lunar

AMO and the Mt tide

/ Paul Pukite (@whut) / 1 Comment

Geophysics is a challenging endeavor — one part geology as historical evidence and the other part current measurements revealing how the forces of nature are continuously shaping the behavior of the Earth. Yet, how much faith can we place on any one interpretation, or on any past consensus?

"But for geophysics on such a massive scale, nothing can be checked via a lab controlled experiment."Someone has described geology!I prefer my own description (though taken from someone else and modified): Geology is like trying to learn about barley by studying beer.

— Compton Scatterbrained (@stommepoes.bsky.social) 2024-09-18T15:13:20.671Z

This goes double for the study of geophysical fluid dynamics — volumes and forces so large that controlled experiments are impossible. So that when a semi-controlled impulse comes about, say from the calving of a glacier, the empirical results may be surprising:

The subsequent mega-tsunami — one of the highest in recent history — set off a wave which became trapped in the bendy, narrow fjord for more than a week, sloshing back and forth every 90 seconds.

The phenomenon, called a “seiche,” refers to the rhythmic movement of a wave in an enclosed space, similar to water splashing backwards and forwards in a bathtub or cup. One of the scientists even tried (and failed) to recreate the impact in their own bathtub.

While seiches are well-known, scientists previously had no idea they could last so long.

“Had I suggested a year ago that a seiche could persist for nine days, people would shake their heads and say that’s impossible,” said Svennevig, who likened the discovery to suddenly finding a new colour in a rainbow. — http://www.msn.com/en-in/news/techandscience/what-caused-the-mysterious-9-day-earth-vibration-scientists-point-to-650-ft-mega-tsunami-that-rocked-greenland/ar-AA1qwIqk

This took place in a large Greenland fjord — massive but not as massive as the ocean. And that’s where massive geophysical forces also take place, such as from tidal pull.

So what about the Atlantic Multidecadal Oscillation (AMO)? The Mt long-period tide is an interference between the Mf nodal tidal cycle (13.66 days) and the Mm anomalistic tidal cycle (27.55 days). When this is synchronized to an annual impulse, a multidecadal response results.

It is much too easy to model the 50-60 year AMO cycle via nonlinear triad frequency-doubling mechanisms, and also simulate the faster cycling from the predominate Mf and Mm interactions with the annual cycle. This is essentially a sloshing behavior operating on the ocean’s thermocline as described in Chapter 12 of Mathematical Geoenergy, applying the nonlinear geophysical dynamics embedded within Laplace’s Tidal Equations.

New colors of the rainbow are waiting to be revealed. No excuse for others to reproduce the tidal forcing models as described and perform cross-validated model fits to replicate the results above. Work smart not hard.

Order overrides chaos

/ Paul Pukite (@whut) / 5 Comments

Dimensionality reduction of chaos by feedbacks and periodic forcing is a source of natural climate change, by P. Salmon, Climate Dynamics (2024)

Bottom line is that a forcing will tend to reduce chaos by creating a pattern to follow, thus the terminology of “forced response”. This has implications for climate prediction. The first few sentences of the abstract set the stage:

The role of chaos in the climate system has been dismissed as high dimensional turbulence and noise, with minimal impact on long-term climate change. However theory and experiment show that chaotic systems can be reduced or “controlled” from high to low dimensionality by periodic forcings and internal feedbacks. High dimensional chaos is somewhat featureless. Conversely low dimensional borderline chaos generates pattern such as oscillation, and is more widespread in climate than is generally recognised. Thus, oceanic oscillations such as the Pacific Decadal and Atlantic Multidecadal Oscillations are generated by dimensionality reduction under the effect of known feedbacks. Annual periodic forcing entrains the El Niño Southern Oscillation.

In Chapters 11 and 12 in Pukite, P., Coyne, D., & Challou, D. (2019). Mathematical Geoenergy. John Wiley & Sons, I cited forcing as a chaos reducer:

“It is well known that a periodic forcing can reduce the erratic fluctuations and uncertainty of a near‐chaotic response function (Osipov et al., 2007; Wang, Yang, Zhou, 2013).“

But that’s just a motivator. Tides are the key, acting primarily on the subsurface thermocline. Salmon’s figure comparing the AMO to Barents sea subsurface temperature is substantiating in terms of linking two separated regions by something more than a nebulous “teleconnection”.

