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## Comments

Paul,

Fine effort applied to the specific lunar contribution to QBO.

Struggling to see whether the convergence seen in the top graph is pure evidence of lunar forcing, or just ongoing smoothing of QBO average over time. Lunar cycles of course start high-Q smooth, and multiple smooth sequences correlate mathematically, if not causally, physically. The bottom graphs are not extremely compelling, as there are so many spurious equivalent peaks compared to supposed hits.

What if historic QBO data is simply still too crude for a reliable measure of correlation? Can we not say that the unspecified causes of noise may represent unidentified forcings that may well be of higher order?

Sensitive systems effectively paint a hologram of their surroundings. QBO statistical "noise" is trying to tell us far more than just tidal information. Its selective attention to focus on the lunar contribution, when complex bulk harmonics and other critical factors remain poorly identified.

`Paul, Fine effort applied to the specific lunar contribution to QBO. Struggling to see whether the convergence seen in the top graph is pure evidence of lunar forcing, or just ongoing smoothing of QBO average over time. Lunar cycles of course start high-Q smooth, and multiple smooth sequences correlate mathematically, if not causally, physically. The bottom graphs are not extremely compelling, as there are so many spurious equivalent peaks compared to supposed hits. What if historic QBO data is simply still too crude for a reliable measure of correlation? Can we not say that the unspecified causes of noise may represent unidentified forcings that may well be of higher order? Sensitive systems effectively paint a hologram of their surroundings. QBO statistical "noise" is trying to tell us far more than just tidal information. Its selective attention to focus on the lunar contribution, when complex bulk harmonics and other critical factors remain poorly identified.`

re: "too crude"

This is daily QBO data from https://cds.climate.copernicus.eu . Note how a short training interval from 1993 to 2001 can recreate the rest of the time series.

This is obviously not a high-Q resonant phenomena anymore than a tidal chart is resonant. The climate science guardians are having a hard time with this finding because they are unable to falsify the agreement. Conceptually it should be trivial to falsify because all one has to do is show that the QBO periods don't match the tidal periods. They do match, so it can't be falsified that way. Even Lindzen, the supposed sage of QBO understanding made the claim in 2 different articles, but unfortunately he didn't seem to understand how to do signal processing and so never made the connection

So some 50 years later, we can give Lindzen a mechanism. But since he is now retired I doubt he would respond.

`> "What if historic QBO data is simply still too crude for a reliable measure of correlation?" re: "too crude" This is daily QBO data from https://cds.climate.copernicus.eu . Note how a short training interval from 1993 to 2001 can recreate the rest of the time series. ![](https://camo.githubusercontent.com/2b305a41d76432421d407a24ce72bc8049285fd8e89d03909d2c273830f7eb79/68747470733a2f2f696d6167697a65722e696d616765736861636b2e636f6d2f696d673932332f333733362f6253704a70732e706e67) This is obviously not a high-Q resonant phenomena anymore than a tidal chart is resonant. The climate science guardians are having a hard time with this finding because they are unable to falsify the agreement. Conceptually it should be trivial to falsify because all one has to do is show that the QBO periods don't match the tidal periods. They do match, so it can't be falsified that way. Even Lindzen, the supposed sage of QBO understanding made the claim in 2 different articles, but unfortunately he didn't seem to understand how to do signal processing and so never made the connection ![](https://imagizer.imageshack.com/img922/8997/92cTTf.png) So some 50 years later, we can give Lindzen a mechanism. But since he is now retired I doubt he would respond.`

Paul, you wrote: "a short training interval from 1993 to 2001 can recreate the rest of the time series"

This is valid if the QBO training interval is not some sort of singularity, like the Feynman Point in the expansion of pi. A quasi-periodic series is at best only simulated, not fully recovered, from a short data sample.

There is a middle ground between the "climate science guardians" not seeing any lunar forcing, and your position of solely seeing lunar forcing. This disagreement represents incomplete explanations on both sides. The Guardians do see a probable solar "quasi-biannual" signal, but with a slipping glitch, like worn gears. I see both Lunar and Solar semi-forcing, from heuristic logic, with no exclusive-or (XOR) dependence.

Can we not entertain a notion of multi-forcing, where various factors multi-chaotically alternate? If "correlation does not imply causation", where is proof of causation as tidal forcing? QBO statistics are not precise enough to exactly match to tidal periods without a lot of noise to confound final existence proof.

A known tidal effect on wind is a velocity maxima during high tide, caused by rising water squeezing wind upward, essentially a Venturi Effect. Conversely, there is a wind velocity minima during low tide. This oscillation is often masked by other weather system variables, but Sailors have long been aware of the effect, and its in the data. No doubt real-time QBO is slightly sensitive to this tidal effect propagating all the way up to the Stratosphere, over ocean. What part is harmonic forcing or asynchronous with QBO is another question.

Late-night early-morning surface level inversion layers also squeeze wind upwards, typically to a far greater magnitude. Like chaotically breaking dawn waves in the upper stratosphere, this is bound to be a cause of QBO noise. There is also annual precession wobble pummeling QBO north and south with Rossby-Hadley cells.

`Paul, you wrote: "a short training interval from 1993 to 2001 can recreate the rest of the time series" This is valid if the QBO training interval is not some sort of singularity, like the Feynman Point in the expansion of pi. A quasi-periodic series is at best only simulated, not fully recovered, from a short data sample. There is a middle ground between the "climate science guardians" not seeing any lunar forcing, and your position of solely seeing lunar forcing. This disagreement represents incomplete explanations on both sides. The Guardians do see a probable solar "quasi-biannual" signal, but with a slipping glitch, like worn gears. I see both Lunar and Solar semi-forcing, from heuristic logic, with no exclusive-or (XOR) dependence. Can we not entertain a notion of multi-forcing, where various factors multi-chaotically alternate? If "correlation does not imply causation", where is proof of causation as tidal forcing? QBO statistics are not precise enough to exactly match to tidal periods without a lot of noise to confound final existence proof. A known tidal effect on wind is a velocity maxima during high tide, caused by rising water squeezing wind upward, essentially a Venturi Effect. Conversely, there is a wind velocity minima during low tide. This oscillation is often masked by other weather system variables, but Sailors have long been aware of the effect, and its in the data. No doubt real-time QBO is slightly sensitive to this tidal effect propagating all the way up to the Stratosphere, over ocean. What part is harmonic forcing or asynchronous with QBO is another question. Late-night early-morning surface level inversion layers also squeeze wind upwards, typically to a far greater magnitude. Like chaotically breaking dawn waves in the upper stratosphere, this is bound to be a cause of QBO noise. There is also annual precession wobble pummeling QBO north and south with Rossby-Hadley cells.`

No such thing as a proof in physics (proofs are for math). Instead, what is done is that one model is compared to another. For example, there is no proof that lunisolar gravitational forcing causes tidal cycles, only that the evidence showing consistency of orbital periods with sea level gauge measurements point to Laplace's Tidal Equations as the "best" model.

https://en.wikipedia.org/wiki/Theory_of_tides#Laplace's_tidal_equations

`> "where is proof of causation" No such thing as a proof in physics (proofs are for math). Instead, what is done is that one model is compared to another. For example, there is no proof that lunisolar gravitational forcing causes tidal cycles, only that the evidence showing consistency of orbital periods with sea level gauge measurements point to Laplace's Tidal Equations as the "best" model. https://en.wikipedia.org/wiki/Theory_of_tides#Laplace's_tidal_equations`

Geophysicists appear equally clueless about the origin of the Chandler wobble (CW), which is a simple applied torque of the lunar nodal cycle mixed with the annual cycle.

In the figure above, the main Chandler wobble frequency is indicated by the upward

GREENarrow in the CW power spectrum. The frequency of 0.843/year is predicted by the aliasing of an annual impulse with the fortnightly draconic/nodal lunar tidal cycle, providing a twice-annual sharp torquing (but variable due to aliasing) and thus sustaining the polar axis cyclic wobble. Consider also that if the southern node torque is equal to the northern node torque, then spectral peaks at 0.157/year and 1.843/year willnotemerge in the calculated Fourier terms. Thus the symmetric-forcing model spectrum inREDdoes not reveal the additional satellite terms, even though these satellite terms do occur in the data, indicated by the pair of downwardGREENarrows pointing to peaks in the theBLUEcurve.This is not

proofthat the Chandler wobble is caused by mixed lunisolar forcing, but no other model will explain it as well, both plausibly and parsimoniously.`> "There is also annual precession wobble" Geophysicists appear equally clueless about the origin of the Chandler wobble (CW), which is a simple applied torque of the lunar nodal cycle mixed with the annual cycle. ![](https://imagizer.imageshack.com/v2/828x597q90/r/923/kVjHaf.png) In the figure above, the main Chandler wobble frequency is indicated by the upward <font color=green>**GREEN**</font> arrow in the CW power spectrum. The frequency of 0.843/year is predicted by the aliasing of an annual impulse with the fortnightly draconic/nodal lunar tidal cycle, providing a twice-annual sharp torquing (but variable due to aliasing) and thus sustaining the polar axis cyclic wobble. Consider also that if the southern node torque is equal to the northern node torque, then spectral peaks at 0.157/year and 1.843/year will *not* emerge in the calculated Fourier terms. Thus the symmetric-forcing model spectrum in <font color=red>**RED**</font> does not reveal the additional satellite terms, even though these satellite terms do occur in the data, indicated by the pair of downward <font color=green>**GREEN**</font> arrows pointing to peaks in the the <font color=blue>**BLUE**</font> curve. This is not *proof* that the Chandler wobble is caused by mixed lunisolar forcing, but no other model will explain it as well, both plausibly and parsimoniously.`

PaulP: "No such thing as proof in physics (proofs are for math)"

It depends on one's Philosophy of Mathematics, whether one thinks Mathematical Proofs somehow exist in a Mathematician's physical brain (or in the Universe).

Many Physicists do in fact accept Existence-Proofs. They believe the Sun and Mathematics co-exist. Existence can be called an Effective Proof. Similarly, Engineering is Applied Physics. The first instance of a novel engineering technology is called Proof-of-Concept; ergo, accepted as a Physical Proof.

You clearly are not arguing that QBO may not exist, for lack of any proof. You are arguing for the existence of Lunar Forcing.

`PaulP: "No such thing as proof in physics (proofs are for math)" It depends on one's Philosophy of Mathematics, whether one thinks Mathematical Proofs somehow exist in a Mathematician's physical brain (or in the Universe). Many Physicists do in fact accept Existence-Proofs. They believe the Sun and Mathematics co-exist. Existence can be called an Effective Proof. Similarly, Engineering is Applied Physics. The first instance of a novel engineering technology is called Proof-of-Concept; ergo, accepted as a Physical Proof. You clearly are not arguing that QBO may not exist, for lack of any proof. You are arguing for the existence of Lunar Forcing.`

An elementary Newtonian physical model would suggest that the effect is there, the question is whether the effect is strong enough. The Chandler wobble is a prime example. If I gave a spinning top a periodic nudge orthogonal to one of its poles, after a transient precessional wobble it will stabilize into a cyclic wobble that matches the nudging period. Any freshman physics lab experiment can show that -- it's called a forced response as opposed to the natural response. It also occurs for any electrical circuit -- and it's essentially why what you hear through an audio amplifier is a scaled and filtered approximation to the input signal (if it was a nonlinear response, it would need to be decoded, as in the Mach-Zehnder-like modulation found in the ENSO model's forced response).

The question is why after ~130 years since Chandler discovered the Earth's wobble, why hasn't this simple relation of the moon and sun doing the nudging been documented anywhere?

Several Russian teams seem to be on the same intuitive track, yet they can't seem to get the math right. I responded to one of the reviewers of my submitted paper here: see reply AC2 https://esd.copernicus.org/preprints/esd-2020-74/#discussion

And there's the case of Grumbine from NASA who was also kind of on the right track, but couldn't quite grasp it either http://moregrumbinescience.blogspot.com/2016/01/earth-sun-distance-and-chandler-wobble.html

Look at all the comments that I added to Grumbine's blog post -- this was 4 years ago and not a peep in response !

