Get a load of this detail:
The first chart above is a model of the QBO that uses the same principal lunar potential frequencies applied in tidal harmonic analysis, but aliased to one year boundaries. Note the richness in the detail of the QBO that the model is matching. The key here is not to filter the QBO data at all — much of the sub-year detail is captured by the higher harmonics of the one-year aliased fundamental.
The second is a back extrapolation, which shows the 18.6 year beat frequency in the lunar nodes.
Richard Ray of NASA Goddard published the following table of rotation rate coefficients last year. What commodity tide matching algorithms do is pick the strongest gravitational coefficients from the table to get a good first-order match to measured tidal gauge data. They apparently don’t blink an eye over what looks like complexity in a model fit. All they have to claim is that (1) this is the known physics of the orbit of the moon wrt the earth and the earth/moon wrt the sun and (2) the rest is essentially fill-in-the-blanks on what the magnitude of the individual factors are. So I follow their basic recipe and apply a multiple linear regression of the strongest factors ( ) to get the fit above.
This is an interim result, as I am not sure where the signal in the QBO stops and the underlying noise (measuring? statistical sampling? random?) in the data takes over. I have a feeling that some further refinement will get the model even closer to the data, since it locks in so closely after just a few aliased lunar cycles are included in the fit.
Frustratingly, I have no idea why this kind of analysis was not performed over the last few decades in which this data has been available. Remember that Richard Lindzen has been studying the QBO for over 50 years, and he even said this in 1974 — “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.”
Nice that he wrote this, as any critical response to these new findings really have to be prefaced with Lindzen’s own words. Blame it all on him if this mechanism sounds too outlandish.
This is a longer passage by Lindzen:
It may be that Lindzen never found this direct connection between lunar tidal gravitation effects and the QBO because he thought it was too weak. He may also never have thought about the impact of physical aliasing, which is second nature and routine to the engineering side of the sciences. Lindzen’s papers are filled with impressive looking sets f partial differential equations, but that is irrelevant if he is unable to come up with a simple first-order physics explanation for an underlying mechanism — like what I am doing here.
On the other hand, stalwart climate scientists such as Kevin Trenberth have always thought there is something more significant to the QBO. In this paper , Trenberth is discussing the link of stratospheric QBO to the tropospheric climate .
The paper further discusses the concept of aliasing and periodic elements in the data. This was published in 1980 but Trenberth’s ideas were not followed through by others, as far as I can trace the citation trail.
If that isn’t enough, the model of ENSO that I have been working on uses these same factors relating to changes in the angular momentum of the earth’s rotation, but weighted to longer periods as the natural response of the ocean damps out faster cycles. Trenberth, with his link of QBO to the tropospheric climate hinted at a periodic connection and I think the lunar/angular momentum idea will become the core mechanism behind ENSO forcing.
The lesson learned is that one has to know who to trust. Do you trust someone like Lindzen, who is a AGW skeptic forced to retract statements and been known to produce ideas such as the debunked Iris theory of cloud feedback? Or do you trust a careful scientist such as Kevin Trenberth to point you in a good direction? This is a tricky landscape to navigate unless you understand the agendas of the scientists involved. Personally, I do not trust a contrarian such as Lindzen — and the science may be agreeing with that assessment.
 K. F. Trenberth, “Atmospheric quasi-biennial oscillations,” Monthly Weather Review, vol. 108, no. 9, pp. 1370–1377, 1980. http://www.gps.caltech.edu/~kl/research/reading/Trenberth_MWR_1980.pdf
9 thoughts on “More refined fit of QBO”
This is really cool, as I take the second derivative of the QBO data and then fit the set of aliased lunar tidal cycles via multiple linear regression. Taking a derivative adds lots of noise to the data, so taking another derivative beyond that just multiplies the noise. Yet the intricate detail that is retained in the model fit is striking.
Why take the second derivative? Because that enables a better match to the wave equation without having to do an integration. This model then becomes very close to the forced response solution to the wave equation of atmospheric winds.
Regarding the semi-diurnal vs. diurnal, one point Ray makes in his paper is that the diurnal tidal potential peaks at latitudes +-45°, while the semi-diurnals peak at the equator. SInce the QBO is an equatorial phenomenon, there may be a mechanism that nulls out the diurnals, e.g., that the tide is forcing a uniquely equatorial phenomenon such as Rossby waves or Kelvin waves within the atmosphere.
