“Wobbling” Moon trending on Twitter

Twitter trending topic

This NASA press release has received mainstream news attention.

The 18.6 year nodal cycle will generate higher tides that will exaggerate sea-level rise due to climate change.

Yahoo news item:

https://news.yahoo.com/lunar-orbit-apos-wobble-apos-173042717.html

So this is more-or-less a known behavior, but hopefully it raises awareness to the other work relating lunar forcing to ENSO, QBO, and the Chandler wobble.

Cited paper

Thompson, P.R., Widlansky, M.J., Hamlington, B.D. et al. Rapid increases and extreme months in projections of United States high-tide flooding. Nat. Clim. Chang. 11, 584–590 (2021). https://doi.org/10.1038/s41558-021-01077-8

Forced Natural Responses to LTE Solution

In Chapter 12 of the book, we describe in detail the solution to Laplace’s Tidal Equations (LTE), which were introduced in Chapter 11.  Like the solution to the linear wave equation, where there are even (cosine) and odd (sine) natural responses, there are also  even and odd responses for nonlinear wave equations such as the Mathieu equation, where the natural response solutions are identified as MathieuC and MathieuS.  So we find that in general the mix of even and odd solutions for any modeled problem is governed by the initial conditions of the behavior along with any continuing forcing. We will describe how that applies to the LTE system next:

Continue reading

Long-Period Tides

In Chapter 12 of the book, we provide a short introduction to ocean tidal analysis. This has an important connection to our model of ENSO (in the same chapter), as the same lunisolar gravitational forcing factors generate the driving stimulus to both tidal and ENSO behaviors. Noting that a recent paper [1] analyzing the so-called long-period tides (i.e. annual, monthly, fortnightly, weekly) in the Drake Passage provides a quantitative spectral decomposition of the tidal factors, it is interesting to revisit our ENSO analysis in the conventional ocean tidal context …


Woodworth and Hibbert [1] use selective bottom pressure recorder (BPR) measurements to extract the tidal factors. Below we reproduce the power spectrum and tidal model fit of the data from their paper.

Continue reading