After working the ENSO model part-time over an extended period if time, it has become clear that the model is a good counter-example to a structurally stable system

https://en.m.wikipedia.org/wiki/Structural_stability

Although the model has an equivalent number of degrees of freedom to a conventional tidal analysis model or to the differential length-of-day (dLOD) model, the non-linearity of the solution makes it exceedingly sensitive to the value and phase of the tidal factors.

What this means is that a 90% accurate estimate of the tidal factors will do a quite adequate job for a conventional tide estimate, but that provides just a starting point for the ENSO model. All the 2nd order factors that don't add much to improving a tidal analysis fit appear to be critical for an ENSO fit. This is just a consequence of the Laplace's Tidal Equation solution in the ENSO regime, where the non-linear multiplier on the forcing will completely change the dynamical trajectory for small perturbations.

But what does this say about the confidence of the results? If it's that sensitive, could matching results simply be fortuitous? The reason I don't think this is the case is that the number of DOF wrt to the set of parameters are as limited in the ENSO model as in the tidal or LOD model. It's just that arriving at the set of values is more difficult with ENSO. For example, one can't simply apply a multiple linear regression algorithm to the ENSO LTE solution like one can with the linearized conventional tidal analysis solution. I am still at the point where I have to exhaustively iterate to get a matching solution.

But after the solution is attained, the primary constituent forcing factors found don't differ that much from the dLOD factors or to representative conventional tidal factors. The strong factor is always the tropical fortnightly term at 13.66 days, with the next largest the anomalistic terms at 27.55 & 13.77 days and then the tropical monthly at 27.32 days. These of course are synched to the annual impulse. The rest of the terms are under an order of magnitude less in spectral power (amplitude * frequency), but because of the sensitivity of the LTE nonlinear multiplier, these need to be iterated to obtain each contributing amplitude.

But with the knowledge that the dLOD results provide a good 1st order starting point, it's no longer a shooting in the dark trial and error approach to iterating on a final solution. The approach I am now using is to take these terms and compact them into an inverse cube law that when Taylor series expanded will generate the primary first-order terms along with all the second-order cross terms. Applying physics to the problem makes it a more plausible model and the reduction in the number of DOFs after doing this makes it more immune to over-fitting.

https://en.m.wikipedia.org/wiki/Structural_stability

Although the model has an equivalent number of degrees of freedom to a conventional tidal analysis model or to the differential length-of-day (dLOD) model, the non-linearity of the solution makes it exceedingly sensitive to the value and phase of the tidal factors.

What this means is that a 90% accurate estimate of the tidal factors will do a quite adequate job for a conventional tide estimate, but that provides just a starting point for the ENSO model. All the 2nd order factors that don't add much to improving a tidal analysis fit appear to be critical for an ENSO fit. This is just a consequence of the Laplace's Tidal Equation solution in the ENSO regime, where the non-linear multiplier on the forcing will completely change the dynamical trajectory for small perturbations.

But what does this say about the confidence of the results? If it's that sensitive, could matching results simply be fortuitous? The reason I don't think this is the case is that the number of DOF wrt to the set of parameters are as limited in the ENSO model as in the tidal or LOD model. It's just that arriving at the set of values is more difficult with ENSO. For example, one can't simply apply a multiple linear regression algorithm to the ENSO LTE solution like one can with the linearized conventional tidal analysis solution. I am still at the point where I have to exhaustively iterate to get a matching solution.

But after the solution is attained, the primary constituent forcing factors found don't differ that much from the dLOD factors or to representative conventional tidal factors. The strong factor is always the tropical fortnightly term at 13.66 days, with the next largest the anomalistic terms at 27.55 & 13.77 days and then the tropical monthly at 27.32 days. These of course are synched to the annual impulse. The rest of the terms are under an order of magnitude less in spectral power (amplitude * frequency), but because of the sensitivity of the LTE nonlinear multiplier, these need to be iterated to obtain each contributing amplitude.

But with the knowledge that the dLOD results provide a good 1st order starting point, it's no longer a shooting in the dark trial and error approach to iterating on a final solution. The approach I am now using is to take these terms and compact them into an inverse cube law that when Taylor series expanded will generate the primary first-order terms along with all the second-order cross terms. Applying physics to the problem makes it a more plausible model and the reduction in the number of DOFs after doing this makes it more immune to over-fitting.