You seem to miss the point that this research is essentially a combination of exploratory metrology approaches and of applied geophysics. Consider that if the data was raw diffraction output (x-ray, electron, etc) and we were simply trying to reverse engineer the structure, the model-based metrology step would be more-or-less straightforward. The hard part would be to determine why the novel structure existed. So there are two models -- the metrology model (which is worked out, via the inverse diffraction physics) and the behavioral model (in that the structure or behavior exists is unknown).
For the geophysics of ENSO and QBO, neither the metrology model nor the behavioral model are close to mature. Straightforward Fourier series doesn't work because of the aliasing and multiple harmonics created, so new metrology approaches have to be devised to go along with the Navier-Stokes/Laplace Tidal Equations behavioral modeling that I previously published. Doing predictions is way down on the list of necessary tasks to complete, but I can see how readers raised with a horse-race mentality would consider it important.