Models and Simulations of the atmosphere
In formal mathematical terms of geometry/topology/homotopy/homology, let’s try proving that a wavenumber=0 cycle of east/west direction inside an equatorial toroidal-shaped waveguide, can only be forced by the Z-component of a (x,y,z) vector where x,y lies in the equatorial plane.
To address this question, let’s dissect the components involved and prove within the constraints of geometry, topology, homotopy, and homology, focusing on valid mathematical principles.
Continue readingBased on the previous post on applying Dynamic Time Warping as a metric for LTE modeling of oceanic indices, it makes sense to apply the metric to the QBO model of atmospheric winds. A characteristic of QBO data is the sharp transitions of wind reversals. As described previously, DTW allows a fit to adjust the alignment between model and data without incurring a potential over-fitting penalty that a conventional correlation coefficient will often lead to.
Continue reading
The above diagram courtesy of Karnauskus
Overall I’m confident with the status of the published analysis of Laplace’s Tidal Equations in Mathematical Geoenergy, as I can model each of these climate indices with precisely the same (save one ***) tidal forcing, all calibrated by LOD. The following Threads allow interested people to contribute thoughts
(*** The odd-one out is QBO, which is a global longitudinally-invariant behavior, which means that only a couple of tidal factors are important.)
Is the utility of this LTE modeling a groundbreaking achievement? => https://www.threads.net/@paulpukite/post/CuvNnwns2la
Sorry to have to point this out, but it’s not my fault that geophysicists and climatologists can’t perform controlled experiments to test out various hypotheses. It’s not their fault either. It’s all nature’s decision to make gravitational forces so weak and planetary objects so massive to prevent anyone from scaling the effect to laboratory size to enable a carefully controlled experiment. One can always create roughly-equivalent emulations, such as a magnetic field experiment (described in the previous blog post) and validate a hypothesized behavior as a controlled lab experiment. Yet, I suspect that this would not get sufficient buy-in, as it’s not considered the actual real thing.
And that’s the dilemma. By the same token that analog emulators will not be trusted by geophysicists and climatologists, so too scientists from other disciplines will remain skeptical of untestable claims made by earth scientists. If nothing definitive comes out of a thought experiment that can’t be reproduced by others in a lab, they remain suspicious, as per their education and training.
It should therefore work both ways. As featured in the previous blog post, the model of the Chandler wobble forced by lunar torque needs to be treated fairly — either clearly debunked or considered as an alternative to the hazy consensus. ChatGPT remains open about the model, not the least bit swayed by colleagues or tribal bias. As the value of the Chandler wobble predicted by the lunar nodal model (432.7 days) is so close to the cited value of 433 days, as a bottom-line it should be difficult to ignore.
There are other indicators in the observational data to further substantiate this, see Chandler Wobble Forcing. It also makes sense in the context of the annual wobble.
As it stands, the lack of an experiment means a more equal footing for the alternatives, as they are all under equal amounts of suspicion.
Same goes for QBO. No controlled experiment is possible to test out the consensus QBO models, despite the fact that the Plumb and McEwan experiment is claimed to do just that. Sorry, but that experiment is not even close to the topology of a rotating sphere with a radial gravitational force operating on a gas. It also never predicted the QBO period. In contrast, the value of the QBO predicted by the lunar nodal model (28.4 months) is also too close to the cited value of 28 to 29 months to ignore. This also makes sense in the context of the semi-annual oscillation (SAO) located above the QBO .
Both the Chandler wobble and the QBO have the symmetry of a global wavenumber=0 phenomena so therefore only nodal cycles allowed — both for lunar and solar.
Next to ENSO. As with LOD modeling, this is not wavenumber=0 symmetry, as it must correspond to the longitude of a specific region. No controlled experiment is possible to test out the currently accepted models, premised as being triggered by wind shifts (an iffy cause vs. effect in any case). The mean value of the ENSO predicted by the tidal LOD-caibrated model (3.80 years modulated by 18.6 years) is too close to the cited value of 3.8 years with ~200 years of paleo and direct measurement to ignore.
In BLUE below is the LOD-calibrated tidal forcing, with linear amplification
In BLUE again below is a non-linear modulation of the tidal forcing according to the Laplace’s Tidal Equation solution, and trained on an early historical interval. This is something that a neural network should be able to do, as it excels at fitting to non-linear mappings that have a simple (i.e. low complexity) encoding — in this case it may be able to construct a Taylor series expansion of a sinusoidal modulating function.
