Jan, The sloshing model is marginally different than the ENSO models that are of current interest and considered the standard models for ENSO. There is the Zebiac-Kane model and various delayed action oscillators, which are described on the Azimuth Project http://www.azimuthproject.org/azimuth/show/ENSO

But those IMO are complicated by the fact that they add nonlinear terms -- I think on the grounds that someone wanted to see chaotic behavior. What happens if you remove the nonlinear terms is that you end up with the basic 2nd-order differential equation called the wave equation, which is the one I have been using recently. The Mathieu sloshing equation is a slight perturbation on the wave equation, which verges toward chaotic behavior, but is a long way from the chaos of the Zebiac-Kane type models. I started with the Mathieu (see note ** below), and frankly probably wasted a of time because I thought that would be my entry in weaning off a fully chaotic model.

Allan Clarke at FSU is the biggest proponent of wave equation type models for ENSO. Read this paper [1] and you can see how the derivation of the wave equation occurs. It is spelled out in its full uncomplicated glory

> ![clarke](http://imageshack.com/a/img673/7682/m57j2Y.gif)

This formulation very hard to argue against because it is a simple model. But if you ever see anyone use it in the literature with periodic forcing terms applied, I would like to know about it.

Thinking about the larger-scale ocean patterns is not on my radar as I am focused on this single standing wave mode.

[1] A. J. Clarke, S. Van Gorder, and G. Colantuono, “Wind stress curl and ENSO discharge/recharge in the equatorial Pacific,” Journal of physical oceanography, vol. 37, no. 4, pp. 1077–1091, 2007.

** I remember reading an aside in one article where the authors dismissed a Mathieu equation type of formulation because the geometry of a spherical earth does not allow the boundary conditions necessary for that kind of solution.

But those IMO are complicated by the fact that they add nonlinear terms -- I think on the grounds that someone wanted to see chaotic behavior. What happens if you remove the nonlinear terms is that you end up with the basic 2nd-order differential equation called the wave equation, which is the one I have been using recently. The Mathieu sloshing equation is a slight perturbation on the wave equation, which verges toward chaotic behavior, but is a long way from the chaos of the Zebiac-Kane type models. I started with the Mathieu (see note ** below), and frankly probably wasted a of time because I thought that would be my entry in weaning off a fully chaotic model.

Allan Clarke at FSU is the biggest proponent of wave equation type models for ENSO. Read this paper [1] and you can see how the derivation of the wave equation occurs. It is spelled out in its full uncomplicated glory

> ![clarke](http://imageshack.com/a/img673/7682/m57j2Y.gif)

This formulation very hard to argue against because it is a simple model. But if you ever see anyone use it in the literature with periodic forcing terms applied, I would like to know about it.

Thinking about the larger-scale ocean patterns is not on my radar as I am focused on this single standing wave mode.

[1] A. J. Clarke, S. Van Gorder, and G. Colantuono, “Wind stress curl and ENSO discharge/recharge in the equatorial Pacific,” Journal of physical oceanography, vol. 37, no. 4, pp. 1077–1091, 2007.

** I remember reading an aside in one article where the authors dismissed a Mathieu equation type of formulation because the geometry of a spherical earth does not allow the boundary conditions necessary for that kind of solution.