In Mathematical Geoenergy, Chapter 12, a biennially-impulsed lunar forcing is suggested as a mechanism to drive ENSO. The current thinking is that this lunar forcing should be common across all the oceanic indices, including AMO for the Atlantic, IOD for the Indian, and PDO for the non-equatorial north Pacific. The global temperature extreme of the last year had too many simultaneous concurrences among the indices for this not to be taken seriously.
NINO34
PDO
AMO
IOD – East
IOD-West
Each one of these uses a nearly identical annual-impulsed tidal forcing (shown as the middle green panel in each), with a 5-year window providing a cross-validation interval. So many possibilities are available with cross-validation since the tidal factors are essentially invariantly fixed over all the climate indices.
The approach follows 3 steps as shown below
The first step is to generate the long-period tidal forcing. I go into an explanation of the tidal factors selected in a Real Climate comment here.
Then apply the lagged response of an annual impulse, in this case alternating in sign every other year, which generates the middle panel in the flow chart schematic (and the middle panel in the indexed models above).
Finally, the Laplace’s Tidal Equation (LTE) modulation is applied, with the lower right corner inset showing the variation among indices. This is where the variability occurs — the best approach is to pick a slow fundamental modulation and generate only integer harmonics of this fundamental. So, what happens is that different harmonics are emphasized depending on the oceanic index chosen, corresponding to the waveguide structure of the ocean basin and what standing waves are maximally resonant or amplified.
Note that for a dipole behavior such as ENSO, the LTE modulation will be mirror-inverses for the maximally extreme locations, in this case Darwin and Tahiti
A machine learning application is free to scrape the following GIST GitHub site for model fitting artifacts.
https://gist.github.com/pukpr/3a3566b601a54da2724df9c29159ce16Another analysis that involved a recursively cycled fit between AMO and PDO. It switched fitting AMO for 2.5 minutes and then PDO for 2.5 minutes, cycling 50 times. This created a common forcing with an optimally shared fit, forcing baselined to PDO.
PDO
AMO
NINO34
IOD-East
IOD-West
Darwin
Tahiti
The table above shows the LTE modulation factors for Darwin and Tahiti model fits. The highlighted blocks show the phase of the modulation, which should have a difference of π radians for a perfect dipole and higher harmonics associated with it. (The K0 wavenumber = 0 has no phase, but just a sign). Of the modes that are shared 1, 45, 23, 36, 18, 39, 44, the average phase is 3.09, close to π (and K0 switches sign).
1.23-(-1.72) = 2.95
1.47-(-2.05) = 3.52
-2.89-(0.166) = -3.056
-0.367-(-2.58) = 2.213
1.59-(-2.175) = 3.765
0.27 - (-2.84) = 3.11
-1.87 -1.14 = -3.01
Average (2.95+3.52+3.056+2.213+3.765+3.11+3.01)/7 = 3.0891
Contrast to the IOD East/West dipole. Only the K0 (wavenumber=0) shows a reversal in sign. The LTE modulation terms are within 1 radian of each other, indicating much less of a dipole behavior on those terms. It’s possible that these sites don’t span a true dipole, either by its nature or from siting of the measurements.
Cross-validating a large interval span on PDO
using CC
using DTW metric, which pulls out more of the annual/semi-annual signal
adding a 3rd harmonic
Complement of the fitting interval, note the spectral composition maintains the same harmonics, indicating that the structure mapped to is stationary in the sense that the tidal pattern is not changing and the LTE modulation is largely fixed.
This is the resolved tidal forcing, finer than the annual impulse sampling used on the models above.
Below can see the primary 27.5545 lunar anomalistic cycle, mixed with the draconic 27.2122/13.606 cycle to create the 6/3 year modulation and the 206 day perigee-syzygy cycle (or 412 full cycle, as 206 includes antipodal full moon or new moon orientation).
(click on any image to magnify)
https://www.realclimate.org/index.php/archives/2024/05/new-journal-nature-2023/#comment-822907
Wind is what’s referred to as a confounding variable in the attribution of ENSO events. The initial changes in SSTs and thermocline levels are more likely driven by oceanic processes, primed by external influences such as tidal and seasonal forcing. Wind patterns respond to these initial changes and then act to amplify and sustain the SST anomalies through a positive feedback loop. Therefore, while winds play a role in the development and intensification of El Niño and La Niña events, they are part of a feedback mechanism rather than the primary causative factor. At best, the interplay between oceanic and atmospheric processes creates a more complex system where multiple feedbacks, including perhaps global warming, contribute to the overall dynamics of ENSO. As everyone in this forum is highly aware of the role of GHGs such as CO2 acting as a feedback mechanism in climate change, it’s odd that wind is not treated the same way with respect to ENSO.