The neural network’s ability to accurately represent a behavior is explained as a simplicity bias — a confounding aspect of machine learning tools such as ChatGPT and neural networks. The YouTube video below explains the counter-intuitive notion of how a NN with a deep set of possibilities tends to find the simplest solution and doing this without over-fitting the final mapping.
So that deep neural networks are claimed to have a built-in Occam’s Razor propensity, finding the most parsimonious input-output mappings when applied to training data. This is spot on with what I am doing with the LTE mapping, but bypassing the NN with a nonlinear sinusoidal modulation optimally fit on training data by a random search function.
I am tempted to try a NN on the ENSO training set as an experiment and see what it finds.
“I am tempted to try a NN on the ENSO training set as an experiment and see what it finds.”
I don’t immediately trust the research published by highly cited atmospheric scientists. By my count many of them seem more keen on presenting their personal views rather than advancing the field. Off the top of my head, Richard Lindzen, Murry Salby, Roy Spencer, Tim Dunkerton, Roger Pielke, Cliff Mass, Judith Curry are all highly cited but come across as political and/or religious zealots. One guy on the list, Dunkerton, is also a racist, who happened to make the Washington Post twice : “Physicist ousted from research post after sending offensive tweet to Hispanic meteorologist” and “Atmospheric scientist loses honor, membership over ethics violation“. Awful stuff and he hasn’t stopped spouting off on Twitter.
Granted that Dunkerton says dumb stuff on Twitter but his highly cited research is also off-base. That’s IMO only because recent papers by others in the field of atmospheric science do continue to cite his ideas as primary, if not authoritative. For example, from a recently published paper “The Gravity Wave Activity during Two Recent QBO Disruptions Revealed by U.S. High-Resolution Radiosonde Data”, citations 1 & 12 both refer to Dunkerton, and specifically to his belief that the QBO period is a property of the atmospheric medium itself
Straight-forward to debunk this Dunkerton theory since the length of the cycle directly above the QBO layer is semi-annual and thus not a property of the medium but of the semi-annual nodal forcing frequency. If we make the obvious connection to the other nodal forcing — that of the moon — then we find the QBO period is fixed to 28 months. I have been highlighting this connection to the authors of new QBO papers under community review, often with some subsequent feedback provided such as here: https://doi.org/10.5194/acp-2022-792-CC1 . Though not visible yet in the comments, I received some personal correspondence that showed that the authors under peer-review are taking the idea seriously and attempting to duplicate the calculations. They seem to be methodical in their approach, asking for clarification and further instructions where they couldn’t follow the formulation. They know about the GitHub software, so hopefully that will be of some help.
In contrast, Dunkerton also knows about my approach but responds in an inscrutable (if not condescending) way. Makes you wonder if scientists such as Dunkerton and Lindzen are bitter and taking out their frustrations via the media. Based on their doggedness, they may in fact be intentionally trying to impede progress in climate science by taking contrarian stances. In my experience, the top scientists in other research disciplines don’t act this way. YMMV
More activity related to my review comment https://doi.org/10.5194/acp-2022-792-CC1
As a review, this was after commenting earlier this year on a Copernicus open-science research article on atmospheric cycles and QBO (with proposed links to sunspots and ENSO) that was undergoing a review, making a suggestion to consider analyses I had presented and published 4 years ago and also prior to that.
Thought that was that and was happy to see that the authors indicated they would revise the manuscript and perhaps advance understanding. But then several days ago, the editor interceded and essentially demanded that the authors not cite my research work. Apparently, the authors were influenced by the editor’s instructions, as they immediately removed my cite and replaced it with a citation to a review article that the editor preferred. The discussion on the article was then closed with no way for me to rebut.
This was all after I spent several hours working with the primary author as they worked to replicate my analysis, sending emails back and forth several times. The editor claimed that my contribution was “a new idea that has not been published in a recognized journal and received peer review”. This is not the case as I said above: Google Scholar citations all ignored.
