This is a followup to the QBOM part 2 post. I showed the machine learning (Eureqa) chart of Figure 1 earlier. The ML exercise mapped the QBOM time series from 1953 to the present time in terms of a set of sinusoidal factors.

Fig. 1: The machine learning fit. The highest complexity solution is shown below.

In the previous post, I focused on the two primary sinusoidal factors and how close they match the aliased Draconic and Synodic (or Tropical as 13 Tropical months = 12 Synodic months) lunar month cycles. The table is reproduced below :

strength  aliased freq   period      in days          actual        % error
78         2.66341033   2.359075219  27.20894362  27.212=draconic  0.011
35         2.29753386   2.734751989  29.53743558  29.531=synodic  -0.021
35         2.29753386   2.734751989  27.32677375  27.322=tropical -0.019

There are a couple more sinusoidal factors involved in the machine learning fit that are not aliased:

strength   frequency    in days       candidate                       % error
30         77.8811187   27.26730124   27.2669=avg(draconic+tropical)  0.0013
26         72.1900786   31.78927972   31.8119=lunar evection cycle   -0.07

These are as well very close to predicted values, if that is what the machine learning is trying to match to. So the temptation is to unalias all the sinusoidal factors and see how well it matches to the harmonic beating of orbital parameters.

This is simple enough to do with a spreadsheet and so we take the solution in Figure 1 and add 13×2π to the radial frequency where it is aliased, leaving the unaliased factors alone. This is shown with a fine sub-monthly resolution in Figure 2.

Fig 2: QBO Forcing unaliased from 1950 to 2000. The long-term modulation is ~17 years.

Richard Ray has constructed a mean square potential over the globe for each day of 1900–1940 for diurnal (m=1) tides [1] shown in Figure 3.

Fig 3: Ray’s tidal amplitude calculation for 1900 to 1940.  With an inset to the left showing finer resolution.

I tried to duplicate this chart by simply squaring the results of Figure 2 and back-extrapolating and sliding the time scale from 1900 to 1940. The result is shown in Figure 4 below.

Fig. 4: The QBO forcing model extrapolated back to 1900 based on the 1953 to 2013 fitting region.

The qualitative agreement between Figure 3 and Figure 4 is striking.  The fact that the high resolution inset does not match in amplitude is less important than the fact that it shows the correct number of peaks.

Thinking this through, the chain of causality inferencing leading from the raw QBO data, to a fitted aliased model, and then to this completely out-of-band extrapolated chart — which shows a remarkable likeness to the calculated tidal amplitude — is more than parsimonious.  It is in fact highly plausible that the QBO oscillations are in fact an aliased version of the familiar ocean tides, caused by the same lunar-solar forcing terms.

According to the cited paper, Richard Ray (of NASA Goddard) does not advocate a strong relationship between climate variability and lunar-solar forces.   He claims that the jury is still out with regards to agreement with the temperature data. (With the CSALT model, I found some agreement via multiple regression here)

Interesting however that the folks at NASA JPL have a different opinion, and one that strongly suggests it is worth pursuing this connection for future research funding. I was able to uncover an internal proposal that Claire Perigaud of JPL wrote concerning a possible collaboration with a French science lab [2]. Read the proposal in detail and you can see the same thought process elaborated here with consideration of aliasing and evidence of strong tidal torque forces operating on climate measures.

“As tides create a strong torque between the bottom of the ocean and its surface, we now think that QSCAT may detect the energy of barotropic tidal currents in the surface currents. It is emphasized by the satellite aliasing due to sun-synchronicity. The energy of tidal currents is proportional to (1/r)^6, where r is the distance of the Earth to the Sun or Moon. The energy of the currents triggered by Lunar tides is ~5 times bigger than that of Solar tides. QuikSCAT alias solar tides permanently and the main diurnal tide K1 into annual.”

(The K1 tide is aliased into a 7.46 year period due to its close proximity to a 24 hour cycle (23.93 hours)).   It is also fascinating reading when Perigaud claims that many of the climate measures introduce contamination and errors when they misguidedly try to subtract the effect of tides.

“But the aliasing is not the only source of uncertainty in monitoring climate from altimetry. Even in a pure hydrodynamic model, one has to take account of the incommensurability of the Lunar motions with the apparent motion of the Sun which makes the number of harmonic constituents infinite. So the coefficients are actually not pure harmonics, they are “packets” of energy around the individual harmonics in the “Darwin spectrum”. These packets were the source of contamination in Fig 5.”

Like I have found with ENSO and QBO here, the connection of lunar forcing with these cyclic phenomena is an idea that needs lots of further consideration.

References

[1] R. D. Ray, “Decadal climate variability: Is there a tidal connection?,” Journal of climate, vol. 20, no. 14, pp. 3542–3560, 2007.  PDF