“Furthermore, by applying ontology‐based approaches for organizing models and techniques, we can set the stage for broader collections of such models discoverable by a general community of designers and analysts. Together with standard access protocols for context modeling,

Energy Transition : Applying Probabilities and Physics

these innovations provide the promise of making environmental context models generally available and reusable, significantly assisting the energy analyst.”

Although we didn’t elaborate on this topic, it is an open area for future development, as our 2017 AGU presentation advocates. The complete research report is available as https://doi.org/10.13140/RG.2.1.4956.3604.

What we missed on the first pass was an ontology for citations titled CiTO (Citation Typing Ontology) which enables better classification and keeping track of research lineage. The idea again is to organize and maintain scientific knowledge for engineering and scientific modeling applications. As an example, one can readily see how the Citation Typing Ontology could be applied, with the * is_extended_by* object property representing much of how science and technology advances — in other words, one finding leading to another.

]]>

- Xiaoqun, C.
*et al.*ENSO prediction based on Long Short-Term Memory (LSTM).*IOP Conference Series: Materials Science and Engineering***, 799**, 012035 (2020).

The x-axis appears to be in months and likely starts in 1979, so it captures the 2016 El Nino (El Nino is negative for SOI). Still have no idea how the neural net arrived at the fit other than it being able to discern the cyclic behavior from the historical waveform between 1979 and 2010. From the article itself, it appears that neither do the authors.

The following are fragments that I am working on.

High-resolution (5-day) MJO model fit

Back extrapolation to historical SOI

The forcing for SOI and high-res MJO is aligned, not degrading at all regions that are outside the training interval (prior to 1980)/

The LTE modulation over the entire span (above) and just over the post 1979 MJO data interval (below)

Power spectrum of forcing shows the expected 13.66 day tropical fortnightly signal, but nearly inseparable from the next strongest 27.55 day anomalistic monthly signal. With the annual impulse mixing these show up as 3.795 year and 3.917 year periods, which thus gives rise to a long beat frequency of 121 years, which is likely the low-frequency peak.

IMPA=399, IMPB=400, SCALING=0.1, SAMPLING=365, REF_TIME=1880

]]>For the tidal forcing that contributes to length-of-day (LOD) variations [1], only a few factors contribute to a plurality of the variation. These are indicated below by the highlighted circles, where the V_{0}/g amplitude is greatest. The first is the nodal 18.6 year cycle, indicated by the N’ = 1 Doodson argument. The second is the 27.55 day “Mm” anomalistic cycle which is a combination of the perigean 8.85 year cycle (p = -1 Doodson argument) mixed with the 27.32 day tropical cycle (s=1 Doodson argument). The third and strongest is twice the tropical cycle (therefore s=2) nicknamed “Mf”.

These three factors also combine as the primary input forcing to the ENSO model. Yet, even though they are strongest, the combinatorial factors derived from multiplying these main harmonics are vital for generating a quality fit (both for dLOD and even more so for ENSO). What I have done in the past was apply the recommended mix of first- and second-order factors that appear in the dLOD spectra for the ENSO forcing.

Yet there is another approach that makes no assumption of the strongest 2nd-order factors. In this case, one simply expands the primary factors as a combinatorial expansion of cross-terms to the 4th level — this then generates a broad mix of monthly, fortnightly, 9-day, and weekly harmonic cycles. A nested algorithm to generate the 35 *constituent *terms is :

Counter := 1; for J in Constituents'Range loop for K in Constituents'First .. J loop for L in Constituents'First .. K loop for M in Constituents'First .. L loop Tf := Tf + Coefficients (Counter) * Fundamental(J) * Fundamental(K) * Fundamental(L) * Fundamental (M); Counter := Counter + 1; end loop; end loop; end loop; end loop;

This algorithm requires the three fundamental terms plus one unity term to capture most of the cross-terms shown in Table 3 above (The annual cross-terms are automatic as those are generated by the model’s annual impulse). This transforms into a *coefficients* array that can be included in the LTE search software.

What is missing from the list are the *evection *terms corresponding to 31.812 (**Msm**) and 27.093 day cycles. They are retrograde to the prograde 27.55 day anomalistic cycle, so would need an additional 8.848 year perigee cycle bring the count from 3 fundamental terms to 4.

The difference between adding an extra level of harmonics, bringing the combinatorial total from 35 to 126, is not very apparent when looking at the time series (below), as it simply adds shape to the main fortnightly tropical cycle.

Yet it has a significant effect on the ENSO fit, approaching a CC of 0.95 (see inset at right for the scatter correlation). Note that the forcing frequency spectra in the middle right inset still shows a predominately tropical fortnightly peak at 0.26/yr and 0.74/yr.

These extra harmonics also helps in matching to the much more busy SOI time-series. Click on the chart below to inspect how the higher-K wavenumbers may be the origin of what is thought to be noise in the SOI measurements.

Is this a case of overfitting? Try the following cross-validation on orthogonal intervals, and note how tight the model matches the data to the training intervals, without degrading too much on the outer validation region.

I will likely add this combinatorial expansion approach to the LTE fitting software on GitHub soon, but thought to checkpoint the interim progress on the blog. In the end the likely modeling mix will be a combination of the geophysical calibration to the known dLOD response together with a refined collection of these 2nd-order combinatorial tidal constituents. The rationale for why certain terms are important will eventually become more clear as well.

