This post follows up on the idea of modeling the historical Southern Oscillation Index (SOI) record with details on how one can apply the SOIM to make accurate predictions. Based on some some early encouraging success, I asserted that a more comprehensive model fitting would be possible. That's what this follow-on post is about -- trying to verify that we can accomplish that "holy-grail" of prediction, the prediction of future El Nino / Southern Oscillation (ENSO) conditions.

To foreshadow what's to come, **Figure 1** shows the comprehensive SOIM fit, which incorporates a grouping of optimally phased Mathieu functions (introduced in the previous post)

This is a very promising result based on the premise of the last post. The principal additions to the simple model are (1) a multi-harmonic basis set of Mathieu functions and (2) a more constraining physical interpretation to the math.

What follows is the explanation and various verification checks, which include:

- Sensitivity of the model to parameter selection
- Comparison to fitting red noise (to show over-fitting is not an issue)
- Hindcasts and forecasts based on restricted training intervals
- Power spectrum of model and data