Also see this post I contributed to the Peak Oil Barrel blog : https://peakoilbarrel.com/predicting-stratospheric-winds/
Trying to understand QBO may lead to madness, if the plights of Richard Lindzen (Macbeth) and Timothy Dunkerton (Hamlet) are any indication. It was first Lindzen — the primary theorist behind QBO — in his quest for scientific notoriety that led to lofty pretentiousness and eventually bad blood with his colleagues. Now it’s the Lindzen-acolyte Dunketon’s turn, avenging his “uncle” with troubling behavior
https://www.washingtonpost.com/weather/2022/02/06/dunkerton-offensive-tweet-nwra-ams/
The behavior of QBO is yet to be explained, but it may be simpler than imagined by Lindzen and Dunkerton
Regarding the gravity waves concentrically emanating from the Tonga explosion
“It’s really unique. We have never seen anything like this in the data before,” says Lars Hoffmann, an atmospheric scientist at the Jülich Supercomputing Centre in Germany.
https://www.nature.com/articles/d41586-022-00127-1
and
“That’s what’s really puzzling us,” says Corwin Wright, an atmospheric physicist at the University of Bath, UK. “It must have something to do with the physics of what’s going on, but we don’t know what yet.”
https://www.nature.com/articles/d41586-022-00127-1
The discovery was prompted by a tweet sent to Wright on 15 January from Scott Osprey, a climate scientist at the University of Oxford, UK, who asked: “Wow, I wonder how big the atmospheric gravity waves are from this eruption?!” Osprey says that the eruption might have been unique in causing these waves because it happened very quickly relative to other eruptions. “This event seems to have been over in minutes, but it was explosive and it’s that impulse that is likely to kick off some strong gravity waves,” he says. The eruption might have lasted moments, but the impacts could be long-lasting. Gravity waves can interfere with a cyclical reversal of wind direction in the tropics, Osprey says, and this could affect weather patterns as far away as Europe. “We’ll be looking very carefully at how that evolves,” he says.
https://www.nature.com/articles/d41586-022-00127-1
This (“cyclical reversal of wind direction in the tropics”) is referring to the QBO, and we will see if it has an impact in the coming months. Hint: the QBO from the last post is essentially modeling gravity waves arising from the tidal forcing as driving the cycle. Also, watch the LOD.
Perhaps the lacking is in applying this simple scientific law: for every action there is a reaction. Always start from that, and also consider: an object that is in motion, tends to stay in motion. Is the lack of observed Coriolis effects to first-order part of why the scientists are mystified? Given the variation of this force with latitude, the concentric rings perhaps were expected to be distorted according to spherical harmonics.
The fit to the ENSO model looks like this
The forcing spectrum like this, with the aliased draconic (27.212d) factor circled:
For QBO, we remove all the lunar factors except for the draconic, as this is the only declination factor with the same spherical group symmetry as the semi-annual solar declination.
And after modifying the annual (ENSO spring-barrier) impulse into a semi-annual impulse with equal and opposite excursions, the resultant model matches well (to first order) the QBO time series.
Although the alignment isn’t perfect, there are indications in the structure that the fit has a deeper significance. For example, note how many of the shoulders in the structure align, as highlighted below in yellow
The peaks and valleys do wander about a bit and might be a result of the sensitivity to the semi-annual impulse and the fact that this is only a monthly resolution. The chart below is a detailed fit of the QBO using data with a much finer daily resolution. As you can see, slight changes in the seasonal timing of the semi-annual pulse are needed to individually align the 70 and 30 hBar QBO time-series data.
This will require further work, especially in considering recently reported perturbations in the QBO periodicity, but it is telling that a shared draconic forcing of the ENSO and QBO models suggests an important cross-validation of the underlying causal mechanism.
Another potential geophysical cross-validation …
The underlying forcing of the ENSO model shows both an 18-year Saros cycle (which is an eclipse alignment cycle of all the tidal periods), along with a 6-year anomalistic/draconic interference cycle. This modulation of the main anomalistic cycle appears in both the underlying daily and monthly profile, shown below before applying an annual impulse. The 6-year is clearly evident as it aligns with the x-axis grid 1880, 1886, 1892, 1898, etc.
The bottom inset shows that a similar 6-year cycle consistently appears in length-of-day (LOD) analyses, this particular trace from a recent paper: [ Leonid Zotov et al 2020 J. Phys.: Conf. Ser. 1705 012002 ].
The 6-year cycle in the LOD is not aligned as strictly as the tidal model and it tends to wander, but it seems a more plausible and parsimonious explanation of the modulation than for example in this paper (where the 6-year LOD cycle is “similarly detected in the variations of C22 and S22, the degree-2 order-2 Stokes coefficients of the Earth’s gravitational field”).