- Ray, R.D. and Erofeeva, S.Y., 2014. Long‐period tidal variations in the length of day.
*Journal of Geophysical Research: Solid Earth*,*119*(2), pp.1498-1509.

In Chapter 12 of the book we model — via LTE — the canonical El Nino Southern Oscillation (ENSO) behavior, fitting to closely-correlated indices such as NINO3.4 and SOI. Another El Nino index was identified circa 2007 that is not closely correlated to the well-known ENSO indices. This index, referred to as El Nino Modoki, appears to have more of a Pacific Ocean centered dipole shape with a bulge flanked by two wing lobes, cycling again as an erratic standing-wave.

If in fact Modoki differs from the conventional ENSO only by a different standing-wave wavenumber configuration, then it should be straightforward to model as an LTE variation of ENSO. The figure below is the model fitted to the El Nino Modoki Index (EMI) (data from JAMSTEC). The cross-validation is included as values post-1940 were used in the training with values prior to this used as a validation test.

The LTE modulation has a higher fundamental wavenumber component than ENSO (plus a weaker factor closer to a zero wavenumber, i.e. some limited LTE modulation as is found with the QBO model).

The input tidal forcing is close to that used for ENSO but appears to lead it by one year. The same strength ordering of tidal factors occurs, but with the next higher harmonic (7-day) of the tropical fortnightly 13.66 day tide slightly higher for EMI than ENSO.

The model fit is essentially a perturbation of ENSO so did not take long to optimize based on the Laplace’s Tidal Equation modeling software. I was provoked to run the optimization after finding a paper yesterday on using machine learning to model El Nino Modoki [1].

It’s clear that what needs to be done is a complete spatio-temporal model fit across the equatorial Pacific, which will be amazing as it will account for the complete mix of spatial standing-wave modes. Maybe in a couple of years the climate science establishment will catch up.

[1] Pal, Manali, et al. “Long-Lead Prediction of ENSO Modoki Index Using Machine Learning Algorithms.” *Scientific Reports*, vol. 10, 2020, doi:10.1038/s41598-019-57183-3.

As can be seen in **Fig 1**, the semi-annual forcing is by far the strongest and sharpest tidal factor. The symmetry is such that the wind is positive (eastward) whenever the sun is at an equinox nodal crossing and negative (westward) whenever the sun is at a solstice extreme. There is a slight tendency for stronger westward excursions during the southern hemisphere summer.

This solar/tidal generation is the most plausible and parsimonious explanation of the driving force for the SAO, as the alternate explanation of the upper atmosphere creating a resonant frequency of exactly 1/2 year would be preposterously coincidental if true. This also creates a seamless explanation for the source of the lower-altitude QBO, as the synchronized lunar + solar nodal crossings generates the exact required period of 28 months.

It’s somewhat odd that others have not made the obvious connection of QBO and SAO to the tidal cycles, but even odder is the recent assertion that annual spiky disturbances of the 1 hPa data at northern latitudes (in this case near Sasso in Italy) are caused by invisible dark forces originating from a galactic flux (or something like that) [1].

The authors provide their own geographical explanation as due to a gravitational lensing of cosmic flux, with the disturbances occurring at a specific earth longitudinal alignment and other planets playing a role in the rapid fluctuations within the cone. See the **blue horizontal line** in the figure below which maps to an average temperature anomaly over a full orbit (one year).

In the Zioutas *et al* model, if the gravitational focusing occurs at a certain longitude of the earth’s orbit around the sun, then inside the cone the disturbance is sharp as the lens focuses, but outside of this cone of focus, normal seasonal temperature cycles occur.

This annual disturbance at ~1 hPa (about 48 km in altitude) has been observed by others [2]. In the article, von Savigny *et al* make the remark that these winter disturbances are *“mainly due to the action of planetary waves”*. Their data originated from near the Eifel mountain region in Germany, and so closely resembles that of **Fig 2** in Italy.

To better understand this annual disturbance feature, I downloaded 1 hPa ERA5 reanalysis data from a location close to Sasso, Italy, and used the GEM model fitting algorithm on an average annualized version to match the analysis of Zioutas *et al*.

Before ascribing this to a cosmic origin, perhaps a more basic question to ask is: What happens if in fact the rapid fluctuations in the annual signal at high-altitudes is simply due to wave breaking?

**Fig 5 **below shows what happens with strong wave-breaking via a cold impulse and LTE Mach-Zehnder-like modulation occurring near the start of northern latitudes winter.

On the right above is what it would look like without the wave-breaking modulation. The basic ideas that that without wave-breaking, the cooling impulses in December would not break up into multiple high-K waves.

As a simplified model view, consider the modulation shown in the figure to the right. The **red profile** is an asymmetric seasonal impulse corresponding to a pair of nodal crossings, with one impulse stronger than the other. As the LTE modulation is applied, the resulting **blue profile** shows a stronger fluctuating disturbance at greater amplitudes.

Another model fit is shown below exclusively using GEM, which takes the annually averaged profile and concatenates them into a time-series to match **Fig 4**. Because of the properties of LTE modulation, only harmonics of the annual cycle are retained in the training, so that the fine details shown in the fitted model are likely high-K standing wave modes corresponding to the seasonal gravity wave forcing. Relatively few degrees of freedom (DOF) are involved in this model, yet the richness and detail in the data is easily duplicated.