I'm willing to keep hammering on this rather elementary explanation as it's bordering on absurdity at this point. Apparently it was Munk and McDonald in 1960 that claimed that externally applied gravitational torques could not cause the wobble, see https://www.google.com/books/edition/The_Rotation_of_the_Earth/klDqPAAACAAJ

`> "You clearly are not arguing that QBO may not exist, for lack of any proof. You are arguing for the existence of Lunar Forcing." An elementary Newtonian physical model would suggest that the effect is there, the question is whether the effect is strong enough. The Chandler wobble is a prime example. If I gave a spinning top a periodic nudge orthogonal to one of its poles, after a transient precessional wobble it will stabilize into a cyclic wobble that matches the nudging period. Any freshman physics lab experiment can show that -- it's called a forced response as opposed to the natural response. It also occurs for any electrical circuit -- and it's essentially why what you hear through an audio amplifier is a scaled and filtered approximation to the input signal (if it was a nonlinear response, it would need to be decoded, as in the Mach-Zehnder-like modulation found in the ENSO model's forced response). The question is why after ~130 years since Chandler discovered the Earth's wobble, why hasn't this simple relation of the moon and sun doing the nudging been documented anywhere? Several Russian teams seem to be on the same intuitive track, yet they can't seem to get the math right. I responded to one of the reviewers of my submitted paper here: see reply AC2 https://esd.copernicus.org/preprints/esd-2020-74/#discussion And there's the case of Grumbine from NASA who was also kind of on the right track, but couldn't quite grasp it either http://moregrumbinescience.blogspot.com/2016/01/earth-sun-distance-and-chandler-wobble.html Look at all the comments that I added to Grumbine's blog post -- this was 4 years ago and not a peep in response ! I'm willing to keep hammering on this rather elementary explanation as it's bordering on absurdity at this point. Apparently it was Munk and McDonald in 1960 that claimed that externally applied gravitational torques could not cause the wobble, see https://www.google.com/books/edition/The_Rotation_of_the_Earth/klDqPAAACAAJ`

PaulP: "Geophysicists appear equally clueless about the origin of the Chandler wobble (and Relative Annual Precession), which is a simple applied torque"

Since the Earth's core is fluidic, these are complex torques, necessarily. Relative Annual Axial Precession is almost as simple as a wobbling top, given the right Galilean Frame of the annual orbit. 26000yr Axial Precession is similarly fairly simple, in its Frame. No one should be "clueless" about these.

Chandler Wobble (CW) was harder to work out, but [Gross 2000 Journal of Geophysical Research] is generally accepted as explaining sustained Excitation of CW:

https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2000GL011450

Excitation is not the same as harmonic forcing. Excitation often occurs anharmonically (ie. violin bowing). [Ray 2013] convincingly showed ocean bottom-pressure oscillation as the major component of CW. It is amply documented in Literature that ocean bottom pressure is indeed tidally dominated, as such an obvious fact to not require much repeating:

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/jgrc.20336

Geophysics is not really "clueless" about any of its major questions. There is a modern abundance of clues to reason from. Again, we can confidently predict weak tidal harmonic forcings (>0) in CW multi-chaos (and might even be close to rough calculations), but inherent first order Helmholtz Resonance of many geophysical oscillators is often dominant.

`PaulP: "Geophysicists appear equally clueless about the origin of the Chandler wobble (and Relative Annual Precession), which is a simple applied torque" Since the Earth's core is fluidic, these are complex torques, necessarily. Relative Annual Axial Precession is almost as simple as a wobbling top, given the right Galilean Frame of the annual orbit. 26000yr Axial Precession is similarly fairly simple, in its Frame. No one should be "clueless" about these. Chandler Wobble (CW) was harder to work out, but [Gross 2000 Journal of Geophysical Research] is generally accepted as explaining sustained Excitation of CW: https://agupubs.onlinelibrary.wiley.com/doi/abs/10.1029/2000GL011450 Excitation is not the same as harmonic forcing. Excitation often occurs anharmonically (ie. violin bowing). [Ray 2013] convincingly showed ocean bottom-pressure oscillation as the major component of CW. It is amply documented in Literature that ocean bottom pressure is indeed tidally dominated, as such an obvious fact to not require much repeating: https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1002/jgrc.20336 Geophysics is not really "clueless" about any of its major questions. There is a modern abundance of clues to reason from. Again, we can confidently predict weak tidal harmonic forcings (>0) in CW multi-chaos (and might even be close to rough calculations), but inherent first order Helmholtz Resonance of many geophysical oscillators is often dominant.`

PaulP,

Perhaps the only problem with your QBO thesis is that does not neutrally account for all statistical drivers on merits. If you would nod to all major known causes of the multi-chaos, that would undercut objections of peer reviewers, meeting them halfway. Hell yes, lunar excitations and partial forcings are formally entailed; so they have to bend too. Once happily published, onto the next adventure.

Back to the general question about proofs in physics, here is a good example of a Nobel Prize-winning physicist (Wilczek) reasonably using the idea and term "proof" in a Mathematical-Physics context. He then assigns "experimental confirmation" as the "next great step". Thus are mathematical proofs traditionally subsumed in Physics:

Title: A landmark proof

Frank Wilczek

Center for Theoretical Physics, MIT 2011

"Researchers finally prove the conjecture that the low-energy excitations of some quantum Hall states are non-Abelian anyons."

https://physics.aps.org/articles/v4/10

`PaulP, Perhaps the only problem with your QBO thesis is that does not neutrally account for all statistical drivers on merits. If you would nod to all major known causes of the multi-chaos, that would undercut objections of peer reviewers, meeting them halfway. Hell yes, lunar excitations and partial forcings are formally entailed; so they have to bend too. Once happily published, onto the next adventure. Back to the general question about proofs in physics, here is a good example of a Nobel Prize-winning physicist (Wilczek) reasonably using the idea and term "proof" in a Mathematical-Physics context. He then assigns "experimental confirmation" as the "next great step". Thus are mathematical proofs traditionally subsumed in Physics: Title: A landmark proof Frank Wilczek Center for Theoretical Physics, MIT 2011 "Researchers finally prove the conjecture that the low-energy excitations of some quantum Hall states are non-Abelian anyons." https://physics.aps.org/articles/v4/10`

There's an annual wobble component. What is that due to? Of course it's due to the annual solar cycle. End of that story because it can't be due to anything else. The non-annual wobble component is known as the Chandler wobble. That follows precisely from the synching of the moon and the sun. What are the odds that these two wobbles are PRECISELY predicted by the EXACT lunar and solar nodal cycles just by chance?

If I measured a 60 Hz hum in the output of an amplifier, I'm not going to waste my time trying to find a resonance in a circuit that matches 60 Hz when I know darn well that the 60 Hz is likely being picked up via the line voltage and passed to the output as a forced response. Let's use some common sense here -- the gyrations that these geophysicists go through to rationalize a root cause is laughable.

`There's an annual wobble component. What is that due to? Of course it's due to the annual solar cycle. End of that story because it can't be due to anything else. The non-annual wobble component is known as the Chandler wobble. That follows precisely from the synching of the moon and the sun. What are the odds that these two wobbles are PRECISELY predicted by the EXACT lunar and solar nodal cycles just by chance? ![](https://imagizer.imageshack.com/img923/9858/ViIcq9.png) If I measured a 60 Hz hum in the output of an amplifier, I'm not going to waste my time trying to find a resonance in a circuit that matches 60 Hz when I know darn well that the 60 Hz is likely being picked up via the line voltage and passed to the output as a forced response. Let's use some common sense here -- the gyrations that these geophysicists go through to rationalize a root cause is laughable.`

Dave said:

I'm not worried about that as I don't necessarily have to account for all possible drivers, as my model accounts for a driver that no one else has accounted for. (Recall that I submitted the short paper to the journal titled Earth Systems Dynamics under their category "ESD

Ideas") So it is up to others to come up with a comparison oftheirmodel tomymodel, and if their statistical drivers can account for the empirical evidence better, that will be fine.`Dave said: > "Perhaps the only problem with your QBO thesis is that does not neutrally account for all statistical drivers on merits. If you would nod to all major known causes of the multi-chaos, that would undercut objections of peer reviewers, meeting them halfway. Hell yes, lunar excitations and partial forcings are formally entailed; so they have to bend too. Once happily published, onto the next adventure." I'm not worried about that as I don't necessarily have to account for all possible drivers, as my model accounts for a driver that no one else has accounted for. (Recall that I submitted the short paper to the journal titled Earth Systems Dynamics under their category ["ESD **Ideas**"](https://esd.copernicus.org/preprints/esd-2020-74/)) So it is up to others to come up with a comparison of *their* model to *my* model, and if their statistical drivers can account for the empirical evidence better, that will be fine.`

Again, CW is accepted to be Tidally Excited by Ocean Bottom Pressure Oscillations, but that is not proof of Tidal Forcing. You seem to assert no one can provide Mathematical-physics Proof of QBO Tidal Forcing, rather than Tidal Excitation, by the high standard Wilczek recognizes. I agree, this has not been done, but think its possible.

QBO and ENSO are obviously hypercomplex multi-chaos cases. Partial statistical models are insufficient. Its the ancient Elephant-in-the-Dark Fallacy, where blind scientists overclaim from partial-clues to a grand puzzle. ENSO and QBO are just such Elephants-

https://en.wikipedia.org/wiki/Blind_men_and_an_elephant

"It is a story of a group of blind men who have never come across an elephant before and who learn and conceptualize what the elephant is like by touching it. Each blind man feels a different part of the elephant...They then describe the elephant based on their limited experience and their descriptions of the elephant are different from each other. In some versions, they come to suspect that the other person is dishonest and they come to blows. The moral of the parable is that humans have a tendency to claim absolute truth based on their limited subjective experience as they ignore other people's limited subjective experiences, which may be equally true."

In your analogy of trivially identifying 60Hz loudspeaker hum, its obviously a high-Q first-order effect; not much like cherry-picking or ignoring squiggles in noisy geophysical data. A closer analogy would be an electric pendulum clock. The pendulum would oscillate at its fundamental frequency, but closer observation would reveal 60Hz excitation. The pendulum would not necessarily be harmonically forced, but could run a bit fast or slow, by various factors well-known to clockmakers.

Broadly laying out the major ENSO-QBO statistical-mechanics controversies would likely be welcomed by the Referees. Your QBO Draft could be the seed of a geophysical grand synthesis, of state-of-the-art multi-chaos analysis, and recover the Elephant.

`Again, CW is accepted to be Tidally Excited by Ocean Bottom Pressure Oscillations, but that is not proof of Tidal Forcing. You seem to assert no one can provide Mathematical-physics Proof of QBO Tidal Forcing, rather than Tidal Excitation, by the high standard Wilczek recognizes. I agree, this has not been done, but think its possible. QBO and ENSO are obviously hypercomplex multi-chaos cases. Partial statistical models are insufficient. Its the ancient Elephant-in-the-Dark Fallacy, where blind scientists overclaim from partial-clues to a grand puzzle. ENSO and QBO are just such Elephants- https://en.wikipedia.org/wiki/Blind_men_and_an_elephant "It is a story of a group of blind men who have never come across an elephant before and who learn and conceptualize what the elephant is like by touching it. Each blind man feels a different part of the elephant...They then describe the elephant based on their limited experience and their descriptions of the elephant are different from each other. In some versions, they come to suspect that the other person is dishonest and they come to blows. The moral of the parable is that humans have a tendency to claim absolute truth based on their limited subjective experience as they ignore other people's limited subjective experiences, which may be equally true." In your analogy of trivially identifying 60Hz loudspeaker hum, its obviously a high-Q first-order effect; not much like cherry-picking or ignoring squiggles in noisy geophysical data. A closer analogy would be an electric pendulum clock. The pendulum would oscillate at its fundamental frequency, but closer observation would reveal 60Hz excitation. The pendulum would not necessarily be harmonically forced, but could run a bit fast or slow, by various factors well-known to clockmakers. Broadly laying out the major ENSO-QBO statistical-mechanics controversies would likely be welcomed by the Referees. Your QBO Draft could be the seed of a geophysical grand synthesis, of state-of-the-art multi-chaos analysis, and recover the Elephant.`

Dave said:

No evidence of this. Regarding linear vs non-linear vs chaotic behaviors in climate models, it’s instructional to consider that even the most subtle non-linear models can wreak havoc on an analysis. And since the number of non-linear formulations is essentially infinite with respect to the number of linear possibilities, this topic of investigation has only begun to be explored. In other words, by punting the football and suggesting that the solutions are chaotic means that one has prematurely eliminated all the non-linear possibilities — and that are only challenging WRT linear models. IOW, they are deterministic and solvable, but with extreme difficulty.

