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).
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Bay of Fundy subbands
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.
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