ENSO

Unified Model of Earth Dynamics

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Lorenz turned out to be a chaotic dead-end in understanding Earth dynamics. Instead we need a new unified model of solid liquid dynamics focusing on symmetries of the rotating earth, applying equations of solid bodies & fluid dynamics. See Mathematical Geoenergy (Wiley, 2018).

Should have made this diagram long ago: here’s the ChatGPT4 prompt with the diagramming plugin.

Graph

Ocean Tides and dLOD have always been well-understood, largely because the mapping to lunar+solar cycles is so obvious. And the latter is getting better all the time — consider recent hi-res LOD measurements with a ring laser interferometer, pulling in diurnal tidal cycles with much better temporal resolution.

That’s the first stage of unification (yellow boxes above) — next do the other boxes (CW, QBO, ENSO, AMO, PDO, etc) as described in the book and on this blog, while calibrating to tides and LOD, and that becomes a cross-validated unified model.

Annotated 10/11/2023

ontological classification according to wavenumber kx, ky, kz and fluid/solid.

Added so would not lose it — highlighted tidal factor is non-standard

Geophysically Informed Machine Learning for Improving Rapid Estimation and Short-Term Prediction of Earth Orientation Parameters

Annual vs Semi-annual

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ENSO models best with alternating sign semi-annual pulses. Operating on the Mf tidal factor this generates a tight forcing with average period 3.8 years.

AMO models best with an annual pulse. Because of the Mt tidal factor the forcing slowly wanders with a period of ~120 years.

PDO models best with an annual pulse but fast decay. Because of the Mt tidal factor the forcing would wander like AMO, but instead it makes biased excursions.

To summarize, the models of ENSO, AMO, and PDO depend on the specific forcing character while keeping the LOD tidal calibration fixed. ENSO likely requires this alternating semi-annual because it is aligned along the equator and so alternates with northern and southern nodal swings. AMO and PDO may require an annual impulse because it’s essentially a northern hemisphere behavior. Why the decay is faster for PDO, or what exactly sets the decay rate after an integrating impulse, is not clear. Perhaps the larger the inertial push the slower the response.

Paleo ENSO

/ Paul Pukite (@whut) / 1 Comment

Two recent articles prompted a few ideas

From last year, https://watchers.news/2022/11/10/study-shows-how-earth-sun-distance-dramatically-influences-annual-weather-cycles-in-the-equatorial-pacific-in-a-22-000-year-cycle/ points to:

Two annual cycles of the Pacific cold tongue under orbital precession

Which says that

“Because the distance effect annual cycle (from perihelion to perihelion, otherwise called the anomalistic year, 365.259636 d (ref. 6)) is slightly longer than the tilt effect annual cycle (from equinox to equinox, otherwise known as the tropical year, 365.242189 d (ref. 6)), the LOP increases over time. A complete revolution of the LOP is the precession cycle, about 22,000 yr (ref. 38). “

The claim is that the exact timing and strength of the annual cycle extreme is important in initiating an El Nino or La Nina cycle. as the Longitude of Perihelion (LOP) moves over time, so that when this aligns with the solstice/equinox events, the ENSO behavior will mirror the strength of the forcing.

Next article

ENSO-related centennial and millennialscale hydroclimate changes recorded from Lake Xiaolongchi in arid Central Asia over the past 8000 years

They note 800 year cycles in the observations

This is not a 22,000 year cycle (as stated its actuallly closer to 21,000), but it’s possible that if tidal cycles play a part of the forcing, then a much shorter paleo cycle may emerge. Consider that the Mf tidal cycle of 13.66 days will generate a cycle of ~3.81 years when non-linearly modulated against the tropical year (seasonal cycle), but ~3.795 years modulated against the perigean or anomalistic year (nearest approach to the sun).

The difference between the two will reinforce every 783 years, which is close to the 800 year cycle. Aliasing and sideband frequency calculations reveal these patterns.

The Power of Darwin

/ Paul Pukite (@whut) / 3 Comments

Using the LTE model on the NINO4 ENSO time-series, I excluded the interval between 1870-1875 for cross-validation. The fit below is from scratch on a dLOD-calibrated initial forcing, then allowing the values to vary slightly but the dLOD remains at 0.9999668 of the initial calibration.