So for solutions to Navier-Stokes, no one really knows what possibilities remain to be explored on a shallow-water 3-D rotating sphere. For my N-S fluid dynamics solution that is analytically similar to Mach-Zehnder modulation. This is good news and bad news — it’s good news because M-Z modulation is a straightforward non-linear formlation, but it’s bad news because M-Z modulation is also used as a highly secure encryption scheme that is very difficult to decode without the nonlinear mapping key.

This means that the model fitting process is computationally intensive because it is essentially a trial-and-error optimizing process using a gradient descent search, if that even gets close to the solution range.

Now consider the computational intensiveness of GCMs and multiplying that by the complexity of a non-linear fitting/decryption algorithm — one hasn’t even approached the scale of computational power needed to make headway. That's all the problem is -- can either join in or move out of the way.

`Dave said: > "QBO and ENSO are obviously hypercomplex multi-chaos cases." No evidence of this. Regarding linear vs non-linear vs chaotic behaviors in climate models, it’s instructional to consider that even the most subtle non-linear models can wreak havoc on an analysis. And since the number of non-linear formulations is essentially infinite with respect to the number of linear possibilities, this topic of investigation has only begun to be explored. In other words, by punting the football and suggesting that the solutions are chaotic means that one has prematurely eliminated all the non-linear possibilities — and that are only challenging WRT linear models. IOW, they are deterministic and solvable, but with extreme difficulty. So for solutions to Navier-Stokes, no one really knows what possibilities remain to be explored on a shallow-water 3-D rotating sphere. For my N-S fluid dynamics solution that is analytically similar to Mach-Zehnder modulation. This is good news and bad news — it’s good news because M-Z modulation is a straightforward non-linear formlation, but it’s bad news because M-Z modulation is also used as a highly secure encryption scheme that is very difficult to decode without the nonlinear mapping key. ![](https://www.researchgate.net/profile/Roberto_Torroba/publication/224038950/figure/fig5/AS:668615602892803@1536421790100/Experimental-arrangement-to-encrypt-the-input-object-Object-path-of-the-Mach-Zehnder.png) This means that the model fitting process is computationally intensive because it is essentially a trial-and-error optimizing process using a gradient descent search, if that even gets close to the solution range. Now consider the computational intensiveness of GCMs and multiplying that by the complexity of a non-linear fitting/decryption algorithm — one hasn’t even approached the scale of computational power needed to make headway. That's all the problem is -- can either join in or move out of the way.`

PaulP: "No evidence (QBO and ENSO are obviously hypercomplex multi-chaos cases)...by punting the football and suggesting that the solutions are chaotic means that one has prematurely eliminated all the non-linear possibilities"

The evidence is the large number of critically interacting multi-physics dimensions, resulting in noisy geophysical data that no simple model can well account for. The applicable math is canonically hypercomplex.

(Multi) Chaos is highly non-linear. Chaos science is hardly "punting", nor "premature elimination". It has a distinguished history in geophysical modeling, from Poincaré to Lorenz, to the present. Chaos may be computationally intractable for accurate long range geophysical prediction, but dismissing ENSO-QBO chaos by invoking football better suggests punting.

`PaulP: "No evidence (QBO and ENSO are obviously hypercomplex multi-chaos cases)...by punting the football and suggesting that the solutions are chaotic means that one has prematurely eliminated all the non-linear possibilities" The evidence is the large number of critically interacting multi-physics dimensions, resulting in noisy geophysical data that no simple model can well account for. The applicable math is canonically hypercomplex. (Multi) Chaos is highly non-linear. Chaos science is hardly "punting", nor "premature elimination". It has a distinguished history in geophysical modeling, from Poincaré to Lorenz, to the present. Chaos may be computationally intractable for accurate long range geophysical prediction, but dismissing ENSO-QBO chaos by invoking football better suggests punting.`

Of course it's punting if you claim any of these behaviors is "multi-chaos" since that implies the solutions are intractable. And it's not only punting but it's punting on 1st down. Good luck with that.

Just like disturbances such as tsunamis will only transiently perturb the clockwork regularity of ocean tides, volcanic disturbances dumping aerosols into the stratosphere will only perturb the regularity of the QBO tides.

`Of course it's punting if you claim any of these behaviors is "multi-chaos" since that implies the solutions are intractable. And it's not only punting but it's punting on 1st down. Good luck with that. --- Just like disturbances such as tsunamis will only transiently perturb the clockwork regularity of ocean tides, volcanic disturbances dumping aerosols into the stratosphere will only perturb the regularity of the QBO tides. <blockquote class="twitter-tweet"><p lang="en" dir="ltr">Decadal Disruption of the QBO by Tropical Volcanic Supereruptions <a href="https://t.co/WGurTmappm">https://t.co/WGurTmappm</a></p>— Scott Osprey (@sosprey) <a href="https://twitter.com/sosprey/status/1355890007106596869?ref_src=twsrc%5Etfw">January 31, 2021</a></blockquote> <script async src="https://platform.twitter.com/widgets.js" charset="utf-8"></script>`

PaulP: "Its punting if you claim any of these behaviors is "multi-chaos" since that implies the solutions are intractable."

Agreed, any such claim would be wrong.

No behavior is multi-chaos in isolation, its in the high-order combinatorics. The solutions are not hopelessly intractable, just as Weather prediction is workable to a useful degree. To dismiss hypercomplex multi-chaos a-priori would be "punting on 1st down".

Systems like ENSO and QBO are indeed sensitive in many ways, so volcanic disturbances is just one more factor of note. We can hypothesize that Ice Ages, Large Meteor Impacts, Anthropogenic Climate Change, and many other events can disrupt these oscillators. In fact, the volcanic simulation cited caused "slightly prolonged periodicity", such that lunar tide excitation could not possibly be synchronous forcing.

We do not stop trying to understand and forecast Weather just because its multi-chaos. In fact, Chaos Science helps us better understand such complex determinism. Its the "quasi" in quasiperiodic.

`PaulP: "Its punting if you claim any of these behaviors is "multi-chaos" since that implies the solutions are intractable." Agreed, any such claim would be wrong. No behavior is multi-chaos in isolation, its in the high-order combinatorics. The solutions are not hopelessly intractable, just as Weather prediction is workable to a useful degree. To dismiss hypercomplex multi-chaos a-priori would be "punting on 1st down". Systems like ENSO and QBO are indeed sensitive in many ways, so volcanic disturbances is just one more factor of note. We can hypothesize that Ice Ages, Large Meteor Impacts, Anthropogenic Climate Change, and many other events can disrupt these oscillators. In fact, the volcanic simulation cited caused "slightly prolonged periodicity", such that lunar tide excitation could not possibly be synchronous forcing. We do not stop trying to understand and forecast Weather just because its multi-chaos. In fact, Chaos Science helps us better understand such complex determinism. Its the "quasi" in quasiperiodic.`

Turns out that ENSO is a straightforward tidal forcing. In 1776, Pierre-Simon Laplace came up with equations that later evolved into the more complex Navier-Stokes equations. However, for many fluid dynamics applications that don't have much viscosity, these so-called Laplace's Tidal Equations are adequate. And so as should be obvious, Laplace's Tidal Equations imply that tides provide the forcing. How can the entire climate science community not be able to solve these equations and apply them properly? Beats me.

One aspect that is tricky about the forcing is that the two major factors -- the tropical fortnightly (

Mf=13.66d) and the anomalistic monthly (Mm=27.55d) are actually aliased quite closely in comparison to the annual impulse. The difference is so small that the repeat cycle for just these two factors is 180 years, which means the fitting process is painful on top of the non-linear iteration required. Yet it is amazing on how few degrees of freedom in the synchronous forcing is required to match to the empirical results and also to cross-validate against the out-of-band testing interval. See below. Detailed tidal analysis has always been about the combinatorics of the primary factor harmonics -- the tropical, draconic, anomalistic cycles interfering with the annual cycle. Then the 1/R^3 gravitational forcing will automatically create the 9-day (Mt) and 6-day (Msq) harmonics, and the solution to LTE will throw it all in to the grinder and one has to decode the non-linear harmonics generation via your choice of iteration. A gradient descent algorithm will work, as will a brute force random descent given enough time.Unfortunately, climate scientists continue to be mystified by all this. Earth sciences is not a discipline that attracts the curious from what I have discovered.

`Turns out that ENSO is a straightforward tidal forcing. In 1776, Pierre-Simon Laplace came up with equations that later evolved into the more complex Navier-Stokes equations. However, for many fluid dynamics applications that don't have much viscosity, these so-called Laplace's Tidal Equations are adequate. And so as should be obvious, Laplace's Tidal Equations imply that tides provide the forcing. How can the entire climate science community not be able to solve these equations and apply them properly? Beats me. One aspect that is tricky about the forcing is that the two major factors -- the tropical fortnightly (**Mf**=13.66d) and the anomalistic monthly (**Mm**=27.55d) are actually aliased quite closely in comparison to the annual impulse. The difference is so small that the repeat cycle for just these two factors is 180 years, which means the fitting process is painful on top of the non-linear iteration required. Yet it is amazing on how few degrees of freedom in the synchronous forcing is required to match to the empirical results and also to cross-validate against the out-of-band testing interval. See below. Detailed tidal analysis has always been about the combinatorics of the primary factor harmonics -- the tropical, draconic, anomalistic cycles interfering with the annual cycle. Then the 1/R^3 gravitational forcing will automatically create the 9-day (**Mt**) and 6-day (**Msq**) harmonics, and the solution to LTE will throw it all in to the grinder and one has to decode the non-linear harmonics generation via your choice of iteration. A gradient descent algorithm will work, as will a brute force random descent given enough time. ![](https://imagizer.imageshack.com/img923/7461/Fj2DqK.png) Unfortunately, climate scientists continue to be mystified by all this. Earth sciences is not a discipline that attracts the curious from what I have discovered.`

PaulP: "ENSO is a straightforward tidal forcing."

Lets carefully define "straightforward tidal forcing". A boat docked at a seaside port subject to lunar tides rises and falls with those tides. This is highly predictable forcing, with very little uncertainty.

ENSO is not that straight forward. There are many sources of non-tidal variation, of noise, of uncertainty; and supposed lunar forcing, with many unexplained aperiodicities in the data, is not as coherent as the boat case.

PaulP: "Earth sciences is not a discipline that attracts the curious from what I have discovered."

That's fortunately untrue for Lunar Tidal Geophysics. Galileo, Newton, Bernoulli, Laplace, Napier, and on and on to our time is a who's who of top tide scientists. In fact, without curiosity, one hardly could become a scientist. Its unclear what a valid test is for identifying non-curious Earth Scientists. You have barely sampled the Earth Scientist population, so not finding the curious could be a statistical Feynman-Point effect.

The problem seems to be that ENSO and QBO are so complex that they are not even rigorously defined (the Elephant problem). ENSO, for example, began as sea-surface temperature oscillation, and then a wind oscillation added. These are not the surface altimetry data parameter lunar tides are traditionally represented by. Given these very disparate properties, there is still no mathematical-physics proof that excitation is being confused for forcing, or vice versa.

This is very interesting Earth Science. I am learning a lot. Surely ENSO-QBO mysteries and controversies will further resolve by continued curiosity...

