I've been wanting to try this for awhile — to see if the solver setup used for fitting to ENSO would work for conventional tidal analysis. The following post demonstrates that if you give it the recommended tidal parameters and let the solver will grind away, it will eventually find the best fitting amplitudes and phases for each parameter.
The context for this analysis is an excellent survey paper on tsunami detection and how it relates to tidal prediction:
S. Consoli, D. R. Recupero, and V. Zavarella, “A survey on tidal analysis and forecasting methods for Tsunami detection,” J. Tsunami Soc. Int.
33 (1), 1–56.
The question the survey paper addresses is whether we can one use knowledge of tides to deconvolute and isolate a tsunami signal from the underlying tidal sea-level-height (SLH) signal. The practical application paper cites the survey paper above:
Percival, Donald B., et al. "Detiding DART® buoy data for real-time extraction of source coefficients for operational tsunami forecasting." Pure and Applied Geophysics 172.6 (2015): 1653-1678.
This is what the raw buoy SLH signal looks like, with the tsunami impulse shown at the end as a bolded line:
After removing the tidal signals with various approaches described by Consoli et al, the isolated tsunami impulse response (due to the 2011 Tohoku earthquake) appears as:
As noted in the caption, the simplest harmonic analysis was done with 6 constituent tidal parameters.
As a comparison, the ENSO solver was loaded with the same tidal waveform (after digitizing the plot) along with 4 major tidal parameters and 4 minor parameters to be optimized. The solver's goal was to maximize the correlation coefficient between the model and the tidal data.
The yellow region is training which reached almost a 0.99 correlation coefficient, with the validation region to the right reaching 0.92.
This is the complex Fourier spectrum (which is much less busy than the ENSO spectra):
The set of constituent coefficients we use is from the Wikipedia page where we need the periods only. Of the following 5 principal tidal constituents, only N2 is a minor factor in this case study.
In practice, multiple linear regression would provide faster results for tidal analysis as the constituents add linearly (see the CSALT model). In contrast, for ENSO there are several nonlinear steps required that precludes a quick regression solution. Yet, this tidal analysis test shows how effective and precise a solution the solver supplies.
The entire analysis only took an evening of work, in comparison to the difficulty of dealing with ENSO data, which is much more noisy than the clean tidal data. Moreover, the parameters for conventional tidal analysis stress the synodic/tropical/sidereal constituents — unfortunately, these are of little consequence for ENSO analysis, which requires the draconic and anomalistic parameters and the essential correction factors. The synodic tide is the red herring for the unwary when dealing with global phenomena such as ENSO, QBO, and LOD. The best way to think about it is that the synodic cycle impacts locally and most immediately, whereas the anomalistic and draconic cycles have global and more cumulative impacts.