The other possibility is that these disturbances are modulated by lunar tidal cycles as during the observation of SSW events. That this doesn’t appear to be modulated evenly over the entire year is why I find this possibility less plausible than the amplitude-dependent LTE modulation. But either is likely more far more plausible than an invisible space force.

In summary, the SAO at the equator is essentially a balanced sum of the annualized cycles that appear north and south of the equator, creating the semi-annual pattern as the nodal orbit crosses the equator.

At correspondingly lower altitudes, the lunar tides take hold. The figure below is data from a recent paper [3] titled “On the forcings of the unusual Quasi-Biennial Oscillation structure in February 2016“, which like the SAO, may not be as unusual as claimed.

Stay tuned and keep aware, as there’s lots of misleading research being published by AGW skeptics claiming that they understand climate indices.

- Zioutas, K.
*et al.*Stratospheric temperature anomalies as imprints from the dark Universe.*Physics of the Dark Universe***28**, 100497 (2020). - von Savigny, C., Peters, D. H. W. & Entzian, G. Solar 27-day signatures in standard phase height measurements above central Europe.
*Atmospheric Chemistry and Physics***19**, 2079–2093 (2019). - Li, H., Pilch Kedzierski, R. & Matthes, K. On the forcings of the unusual Quasi-Biennial Oscillation structure in February 2016.
*Atmospheric Chemistry and Physics***20**, 6541–6561 (2020).

In research articles published ~50 years ago, Richard Lindzen made these assertions:

“For oscillations of tidal periods, the nature of the forcing is clear”

Lindzen, Richard S. “Planetary waves on beta-planes.”Mon. Wea. Rev95.7 (1967): 441-451.

and

“

5. Lunar semidiurnal tideOne rationale for studying tides is that they are motion systems for which we know the periods perfectly, and the forcing almost as well (this is certainly the case for gravitational tides). Thus,

it is relatively easy to isolate tidal phenomena in the data, to calculate tidal responses in the atmosphere, and to compare the two. Briefly, conditions for comparing theory and observation are relatively ideal. Moreover, if theory is incapable of explaining observations for such a simple system,we may plausibly be concerned with our ability to explain more complicated systems.Lindzen, R.S. and Hong, S.S., 1974. “Effects of mean winds and horizontal temperature gradients on solar and lunar semidiurnal tides in the atmosphere“.

Lunar tides are especially well suited to such studies since it is unlikely that lunar periods could be produced by anything other than the lunar tidal potential.“Journal of the atmospheric sciences,31(5), pp.1421-1446.

With that in mind, it should be possible to rule out the role of tidal forcing as the driving stimulus to a phenomenon such as the ~2.37-year cycle of the QBO. If the cycles of QBO and known tidal periods don’t match, then end-of-story according to Lindzen and tidal forcing isn’t and cannot be the forcing stimulus. Yet, when one checks the numbers for the longitudinally-invariant nodal tidal cycle against the annual solar nodal cycle (a strongly non-linear coupling), it comes out calibrating precisely on period:

1 / (365.242/27.2122 -13) = **2.369** years

This is simply an aliasing frequency formula, easily found as a FAQ on signal processing forums. It can also be graphically checked by multiplying an annual impulse train with the tidal cycle and plotting the result, as shown below.

After providing a lagged response to filter out the impulse, the agreement to the QBO data is obviously evident as shown below (plot generated from the GEM library).

So why didn’t Lindzen see this connection 50 years ago, while it is so evidently obvious?

Being charitable, it could be because the possibility of the nonlinear interaction of an annual signal with the tidal cycle was never considered by Lindzen back then, and it has since got lost in the interim. To be non-charitable, it may be that Lindzen lacked the insight to consider what is quite commonly encountered (i.e. waveform aliasing) in other disciplines.

One aspect that has become more obvious over time is that the stronger the annual impulse, the greater the delineation of the cycle via the nonlinear modulation. A recent paper by Alexander & Vincent [1] provides evidence for a very sharp gravity wave impulse, see the narrow impulse labeled in the 2-D plot below, with empirical data collected from airborne measurements.

And this result in the figure below from Hindley *et al *presented at this year’s EGU ([2] and discussed here) clearly shows how striking the annual impulse train is.

What is somewhat perplexing about the consensus surrounding QBO is that there is some indication (*i.e. unwritten understanding*) that the cycle is fixed — otherwise there wouldn’t be dozens of research papers discussing the QBO anomaly/disruption of 2016 and how it transiently disrupted the cycle. In other words, how can they say there is a disruption unless the underlying cycle is well understood?

These are all attempts to model QBO, taken from this paper doi:10.1029/2019jd032362 Why all so different for such a simple behavior? Unless there is consistency, any explanation of an anomaly would have to consider each of these plots individually.

Whereas with a lunisolar forcing, only one model is required as a baseline for further understanding. That’s why Lindzen’s jumping the gun on a mechanism behind QBO was so unfortunate — as it has likely deferred advances toward a common understanding for decades. As Lindzen himself said in the quote at the top of this post, that “*(without)* ** such a simple system, we may plausibly be concerned with our ability to explain more complicated systems**“.