`PaulP: "ENSO is a straightforward tidal forcing." Lets carefully define "straightforward tidal forcing". A boat docked at a seaside port subject to lunar tides rises and falls with those tides. This is highly predictable forcing, with very little uncertainty. ENSO is not that straight forward. There are many sources of non-tidal variation, of noise, of uncertainty; and supposed lunar forcing, with many unexplained aperiodicities in the data, is not as coherent as the boat case. PaulP: "Earth sciences is not a discipline that attracts the curious from what I have discovered." That's fortunately untrue for Lunar Tidal Geophysics. Galileo, Newton, Bernoulli, Laplace, Napier, and on and on to our time is a who's who of top tide scientists. In fact, without curiosity, one hardly could become a scientist. Its unclear what a valid test is for identifying non-curious Earth Scientists. You have barely sampled the Earth Scientist population, so not finding the curious could be a statistical Feynman-Point effect. The problem seems to be that ENSO and QBO are so complex that they are not even rigorously defined (the Elephant problem). ENSO, for example, began as sea-surface temperature oscillation, and then a wind oscillation added. These are not the surface altimetry data parameter lunar tides are traditionally represented by. Given these very disparate properties, there is still no mathematical-physics proof that excitation is being confused for forcing, or vice versa. This is very interesting Earth Science. I am learning a lot. Surely ENSO-QBO mysteries and controversies will further resolve by continued curiosity...`

Dave said:

For ENSO, the wind oscillation is a result

nota cause. ENSO is a sloshing of the ocean's surface temperature caused by a tidally forced perturbation of the thermocline. The cycling standing wave in surface temperature causes changes in atmospheric pressure via the inverse barometer effect and then the gradient in pressure drives the wind (air flows from high pressure to low pressure obviously).So essentially my work and the substantiating work by Lin & Qian (2019) blows a gigantic hole in the consensus understanding of ENSO. Read Lin's paper in the link below:

"Switch Between El Nino and La Nina is Caused by Subsurface Ocean Waves Likely Driven by Lunar Tidal Forcing"

This is being treated as bad mojo by climate scientists IMO. From my experience, in any other scientific discipline, curious researchers would be all over it.

`Dave said: > ".... and then a wind oscillation added. " For ENSO, the wind oscillation is a result *not* a cause. ENSO is a sloshing of the ocean's surface temperature caused by a tidally forced perturbation of the thermocline. The cycling standing wave in surface temperature causes changes in atmospheric pressure via the [inverse barometer effect](https://www.swellnet.com/news/swellnet-analysis/2016/04/19/inverse-barometer-effect) and then the gradient in pressure drives the wind (air flows from high pressure to low pressure obviously). So essentially my work and the substantiating work by Lin & Qian (2019) blows a gigantic hole in the consensus understanding of ENSO. Read Lin's paper in the link below: ["Switch Between El Nino and La Nina is Caused by Subsurface Ocean Waves Likely Driven by Lunar Tidal Forcing"](https://www.nature.com/articles/s41598-019-49678-w) ![](https://media.springernature.com/lw685/springer-static/image/art%3A10.1038%2Fs41598-019-49678-w/MediaObjects/41598_2019_49678_Fig4_HTML.png) This is being treated as bad mojo by climate scientists IMO. From my experience, in any other scientific discipline, curious researchers would be all over it.`

No one says the wind is the ENSO cause, simply the SO component, as ENSO was first defined.

Here is a science team that addresses ENSO Chaos via Lyapunov Exponent analysis (no "punting"):

Title: ENSO’s Decadal Dance viewed through a Local Lyapunov Lens

Karamperidou, Cane, Wittenberg, Lall

Columbia NYC, NOAA, Princeton,

https://extranet.gfdl.noaa.gov/~atw/yr/2011/karamperidou_WCRP.pdf

`No one says the wind is the ENSO cause, simply the SO component, as ENSO was first defined. Here is a science team that addresses ENSO Chaos via Lyapunov Exponent analysis (no "punting"): Title: ENSO’s Decadal Dance viewed through a Local Lyapunov Lens Karamperidou, Cane, Wittenberg, Lall Columbia NYC, NOAA, Princeton, https://extranet.gfdl.noaa.gov/~atw/yr/2011/karamperidou_WCRP.pdf`

[Lin & Qian 2019] offers partial Lunar Tidal Forcing as a refinement to previous models, as they take pains to explain. The eastward subsurface wave and its "likely" tidal coupling is just part of the total ENSO cycle and basket of effects, like winds and distant climate signals. They make no stronger claim than improving on current predictive models. They don't account for asynchronous excitation. This is all fully consistent with our consensus here, that there must be some tidal forcing in the complex mix of ENSO effects. There is still the fundamental Hemholtz resonances as partial non-lunar forcings. Its not just straightforward tidal forcing, like a boat docked in a tide. The ENSO Elephant is not yet fully grasped.

`[Lin & Qian 2019] offers partial Lunar Tidal Forcing as a refinement to previous models, as they take pains to explain. The eastward subsurface wave and its "likely" tidal coupling is just part of the total ENSO cycle and basket of effects, like winds and distant climate signals. They make no stronger claim than improving on current predictive models. They don't account for asynchronous excitation. This is all fully consistent with our consensus here, that there must be some tidal forcing in the complex mix of ENSO effects. There is still the fundamental Hemholtz resonances as partial non-lunar forcings. Its not just straightforward tidal forcing, like a boat docked in a tide. The ENSO Elephant is not yet fully grasped.`

Dave said:

In case you are unaware, it's known that calculating a Lyapunov Exponent can only be done on a mathematical formulation, i,e. on a hypothetical model of the empirical data. It can't be done on the actual data because it requires a perturbation of the internal variables to be able to gauge output sensitivity to a change in the input. Since one does not know what these internal variables are, it's all just a guess as to whether the actual behavior is chaotic. It's basically a chicken-and-egg problem,

So any Lyapunov Exponent you see quoted is with respect to a mathematical model and it does not really show anything but a characterization of how much the modeler thinks the resulting behavior is chaotic.

I don't think my model is chaotic as it does have a repeat period (however long that may be) and so the Lyaponuv Exponent holds little relevance. Moreover, it's possible to show that the measured ENSO time-series contains long term coherence. This is related to the annual spring behavior which synchronizes the behavior. The following intra-spectral cross-correlation demonstrates clearly that the physical response is based on an annual impulse. There is a symmetry in the spectrum about the 0.5/yr frequency value.

Likely not chaotic

You say:

Dave, That's an argument of Appeal to Authority mixed in with Appeal To Complexity. If you want to pick apart some aspect of the model, then do that.

You say:

It appears that the discussion along this track will continue.

And a Russian team (Serykh & Sonechkin) is also looking at this as well

"Interrelations Between Temperature Variations in Oceanic Depths and the Global Atmospheric Oscillation"

They think it is somehow associated with the pole tide, which is connected to the Chandler wobble, bringing it full circle.

Look at the upper left of the curve and the spectral spike at ~0.85/yr labelled Chandler Wobble.

ENSO doesn't have wavenumber 0 symmetry so the regional tidal factors should be more of a factor than the Chandler wobble forcing. The Russians are essentially where I was about 5 years ago, when I spotted some correlation

https://forum.azimuthproject.org/discussion/comment/14538/#Comment_14538

The same Russian team is aware of our work as you can see Serykh is commenting here: https://esd.copernicus.org/preprints/esd-2020-74/#discussion

`Dave said: > "Here is a science team that addresses ENSO Chaos via Lyapunov Exponent analysis (no "punting"):" In case you are unaware, it's known that calculating a Lyapunov Exponent can only be done on a mathematical formulation, i,e. on a hypothetical model of the empirical data. It can't be done on the actual data because it requires a perturbation of the internal variables to be able to gauge output sensitivity to a change in the input. Since one does not know what these internal variables are, it's all just a guess as to whether the actual behavior is chaotic. It's basically a chicken-and-egg problem, So any Lyapunov Exponent you see quoted is with respect to a mathematical model and it does not really show anything but a characterization of how much the modeler thinks the resulting behavior is chaotic. I don't think my model is chaotic as it does have a repeat period (however long that may be) and so the Lyaponuv Exponent holds little relevance. Moreover, it's possible to show that the measured ENSO time-series contains long term coherence. This is related to the annual spring behavior which synchronizes the behavior. The following intra-spectral cross-correlation demonstrates clearly that the physical response is based on an annual impulse. There is a symmetry in the spectrum about the 0.5/yr frequency value. ![](https://imagizer.imageshack.com/v2/1242x470q90/r/922/YmyFPN.png) Likely not chaotic You say: > " The ENSO Elephant is not yet fully grasped." Dave, That's an argument of Appeal to Authority mixed in with Appeal To Complexity. If you want to pick apart some aspect of the model, then do that. You say: > "[Lin & Qian 2019] offers partial Lunar Tidal Forcing as a refinement to previous models, as they take pains to explain." It appears that the discussion along this track will continue. > "Dear Dr. Pukite, >Thank you very much for your comments. It’s great to know that a mathematical model of tidally forced ENSO is being developed. Hope it could make great long-lead forecasts. I’m editing an AGU monograph in which I’ll emphasize the importance of tidal forcing (attached). >Cheers, >Jialin Lin" And a Russian team (Serykh & Sonechkin) is also looking at this as well ["Interrelations Between Temperature Variations in Oceanic Depths and the Global Atmospheric Oscillation"](https://link.springer.com/article/10.1007/s00024-020-02615-9) They think it is somehow associated with the pole tide, which is connected to the Chandler wobble, bringing it full circle. Look at the upper left of the curve and the spectral spike at ~0.85/yr labelled Chandler Wobble. ![](https://imagizer.imageshack.com/img923/7461/Fj2DqK.png) ENSO doesn't have wavenumber 0 symmetry so the regional tidal factors should be more of a factor than the Chandler wobble forcing. The Russians are essentially where I was about 5 years ago, when I spotted some correlation https://forum.azimuthproject.org/discussion/comment/14538/#Comment_14538 The same Russian team is aware of our work as you can see Serykh is commenting here: https://esd.copernicus.org/preprints/esd-2020-74/#discussion`

Me: " The ENSO Elephant is not yet fully grasped."

PaulP: "That's an argument of Appeal to Authority mixed in with Appeal To Complexity."

Those two fallacies are mutually exclusive. An argument must specifically endorse an Authority to be such, like "based on NOAA...". As for Appeal to Complexity, that fallacy requires all arguments to be conflated as equally hopeless.

In fact, I am strongly favoring a specific argument that ENSO-QBO science is hypercomplex multi-chaos combined from various causal factors validated, with Helmholtz resonances hypothesized as dominant, with partial tidal forcings and excitations included.

Thanks for carefully accounting for the many specific details offered here in explanation. Its not just saying "Elephant" or "Chaos" anymore than saying "punting".

A particular insight is that the Tidal and Helmholtz harmonics would preferentially resonate together at specific shared frequencies, if you want to relate these two aspects.

Also, one can either predict stability statistics of a dynamical system with Lyapunov exponents, to then compare with real-world data, or use data to estimate Lyapunov exponents. The NOAA, Princeton, Columbia team are simply applying standard dynamical system math to ENSO.

There is no dishonor if you self-publish your ENSO-QBO science without formal peer review approval, if it nevertheless is correct, original, and significant. Many of the greatest science ideas were published so.

`Me: " The ENSO Elephant is not yet fully grasped." PaulP: "That's an argument of Appeal to Authority mixed in with Appeal To Complexity." Those two fallacies are mutually exclusive. An argument must specifically endorse an Authority to be such, like "based on NOAA...". As for Appeal to Complexity, that fallacy requires all arguments to be conflated as equally hopeless. In fact, I am strongly favoring a specific argument that ENSO-QBO science is hypercomplex multi-chaos combined from various causal factors validated, with Helmholtz resonances hypothesized as dominant, with partial tidal forcings and excitations included. Thanks for carefully accounting for the many specific details offered here in explanation. Its not just saying "Elephant" or "Chaos" anymore than saying "punting". A particular insight is that the Tidal and Helmholtz harmonics would preferentially resonate together at specific shared frequencies, if you want to relate these two aspects. Also, one can either predict stability statistics of a dynamical system with Lyapunov exponents, to then compare with real-world data, or use data to estimate Lyapunov exponents. The NOAA, Princeton, Columbia team are simply applying standard dynamical system math to ENSO. There is no dishonor if you self-publish your ENSO-QBO science without formal peer review approval, if it nevertheless is correct, original, and significant. Many of the greatest science ideas were published so.`

Lets try a reboot from first principles:

ENSO has been recorded to occur with periods ranging from 2 to 7 years.

How do Lunar Tide statistics allow (or not) validated prediction of this variation?

`Lets try a reboot from first principles: ENSO has been recorded to occur with periods ranging from 2 to 7 years. How do Lunar Tide statistics allow (or not) validated prediction of this variation?`

Look at the top 3 tidal constituents (Mf, Mm, and 18.6 year) in the following chart (note its plotted on a log scale) and then compare to the table below it adapted from R.D.Ray.

