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.
① 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.
② 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.
③ 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
④ 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.
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.