The SOIM Differential Equation

[mathjax]Is there such a thing as too simple a model? Take a look at this fit to ENSO

Fig 1: The SOI fit explained in this post.  The time axis is in months from 1880.

My original approach to reconstructing the SOI time series using basis Mathieu functions is useful but not the only way to do the modeling.  I believe that I took that as far as I could go and so decided to bite the bullet and solve the SOIM (Southern Oscillation Index Model) differential equations numerically.  What pops out is a gloriously simple climate model that fits the data remarkably well — and BTW, one of those models deemed not to exist by the climate science deniers.

What follows is the description of the model and how it connects to the previously described Chandler Wobble along with a crucial link to the quasi-biennial oscillation (QBO). Some type of forcing is responsible for providing the necessary energy to get the ENSO sloshing behavior going, and these are as good of candidates as any.

Read on to see how it can’t possible be done 🙂

Continue reading

The SOIM: substantiating the Chandler Wobble and tidal connection to ENSO

(see later posts here)

[mathjax]My previous posts on modeling the Southern Oscillation Index as a periodically modulated wave equation — in particular via the Mathieu equation — are listed below:

  1. The Southern Oscillation Index Model
  2. SOIM and the Paul Trap
  3. The Chandler Wobble and the SOIM

The first post introduced the Mathieu equation and established a premise for mathematically modeling the historical SOI time-series of ENSO, the Southern Oscillation part of the El Nino/Southern Oscillation phenomenon.  The second post was an initial evaluation of a multivariate fit, evaluated by exploring the parameter space.  The third post was a bit of a breakthrough, which focused on a specific periodic process — the Chandler Wobble (CW) — which appeared to have a strong causal connection to the underlying SOI model.

This short post effectively substantiates the Chandler Wobble connection and provides nearly as strong support that other tidal beat periodicities force the modulation as well.

Continue reading