All the modelled ENSO time-series peaks align based on the assignment of tidal gravitational forcings in the last column $$V_0/g$$

The ranking matched the falloff in strength $$ Mf > Mm > 18.6y > Mt > Msm > Msq $$

Everything below this in strength are essentially secondary factors

This doesn't happen by accident, it happens as a result of a solution to Laplace's Tidal Equations applied to an equatorial waveguide topology consisting of standing-wave modes. Alas, the consensus will point to ENSO as being a chaotically-driven behavior as that is a default rationale if they are not able to come up with an adequate physics-based model.

`Look at the top 3 tidal constituents (Mf, Mm, and 18.6 year) in the following chart (note its plotted on a log scale) and then compare to the table below it adapted from R.D.Ray. ![](https://imagizer.imageshack.com/img923/7461/Fj2DqK.png) ![](https://imagizer.imageshack.com/img922/4118/LDtvyM.png) All the modelled ENSO time-series peaks align based on the assignment of tidal gravitational forcings in the last column $$V_0/g$$ The ranking matched the falloff in strength $$ Mf > Mm > 18.6y > Mt > Msm > Msq $$ Everything below this in strength are essentially secondary factors ![](https://imagizer.imageshack.com/img924/8088/u05MbM.png) This doesn't happen by accident, it happens as a result of a solution to Laplace's Tidal Equations applied to an equatorial waveguide topology consisting of standing-wave modes. Alas, the consensus will point to ENSO as being a chaotically-driven behavior as that is a default rationale if they are not able to come up with an adequate physics-based model.`

Paul, you did not address the question as stated. What is your model's Tidal-based ENSO Prediction for the next few cycles? It should reliably predict when short or long periods will occur.

You write: "Alas, the consensus will point to ENSO as being a chaotically-driven behavior as that is a default rationale if they are not able to come up with an adequate physics-based model."

"Chaotically-driven behavior" is in fact "an adequate physics-based model," at least since Poincaré. Chaos science is well established, not just a "default rationale".

`Paul, you did not address the question as stated. What is your model's Tidal-based ENSO Prediction for the next few cycles? It should reliably predict when short or long periods will occur. You write: "Alas, the consensus will point to ENSO as being a chaotically-driven behavior as that is a default rationale if they are not able to come up with an adequate physics-based model." "Chaotically-driven behavior" is in fact "an adequate physics-based model," at least since Poincaré. Chaos science is well established, not just a "default rationale".`

Dave asked:

One step better -- here is an extrapolation for two centuries from now

There's still much structural uncertainty remaining in the model. As I said, we have yet to reach the repeat cycle of the Mm,Mf+annual combination which is a basic calibration interval for discriminating & training of the forcing amplitudes.

The rule of thumb is that one day for conventional tidal analysis training is equivalent to at least a year's worth of long-period tidal training analysis. And the nonlinear modulation makes it progressively harder.

`Dave asked: > "What is your model's Tidal-based ENSO Prediction for the next few cycles? It should reliably predict when short or long periods will occur." One step better -- here is an extrapolation for two centuries from now ![](https://imagizer.imageshack.com/img923/1623/ZBWOJr.png) There's still much structural uncertainty remaining in the model. As I said, we have yet to reach the repeat cycle of the Mm,Mf+annual combination which is a basic calibration interval for discriminating & training of the forcing amplitudes. The rule of thumb is that one day for conventional tidal analysis training is equivalent to at least a year's worth of long-period tidal training analysis. And the nonlinear modulation makes it progressively harder.`

Not better, worse, because prediction starting at year 2280 cannot be falsified until then.

Again, what does your Model predict for the next few ENSO cycles? Identify the shorter and longer periods. Then today's geophysical community will see just how valid your Model is in the most fundamental parameter of period prediction.

The Hypercomplex Multi-Chaos Geophysics prediction is that a purely Tidal-forcing ENSO Model will be unable to make sound specific predictions of individual cycle periods, because it neglects applicable physics.

`Not better, worse, because prediction starting at year 2280 cannot be falsified until then. Again, what does your Model predict for the next few ENSO cycles? Identify the shorter and longer periods. Then today's geophysical community will see just how valid your Model is in the most fundamental parameter of period prediction. The Hypercomplex Multi-Chaos Geophysics prediction is that a purely Tidal-forcing ENSO Model will be unable to make sound specific predictions of individual cycle periods, because it neglects applicable physics.`

Dave said:

Knock yourself out and run the model. Then you can frame it any way you want.

for the source code: https://github.com/pukpr/GeoEnergyMath

`Dave said: > "Again, what does your Model predict for the next few ENSO cycles?" Knock yourself out and run the model. Then you can frame it any way you want. for the source code: https://github.com/pukpr/GeoEnergyMath`

Its framed as the simplest ENSO Model test of predicting timing of upcoming cycles, by short or long events; as well established in the domain. Burden of validation of claimed predictive value of your Model is above all yours. "Knock yourself out", or "punt"; as you put it. Its odd to bother to predict year 2280 onward, but not this decade.

If your Model can do no better (maybe worse) than the year or so of predictive power of competing ENSO models, its because of the interesting deterministic chaos physics. Like weather prediction, predictive ENSO geoscience will advance, and the ENSO prediction window will expand, only by diligently accounting for more critical factors, at higher fidelity.

Your codebase is not very user-friendly yet. The user would first have to download and install GNATStudio and compile an executable. Its your baby; a major work in progress. Publishing imminent ENSO predictions would be kinder on your reviewers than demanding they run poorly supported code. TIA

`Its framed as the simplest ENSO Model test of predicting timing of upcoming cycles, by short or long events; as well established in the domain. Burden of validation of claimed predictive value of your Model is above all yours. "Knock yourself out", or "punt"; as you put it. Its odd to bother to predict year 2280 onward, but not this decade. If your Model can do no better (maybe worse) than the year or so of predictive power of competing ENSO models, its because of the interesting deterministic chaos physics. Like weather prediction, predictive ENSO geoscience will advance, and the ENSO prediction window will expand, only by diligently accounting for more critical factors, at higher fidelity. Your codebase is not very user-friendly yet. The user would first have to download and install GNATStudio and compile an executable. Its your baby; a major work in progress. Publishing imminent ENSO predictions would be kinder on your reviewers than demanding they run poorly supported code. TIA`

The reason that I mentioned the framing is that it seems that you have a plan on how to proceed, as if you have a sure-fire recipe for gaining acceptance. So you recommend that I make a prediction and place it in some sort of "official" location where it can't be tampered with, and only then will climate scientists become interested in the approach? I presume that once it is uploaded to this location that someone will be appointed to monitor how the prediction is faring in comparison to the most recent data, and once it has passed some trial period, and it is deemed successful that the scientific media will be duly alerted, and then they will ask me to write a paper describing how I came up with the model?

Well .... I'm not familiar with that approach to scientific innovation, having been educated in a real R&D environment populated by lab rats and inventors and risk-takers. This may give you an idea of where my head is at. One academic researcher that I was aware of early on in my research was Nick Holonyak Jr at UIUC. An interview with him came up in my feed today and summarizes well a collective attitude:

https://news.illinois.edu/view/6367/943749387

Believe it or not, that's the way scientific innovation should work and has worked in the past. You show others what you have, and presume that a colleague has enough intellectual curiosity to pick up on it and run with it. You don't argue with people that suggest nothing can be done because someone else claimed "multi-chaos geophysics" LOL

It demonstrated that it's a well-behaved stationary process and won't blow up after sufficient time has passed. I did it a day ago. If you want to see what it is for this decade, that is right there on the previous figure I displayed.

`The reason that I mentioned the framing is that it seems that you have a plan on how to proceed, as if you have a sure-fire recipe for gaining acceptance. So you recommend that I make a prediction and place it in some sort of "official" location where it can't be tampered with, and only then will climate scientists become interested in the approach? I presume that once it is uploaded to this location that someone will be appointed to monitor how the prediction is faring in comparison to the most recent data, and once it has passed some trial period, and it is deemed successful that the scientific media will be duly alerted, and then they will ask me to write a paper describing how I came up with the model? Well .... I'm not familiar with that approach to scientific innovation, having been educated in a real R&D environment populated by lab rats and inventors and risk-takers. This may give you an idea of where my head is at. One academic researcher that I was aware of early on in my research was Nick Holonyak Jr at UIUC. An interview with him came up in my feed today and summarizes well a collective attitude: > “It’s a good thing I was an engineer and not a chemist. When I went to show them my LED, all the chemists at GE said, ‘You can’t do that. If you were a chemist, you’d know that wouldn’t work.’ I said, ‘Well, I just did it, and see, it works!’” Holonyak said. https://news.illinois.edu/view/6367/943749387 Believe it or not, that's the way scientific innovation should work and has worked in the past. You show others what you have, and presume that a colleague has enough intellectual curiosity to pick up on it and run with it. You don't argue with people that suggest nothing can be done because someone else claimed "multi-chaos geophysics" LOL > "Its odd to bother to predict year 2280 onward, but not this decade." It demonstrated that it's a well-behaved stationary process and won't blow up after sufficient time has passed. I did it a day ago. If you want to see what it is for this decade, that is right there on the previous figure I displayed.`

Its not my plan here, but how science is done traditionally, with semantically clear predictions that I don't see yet in your Model (my bad). Just emulate Galileo or Mendel, and many others, who published against orthodoxy with definite falsifiable predictions. You don't have to publish in some "official" journal with "guardians". If nothing else, just predicting an accurate sequence of anomalously short and long ENSO periods, right here, would be enough.

If your ENSO Model is correct, you are ready to make validated predictions of the next few ENSO cycles, of "confirmation", as the "next great step", as Wilczek put it, then many will look closely at your Model.

`Its not my plan here, but how science is done traditionally, with semantically clear predictions that I don't see yet in your Model (my bad). Just emulate Galileo or Mendel, and many others, who published against orthodoxy with definite falsifiable predictions. You don't have to publish in some "official" journal with "guardians". If nothing else, just predicting an accurate sequence of anomalously short and long ENSO periods, right here, would be enough. If your ENSO Model is correct, you are ready to make validated predictions of the next few ENSO cycles, of "confirmation", as the "next great step", as Wilczek put it, then many will look closely at your Model.`

The difference there is that they can do

controlled experiments. There is no control possible with climate science, geophysics, or astrophysics.And are you not familiar with the idea behind cross-validation?

`>" don't see semantically clear predictions in your Model yet, and was thinking more along the lines of Galileo or Mendel, and many others, who published against orthodoxy with definite predictions." The difference there is that they can do *controlled experiments*. There is no control possible with climate science, geophysics, or astrophysics. And are you not familiar with the idea behind [cross-validation](https://en.wikipedia.org/wiki/Cross-validation_(statistics))? > " It is mainly used in settings where the goal is prediction, and one wants to estimate how accurately a predictive model will perform in practice. "`

Galileo and Copernicus got into trouble with orthodoxy not from controlled experiment, but for matching a heretical model to geophysical observation.

Contending ENSO models do in fact amount to a controlled experiment. The test is how well they predicted ENSO as the observational data comes in. Your model effectively tests directly against best orthodoxy. That is empirical cross-validation.

`Galileo and Copernicus got into trouble with orthodoxy not from controlled experiment, but for matching a heretical model to geophysical observation. Contending ENSO models do in fact amount to a controlled experiment. The test is how well they predicted ENSO as the observational data comes in. Your model effectively tests directly against best orthodoxy. That is empirical cross-validation.`

The most comprehensive cross-validation is that Chandler wobble, ENSO, QBO, and several other climate indices can all be straightforwardly interpreted as tidally forced behaviors. Cross-validation via parsimony says that since one model can explain many diverse behaviors simultaneously, it likely means that is indeed the correct explanation.

FYI, I presented this idea at the 2018 AGU, download the PDF which describes several possible cross-validation approaches

https://www.essoar.org/doi/abs/10.1002/essoar.10500568.1

`The most comprehensive cross-validation is that Chandler wobble, ENSO, QBO, and several other climate indices can all be straightforwardly interpreted as tidally forced behaviors. Cross-validation via parsimony says that since one model can explain many diverse behaviors simultaneously, it likely means that is indeed the correct explanation. FYI, I presented this idea at the 2018 AGU, download the PDF which describes several possible cross-validation approaches https://www.essoar.org/doi/abs/10.1002/essoar.10500568.1`

This is all very interesting. I suspect both the inherent risk of overfitting from noisy data that you cite, and also risk of underfitting, from still-incomplete identification of chaotic ENSO multi-physics. Poor predictions either or both ways.