The cross-validation doesn’t look good and actually is anti-correlated to a CC = -0.5 over that interval. But the region before 1875 appears suspiciously flat in any case, see the data on the KNMI site — it’s only a certainty that the El Nino peak at 1877-1878 is real and not estimated.

So, the next step is to take the fit to NINO4 and apply it to the Darwin (SOI) time-series, applying the same fitting interval from 1875-present. Immediately, it captures the 3 positive excursions in the interval 1870 to 1875. And then letting the fit proceed to a high CC, the result is shown below:

The resultant fit in the excluded cross-validation region reaches 0.58, thus reversing the anti-correlation and confirming that the NINO4 time-series data prior to 1875 is likely incorrect.

The fit data is at https://gist.github.com/pukpr/c26f1da00337e92dbb47671ca48af2cf?permalink_comment_id=4639783#gistcomment-4639783. The main modifications to tidal factors are in the very long periods — these values start small due to the dLOD calibration (the differential filters out low frequencies) but the 4.42 year amplitude is nearly tripled after the fit, the 8.85 & 9.3 year up by 50%. The 18.6 year is only up 14%, and the 3rd order 6 year and 15.9 year are down 63% and up 45% respectively. All the fortnightly and monthly values are stable. This is perhaps reasonable considering how much the LOD drifts over time at low frequency, and that the calibration is restricted to post-1962.

The Big 10 Climate Indices

/ Paul Pukite (@whut) / 2 Comments

The above diagram courtesy of Karnauskus

These correspond to the geographically defined climate indices

Overall I’m confident with the status of the published analysis of Laplace’s Tidal Equations in Mathematical Geoenergy, as I can model each of these climate indices with precisely the same (save one ***) tidal forcing, all calibrated by LOD. The following Threads allow interested people to contribute thoughts

  1. ENSO – https://www.threads.net/@paulpukite/post/CuWS8MFu8Jc
  2. AMO – https://www.threads.net/@paulpukite/post/Cuh4krjJTLN
  3. PDO – https://www.threads.net/@paulpukite/post/Cuu0VCypIi5
  4. QBO – https://www.threads.net/@paulpukite/post/CuiKQ5tsXCQ
  5. SOI (Darwin & Tahiti) – https://www.threads.net/@paulpukite/post/Cuu2IkBJh55 => MJO
  6. IOD (East & West) – https://www.threads.net/@paulpukite/post/Cuu9PYvJAG2
  7. PNA – https://www.threads.net/@paulpukite/post/CuvAVR7JN7R
  8. AO – https://www.threads.net/@paulpukite/post/CuvEz37JPFV
  9. SAM – https://www.threads.net/@paulpukite/post/CuvLZ2CMt1X
  10. NAO – https://www.threads.net/@paulpukite/post/CuvNnwns2la

(*** The odd-one out is QBO, which is a global longitudinally-invariant behavior, which means that only a couple of tidal factors are important.)

Is the utility of this LTE modeling a groundbreaking achievement? => https://www.threads.net/@paulpukite/post/CuvNnwns2la

A Digital Twin of ENSO

/ Paul Pukite (@whut) / 3 Comments

The idea of a digital twin is relatively new in terms of coinage of terms, but the essential idea has been around for decades. In the past, a digital twin was referred to as a virtual simulation of a specific system, encoded via a programming language. In the case of a system that was previously built, the virtual simulation emulated all the behaviors and characteristics of that system, only operated on a computer, with any necessary interactive controls and displays provided on a console, either real or virtual. A widely known example of a VS is that of a flight simulator, which in historical terms was the industrial forerunner to today’s virtual reality. A virtual simulation could also be used during the design of the system, with the finished digital twin providing a blueprint for the actual synthesis of the end-product. This approach has also been practiced for decades, both in the electronics industry via logic synthesis of integrated circuits from a hardware description language and with physical products via 3D printing from CAD models.

Continue reading →

Gist Evaluation

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The Gist site on GitHub allows you to comment on posts very easily. For example, images of charts can be pasted in the discussion area. Also snippets of code can be added and updated, which is useful for neural net evaluation. The following is a link to an initial Gist area for evaluating LTE models.

Comparison of LTE models applying slight variations of tidal forcing but larger allowance of basin tidal modulation

AMO

NINO4

IOD-East

IOD-West

PDO

Comparison of forcing

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