This blog is late to the game in commenting on the physics of the Hollywood film Moonfall — but does that really matter? Geophysics research and glacially slow progress seem synonymous at this point. In social media, unless one jumps on the event of the day within an hour, it’s considered forgotten. However, difficult problems aren’t unraveled quickly, and that’s what he have when we consider the Moon’s influence on the Earth’s geophysics. Yes, tides are easy to understand, but any other impact of the Moon is considered warily, perhaps over the course of decades, not as part of the daily news & entertainment cycle.

My premise: The movie Moonfall is a more pure climate-science-fiction film than Don’t Look Up. Discuss.

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

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.

“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.”

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.

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 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.

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 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.

Addendum: After this presentation was submitted, a ground-breaking paper by a group at the University of Paris came on-line. Their paper, “On the Shoulders of Laplace” covers much the same ground as the EGU presentation linked above.

F. Lopes, J.L. Le Mouël, V. Courtillot, D. Gibert, On the shoulders of Laplace, Physics of the Earth and Planetary Interiors, 2021, 106693, ISSN 0031-9201, https://doi.org/10.1016/j.pepi.2021.106693.

Excerpts from the paper “On the shoulders of Laplace”

Moreover Lopes et al claim that this celestial gravitational forcing carries over to controlling cyclic climate indices, following Laplace’s mathematical formulation (now known as Laplace’s Tidal Equations) for describing oceanic tides.

This view also aligns with the way we model climate indices such as ENSO and QBO via a solution to Laplace’s Tidal Equations, as described in the linked EGU presentation above.

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.

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

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

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

In our book Mathematical GeoEnergy, several geophysical processes are modeled — from conventional tides to ENSO. Each model fits the data applying a concise physics-derived algorithm — the key being the algorithm’s conciseness but not necessarily subjective intuitiveness.

I’ve followed Gell-Mann’s work on complexity over the years and so will try applying his qualitative effective complexity approach to characterize the simplicity of the geophysics models described in the book and on this blog.

Here’s a breakdown from least complex to most complex

In Chapter 11 of the book Mathematical GeoEnergy, we model the QBO of equatorial stratospheric winds, but only touch on the related cycle at even higher altitudes, the semi-annual oscillation (SAO). The figure at the top of a recent post geometrically explains the difference between SAO and QBO — the basic idea is that the SAO follows the solar tide and not the lunar tide because of a lower atmospheric density at higher altitudes. Thus, the heat-based solar tide overrides the gravitational lunar+solar tide and the resulting oscillation is primarily a harmonic of the annual cycle.

One 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.

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. “