1.Alexander, M. J. & Vincent, R. A. *Balloon-borne observations of short vertical wavelength gravity waves and interaction with QBO winds*. http://www.essoar.org/doi/10.1002/essoar.10502563.2 (2020) doi:10.1002/essoar.10502563.2.

2. Neil Hindley, Corwin Wright, Lars Hoffmann, M. Joan Alexander, Nicholas Mitchell, *Exploring long-term satellite observations of global 3-D gravity wave characteristics in the stratosphere*, **EGU2020-19821** https://presentations.copernicus.org/EGU2020/EGU2020-19821_presentation.pdf

This works best with a cosine amplitude spectrum, as the sine amplitude spectrum will reveal an anti-symmetry.

Across the next equivalent Brillouin zone — corresponding to the semi-annual harmonic — the mirror symmetry is still there but spotty in terms of alignment as shown in **Fig 2**.

This mirror symmetry also appears for more obscure climate indices such as the Pacific North America (PNA) pattern as shown in **Fig 3** below.

As with ENSO, the PNA essentially characterizes the USA climate variability in ways that a *“lot of management policies depend”*, governing fisheries, agriculture, irrigation, etc. So even though ENSO and PNA don’t match in terms of time-series comparison, they do share this mirror symmetry characterization.

The basis for this symmetry, the math behind Double-Sideband Suppressed-Carrier Modulation was covered in the previous post, but I return to it based on a presentation at the virtual EGU meeting that I only got around to in the past few days.

**Experimental internal gravity wave turbulence**_{Géraldine Davis, Thierry Dauxois, Sylvain Joubaud, Timothée Jamin, Nicolas Mordant, and Clément Savaro}

Davis et al stimulate a partially trapezoidal fluid reservoir with a primary frequency and find that richer harmonics are created with increased forcing as shown in **Fig 4 **below

Their interpretation of the experimental results are somewhat inscrutable (IMO) for the time being, but they do call attention to the role of triadic interactions. Triads were discussed in a recent post but the twist here is to make the connection of the mirror folding to the algebraic construction of a triad. In each case shown in **Fig 5** below, a peak identified in the Davis presentation shows the same folded mirror symmetry. This reappears across 3 zones as indicated by the arrow annotations.

The tenuous connection that I am exploring is how the triad frequencies bifurcate with increasing forcing levels. Based on the ENSO model, the mirror symmetry is due to the amplification of the carrier signal — i.e. the annual impulse — against the tidal cycle forcing. This is then fed in to the solution of Laplace’s Tidal Equations, producing a modulated time series rich in additional harmonics. Importantly, this preserves the mirror symmetry.

For comparison, Davis et al generate the chart in **Fig 6** to show the progression in richness with increased forcing. Their *N* is a characteristic buoyancy frequency that figures in to the value of the resonant frequencies.

The LTE complement is shown in **Fig 7** below where the interaction of a single selected frequency (which could be a resonant frequency such as *N*) is modulated by the main carrier impulsed wave-train. At the top with a relatively weak LTE modulation of 1, only a single side-band satellite pair is seen for each harmonic zone. With a LTE modulation of 3, another pair of side-band satellites fully emerges, with a third pair beginning to emerge. With modulation of 5 and 7, the strengths of these side-bands begins to equalize across the spectrum. This is all a consequence of higher and thus more energetic standing wavenumbers being added to the system, as a specific value of LTE modulation is linearly related to a standing-wave wavenumber.

That’s essentially a demonstration of the DSSC modulation mixing with the LTE modulation to generate the triads — a different yet complementary interpretation that I covered a few weeks ago before attending the EGU sessions.

Here is a link to a recent paper from Davis *et al* on arXiv that covers their EGU presentation in greater depth : Succession of resonances to achieve internal wave turbulence. This is required reading to remove some of the inscrutability, yet still something seems over-cooked. It’s entirely possible that a natural resonance is interacting with the forcing wave — the fact that the LTE solution requires a single natural response frequency and yet all the satellite side-band pairs (counting 3) clearly align in **Fig 7** may not be a coincidence.

They present it as below, with the caveat that the tailing off at high wavenumber (or shorter wavelength) disperses with a k^{-5/3 }dependence referred to Kologorov’s 5/3 spectrum and arising due to turbulence, though still controversial as the authors claim in the bullet points.

In our interpretation, the piece-wise power-law roll-off shown above is replaced by a smooth continuum with inflection points determined by the specific shape of the Cauchy density function. The Cauchy characterizes a stochastic distribution of some mix of standing and traveling wavetrains, with a preferred wavenumber defined by the cusp location. This disordered distribution is in contrast to the highly ordered nature of the QBO and of standing waves in a constrained container.

The continuum from deterministic to stochastic is essentially described as:

- Highly ordered deterministic waves, potentially including harmonics (see QBO with characteristic squared off waves)
- A specific amount of disorder applied as a semi-Markov process, maintaining harmonics
- Dispersion applied to the waves as semi-Markov without harmonics (Cauchy)

In the study’s presentation, the authors consider an experimental apparatus and try to recreate wave-trains as they may be represented in an actual atmosphere. One set of results is shown in slide 7 in their PDF. There is clearly a strong periodic component in the wave-train spectrum, so can’t be characterized as a Cauchy.

My first attempt at extracting what appears to be a semi-random sawtooth wave from the spectra as shown in the figure below with the model spectrum in dashed **GREEN**.

