Thinking about Jan's comment some more, emphasizing the trees and leaves analogy.
> "Model the real world as a *tree* (perhaps but not necessarily a random tree or random forest) with closed-form solutions applicable to tiny bits of physics at each of its *leaves*"
ENSO is likely a forest of trees with leaves. If the ENSO model is fit to the coarser time resolution of the NINO34 time-series, that represents the trees in the forest. Yet the leaves can be observed if we take the finer resolution of the SOI time-series into consideration. The physics is the same but the SOI reveals the high-wave-number components of the standing wave modes.
The upper panel with the brown background is the NINO34 complete time-series from 1880 to the present time. This represents the forest of trees
The middle panel with the green background is the SOI time-series representing a high-resolution view since 1992. This represents the leaves on each tree. The inset shows how it is represented on the lower-resolution scale. Some low-pass filtering was applied to reveal how the model matches to the data, which was fit only to the upper graph. In other words, the leaves are emergent based on needing some high-K components to fit the sharpness of the low-res time-series.
The lower panel is the frequency spectrum of SOI in the high-resolution mode.
The question is how much information we can glean from continuing to characterize the high-res leaves of ENSO. These high-K standing wave nodes may not be particularly stationary in time, as they are not as bound to the container as the primary low-K standing wave dipole of ENSO is. The diagram below indicates how the characterization works along the step edge of the 1998 El Nino transition.