But of course, these are just words. If g(t) is a seasonally impulsed tidal forcing then ENSO = f1(g(t)) and AMO = f2(g(t)) and PDO = f3(g(t)), where f1, f2, f3 are different LTE standing wave mode modulation functions. LTE standing wave modes are solutions to Laplace’s Tidal Equations, a simplified form as described in Mathematical Geoenergy (Wiley/AGU, 2018). Oceanic climate indices are a rich source of data for cross-validating such models. I don’t even treat wind as a driving factor, as it is subsumed as an amplifying scale factor, to first-order invariant across the time interval that ENSO and the other indices have been measured.
A likely role for stratification in long-term changes of the global ocean tides
https://www.nature.com/articles/s43247-024-01432-5#citeas
Thesis: The El Niño-Southern Oscillation and the Signal-to-Noise Paradox
Williams, N
https://ore.exeter.ac.uk/repository/handle/10871/136337
Dimensionality reduction of chaos by feedbacks and periodic forcing is a source of natural climate change, P. Salmon
https://link.springer.com/article/10.1007/s00382-024-07191-5
Long Period Tidal Force Variations and Regularities in Orbital Motion of the Earth-Moon Binary Planet System
https://link.springer.com/article/10.1007/s11038-011-9381-8
“The formula (4) does not contain angular distances between heavenly bodies and a celestial equator. This means that the declination of the Moon and Sun relative to the Earth’s equator is a secondary factor for the generation of tidal periodicities of 206 and 412 days. This fact was mentioned also by Desplanque and Mossman (2004, Fig. 68, p.106) in their study of the Bay of Fundy tides.”
https://media.springernature.com/lw685/springer-static/image/art%3A10.1007%2Fs11038-011-9381-8/MediaObjects/11038_2011_9381_Fig5_HTML.gif
Do periodic consolidations of Pacific countercurrents trigger global cooling by equatorially symmetric La Niña?
https://cp.copernicus.org/preprints/cp-2010-28/
“Surprising coincidences of WWB with perigean eclipses suggest a parallel atmospheric tide influence. Proposed PCC-ESLN forcing operates in multiple timescales, beginning where the annual cycle of strong equinoctial tides coincides with the minimum perigee cycle. This forcing corresponds with El Niño Southern Oscillation (ENSO) events in 1997, 2002, and 2006. Next, extreme central eclipses that perturb perigee-sysygy intervals”
Rejected, even though the author clearly stated that this is something to look into. May have been too enamored with climate change
“The striking observation of ENSO activity in years of maximum tidal excursions near the
vernal equinox (Fig. 8) suggests that this may be the key to the so-called spring predictability barrier. If verified, such a predictive tool would have great societal value in agricultural planning and tropical cyclone risk assessment.”
—
Long-Period Tides in an Atmospherically Driven, Stratified Ocean
RUI M. PONTE AND AYAN H. CHAUDHURI
DOI: 10.1175/JPO-D-15-0006.1
On Dynamical Decomposition of Multiscale Oceanic Motions
https://agupubs.onlinelibrary.wiley.com/doi/pdfdirect/10.1029/2022MS003556
Tides and their seminal impact on the geology, geography, history, and socio-economics of the Bay of Fundy, eastern Canada
https://www.erudit.org/en/journals/ageo/2004-v40-n1-ageo_40_1/ageo40_1art01/
“Overlapping of the cycles of spring and perigean tides every 206 days results in an annual progression of 1.5 months in the periods of especially high tides. Depending on the year, these strong tides can occur at all seasons. The strongest Fundy tides occur when the three elements – anomalistic, synodical, and tropical monthly cycles – peak simultaneously. The closest match occurs at intervals of 18.03 years, a cycle known as the Saros.
Extra-high tides can occur at all seasons in the Bay of Fundy, depending on the year in question. The result is considerable tidal variation throughout the year. Distinct cycles of 12.4 hours, 24.8 hours, 14.8 days, 206 days, 4.53 years, and 18.03 years are recognized.”
https://www.physicsforums.com/threads/orientation-of-the-earth-sun-and-solar-system-in-the-milky-way.888643/page-5#post-7076902
Lunar rotational dissipation in solid body and molten core
https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2000JE001396
“The Moon keeps one face toward the Earth. This simple statement of the equality of the rotational and orbital periods has
a deeper implication. Since there is no reason to expect that the Moon formed in such a special rotational state, there must have
been one or more mechanisms for changing the lunar rotational angular momentum and energy”
“The most important dissipation terms are at monthly, 206 day, annual, 3 year, and 6 year periods. The series of this section will
be used for interpretation of LLR data fits (section 18).”
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