The Fourier analysis method is described in Chapter 16, with the formula to the right from page 194. The upper formula is for a symmetric square wave and the lower formula for an asymmetric or skewed wave.

The fit to first-order does show all the harmonics of the fundamental so it is definitely a skewed waveform (as a symmetric waveform would show only the odd harmonics). Yet the peaks are too sharp, and likely the width of the spectral lobes is due to the sampling being limited to a few cycles. By fitting to a cusped asymmetric sawtooth-like waveform of ~4 cycles (shown in the upper right inset in the figure below), the power spectra can be duplicated precisely, as shown in the figure below with the model shown in **PURPLE**.

The extra side-lobes are due to fixed sampling size, so am sure that this is close to the actual waveform shape. One author of the presentation seems to agree — after adding these observations to the comment page, he said:

“

Uwe Harlander, 12 May 2020thank you very much for your interesting comments. You are right, due to the length of the measured time series the low-frequency wave part is indeed limited to a few waves and also the skewness of the wave form you have shown seems to be rather realistic to me. The low-frequency part consists of Rossby waves (or their relatives, Eady waves) and the cold front is usually steeper as the warm front of the wave.“

The point is that the more you can characterize the data the better that you can extract and discriminate the finer structure that you are interested in — in this case, to extract the high wavenumber turbulence one must first distinguish the highly-ordered wave components.

Moreover, this kind of analysis provides confidence that other atmospheric and oceanic gravity wave features [3] can be similarly characterized — as other EGU presentations [4] focus on a similar lab-based experimental apparatus to understand these type of waves. Consider my comments here, as phenomena such as QBO may be simple enough to understand without resorting to a limited physical emulation.

- Rodda, C. & Harlander, U.
*Transition from geostrophic flows to inertia-gravity waves in the spectrum of a differentially heated rotating annulus experiment.*https://meetingorganizer.copernicus.org/EGU2020/EGU2020-9374.html (2020) doi:10.5194/egusphere-egu2020-9374. - Nastrom, G. & Gage, K. S. A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft.
*Journal of the atmospheric sciences***42**, 950–960 (1985). - Bushell, A. C.
*et al.*Parameterized Gravity Wave Momentum Fluxes from Sources Related to Convection and Large-Scale Precipitation Processes in a Global Atmosphere Model.*http://dx.doi.org/10.1175/JAS-D-15-0022.1*https://journals.ametsoc.org/doi/abs/10.1175/JAS-D-15-0022.1 (2015) doi:10.1175/JAS-D-15-0022.1. - Léard, P., Lecoanet, D. & Le Bars, M.
*A multi-wave model for the Quasi-Biennial Oscillation: Plumb’s model extended*. https://meetingorganizer.copernicus.org/EGU2020/EGU2020-7375.html (2020) doi:10.5194/egusphere-egu2020-7375.

Notes from the EGU 2020 meeting from last week. The following list of presentation pages are those those that I have commented on, with responses from authors or from chat sessions included. What’s useful about this kind of virtual meeting is that the exchange is concrete and there’s none of the ambiguity in paraphrasing one-on-one discussions that take place at an on-site gathering.

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-12346.html

I pointed out in response to another commenter’s (Bruun) claim *“The ENSO process is a resonant wave phenomena of the earth system “* that *“The evidence doesn’t support this. It appears to be more driven by tidal forces as can be seen by calibrating against the known angular momentum changes (from dLOD) and then applying a solution to Laplace’s Tidal Equations along the equator.”*

Some back and forth where Bruun said diurnal and semidiurnal tidal cycles (which are much too fast IMO to invoke a response) should *“play a role”*.

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-21756.html

In the chat:

In the permanent comment, I clarified as to how a *“recharge oscillator model fits into GCMs, in that it is more a simplifying model trained from the output data, so it provides a phenomenological interpretation.”*

The author **Crespo** responded *“I am glad to hear that my explanation was clarifying. I can try to expand here now with more time. As I said in the chat we train the model with CMIP5 models output data. In practice this means that we fit the recharge oscillator conceptual model to the output data of the CMIP5 models to obtain the parameters of the model (see my slides). Once we have the parameters we can run the model freely and build some statistics with the output variables of the ReOsc mode; SST and thermocline.By doing this we can investigate if the recharge-discharge mechanism is well represented by each CMIP model, how is the amplitude of it and if there is a decadal modulation in this mechanism in the models.”*

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-18545.html

I asked if the Chandler Wobble may be a *“434 day wobble a result of the lunar nodal torqueing cycle (13.606 day) acting on a non-spheroidal earth”*

The response is *“Your hypothesis indeed sounds reasonable in theory. However, in practice, on the plots of my slide 4 you can see a very good match between the C21/S21 series I derived (in blue), removing all the known tidal effects, and the Chandler polar motion evolution (in red). This shows that tidal effects cannot be the source of this ~430-day oscillation.”*

Provoked another response after I posted this chart and the recent paper by Na

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-11931.html

I mentioned that *“An annual forcing is observed in the ENSO cross-spectrum with a mirror symmetry about the 0.5/yr point. It’s referred to as d ouble-sideband suppressed-carrier modulation“*

One of the authors (Stenchikov) responded *“I am not sure I understand it correctly. Volcanic forcing is sporadic and the system is nonlinear. So you should see multiple subharmonics generated.”*

A subharmonic would be a lower (i.e. half) frequency but he may have meant higher. Assuming that, I countered with a recent chart showing the mirror symmetry at higher (super) harmonics but no further response

In the chat session, I asked a question as follows but no response, as they ran out of time apparently.

