of the conventional climate science methods -- I am not comfortable at all with EOFs for instance. I base my entire premise on the fact that we have this humongous body of water in the Pacific and trying to understand what happens when it starts to slosh back and forth. There is very little viscosity in this motion from what I understand, so that it should oscillate once it gets set in motion. And the simplest first-order inviscid perturbation to the oscillation has the form of the Mathieu differential equation.
There could be two major modes of the oscillation, separable I am guessing in orthogonal directions aligned with the geographic axis.
In the past I had noticed that one of the authors, O'Brien a highly regarded emeritus climatologist, had written several papers (again low-cited) on solving the hydrodynamics problem with a co-author D.Muller.
D. Müller and J. J. O’Brien, Shallow water waves on the rotating sphere, Phys. Rev. E 51, 4418 , 1995
As I recall, they had some references to a Mathieu equation formulation, but did not pursue it. I will dig this paper out in my PDF stash. EDIT: [PDF here](http://coaps.fsu.edu/bios/95-4.pdf)
Amazing how these guys can keep any of this straight in their minds.
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This is an extract from the Muller & O'Brien paper referenced above
Because of the spheroid nature of the earth, they punted on the problem. They may be formally correct that one can not apply a full 2D treatment to a spheroidal problem, but that does not mean we should avoid a first-order perturbation approach to at least capture the quasi-periodidicity.
There is a gaping hole in the research on this topic. Nothing below the horribly complex.