This is a continuation from the previous Length of Day post showing how closely the ENSO forcing aligns to the dLOD forcing.
Ding & Chao apply an AR-z technique as a supplement to Fourier and Max Entropy spectral techniques to isolate the tidal factors in dLOD
- H. Ding and B. F. Chao, “Application of stabilized AR‐z spectrum in harmonic analysis for geophysics,” Journal of Geophysical Research: Solid Earth, vol. 123, no. 9, pp. 8249–8259, 2018.
The red data points are the spectral values used in the ENSO model fit.
The top panel below is the LTE modulated tidal forcing fitted against the ENSO time series. The lower panel below is the tidal forcing model over a short interval overlaid on the dLOD/dt data.
That’s all there is to it — it’s all geophysical fluid dynamics. Essentially the same tidal forcing impacts both the rotating solid earth and the equatorial ocean, but the ocean shows a lagged nonlinear response as described in Chapter 12 of the book. In contrast, the solid earth shows an apparently direct linear inertial response. Bottom line is that if one doesn’t know how to do the proper GFD, one will never be able to fit ENSO to a known forcing.
GeoEnergy Math 
Context on the AR-z amplitudes : “An AR-z (Lorentzien) peak will appear in the frequency spectrum whenever a pole exists, signifying a harmonic signal at the frequency in question, where the spectral peak height is inversely proportional to the square of the distance to the pole in question in the complex z-plane. Here we re-emphasize that the latter does not contain information about the actual signal amplitude, as noted above. The non-zero amplitude, though, is what makes possible the estimation of the complex frequency in the first place; and a higher SNR would render better estimated AR coefficients and pole position.”
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