The author did answer Bruun’s question though: *“ Evgeniya Predybaylo KAUST/MPIC (07:13) @John Bruun Exeter Well, according to our simulations, the tropical Pacific response can show the variety of responses – from La Nina-like to El Nino-like depending on what was the state of the Pacific during the eruption. So, the effect is actually significant. “*

The Pacific Ocean dynamics seems to be immune from volcanic forcing, so the response is questionable at best.

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-17743.html

I tried asking during the chat session and on the presentation linked above but got no reply in either case:

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-19240.html

I asked *“Why isn’t the 434 day wobble a result of the lunar nodal torqueing cycle (13.606 day) acting on a non-spheroidal earth? “*

A very detailed answer from Bizouard: *“According to our present understanding, the 434 day wobble is a normal mode of the Earth rotation, produced by the Earth flattening (the Euler mode with a period of 304 days). The departure of the 434 period from the Euler period predicted for a rigid Earth results from the Earth deformation (the pole tide), produced by the tiny centrifugical variation accompagnying the polar motion. Effect of the Moon has never been proved, even if some authors invoke a possible synchronisation of the Chandler wobble with tidal cycles through non-linear processes, that has to be demonstrated. Dissipation accompaniying the pole tide results in a decay of the Chandler wobble: after 200 years its amplitude would be divided by 8-100 in abscence of excitation. So, its maintenance, at an amplitude of 50-200 mas, requires a forcing. According to my own studies, that one stems from atmospheric and oceanic mass transports.”*

I responded at some length starting with *“The expected value is 365.242/(365.242/13.606-26) = 433 days, which matches the established value of the Chandler wobble cycle. …. “*

This response:

BTW, the author Bizouard is the Director of the EOP (Earth Orientation Parameters) Product Center at http://obspm.fr which is the observatory in Paris that keeps track of the earth’s rotation parameters, see http://hpiers.obspm.fr/eop-pc/index.php. So it’s good to get a response with such conviction.

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-13127.html

This presentation discusses the 6-year cycle in dLOD so I asked this question “*Since the dLOD is dominated by variations caused by tidal/gravitational forcing, why isn’t the 6-year cycle traced to the interaction between the nodal (18.6y) and perigean (8.85y) cycle?*“

The author responded *“It was shown by Gillet et al. (2010) that the 6-year varaition in LOD can be linked to variations in the geomagnetic field produced in the Earth’s fluid outer core by Alfven waves and torssional oscillations of the appropriate period. We do not reject the possibility that two lunar cycles contribute as well. Thanks.”*

I countered with good on being able to extract the signal because it is quite weak in my opinion. As I mentioned, the 18.6 year cycle is very apparent in dLOD but I have had hit-or-miss success in trying to isolate it definitively.

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-7088.html

I commented as follows:* “The changes in the LOD or angular momentum will likely be felt most strongly in the ocean’s thermocline, where the highly reduced effective gravity at the thermocline density interface is most suceptible to inertial changes. And since dLOD is largely governed by tidal forcing cycles, the thermocline sloshing will transitively be accounted for by the tidal pattern. This has recently been shown to be the case with ENSO, see Lin, J. & Qian, T. Switch Between El Nino and La Nina is Caused by Subsurface Ocean Waves Likely Driven by Lunar Tidal Forcing. Sci Rep 9, 1–10 (2019).”*

The author responded: *“Thank you for the interesting comment! We will have a look at the article.”*

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-19806.html

Based on a comment in their presentation that MJO is *“yet poorly simulated in most atmospheric circulation models”*, I commented : *“Is that because it’s not well known that it is connected directly to ENSO via the SOI measure with a 21-day lag?”*

The author responded : * “What index do you use for the MJO?Did you try to calculate the correlation with the interannual variability removed?*”

I answered that here in CC4, showing the cross-correlation chart at short (much less than interannual) time intervals.

The author concluded with an answer to someone else’s question: *“In think the energy source for Rossby waves is the organized convection trough atmospheric column stretching. Citing Geoffrey K. Vallis (pag. 326, 2017) ”From the perspective of potential vorticity, then to the extent that the flow is adiabatic the quantity (𝑓 + 𝜁)/ℎ is conserved following the flow. The heating increases the value of ℎ (the stretching), so that 𝑓 + 𝜁 also tends to increase in magnitude. The flow finds it easier to migrate polewards to increase its value of 𝑓 than to increase its relative vorticity alone, for the latter would require more energy.” Then a pair of cyclonic centers is formed straddling the equator.”*

That may be how the MJO spins off the equator as a wave-train, transforming the standing waves of ENSO into the vortex-like equatorial traveling Tropical Instability Waves and then peeling those off as the off-equatorial MJO waves. This is all a lunisolar energy source though, imho.

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-17014.html

I asked whether *“these cycles due to synodic tides?”*

The author answered *“The 14 day variation that you mention is the spring-neap cycle. That is caused by the interaction of the two semi-diurnal constituents, M2 and S2”*

True, and when an inertial response is factored in, then the 14 day cycle is what impacts behaviors such as dLOD and ENSO.

