An intriguing discovery is that the higher-resolution aspects of the SOI time-series (as illustrated by the Australian BOM 30-day SOI moving average) may also have a tidal influence. Note the fast noisy envelope that rides on top of the deep El Nino of 2015-2016 shown below:
For the standard monthly SOI as reported by NCAR and NOAA, this finer detail disappears. BOM provides the daily SOI value for about the past ~ 3 years here.
Yet if we retain this in the 1880-present monthly ENSO model, by simultaneously isolating [1] the higher frequency fine structure from 2015-2017, the fine structure also emerges in the model. This is shown in the lower panel below.
This indicates that the differential equation being used currently can possibly be modified to include faster-responding derivative terms which will simultaneously show the multi-year fluctuations as well as what was thought to be a weekly-to-monthly-scale noise envelope. In fact, I had been convinced that this term was due to localized weather but a recent post suggested that this may indeed be a deterministic signal.
Lunisolar tidal effects likely do impact the ocean behavior at every known time-scale, from the well-characterized diurnal and semi-diurnal SLH tides to the long-term deep-ocean mixing proposed by Munk and Wunsch. It’s not surprising that tidal forces would have an impact on the intermediate time-scale ENSO dynamics, both at the conventional low resolution (used for El Nino predictions) and at the higher-resolution that emerges from SOI measurements (the 30-day moving average shown above). Obviously, monthly and fortnightly oscillations observed in the SOI are commensurate with the standard lunar tides of periods 13-14 days and 27-28 days. And non-linear interactions may result in the 40-60 day oscillations observed in LOD.
from Earth Rotational Variations Excited by Geophysical Fluids, B.F. Chao, http://ivs.nict.go.jp/mirror/publications/gm2004/chao/
It’s entirely possible that removing the 30-day moving average on the SOI measurements can reveal even more detail/
Footnote
[1] Isolation is accomplished by subtracting a 24-day average about the moving average value, which suppresses the longer-term SOI variation.
GeoEnergy Math 
Going from right to left in the Chao figure
Semi-diurnal tides –> Tidal forcing
Diurnal tides –> Tidal forcing
Long-period tides –> Tidal forcing
40-60 day oscillation –> (is this tidal too?)
Semi-annual –> Solar + Tidal
Annual –> Solar + Tidal
Core –> ???
ENSO –> Tidal forcing
QBO –> Tidal forcing
Secular –> ???
It’s just about all tidal.
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Attempt at combining the long-term fit 1880-2016 data with the short-term hiRes SOI model by summing the two (the intensity is inverted according to SOI definition):
The long-term fit does not excessively favor the years post-2015 so that particular fit is not especially tight. Overall it is promising.
I am thinking the faster ENSO mode may be a different zonal harmonic solution to Laplace’s tidal equations. Where the primary solution is a zonal 6 but the faster is a zonal 7. This may alter the diffEq parameters enough to capture a higher frequency bandwidth closer to the monthly tidal forcing periods.
This is what the resolution looks like in comparison to the monthly data. Note how much potential detail is lost by only looking at monthly!
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