Likely every ocean index has a common-mode mechanism. The tidal forcing by itself is close to providing an external synchronizing source, but requires what I refer to as a LTE modulation to zero in on the exact forced response. Read the previous blog post to get a feel how this works:

Common forcing for ocean indices

As Salmon notes, it’s known at some level that an annual/seasonal impulse is entraining or synchronizing ENSO, and also likely PDO and AMO. The top guns at NASA JPL point out that the main lunisolar terms are at monthly, 206 day, annual, 3 year, and 6 year periods, and this is what is used to model the forcing, see the following two charts

Now note how the middle panel in each of the following modeled climate indices does not change markedly. The most challenging aspect is the inherent structural sensitivity of the manifold1 mapping involved in LTE modulation. As the Darwin fit shows, the cross-validation is better than it may appear, as the out-of-band interval does not take much of a nudge to become synchronized with the data. Note also that the multidecadal nature of an index such as AMO may be ephemeral — the yellow cross-validation band does show valleys in what appears to be a longer multidecadal trend, capturing the long-period variations in the tides when modulated by an annual impulse – biennial in this case.

Model config repo: https://gist.github.com/pukpr/3a3566b601a54da2724df9c29159ce16?permalink_comment_id=5108154#gistcomment-5108154

1 The term manifold has an interesting etymology. From the phonetics, it is close to pronounced as “many fold”, which is precisely what’s happening here — the LTE modulation can fold over the forcing input many times in proportion to the mode of the standing wave produced. So that a higher standing wave will have “many folds” in contrast to the lowest standing wave model. At the limit, the QBO with an ostensibly wavenumber=0 mode will have no folds and will be to first-order a pass-through linear amplification of the forcing, but with likely higher modes mixed in to give the time-series some character.

Common forcing for ocean indices

/ Paul Pukite (@whut) / 6 Comments

In Mathematical Geoenergy, Chapter 12, a biennially-impulsed lunar forcing is suggested as a mechanism to drive ENSO. The current thinking is that this lunar forcing should be common across all the oceanic indices, including AMO for the Atlantic, IOD for the Indian, and PDO for the non-equatorial north Pacific. The global temperature extreme of the last year had too many simultaneous concurrences among the indices for this not to be taken seriously.

NINO34

PDO

AMO

IOD – East

IOD-West

Each one of these uses a nearly identical annual-impulsed tidal forcing (shown as the middle green panel in each), with a 5-year window providing a cross-validation interval. So many possibilities are available with cross-validation since the tidal factors are essentially invariantly fixed over all the climate indices.

The approach follows 3 steps as shown below

The first step is to generate the long-period tidal forcing. I go into an explanation of the tidal factors selected in a Real Climate comment here.

Then apply the lagged response of an annual impulse, in this case alternating in sign every other year, which generates the middle panel in the flow chart schematic (and the middle panel in the indexed models above).

Finally, the Laplace’s Tidal Equation (LTE) modulation is applied, with the lower right corner inset showing the variation among indices. This is where the variability occurs — the best approach is to pick a slow fundamental modulation and generate only integer harmonics of this fundamental. So, what happens is that different harmonics are emphasized depending on the oceanic index chosen, corresponding to the waveguide structure of the ocean basin and what standing waves are maximally resonant or amplified.

Note that for a dipole behavior such as ENSO, the LTE modulation will be mirror-inverses for the maximally extreme locations, in this case Darwin and Tahiti

A machine learning application is free to scrape the following GIST GitHub site for model fitting artifacts.

https://gist.github.com/pukpr/3a3566b601a54da2724df9c29159ce16

Another analysis that involved a recursively cycled fit between AMO and PDO. It switched fitting AMO for 2.5 minutes and then PDO for 2.5 minutes, cycling 50 times. This created a common forcing with an optimally shared fit, forcing baselined to PDO.

PDO

AMO

NINO34

IOD-East

IOD-West

Darwin

Tahiti

The table above shows the LTE modulation factors for Darwin and Tahiti model fits. The highlighted blocks show the phase of the modulation, which should have a difference of π radians for a perfect dipole and higher harmonics associated with it. (The K0 wavenumber = 0 has no phase, but just a sign). Of the modes that are shared 1, 45, 23, 36, 18, 39, 44, the average phase is 3.09, close to π (and K0 switches sign).

1.23-(-1.72) = 2.95 
1.47-(-2.05) = 3.52
-2.89-(0.166) = -3.056 
-0.367-(-2.58) = 2.213 
1.59-(-2.175) = 3.765 
0.27 - (-2.84) = 3.11 
-1.87 -1.14 = -3.01 

Average (2.95+3.52+3.056+2.213+3.765+3.11+3.01)/7 = 3.0891

Contrast to the IOD East/West dipole. Only the K0 (wavenumber=0) shows a reversal in sign. The LTE modulation terms are within 1 radian of each other, indicating much less of a dipole behavior on those terms. It’s possible that these sites don’t span a true dipole, either by its nature or from siting of the measurements.