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-6394.html

I asked : *“Why do the SOI and MJO track each other so closely but with lag of 21 days separating them?”*

The author responded :

“What kind of MJO time series do you use? Is it RMM index or something like that?As the MJO convection propagates from equatorial Indian Ocean to equatorial Pacific, it may cause SLP variations that resemble the SO. Therefore, the correlation between MJO and SOI could be a reflection of the influence of SLP variation by the MJO. The time lag between them is probably due to the time lag between the positve phase describe by the MJO time series you used and the MJO phase that cause SO-like SLP pattern.I don’t think MJO is a slave to ENSO. “

I responded with a link to the pentad MJO source at NOAA but that was essentially the last comment so far. They have a journal article here:

Chen, G. & Wang, B. Circulation factors determining the propagation speed of the Madden-Julian Oscillation.

Journal of Climate(2020).

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-8885.html

I pointed out that the SAM index may share a common forcing with ENSO. Provided a reference to Mathematical Geoenergy

*“Thanks, will have a look.”*

Also tried a link but that did not go through.

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-13481.html

I mentioned the common-mode lunisolar forcing between NAO and other climate indices and received this response:

“Thanks Paul for this interesting comment!

We did not look at the spectra of the NAO, we msotly looked at the time domain focussing on the nonlinear aspect of predictability. The lunisolar forcing seems to be all over (NAO, Arctic Oscillation, plant growth …). which frequency precisely you are talking about – From the figure you posted, you seem to tal about quite low frequency, righ!

/Abdel”

Yes, indeed. He later requested our most recent AGU paper.

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-7171.html

I asked *“why is it that ENSO has such a strong correlation to MJO when a 21 day lag is applied?”*

Read the full conversation but part of the response by Chen Schwartz:

The fluctuations in the SOI index that are correlated with the MJO could be possibly, in part, related to the surface westerly anomalies induced by the MJO, but this is something I’ve never looked on (the ENSO signal is usually has to be separated from the MJO).The connection to El-Nino events is more complex as far as I know, and it’s on timescales longer than 3 weeks.

responded with a suggestion about MJO being a traveling wave offshoot of ENSO but this was the extent

“As far as I know, ENSO can modulate the MJO and also its extratropical response, but it does not trigger it (their timescales are not the same). Nevertheless, tropical meteorology is not my expertise, so you may want to attend the Tropical Meteorology session tomorrow, so you can get more in-depth answers. “

This insight is much better than nothing!

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-20845.html

I asked : *“How can one extract a description of the differential equation when the forcing is unknown?”*

response

“I believe that when the forcing overrides the natural response of a system, the extracted model naturally (due to the learning criterion) relates the forcing signature to the dynamics and thus, approximates the forced system with a non-foreced one. This approximation may be crude but one can add a learnable forcing signatures (similarly to what we did with the learnable embedding) to find an approximate forced system. However, without any prior knowledge of either the dynamics or the forcing, the latter approximation will not be quite informative since forcing signatures will mixed with the natural dynamics of the system.”

That’s a good response. I added *“Both the initial conditions (as you say) and the running boundary values as either ongoing temporal forcing or spatial boundary conditions play a role. Thank you.”*

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-7569.html

I wanted to point out that flows in their reference “global sea-level pressure data for the past 40 years” may not be chaotic: *“The longest continuous sea-level pressure (SLR) time series may be the SOI differential between Tahiti and Darwin which characterizes ENSO. This is not chaotic as it arises directly from tidal forcing patterns, which are similar to the pattern found in the earth’s length-of-day variations but modulated by the ocean’s fluid dynamic response.”*

No response so far. Good figures though and some good insight into where machine learning will have problems when they assume a chaotic solution. Note the value of being able to solve Navier-Stokes as we can with the LTE approach.

*It is not straightforward to apply Machine Learning techniques to geophysical flows: turbulence and intermittency worsen the performance**Partial predictability can be recovered by separating large from small scale dynamics (e.g moving average, PCA, wavelets)**Possible developments will largely benefit from interactions with the stochastic dynamical systems community*

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-2113.html

Quite the complex model so I posed a simple question: *“Is switching between El Nino and La Nina caused by subsurface ocean waves driven by lunar tidal forcing ?”*

Response:

“No. the tidal forcing may influence the switching but not the major reason. The transition between El Nino and La Nina can be explained by the theories of the delayed oscillation, charge-dischage …. The easterward subsurface ocean waves (i.e., kevin waves) are due to the beta-plane.”

So apparently from the GCMs they are creating an *“intermediate complex model (ICM) and makes the ICM output closer to the observations”*.

In the presentation, they mention that the ICM is unable to model Tropical Instability Waves (TIW). Their longer paper here: https://journals.ametsoc.org/doi/full/10.1175/WAF-D-19-0050.1

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-2235.html

They are tying to find commonality between Pacific ocean climate indices.

Asked this loaded question ~~but no response~~: *“Are these teleconnections or are they actually related by a common-mode mechanism, such as the erratic nature of long-period tidal cycles?”*

RESPONSE 5/20/2020 – *“It is a interesting question, but tide changes are not the focus of our research*.”

