ESD Ideas article for review

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The simple idea is that tidal forces play a bigger role in geophysical behaviors than previously thought, and thus helping to explain phenomena that have frustrated scientists for decades.

The idea is simple but the non-linear math (see figure above for ENSO) requires cracking to discover the underlying patterns.

The rationale for the ESD Ideas section in the EGU Earth System Dynamics journal is to get discussion going on innovative and novel ideas. So even though this model is worked out comprehensively in Mathematical Geoenergy, it hasn’t gotten much publicity.

Stratospheric Sudden Warming

Chapter 11 of the book describes a model for the QBO of stratospheric equatorial winds. The stratified layers of the atmosphere reveal different dependencies on the external forcing depending on the altitude, see Fig 1.

Figure 1 : At high altitudes, only the sun’s annual cycle impacts the stratospheric as a semi-annual oscillation (SAO). Below that the addition of the lunar nodal cycle forces the QBO. The earth itself shows a clear wobble with the lunar cycle interacting with the annual.

Well above these layers are the mesosphere, thermosphere, and ionosphere. These are studied mainly in terms of space physics instead of climate but they do show tidal interactions with behaviors such as the equatorial electrojet [1].

The behaviors known as stratospheric sudden warmings (SSW) are perhaps a link between the lower atmospheric behaviors of equatorial QBO and/or polar vortex and the much higher atmospheric behavior comprising the electrojet. Papers such as [1,2] indicate that lunar tidal effects are showing up in the SSW and that is enhancing characteristics of the electrojet. See Fig 2.

Figure 2 : During SSW events, a strong modulation of period ~14.5 days emerges, close to the lunar fortnightly period as seen in these spectrograms. Taken from ref [2] and see quote below for more info.

“Wavelet spectra of foEs during two SSW events exhibit noticeable enhanced 14.5‐day modulation, which resembles the lunar semimonthly period. In addition, simultaneous wind measurements by meteor radar also show enhancement of 14.5‐day periodic oscillation after SSW onset.”

Tang et al [2]

So the SSW plays an important role in ionospheric variations, and the lunar tidal effects emerge as the higher atmospheric density of a SSW upwelling becomes more sensitive to lunar tidal forcing. That may be related to how the QBO also shows a dependence on lunar tidal forcing due to its higher density.


  1. Siddiqui, T. A. Relationship between lunar tidal enhancements in the equatorial electrojet and stratospheric wind anomalies during stratospheric sudden warmings. (2020). Originally presented at AGU 2018 Fall Meeting
  2. Tang, Q., Zhou, C., Liu, Y. & Chen, G. Response of Sporadic E Layer to Sudden Stratospheric Warming Events Observed at Low and Middle Latitude. Journal of Geophysical Research: Space Physics e2019JA027283 (2020).

Chandler Wobble according to Na

In Chapter 13 of the book, we have a description of the mechanism forcing the Chandler Wobble in the Earth’s rotation. As a counter to a recent GeoenergyMath post suggesting there is little consensus behind this mechanism, a recent paper by Na et al provides a foundation to understand how the lunar forcing works. 

Chandler wobble and free core nutation are two major modes of perturbation in the Earth rotation. Earth rotation status needs to be known for the coordinate conversion between celestial reference frame and terrestrial reference frame. Due mainly to the tidal torque exerted by the moon and the sun on the Earth’s equatorial bulge, the Earth undergoes precession and nutation.

Na, S.-H. et al. Chandler Wobble and Free Core Nutation: Theory and Features. Journal of Astronomy and Space Sciences 36, 11–20 (2019).
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Lunisolar Forcing of the Chandler Wobble

In Chapter 13 of the book, we have a description of the mechanism forcing the Chandler Wobble in the Earth’s rotation. Even though there is not yet a research consensus on the mechanism, the prescribed lunisolar forcing seemed plausible enough that we included a detailed analysis in the text.  Recently we have found a recent reference to a supporting argument to our conjecture, which is presented below …

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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)
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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The Chandler Wobble Challenge

In the last post I mentioned I was trying to simplify the ENSO model. Right now the forcing is a mix of angular momentum variations related to Chandler wobble and lunisolar tidal pull. This is more complex than I would like to see, as there are a mix of potentially confounding factors. So what happens if the Chandler wobble is directly tied to the draconic/nodal cycles in the lunar tide? There is empirical evidence for this even though it is not outright acknowledged in the consensus geophysics literature. What you will find are many references to the long period nodal cycle of 18.6 years (example), which is clearly a lunar effect. If that is indeed the case, then the behavior of ENSO is purely lunisolar, as the Chandler wobble behavior is subsumed. That simplification would be significant in further behavioral modeling.

The figure below is my fit to the Chandler wobble, seemingly matching the aliased lunar draconic cycle rather precisely, taken from a previous blog post:


The consensus is that it is impossible for the moon to induce a nutation in the earth’s rotation to match the Chandler wobble. Yet, the seasonally reinforced draconic pull leads to an aliasing that is precisely the same value as the Chandler wobble period over the span of many years. Is this just coincidence or is there something that the geophysicists are missing?

It’s kind of hard to believe that this would be overlooked, and I have avoided discussing the correlation out of deference to the research literature. Yet the simplification to the ENSO model that a uniform lunisolar forcing would result in shouldn’t be dismissed. To quote Clinton: “What if it is the moon, stupid?”

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ENSO model maps to LOD cycles

Elaborating on this comment attached to an LOD post,  noting this recent paper:

Shen, Wenbin, and Cunchao Peng. 2016. “Detection of Different-Time-Scale Signals in the Length of Day Variation Based on EEMD Analysis Technique.” Special Issue: Geodetic and Geophysical Observations and Applications and Implications 7 (3): 180–86.  doi:10.1016/j.geog.2016.05.002.

Because of the law of conservation of momentum sloshing can change the velocity of a container full of liquid, momentarily speeding it up or slowing it down as the liquid sloshes back and forth.  By the same token, suddenly slowing or speeding of that container can also cause the sloshing.   So there is a chicken and egg quality to the analysis of sloshing, making it difficult to ascertain the origin of the effect.

If ENSO is a manifestation of a liquid sloshing in a container and if the length-of-day (LOD) is a measurement of the angular momentum changes of the Earth’s rotation, then it is perhaps useful to compare the fundamental time-varying signals in each measurement.

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ENSO Model Final Stretch (maybe)

[mathjax]I recently posted a bog article called QBO Model Final Stretch. The idea with that post was to give an indication that the physics and analytical math model explaining the behavior of the QBO was in decent shape. I would like to do the same thing with the ENSO model but retain the context of the QBO model.  Understanding the QBO was a boon to making progress with ENSO as it provided an excellent training ground for time-series analysis and also provided some insight into the underlying forcing functions.  In the literature, there is a clear indication that ENSO and QBO are somehow related, but the causality chain remains unclear.

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