Cross-validating a large interval span on PDO

using CC

using DTW metric, which pulls out more of the annual/semi-annual signal

adding a 3rd harmonic

Complement of the fitting interval, note the spectral composition maintains the same harmonics, indicating that the structure mapped to is stationary in the sense that the tidal pattern is not changing and the LTE modulation is largely fixed.

This is the resolved tidal forcing, finer than the annual impulse sampling used on the models above.

Below can see the primary 27.5545 lunar anomalistic cycle, mixed with the draconic 27.2122/13.606 cycle to create the 6/3 year modulation and the 206 day perigee-syzygy cycle (or 412 full cycle, as 206 includes antipodal full moon or new moon orientation).

(click on any image to magnify)

Fundy-mental (continued)

/ Paul Pukite (@whut) / 1 Comment

I’m looking at side-band variants of the lunisolar orbital forcing because that’s where the data is empirically taking us. I had originally proposed solving Laplace’s Tidal Equations (LTE) using a novel analytical derivation published several years ago (see Mathematical Geoenergy, Wiley/AG, 2019). The takeaway from the math results — given that LTEs form the primitive basis of the GCM-specific shallow-water approximation to oceanic fluid dynamics — was that my solution involved a specific type of non-linear modulation or amplification of the input tidal. However, this isn’t the typical diurnal/semi-diurnal tidal forcing, but because of the slower inertial response of the ocean volume, the targeted tidal cycles are the longer period monthly and annual. Moreover, as very few climate scientists are proficient at signal processing and all the details of aliasing and side-bands, this is an aspect that has remained hidden (again thank Richard Lindzen for opening the book on tidal influences and then slamming it shut for decades).

Continue reading →

Bay of Fundy subbands

/ Paul Pukite (@whut) / 1 Comment

With the recent total solar eclipse, it revived lots of thought of Earth’s ecliptic plane. In terms of forcing, having the Moon temporarily in the ecliptic plane and also blocking the sun is not only a rare and (to some people) an exciting event, it’s also an extreme regime wrt to the Earth as the combined reinforcement is maximized.

In fact this is not just any tidal forcing — rather it’s in the class of tidal forcing that has been overlooked over time in preference to the conventional diurnal tides. As many of those that tracked the eclipse as it traced a path from Texas to Nova Scotia, they may have noted that the moon covers lots of ground in a day. But that’s mainly because of the earth’s rotation. To remove that rotation and isolate the mean orbital path is tricky.  And that’s the time-span duration where long-period tidal effects and inertial motion can build up and show extremes in sea-level change. Consider the 4.53 year extreme tidal cycle observed at the Bay of Fundy (see Desplanque et al) located in Nova Scotia. This is predicted if the long-period lunar perigee anomaly (27.554 days and the 8.85 absidal precessional return cycle) amplifies the long period lunar ecliptic nodal cycle, as every 9.3 years the lunar path intersects the ecliptic plane, one ascending and the other descending as the moon’s gravitational pull directly aligns with the sun’s.  The predicted frequencies are 1/8.85 ± 2/18.6 = 1/4.53 & 1/182, the latter identified by Keeling in 2000.  The other oft-mentioned tidal extreme is at 18.6 years, which is identified as the other long period extreme at the Bay of Fundy by Desplanque, and that was also identified by NASA as an extreme nuisance tide via a press release and a spate of “Moon wobble” news articles 3 years ago.

What I find troubling is that I can’t find a scholarly citation where the 4.53 year extreme tidal cycle is explained in this way. It’s only reported as an empirical observation by Desplanque in several articles studying the Bay of Fundy tides. 

Continue reading →

Proof for allowed modes of an ideal QBO

/ Paul Pukite (@whut) / 6 Comments

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 reading →

Are the QBO disruptions anomalous?

/ Paul Pukite (@whut) / 10 Comments

Based 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 →

Unified Model of Earth Dynamics

/ Paul Pukite (@whut) / Leave a comment

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

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

Graph

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

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

Annotated 10/11/2023

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

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

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

Paleo ENSO

/ Paul Pukite (@whut) / 1 Comment

Two recent articles prompted a few ideas

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

Two annual cycles of the Pacific cold tongue under orbital precession

Which says that

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

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

Next article

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

They note 800 year cycles in the observations

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

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