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-2560.html

I added an observation based on the latest QBO data *“It has been a few years since the 2015-2016 QBO anomaly and the QBO cycle has re-aligned to the predicted lunisolar-nodal cycle of 28.436 months. This is the expected wave response from the gravitational forcing.”*

Surprised by the response:

“Thank you. This is a good perspective. And how much variance contribution the 28 month periodicity of QBO can explain may also affect its predictability.”

They think there was a higher energy density feeding the gravity wave during the 2015-2016 time frame. Compare against our model of QBO. This may have transitioned first around 2006 and ended in 2016.

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-16682.html

Offered this comment *“This might help in understanding QBO — consider the forcing the lunisolar nodal cycle interacting with the topology of the equatorial toroid generates the corrects period”* but no response.

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-15897.html

Offered a similar comment *“There is no real snchronization between the QBO and ENSO since QBO has a wavenumber of 0 implying only tidal forces of hemispherical symmetry will be involved, such as the lunar and solar nodal tide. On the other hand, since ENSO is a tropical Pacific with non-zero longitudinal wavenumber, the lunar tropical/synodic tide provides the greater forcing.”* but also no response.

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-5635.html

Another commenter asked this:

“MIROC-AGCM-LL does have realistic QBO without gravity wave prameterization. Does it imply GW drag is not necessary in simulaiting QBO?”

I responded “How can QBO not require gravity wave parameterization? The QBO cycle of 28 months is clearly an exact alignment with the lunar nodal gravitational cycle. This is such a strong synchronizing force that even the QBO anomaly of 2015-2016 couldn’t permanently disrupt the alignment, as it is now has synched back to the prior cycle.” but that’s as far as the discussion went.

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-17338.html

No response to this comment:* “Have you been aware that the 28-month QBO cycle has been verified to be aligned to the atmospheric lunar nodal tide? This was cross-validated when after the 2015-2016 QBO anomaly, the alignment re-established itself, much like tidal signals will re-align after a tsunami.”*

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-8789.html

During the chat session I asked:

This makes sense as at the polar latitudes (northern Norway is the focus of this study), a seasonal signal will be strongest, while the equator will show a semiannual oscillation for each nodal crossing.

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-6118.html

My chat session comment:

his response

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-8503.html

Chat session question that was promptly answered

In many of the papers on internal tide generation, the waves arise from interactions from tides with abyssal hills and ridges, so it is interesting to learn that the thermocline interface can also spawn the waves. The soliton response is intriguing since I made the connection between traveling waves and solitons on a recent MJO post. BTW, they don’t say anything about the thermocline in their presentation. The Drake passage also mentioned.

I added the Qian & Lin reference for good measure to the chat.

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-8371.html

Added a comment during the chat session:

This triad feature shows up frequently as I discussed in a recent blog post titled Triad Waves, where I mention the work of Bruce Sutherland.

There was a related presentation on experimental work : **The long-time spatial and temporal development of Triadic Resonance Instability** which has flow along diagonal beams

Reminding of these Sutherland waveforms that occur in stratified layers and that we can reproduce

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-7375.html

A comment during the chat session on internal gravity waves (IGW):

added a comment to the presentation page: *“I never understood the rationale for the Plumb experiment to act as a validation for the QBO mechanism. First of all, the Plumb apparatus is a rotating cylinder and not a rotating sphere, so it does not allow the apparently important Coriolis effect. Secondly, the lab-sized nature of the apparatus prevents the emulation of any gravitational effect. There are centrifugal acceleration aspects but these aren’t balanced by gravity, and what’s more, any gravitational effects are along the length of the cylinder and not radial. Overall and at best, it may help explain certain stratification properties, but validates nothing about the fundamental QBO oscillation.*“

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-9374.html

inertia-gravity waves in the spectrum of a

differentially heated rotating annulus experiment

I added a comment to the chat session, but it was at the end so never got addressed:

Interesting chart here from their uploaded presentation:

In Chapter 11 of our book on wind energy, we model the Nastrom and Gage data via a damped correlation model for a peaked wavenumber with figure reproduced below. The piece-wise power-law roll-off shown above is replaced by a smooth continuum with inflection points determined by the specific shape of the Cauchy density function.

May write a longer post on this because it does address the concept of dispersion in the context of wave spectrum that also shows distinctly more likely (i.e. peaked) wavenumbers.

Asked about this on the comment page

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-8835.html

Asked a question during the chat session

No response.

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-7527.html

During the chat, asked a question about the spring barrier:

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-7263.html

Since this concerned Australia, asked a question about IOD:

The IOD has a common-mode connection to ENSO shown here, based on the standing-wave mode.

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-16656.html

How can they determine what ENSO does in a warming world if they don’t understand the fundamentals behind ENSO? Asked in a chat session

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-8916.html

In chat session:

At the end of this session, someone took a potshot at me

https://meetingorganizer.copernicus.org/EGU2020/EGU2020-6137.html

“

Nonlinearities prominent in some setups, but vary strongly with location or season of the year”

In the chat on a session devoted to primarily paleoclimate topics :

- I am
**pukpr**in the chat sessions - The chat sessions averaged >100 participants from what I heard but were not archived.
- The uploaded presentations have relatively few comments attached so far but are permanent. New comments will be accepted until May 31
- This virtual conference was instead of the yearly meeting in Vienna. I debated submitting an abstract but didn’t.
- Will add more in the comments below