Let me take some time to study and ponder the issues as you present them. Accurate real-world prediction will still be the truest test of your model, of "straightforwardly...tidally forced behaviors" (ie. not highly chaotic). Lunisolar Earth tides start as a three-body system, so chaos is predicted from the start.

Yikes, Vertical Coriolis Effect at the equator seems like a huge source of Earth Rotational Energy to account for, but I am not seeing much in the literature. I suspect ENSO of some sort would occur if the Moon did not exist, and this would be a likely driver. Lunisolar signal may just be a coherent source of noise overlaid on the underlying harmonics, that could be interpreted as "forcing". Take the loudspeaker 60Hz hum case, with 60Hz as the tidal signal, and posit a quasiperiodic lower frequency drumbeat in the audio. 60Hz periodicity could be interpreted as "forcing" the quasi-periodic signal, by observation of superposition.

On a related tack, consider ENSO and tides as planetary-scale phonons that are constantly created and annihilated. A high tide is one phonon, and a low tide is its antiparticle. Similarly, El Nino and La Nina are an anti-pair, and Tidal and ENSO phonons constantly super-pose. In this physical interpretation, heuristically, the Tidal and Coriolis energy hardly interact, although they seem to when compounded into one signal stream.

A terrific ENSO clue is the original observation of Peruvian fishermen of the onset of major change in December ("El Nino"). This is obviously a Solar seasonal year signal, not a Lunar signal. We may posit equatorial oceanic ITCZ flow as a band wandering north and south, seasonally, and that ENSO's state is carried along with it, sweeping the coast. To an observer on the coast, the onset seems to happen suddenly, when the sweep arrives.

A huge problem nailing down ENSO is Heisenberg Uncertainty with regard to its position and velocity. Overlaying the Lunisolar signal on a fuzzy ENSO signal is fraught with imprecision.

Axiom: LaPlace's Demon is smarter than LaPlace.

Commentary: LaPlace would not have stopped at his Tidal Equations to explain ENSO. His Demon could best resolve ENSO's deterministic chaos.

`This is all very interesting. I suspect both the inherent risk of overfitting from noisy data that you cite, and also risk of underfitting, from still-incomplete identification of chaotic ENSO multi-physics. Poor predictions either or both ways. Let me take some time to study and ponder the issues as you present them. Accurate real-world prediction will still be the truest test of your model, of "straightforwardly...tidally forced behaviors" (ie. not highly chaotic). Lunisolar Earth tides start as a three-body system, so chaos is predicted from the start. Yikes, Vertical Coriolis Effect at the equator seems like a huge source of Earth Rotational Energy to account for, but I am not seeing much in the literature. I suspect ENSO of some sort would occur if the Moon did not exist, and this would be a likely driver. Lunisolar signal may just be a coherent source of noise overlaid on the underlying harmonics, that could be interpreted as "forcing". Take the loudspeaker 60Hz hum case, with 60Hz as the tidal signal, and posit a quasiperiodic lower frequency drumbeat in the audio. 60Hz periodicity could be interpreted as "forcing" the quasi-periodic signal, by observation of superposition. On a related tack, consider ENSO and tides as planetary-scale phonons that are constantly created and annihilated. A high tide is one phonon, and a low tide is its antiparticle. Similarly, El Nino and La Nina are an anti-pair, and Tidal and ENSO phonons constantly super-pose. In this physical interpretation, heuristically, the Tidal and Coriolis energy hardly interact, although they seem to when compounded into one signal stream. A terrific ENSO clue is the original observation of Peruvian fishermen of the onset of major change in December ("El Nino"). This is obviously a Solar seasonal year signal, not a Lunar signal. We may posit equatorial oceanic ITCZ flow as a band wandering north and south, seasonally, and that ENSO's state is carried along with it, sweeping the coast. To an observer on the coast, the onset seems to happen suddenly, when the sweep arrives. A huge problem nailing down ENSO is Heisenberg Uncertainty with regard to its position and velocity. Overlaying the Lunisolar signal on a fuzzy ENSO signal is fraught with imprecision. Axiom: LaPlace's Demon is smarter than LaPlace. Commentary: LaPlace would not have stopped at his Tidal Equations to explain ENSO. His Demon could best resolve ENSO's deterministic chaos.`

You may be inadvertently supporting my lunar-induced Chandler wobble model. The 3-body system is intractable because of the mutual dynamics between the bodies. But what else is the moon's torque on the earth's axis due to its declination cycle -- and a synchronization with the solar declination cycle (i.e. seasonal) -- but a mutual interaction? This is a slight effect of course and it is not chaotic on human-scales because it really is just a perturbation of a small body acting on a larger body.

As far as overfitting is concerned, it is entirely possible, but I take pains to minimize the degrees of freedom (DOF) in the model. For the ENSO tidal model, the precise formulation of parameters has to fit into a narrow range so as to follow the orbital path.

This is a good recent reference that lays out the resolved tidal forcing http://phy.hk/PP/How_tidal_forces_cause_ocean_tides.pdf

The important projection is described in the figure below where it is critical to consider the horizontal tidal force, which then not only brings the lunar distance into the equation (the monthly anomalistic tidal cycle

Mm) but also the lunar declination with respect to the equator (the nearly symmetric fortnightly draconic or nodal cycleMf).So the simplest formulation I applied is a linear combination of the two applied to a 1/R^3 gravitational pull.

$$~\frac{1}{(1 + a Mf + b Mm)^3}$$ This minimal expression generates a simple waveform in the denominator

which is large enough in amplitude to match the rich spectrum of tidal harmonics observed when the R^3 Taylor series expansion is applied. It also fits the ENSO time-series with the LTE modulation applied, along with a few secondary correction terms as shown above.

So essentially only 3 DOF -- 1 each for

MmandMf, and a third for the LTE modulation is not overfitting at all to get an impressive fit for the ENSO time-series. It is only difficult because the slight differences inMmandMfgive a nonlinearly modulated repeat cycle of over 180 years, so no wonder that the pattern has remained elusive for these many years. It's all straightforward to do but the results are unforgiving if you don't formulate the set of parameters precisely.Good news is that my abstract for the upcoming EGU meeting was accepted today so that I will once again be able to present the findings to a wider audience.

`> "Lunisolar Earth tides start as a three-body system, so chaos is predicted from the start." You may be inadvertently supporting my lunar-induced Chandler wobble model. The 3-body system is intractable because of the mutual dynamics between the bodies. But what else is the moon's torque on the earth's axis due to its [declination cycle](https://en.wikipedia.org/wiki/Lunar_standstill) -- and a synchronization with the solar declination cycle (i.e. seasonal) -- but a mutual interaction? This is a slight effect of course and it is not chaotic on human-scales because it really is just a perturbation of a small body acting on a larger body. > "I suspect both the inherent risk of overfitting from noisy data that you cite" As far as overfitting is concerned, it is entirely possible, but I take pains to minimize the degrees of freedom (DOF) in the model. For the ENSO tidal model, the precise formulation of parameters has to fit into a narrow range so as to follow the orbital path. ![](https://upload.wikimedia.org/wikipedia/commons/thumb/3/34/Lunar_orbit.png/450px-Lunar_orbit.png) This is a good recent reference that lays out the resolved tidal forcing http://phy.hk/PP/How_tidal_forces_cause_ocean_tides.pdf The important projection is described in the figure below where it is critical to consider the horizontal tidal force, which then not only brings the lunar distance into the equation (the monthly anomalistic tidal cycle **Mm**) but also the lunar declination with respect to the equator (the nearly symmetric fortnightly draconic or nodal cycle **Mf**). ![](https://imagizer.imageshack.com/img922/2346/2B80I9.png) So the simplest formulation I applied is a linear combination of the two applied to a 1/R^3 gravitational pull. $$~\frac{1}{(1 + a Mf + b Mm)^3}$$ This minimal expression generates a simple waveform in the denominator ![](https://imagizer.imageshack.com/img924/8088/u05MbM.png) which is large enough in amplitude to match the rich spectrum of tidal harmonics observed when the R^3 Taylor series expansion is applied. It also fits the ENSO time-series with the LTE modulation applied, along with a few secondary correction terms as shown above. So essentially only 3 DOF -- 1 each for **Mm** and **Mf**, and a third for the LTE modulation is not overfitting at all to get an impressive fit for the ENSO time-series. It is only difficult because the slight differences in **Mm** and **Mf** give a nonlinearly modulated repeat cycle of over 180 years, so no wonder that the pattern has remained elusive for these many years. It's all straightforward to do but the results are unforgiving if you don't formulate the set of parameters precisely. Good news is that my abstract for the upcoming EGU meeting was accepted today so that I will once again be able to present the findings to a wider audience.`

Paul: "You may be inadvertently supporting my lunar-induced Chandler wobble model."

Its not inadvertent. Read back carefully; I have endorsed a definite component of Lunisolar Tidal causality all along, to all these planetary dynamics.

The question is how much influence to assign to each of a long list of factors, that together often act chaotically rather than "straightforwardly". Your strength is in Lunisolar statistics, but there is lot more going on. Its becoming clear that ENSO data noise causes overfitting of virtually all numeric models to date, and incomplete model identification similarly causes pervasive underfitting.

Its kind of nice these rich geophysical dynamics are smarter than we are.

`Paul: "You may be inadvertently supporting my lunar-induced Chandler wobble model." Its not inadvertent. Read back carefully; I have endorsed a definite component of Lunisolar Tidal causality all along, to all these planetary dynamics. The question is how much influence to assign to each of a long list of factors, that together often act chaotically rather than "straightforwardly". Your strength is in Lunisolar statistics, but there is lot more going on. Its becoming clear that ENSO data noise causes overfitting of virtually all numeric models to date, and incomplete model identification similarly causes pervasive underfitting. Its kind of nice these rich geophysical dynamics are smarter than we are.`

I doubt that noise is much of an issue -- we are considering an ocean basin with a significant inertia associated with the thermocline. Nothing has been known to disturb the cycles of ENSO, not even volcanic events. Contrast that to atmospheric cycles, where the lower density and thus lower inertia will make it more sensitive to disturbances, which is likely why the QBO shows more noisy anomalies.

You said:

Let's place some context into the fitting issue. Recall that

only twoprimary lunar cycles are required to match the ENSO time-series, subject to the non-linear transformation derived from solving Laplace's Tidal Equations. Here,F(t)is the tidal forcing$$ \sin (A F(t)) $$ In contrast, conventional tidal analysis is just the linear transformation

$$ A F(t) $$ The difference between the two in terms of structural sensitivity is like the diff between night and day. For conventional tidal analysis, changing the forcing scale factor

Awill maintain the integrity of the underling pattern. So one can add additional tidal harmonics and understand precisely what it will do to the result.$$ dA \cdot F(t) + A \cdot dF(t) $$ Unfortunately that is not the case with the non-linear LTE. A differential applied as such

$$ \cos (A F(t)) ( dA \cdot F(t) + A \cdot dF(t) ) $$ obviously does a non-intuitive squirrelly scaling, almost 90 degrees to what one would expect to a linear tidal response -- since the cosine is orthogonal to the sine. The outcome of this is that the iteration to an optimal fit takes time, and even a slight delta change can wreak havoc on a good fit.

So both under-fitting and over-fitting will be sub-optimal and only a precise fit will do the job properly. There are a number of non-chaotic physical processes that are analogous to "threading the needle" and can only be analyzed by nailing the pattern exactly right. Not surprisingly the analysis of liquid sloshing in a tank has the same exacting requirements.

This essentially explains where I spend most of my time in the analysis, calibrating and cross-validating all the forces required to thread the needle.

BTW, what's crucial about the finding is that there is a new initiative in climate modeling (https://clima.caltech.edu/) that plans to use alternative approaches such as machine learning to discover climate and ocean patterns.

This project has significant government and private funding so I have no doubt that some deep learning algorithm will discover the same underlying pattern I have, but instead of by a careful application of physics it will do it via brute force means. Then watch what happens when they try to reverse engineer the ML results.

