In Chapter 12 of the book, we provide a short introduction to ocean tidal analysis. This has an important connection to our model of ENSO (in the same chapter), as the same lunisolar gravitational forcing factors generate the driving stimulus to both tidal and ENSO behaviors. Noting that a recent paper [1] analyzing the so-called *long-period* tides (i.e. annual, monthly, fortnightly, weekly) in the Drake Passage provides a quantitative spectral decomposition of the tidal factors, it is interesting to revisit our ENSO analysis in the conventional ocean tidal context …

Woodworth and Hibbert [1] use selective bottom pressure recorder (BPR) measurements to extract the tidal factors. Below we reproduce the power spectrum and tidal model fit of the data from their paper.

In comparison, for the ENSO model, we extract the following spectrum for the tidal forcing (time-domain shown in upper right inset). This is a log scale so note that most of the constituent tidal factors are weaker than the primary factors Mf/Sidereal (13.66/27.32 day) and Msf/Synodic (14.77/29.53 day).

The factors scale in proportion to the Drake Passage BPR spectrum, with the addition of the smaller amplitude features which emerge from the best ENSO fit. The red arrows indicate the location of the nodal (18.6 year) satellite peaks. Only the peak labelled “A” is not identifiable straightforwardly from catalogued tidal harmonic constituents, as described in [2]. *(added 9-27-2019 : “A” is the 14.192 day tidal constituent listed in R.D.Ray et al “Long‐period tidal variations in the length of day” Table 3)*

The time domain comparison is shown below, with the GREEN dashed line indicating the ENSO tidal forcing input, shifted slightly to align with the Drake Passage tidal data/model.

Chapter 12 in the book describes the detailed ENSO model including the modulation with an annual impulse *plus* the Laplace’s Tidal Equation dynamical response, which transforms the input tidal forcing to the full range (1880-present) ENSO behavior as fitted below.

The rather simple input forcing produces a rich waveform as a response, which is most plausibly explained in terms of the modeled LTE response function along the constrained equatorial topology. In other words, WYSIWYG for conventional tidal analysis, but for topologically constrained behaviors such as ENSO, the forcing is only a first step.

#### References

[1] P. L. Woodworth and A. Hibbert, “The nodal dependence of long-period ocean tides in the Drake Passage,” Ocean Science, vol. 14, no. 4, pp. 711–730, 2018.

[2] R. M. Ponte, A. H. Chaudhuri, and S. V. Vinogradov, “Long-Period Tides in an Atmospherically Driven, Stratified Ocean,” Journal of Physical Oceanography, vol. 45, no. 7, pp. 1917–1928, Jul. 2015.

The spike to the right of Mt in the ENSO forcing spectrum, lined up at 40/year, is Mtm or 9.13 days

Long-period constituent list

https://www.iho.int/mtg_docs/com_wg/IHOTC/IHOTC_Misc/TWCWG_Constituent_list.pdf

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