Cross-validation confidence improves as the number of mutually agreeing alignments increase. Given the fact that controlled experiments are impossible to perform, this category of analyses is the best way to validate the geophysical models.
Revisiting earlier modeling of the North Atlantic Oscillation (NAO) and Arctic Oscillation (AO) indices with the benefit of updated analysis approaches such as negative entropy. These two indices in particular are intimidating because to the untrained eye they appear to be more noise than anything deterministically periodic. Whereas ENSO has periods that range from 3 to 7 years, both NAO and AO show rapid cycling often on a faster-than-annual pace. The trial ansatz in this case is to adopt a semi-annual forcing pattern and synchronize that to long-period lunar factors, fitted to a Laplace’s Tidal Equation (LTE) model.
Start with candidate forcing time-series as shown below, with a mix of semi-annual and annual impulses modulating the primarily synodic/tropical lunar factor. The two diverge slightly at earlier dates (starting at 1880) but the NAO and AO instrumental data only begins at the year 1950, so the two are tightly correlated over the range of interest.
The intensity spectrum is shown below for the semi-annual zone, noting the aliased tropical factors at 27.32 and 13.66 days standing out.
The NAO and AO pattern is not really that different, and once a strong LTE modulation is found for one index, it also works for the other. As shown below, the lowest modulation is sharply delineated, yet more rapid than that for ENSO, indicating a high-wavenumber standing wave mode in the upper latitudes.
The model fit for NAO (data source) is excellent as shown below. The training interval only extended to 2016, so the dotted lines provide an extrapolated fit to the most recent NAO data.
Same for the AO (data source), the fit is also excellent as shown below. There is virtually no difference in the lowest LTE modulation frequency between NAO and AO, but the higher/more rapid LTE modulations need to be tuned for each unique index. In both cases, the extrapolations beyond the year 2016 are very encouraging (though not perfect) cross-validating predictions. The LTE modulation is so strong that it is also structurally sensitive to the exact forcing.
Both NAO and AO time-series appear very busy and noisy, yet there is very likely a strong underlying order due to the fundamental 27.32/13.66 day tropical forcing modulating the semi-annual impulse, with the 18.6/9.3 year and 8.85/4.42 year providing the expected longer-range lunar variability. This is also consistent with the critical semi-annual impulses that impact the QBO and Chandler wobble periodicity, with the caveat that group symmetry of the global QBO and Chandler wobble forcings require those to be draconic/nodal factors and not the geographically isolated sidereal/tropical factor required of the North Atlantic.
It really is a highly-resolved model potentially useful at a finer resolution than monthly and that will only improve over time.
(as a sidenote, this is much better attempt at matching a lunar forcing to AO and jet-stream dynamics than the approach Clive Best tried a few years ago. He gave it a shot but without knowledge of the non-linear character of the LTE modulation required he wasn’t able to achieve a high correlation, achieving at best a 2.4% Spearman correlation coefficient for AO in his Figure 4 — whereas the models in this GeoenergyMath post extend beyond 80% for the interval 1950 to 2016! )
In Chapter 12, we described the model of QBO generated by modulating the draconic (or nodal) lunar forcing with a hemispherical annual impulse that reinforces that effect. This generates the following predicted frequency response peaks:
The 2nd, 3rd, and 4th peaks listed (at 2.423, 1.423, and 0.423) are readily observed in the power spectra of the QBO time-series. When the spectra are averaged over each of the time series, the precisely matched peaks emerge more cleanly above the red noise envelope — see the bottom panel in the figure below (click to expand).
The inset shows what these harmonics provide — essentially the jagged stairstep structure of the semi-annual impulse lag integrated against the draconic modulation.
It is important to note that these harmonics are not the traditional harmonics of a high-Q resonance behavior, where the higher orders are integral multiples of the fundamental frequency — in this case at 0.423 cycles/year. Instead, these are clear substantiation of a forcing response that maintains the frequency spectrum of an input stimulus, thus excluding the possibility that the QBO behavior is a natural resonance phenomena. At best, there may be a 2nd-order response that may selectively amplify parts of the frequency spectrum.
See my latest submission to the ESD Ideas issue : ESDD – ESD Ideas: Long-period tidal forcing in geophysics – application to ENSO, QBO, and Chandler wobble (copernicus.org)
GeoEnergy Math 