`I doubt that noise is much of an issue -- we are considering an ocean basin with a significant inertia associated with the thermocline. Nothing has been known to disturb the cycles of ENSO, not even volcanic events. Contrast that to atmospheric cycles, where the lower density and thus lower inertia will make it more sensitive to disturbances, which is likely why the QBO shows more noisy anomalies. You said: > "Its becoming clear that ENSO data noise causes overfitting of virtually all numeric models to date, and incomplete model identification similarly causes pervasive underfitting." Let's place some context into the fitting issue. Recall that *only two* primary lunar cycles are required to match the ENSO time-series, subject to the non-linear transformation derived from solving Laplace's Tidal Equations. Here, *F(t)* is the tidal forcing $$ \sin (A F(t)) $$ In contrast, conventional tidal analysis is just the linear transformation $$ A F(t) $$ The difference between the two in terms of structural sensitivity is like the diff between night and day. For conventional tidal analysis, changing the forcing scale factor *A* will maintain the integrity of the underling pattern. So one can add additional tidal harmonics and understand precisely what it will do to the result. $$ dA \cdot F(t) + A \cdot dF(t) $$ Unfortunately that is not the case with the non-linear LTE. A differential applied as such $$ \cos (A F(t)) ( dA \cdot F(t) + A \cdot dF(t) ) $$ obviously does a non-intuitive squirrelly scaling, almost 90 degrees to what one would expect to a linear tidal response -- since the cosine is orthogonal to the sine. The outcome of this is that the iteration to an optimal fit takes time, and even a slight delta change can wreak havoc on a good fit. So both under-fitting and over-fitting will be sub-optimal and only a precise fit will do the job properly. There are a number of non-chaotic physical processes that are analogous to "threading the needle" and can only be analyzed by nailing the pattern exactly right. Not surprisingly the analysis of [liquid sloshing in a tank](https://asmedigitalcollection.asme.org/fluidsengineering/article/137/9/090801/472122/Recent-Advances-in-Physics-of-Fluid-Parametric) has the same exacting requirements. This essentially explains where I spend most of my time in the analysis, calibrating and cross-validating all the forces required to thread the needle. --- BTW, what's crucial about the finding is that there is a new initiative in climate modeling (https://clima.caltech.edu/) that plans to use alternative approaches such as machine learning to discover climate and ocean patterns. > "CLIMATE MACHINE -- We are developing the first Earth system model that automatically learns from diverse data sources. Our model will exploit advances in **machine learning** and data assimilation to learn from observations and from data generated on demand in targeted high-resolution simulations, for example, of clouds or **ocean turbulence**. This will allow us to reduce and quantify uncertainties in climate predictions." This project has significant government and private funding so I have no doubt that some deep learning algorithm will discover the same underlying pattern I have, but instead of by a careful application of physics it will do it via brute force means. Then watch what happens when they try to reverse engineer the ML results.`

ENSO cycles are inherently very disturbed, since they range from 2-7 years; periods no one can reliably predict yet.

Not bulk ENSO noise warned, but pervasive and itself chaotic sampling and sensor noise from ocean waves, clouds, temperature fluctuations, sea-bottom features, coastal irregularities, sensing array gaps, you name it. Lots of noise. Of course, if you are right, you'll predict lunisolar driven ENSO periods regardless of all concerns. But if your predictions don't match actual outcomes, at least a long list of suspected noise sources is already going.

Machine learning? Great. Lets see how statistical mechanics and knowledge based heuristics compare with a Black Box. Don't expect an exact match to your model. All models overlaid could beat any one model. Weather is best predicted by multi-models.

Many unidentified squiggles in the data will turn out to be stochastic superpositions of factors, not discrete "straightforward" events. "Noise" is indeed punting, but "deterministic chaos" is running the ball.

`ENSO cycles are inherently very disturbed, since they range from 2-7 years; periods no one can reliably predict yet. Not bulk ENSO noise warned, but pervasive and itself chaotic sampling and sensor noise from ocean waves, clouds, temperature fluctuations, sea-bottom features, coastal irregularities, sensing array gaps, you name it. Lots of noise. Of course, if you are right, you'll predict lunisolar driven ENSO periods regardless of all concerns. But if your predictions don't match actual outcomes, at least a long list of suspected noise sources is already going. Machine learning? Great. Lets see how statistical mechanics and knowledge based heuristics compare with a Black Box. Don't expect an exact match to your model. All models overlaid could beat any one model. Weather is best predicted by multi-models. Many unidentified squiggles in the data will turn out to be stochastic superpositions of factors, not discrete "straightforward" events. "Noise" is indeed punting, but "deterministic chaos" is running the ball.`

Umm, all you are describing is the problem statement.

We all know that.

At some point are you planning on doing something other than punting on the problem?

ENSO exists only along the equatorial waveguide, creating stable standing waves with nodes that never change their spatial geometry. As with a topological insulator, the behavior appears to be stable against irregularities. Consider that every time that Tropical Instability Waves (TIW) arise during La Nina, the wavetrains

alwayshave a wavelength of 1200 kilometers.Very few behaviors on this scale with such a large inertial mass will show statistical noise. It's one big standing wave, but with higher-order wavenumbers (via TIW) that constructively sharpen the peaks in the time-series

The model I have published is a comprehensive spatio-temporal model of standing wave behavior, separating the stable spatial nodes from nonlinear wave-breaking modes which create complex harmonics in the temporal domain.

The bottom-line is that the spatial pattern is easily predicted, and only the temporal pattern is challenging to those not aware of the LTE solution approach.

`> "ENSO cycles are inherently very disturbed, since they range from 2-7 years; periods no one can reliably predict yet." Umm, all you are describing is the problem statement. We all know that. At some point are you planning on doing something other than punting on the problem? > "Not bulk ENSO noise warned, but pervasive and itself chaotic sampling and sensor noise from ocean waves, clouds, temperature fluctuations, sea-bottom features, coastal irregularities, sensing array gaps, you name it." ENSO exists only along the equatorial waveguide, creating stable standing waves with nodes that never change their spatial geometry. As with a topological insulator, the behavior appears to be stable against irregularities. Consider that every time that Tropical Instability Waves (TIW) arise during La Nina, the wavetrains *always* have a wavelength of 1200 kilometers. ![](https://imagizer.imageshack.com/img921/1200/IoAbZy.gif) Very few behaviors on this scale with such a large inertial mass will show statistical noise. It's one big standing wave, but with higher-order wavenumbers (via TIW) that constructively sharpen the peaks in the time-series ![](https://imagizer.imageshack.com/v2/927x597q90/r/924/2C7dWn.png) The model I have published is a comprehensive spatio-temporal model of standing wave behavior, separating the stable spatial nodes from nonlinear wave-breaking modes which create complex harmonics in the temporal domain. The bottom-line is that the spatial pattern is easily predicted, and only the temporal pattern is challenging to those not aware of the LTE solution approach.`

PaulP: "Nothing has been known to disturb the cycles of ENSO"

So I pointed out ENSO cycles are known inherently disturbed, which is as you say, the "Problem Statement" (not punting).

In fact, many things can throw ENSO. Plate tectonics are heuristically guaranteed to "disturb (create-change-destroy) cycles of ENSO", and many other probable events must be able to throw ENSO, like Ice-Age/SnowBall-Earth phases, major Asteroid Strikes, or Anthropogenic Climate Change.

The photo of TIW in fact shows Doppler wavelength variation (see right side). TIW is an apparent non-lunisolar Helmholz resonance. The equatorial wave guide is not perfect. Its subject to seasonal kicks like the ITCZ itself is. Its far from a perfect Topological Insulator either. Speaking of which, the sea surface and internal thermocline are Anyonic channels, further hyper-complicating the hyper-chaotic picture. "Noise" is simply what we call deterministic chaos before we sort out the details.

Geophysical sensor networks are made of small cells subject to lots of local noise, even if the bulk event is relatively immune to local noise, as you claim. Bulk events are hard to pinpoint in spacetime, and in principle embody micro-chaos around an idealized center and relativistic time-base very hard to actually observe.

In the 60Hz analogy, just as you argue, "the spatial pattern is easily predicted", but if overlaid on Beethoven, it does not follow that its forcing the music signal. Ideally you want to prove lunisolar forcing, not just leave open that tidal signals may be corrupting ENSO data. If you still doubt there is any proof possible in mathematical physics, that may stop you from persevering.

Here is NASA studying Jupiter's QQO version of Earth's QBO. Obviously, Jupiter's oscillation is not forced by huge lunisolar tides:

https://www.youtube.com/watch?v=4tJkhPmMAl4&feature=emb_logo

https://www.nasa.gov/feature/goddard/2017/nasa-solves-how-a-jupiter-jet-stream-shifts-into-reverse

Jupiter's year is 11.86 Earth years, its day is 9hr 55min, and its moons are tiny by comparison.

`PaulP: "Nothing has been known to disturb the cycles of ENSO" So I pointed out ENSO cycles are known inherently disturbed, which is as you say, the "Problem Statement" (not punting). In fact, many things can throw ENSO. Plate tectonics are heuristically guaranteed to "disturb (create-change-destroy) cycles of ENSO", and many other probable events must be able to throw ENSO, like Ice-Age/SnowBall-Earth phases, major Asteroid Strikes, or Anthropogenic Climate Change. The photo of TIW in fact shows Doppler wavelength variation (see right side). TIW is an apparent non-lunisolar Helmholz resonance. The equatorial wave guide is not perfect. Its subject to seasonal kicks like the ITCZ itself is. Its far from a perfect Topological Insulator either. Speaking of which, the sea surface and internal thermocline are Anyonic channels, further hyper-complicating the hyper-chaotic picture. "Noise" is simply what we call deterministic chaos before we sort out the details. Geophysical sensor networks are made of small cells subject to lots of local noise, even if the bulk event is relatively immune to local noise, as you claim. Bulk events are hard to pinpoint in spacetime, and in principle embody micro-chaos around an idealized center and relativistic time-base very hard to actually observe. In the 60Hz analogy, just as you argue, "the spatial pattern is easily predicted", but if overlaid on Beethoven, it does not follow that its forcing the music signal. Ideally you want to prove lunisolar forcing, not just leave open that tidal signals may be corrupting ENSO data. If you still doubt there is any proof possible in mathematical physics, that may stop you from persevering. Here is NASA studying Jupiter's QQO version of Earth's QBO. Obviously, Jupiter's oscillation is not forced by huge lunisolar tides: https://www.youtube.com/watch?v=4tJkhPmMAl4&feature=emb_logo https://www.nasa.gov/feature/goddard/2017/nasa-solves-how-a-jupiter-jet-stream-shifts-into-reverse Jupiter's year is 11.86 Earth years, its day is 9hr 55min, and its moons are tiny by comparison.`

Who cares? ... next

At this point, if I notice something useful that you're contributing, will let you know.

The spatial nodes are tied to the temporal LTE scaling by a linear dispersion curve.

$$ \omega \sim k $$ I haven't even really begun to tap into mapping the complete spatio-temporal data set but no doubt it will work because it has to obey Laplace's Tidal Equations according to the following, w/ model on the right

`> Plate tectonics are heuristically guaranteed to ... Who cares? ... next At this point, if I notice something useful that you're contributing, will let you know. --- The spatial nodes are tied to the temporal LTE scaling by a linear dispersion curve. $$ \omega \sim k $$ I haven't even really begun to tap into mapping the complete spatio-temporal data set but no doubt it will work because it has to obey Laplace's Tidal Equations according to the following, w/ model on the right ![](https://imagizer.imageshack.com/img924/2853/qRlhIH.png)`

"Who cares?"

I do. You claimed nothing was known to disturb ENSO cycles, so I corrected that misimpression with several counter-examples both shorter and longer in time. Plate tectonics is of keen interest to geophysicists interested in how ENSO ever set up in the first place. Invoking football when ENSO chaos is brought up is similarly allowed, as you care to do. Jupiter does not seem to have a direct equivalent of ENSO, for lack of continental plates.

What if the ENSO-QBO Lunisolar forcing hypothesis is mistaken, for the many specific possible reasons being supplied? Would that not be "useful"? The Jupiter QQO case and the elaboration of your 60Hz hum analogy should be addressed. Its also not enough to claim a statistical model is correct. You want to prove prediction empirically and also explain the detailed physics of forcing every causal step of the way.

Lin & Qian rightly propose to add Lunisolar dynamics into the most advanced multi-physics models, rather than negate and replace them. Ironically, this may eventually take the form of cancelling Lunisolar component signals that cause noise in the data, while recognizing those that may add some weak forcing. Then there is the excitation factor to separate out. Lunisolar excitation might be predicted to increase ENSO cycle frequency. These are fine open questions.

