Scaling El Nino

Recently, the rock climber Alex Honnold took a route up El Capitan without ropes.There's no room to fail at that. I prefer a challenge that one can fail at, and then keep trying.  This is the ascent to conquering El Nino:

The Free-thought Route*

Χ  Base camp:  ENSO (El Nino/Southern Oscillation) is a sloshing behavior, mainly in the thermocline where the effective gravity makes it sensitive to angular momentum changes.
Χ  Faster forcing cycles reinforce against the yearly cycle, creating aliased periods. How?
Χ  Monthly lunar tidal cycles provide the aliased factors: Numbers match up perfectly.
This aliasing also works for QBO, an atmospheric analog of ENSO.
Χ  A biennial meta-stability appears to be active. Cycles reinforce on alternating years.
Χ  The well-known Mathieu modulation used for sloshing simulations also shows a biennial character.
Machine learning experiments help ferret out these patterns.
Χ  The delay differential equation formulation matches up with the biennial Mathieu modulation with a delay of one-year.  That's the intuitive yearly see-saw that is often suggested to occur.
  The Chandler wobble also shows a tidal forcing tendency, as does clearly the earth's LOD (length-of-day) variations.
Χ  Integrating the DiffEq model provides a good fit, including long-term coral proxy records
Χ  Solving the Laplace tidal equation via a Sturm-Liouville expression along the equator helps explain details of QBO and ENSO
  Close inspection of sea-level height (SLH) tidal records show evidence of both biennial and ENSO characteristics
Δ Summit: Final validation of the geophysics comparing ENSO forcing against LOD forcing.

Model fits to ENSO using a training interval

The route encountered several dead-ends with no toe-holds or hand-holds along the way (e.g. the slippery biennial phase reversal, the early attempts at applying Mathieu equation). In retrospect many of these excursions were misguided or overly complex, but eventually other observations pointed to the obvious route.

This is a magnification of the fitting contour around the best forcing period values for ENSO. These pair of peak values are each found to be less than a minute apart from the known values of the Draconic cycle (27.2122 days) and Anomalistic cycle (27.5545 days).

The forcing comes directly from the angular momentum variations in the Earth's rotation. The comparison between what the ENSO model uses and what is measured via monitoring the length-of-day (LOD) is shown below:

 

 

*  This is not the precise route I took, but how I wish it was in hindsight.

ENSO model fit 1880-1980

This is an ENSO fit that only has knowledge of data prior to 1980. The data is 80% NINO34 and 20% SOI, with the latter providing finer structure.The lower fit includes a slight variation of the Draconic month according to this NASA page. It doesn't seem to do much.

A previous fit used values of A=0.785, M=0.3, K=-0.15 to 1920. This used A=0.866, M=0.207, K=-0.16.

The Lunar Geophysical Connection

The conjecture out of NASA JPL is that the moon has an impact on the climate greater than is currently understood:

Claire Perigaud (Caltech/JPL)
and
Has this research gone anywhere?  Looks as if has gone to this spin-off.
According to the current consensus, variability in wind is what contributes to forcing for behaviors such as the El Nino/Southern Oscillation (ENSO).
OK, but what forces the wind? No one can answer that apart from saying wind variability is just a part of the dynamic climate system.  And so we are lead to believe that a wind burst will cause an ENSO and then the ENSO event will create a significant disruptive transient to the climate much larger than the original wind stimulus. And that's all due to positive feedback of some sort.
I am only paraphrasing the current consensus.
A much more plausible and parsimonious explanation lies with external lunar forcing reinforced by seasonal cycles.

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ENSO Proxy Validation

This is a straightforward validation of the ENSO model presented at last December's AGU.

What I did was use the modern instrumental record of ENSO — the NINO34 data set — as a training interval, and then tested across the historical coral proxy record — the UEP data set.

The correlation coefficient in the out-of-band region of 1650 to 1880 is excellent, considering that only two RHS lunar periods (draconic and anomalistic month) are used for forcing. As a matter of fact, trying to get any kind of agreement with the UEP using an arbitrary set of sine waves is problematic as the time-series appears nearly chaotic and thus requires may Fourier components to fit. With the ENSO model in place, the alignment with the data is automatic. It predicts the strong El Nino in 1877-1878 and then nearly everything before that.

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Shortest Training Fit for ENSO

This is remarkable. Using the spreadsheet linked in the last post, the figure below is a model of ENSO derived completely by a training fit over the interval 1900 to 1920, using the Nino3.4 data series and applying the precisely phased Draconic and Anomalistic long-period tidal cycles.

Fig. 1 : The ENSO model in red. The blue BG region is used for training of the lunar tidal amplitudes against the Nino3.4 data in green. That data is square root compacted to convert it to an equivalent velocity.

Not much more to say. There is a major disturbance starting in the mid-1980's, but that is known from a Takens embedding analysis described in the first paper in this post.

Tidal Model of ENSO

The input forcing to the ENSO model includes combinations of the three major lunar months modulated by the seasonal solar cycle. This makes it conceptually similar to an ocean tidal analysis, but for ENSO we are more concerned about the long-period tides rather than the diurnal and semi-diurnal cycles used in conventional tidal analysis.

The three constituent lunar month factors are:

Month type Length in days
anomalistic 27.554549
tropical 27.321582
draconic 27.212220

So the essential cyclic terms are the following phased sinusoids

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