If your model by itself is not the most predictive of upcoming ENSO cycles, you could sort out all the open questions in order to join rather than stand apart from the major ENSO modelling team efforts, adding your particular expertise in Lunisolar factors, as a key aspect of a most-complete ENSO picture, with best-prediction.

ENSO effect on sea-surface height does not exactly match "straightforward" LaPlace Tidal Equation predictions. Heat and downwind vertical sea-surface expansion components are missing.

Science is following a trail of inquiry wherever it eventually leads; not sticking to an idée fixe starting-point. I am learning a lot here. QBO dynamics are particularly beautiful to first grasp, less of a confused morass than ENSO, with all its surface complications.

`"Who cares?" I do. You claimed nothing was known to disturb ENSO cycles, so I corrected that misimpression with several counter-examples both shorter and longer in time. Plate tectonics is of keen interest to geophysicists interested in how ENSO ever set up in the first place. Invoking football when ENSO chaos is brought up is similarly allowed, as you care to do. Jupiter does not seem to have a direct equivalent of ENSO, for lack of continental plates. What if the ENSO-QBO Lunisolar forcing hypothesis is mistaken, for the many specific possible reasons being supplied? Would that not be "useful"? The Jupiter QQO case and the elaboration of your 60Hz hum analogy should be addressed. Its also not enough to claim a statistical model is correct. You want to prove prediction empirically and also explain the detailed physics of forcing every causal step of the way. Lin & Qian rightly propose to add Lunisolar dynamics into the most advanced multi-physics models, rather than negate and replace them. Ironically, this may eventually take the form of cancelling Lunisolar component signals that cause noise in the data, while recognizing those that may add some weak forcing. Then there is the excitation factor to separate out. Lunisolar excitation might be predicted to increase ENSO cycle frequency. These are fine open questions. If your model by itself is not the most predictive of upcoming ENSO cycles, you could sort out all the open questions in order to join rather than stand apart from the major ENSO modelling team efforts, adding your particular expertise in Lunisolar factors, as a key aspect of a most-complete ENSO picture, with best-prediction. ENSO effect on sea-surface height does not exactly match "straightforward" LaPlace Tidal Equation predictions. Heat and downwind vertical sea-surface expansion components are missing. Science is following a trail of inquiry wherever it eventually leads; not sticking to an idée fixe starting-point. I am learning a lot here. QBO dynamics are particularly beautiful to first grasp, less of a confused morass than ENSO, with all its surface complications.`

That's fine, you can go ahead and study processes that evolve over geologic time. I am not working that angle, only the climate changes that happen over the course of days to years.

There are only two forcing mechanisms that are operational -- the sun and the moon, along with the man-made component that mainly impacts the trend to 1st-order, and the occasional volcanic disturbance.

`>> "Who cares?" >I do. That's fine, you can go ahead and study processes that evolve over geologic time. I am not working that angle, only the climate changes that happen over the course of days to years. There are only two forcing mechanisms that are operational -- the sun and the moon, along with the man-made component that mainly impacts the trend to 1st-order, and the occasional volcanic disturbance.`

PaulP: "There are only two forcing mechanisms that are operational -- the sun and the moon."

There are more than that. Inherent Helmholtz resonances of the geographic structure with excitation by Vertical and Horizontal Coriolis and ITCZ and Trade Wind Belts. Major Asteroids and Volcanic Eruptions happen fast and do disrupt. Solar radiation and cloud-cover interaction play roles. Being curious about geological time-scale does not hurt. Your personal experience of lack of peer curiosity in geoscience is not everyone. This is all cool stuff.

Jupiter non-lunisolar QQO dynamics are strongly driven by planetary rotation, as its QBO analog. ENSO and QBO get lots of non-lunisolar excitation energy from Earth rotation (Vertical Coriolis). They would be quite active even without the Moon. Lunisolar data noise on ENSO geo-sensor networks is a serious issue to rule-out or embrace. Have you seen that hypothesis before? Scrutinizing the geo-sensors for direct tidal sensitivity will sort it out.

Don't be too unhappy if the lunisolar correlations you clearly see have a more complex explanation than first thought. You would still be first to publish, if a needed pivot is not too much. Beware of confirmation bias preventing validating lunisolar signal explanations you consider unhelpful a priori. Correlation is not always causation. Not all excitation is direct harmonic period-forcing. Inherent resonance makes for sensitive forcing.

`PaulP: "There are only two forcing mechanisms that are operational -- the sun and the moon." There are more than that. Inherent Helmholtz resonances of the geographic structure with excitation by Vertical and Horizontal Coriolis and ITCZ and Trade Wind Belts. Major Asteroids and Volcanic Eruptions happen fast and do disrupt. Solar radiation and cloud-cover interaction play roles. Being curious about geological time-scale does not hurt. Your personal experience of lack of peer curiosity in geoscience is not everyone. This is all cool stuff. Jupiter non-lunisolar QQO dynamics are strongly driven by planetary rotation, as its QBO analog. ENSO and QBO get lots of non-lunisolar excitation energy from Earth rotation (Vertical Coriolis). They would be quite active even without the Moon. Lunisolar data noise on ENSO geo-sensor networks is a serious issue to rule-out or embrace. Have you seen that hypothesis before? Scrutinizing the geo-sensors for direct tidal sensitivity will sort it out. Don't be too unhappy if the lunisolar correlations you clearly see have a more complex explanation than first thought. You would still be first to publish, if a needed pivot is not too much. Beware of confirmation bias preventing validating lunisolar signal explanations you consider unhelpful a priori. Correlation is not always causation. Not all excitation is direct harmonic period-forcing. Inherent resonance makes for sensitive forcing.`

An external force is needed to cause the winds to change. Amazing how something so elementary can stump so many people,

Coriolis is constant.

You must be under the mistaken impression that none of this is published. It is ... https://scholar.google.com/scholar?q="mathematical+geoenergy"

Handy index: https://geoenergymath.com/2020/03/12/groundbreaking-research/

`> "There are more than that. Inherent Helmholtz resonances of the geographic structure with excitation by Vertical and Horizontal Coriolis and ITCZ and Trade Wind Belts. " An external force is needed to cause the winds to change. Amazing how something so elementary can stump so many people, Coriolis is constant. > "You would still be first to publish" You must be under the mistaken impression that none of this is published. It is ... https://scholar.google.com/scholar?q=%22mathematical+geoenergy%22 Handy index: https://geoenergymath.com/2020/03/12/groundbreaking-research/`

PaulP: "An external force is needed to cause the winds to change. Amazing how something so elementary can stump so many people"

Unsure what you mean by stumped. Winds do not remain constant by absence of external force. They run down by approaching pressure equilibrium. Internal vortices would decay into progressively smaller vortices. Winds must change regardless of externalities. They are not a perpetual motion fallacy case.

Here we are talking about ITCZ wind flow across the entire Pacific piling up water in the West that then sloshes somewhat chaotically. That's scarcely Lunisolar period-forced, but more dependent on geographic structural harmonic periods.

PaulP: "Coriolis is constant"

Not really. Coriolis is not locally constant, as the variable interaction of turbulent convective flow with planetary rotation. A lot of convective flow starts thermally, from insolation and geothermal sources, that then interacts with rotation as Coriolis Effect. This is the Geostrophic Balance. Its not even fully constant in bulk, only roughly so, since the Sun is dynamic, Earth's core is cooling, and various other dynamical details.

PaulP: "You must be under the mistaken impression that none of this is published."

I am reviewing here multiple alternative explanations to your forcing-only hypothesis to account for Lunisolar artifacts in geophysical data. I have not yet seen most of these published by you or anyone else, but perhaps you can pinpoint such prior instances, being better acquainted with the literature. These would help explain why your model might not prove able to predict the next few ENSO cycles, if that is the outcome.

If any of these alternative explanations are novel to the literature, and have significance, you got first crack to peer-publish.

`PaulP: "An external force is needed to cause the winds to change. Amazing how something so elementary can stump so many people" Unsure what you mean by stumped. Winds do not remain constant by absence of external force. They run down by approaching pressure equilibrium. Internal vortices would decay into progressively smaller vortices. Winds must change regardless of externalities. They are not a perpetual motion fallacy case. Here we are talking about ITCZ wind flow across the entire Pacific piling up water in the West that then sloshes somewhat chaotically. That's scarcely Lunisolar period-forced, but more dependent on geographic structural harmonic periods. PaulP: "Coriolis is constant" Not really. Coriolis is not locally constant, as the variable interaction of turbulent convective flow with planetary rotation. A lot of convective flow starts thermally, from insolation and geothermal sources, that then interacts with rotation as Coriolis Effect. This is the Geostrophic Balance. Its not even fully constant in bulk, only roughly so, since the Sun is dynamic, Earth's core is cooling, and various other dynamical details. PaulP: "You must be under the mistaken impression that none of this is published." I am reviewing here multiple alternative explanations to your forcing-only hypothesis to account for Lunisolar artifacts in geophysical data. I have not yet seen most of these published by you or anyone else, but perhaps you can pinpoint such prior instances, being better acquainted with the literature. These would help explain why your model might not prove able to predict the next few ENSO cycles, if that is the outcome. If any of these alternative explanations are novel to the literature, and have significance, you got first crack to peer-publish.`

Of course it is. As I said the orbital dynamics causing the daily cycle and the annual cycle are responsible for most of the variability -- this is not due to "the wind". Then, adding in the external gravitational forcing, we get such variability as the tidal cycles, LOD cycles, and these other mysterious behaviors known as ENSO, QBO, Chandler Wobble, MJO, TIW, AMO, PDO, PNA, NAO, IOD, AO, AAO, which all share a common-mode mechanism.

BTW

You think I care one iota about being able to predict the next few ENSO cycles? Taking that by itself, predicting the next few cycles will only raise the question as whether that happened purely by chance.

`> "only roughly so, since the Sun is dynamic" Of course it is. As I said the orbital dynamics causing the daily cycle and the annual cycle are responsible for most of the variability -- this is not due to "the wind". Then, adding in the external gravitational forcing, we get such variability as the tidal cycles, LOD cycles, and these other mysterious behaviors known as ENSO, QBO, Chandler Wobble, MJO, TIW, AMO, PDO, PNA, NAO, IOD, AO, AAO, which all share a common-mode mechanism. BTW > "These would help explain why your model *might not prove able* to predict the next few ENSO cycles, if that is the outcome." You think I care one iota about being able to predict the next few ENSO cycles? Taking that by itself, predicting the next few cycles will only raise the question as whether that happened purely by chance.`

PaulP:"You think I care one iota about being able to predict the next few ENSO cycles? Taking that by itself, predicting the next few cycles will only raise the question as whether that happened purely by chance."

You got me there; thought you cared. Would you not rightly celebrate if your Model duly predicted upcoming cycles? You instead raise the question whether your Model is truly predictive, by willfully not predicting any cycle right as it comes.

I question whether any correct Model would likely long fail to predict cycles, "purely by chance", and predict the Lunisolar signal will be mostly seen as sensor noise in ENSO data, past, present, and future. Let the question therefore be, "whether that happened purely by chance". Not likely.

As for identifying the common-mode of ENSO, QBO, Chandler Wobble, MJO, TIW, AMO, PDO, PNA, NAO, IOD, AO, AAO; these are all spring-mass oscillators, either singly or as networks; and Yes, the Lunisolar signal would appear as noise in all their sensor data networks, as well as adding a some excitation, and even a tiny bit of period-forcing in the multi-chaos statistics.

`PaulP:"You think I care one iota about being able to predict the next few ENSO cycles? Taking that by itself, predicting the next few cycles will only raise the question as whether that happened purely by chance." You got me there; thought you cared. Would you not rightly celebrate if your Model duly predicted upcoming cycles? You instead raise the question whether your Model is truly predictive, by willfully not predicting any cycle right as it comes. I question whether any correct Model would likely long fail to predict cycles, "purely by chance", and predict the Lunisolar signal will be mostly seen as sensor noise in ENSO data, past, present, and future. Let the question therefore be, "whether that happened purely by chance". Not likely. As for identifying the common-mode of ENSO, QBO, Chandler Wobble, MJO, TIW, AMO, PDO, PNA, NAO, IOD, AO, AAO; these are all spring-mass oscillators, either singly or as networks; and Yes, the Lunisolar signal would appear as noise in all their sensor data networks, as well as adding a some excitation, and even a tiny bit of period-forcing in the multi-chaos statistics.`