Keith, I agree that it likely has something to do with the relative latitudinal strength of the effect.
I had been suggesting that the Anomalous lunar tide has much less an effect, based on the weakness of the 3.918 year aliased period. But I started looking at the complementary -2*pi folded period, which is at -1.343 years, and that one is relatively strong! (the negative sign on the folded period is a consequence of subtracting 2*pi from 2*pi/3.918)
The Draconic (nodal) lunar tide is still the strongest, and it is strong enough that it shows power at both +/- 2*pi side-lobed aliased periods. In other words, the aliased periods corresponding to frequencies 2*pi/2.37+2*pi and 2*pi/2.37-2*pi.
Doing this step of looking at the near-by harmonics is what is starting to pull out the most amazingly intricate detail. And that detail seems to match to the data !
This is a representative table of the forcing factors that go into the prior figures. One for f(t) and one for f ” (t). The latter is more sensitive to the higher forcing frequencies, as the fine sub-yearly structure is expose on taking the second derivative. The main factor again is the Draconic or Nodal aliased lunar month forcing. The only questionable factor is the 2.96 year period, which I haven’t been able to identify from the known lunar tidal factors but is possibly related to a spin-orbit coupling perturbation in the moon’s rotation, which I have seen cited as 2.9 years. At this stage 2.9 vs 2.96 is actually a significant difference. Yet, this unknown 2.96 factor is only the 10th strongest factor and doesn’t actually make a big difference in the overall fit.
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The following is a rant by an insane person from Australia. I don’t know why so many come from down under.
here telescope: The Warmist only weapon: Stefan Boltzmann’s crappy experiment 160y ago: heating CO2 in a tube is not same as warmed CO2 in the atmosphere- which goes instantly up, when warmed, to cool down! Even the cavemen knew that; reason they invented the chimney!!! In the tube/ sealed chamber, warmed CO2 cannot expend, but keeps warming up when heated, AND CREATING IT’S OWN PRESSURE – on the other hand: in the air, as soon as CO2 warms up-> INSTANTLY goes UP, where is thinner air and much colder, to release the heat!!! Comparing CO2 warming in the sealed tube AND: free CO2 in the air, is same as comparing a bird on the branch of the tree, with a bird in the pressure cooker. That’s what the 30000 criminally oriented ‘’questionable scientist in what fields’’ are trying to con the public, for fleecing the Urban Sheep! And for Marxist /Bolsheviks model oppression! #2: Methane & carbon dioxide (CO2&CH4) are the new western Marxist Hammer and Sickle. P.s. the 160y old Stefan Boltzmann’s law / experiment was not mentioned ones, in the 60’s-70’s! Because same shonks at that time were promoting; because of CO2 dimming effect, will be Ice Age by year 2000.
More gibberish by an insane person from Australia.
here telescope: ICE FREE POLAR CAPS CRAP, MISLEADING: on the Polar caps the temp is minus -75C (-103F); for both polar caps to melt, the planet’s temp needs to warm up by 76C. cool – if the planet warmed by 76C and add another 37C (98F)which is the temperature today in the tropics and subtropics 76 + 37 = 113C which is (235,8F). 113C is 13C above the water BOILING point (23,8F above water boiling point) From bacteria, trees, grass, animals and birds; all of them have water in their body = everything would have being cooked and sterilized in less than 10 minutes in the tropics and subtropics!!! Do you believe that the planet got sterilized?! ”Pagan beliefs” which are the ”Skeptic’s” gospel AND the Warmist used those same pagan beliefs, to create their LIE that is going to be warmer planet in 100 years is 100% WRONG! On 70C everything gets Pasteurized / killed, dead, kaput in 10 minutes, 113C is another 43C on top of that! In US, Europe where the propaganda is created – say that polar ice will melt again… well, if in US &Europe get warmer only by 8C above water boiling point… make an experiment: deep your hand in a pot of boiling water for 20 minutes, AND: pretend that outside the pot is 8C warmer than in the pot’’ I bet on that temp, you are not going to worry much about the polar bears and Bangladesh; because Bangladesh would have being 10C above water boiling point. Q: are university books and ”peer reviewed papers” correct, or me?! They were coming up with any crap in the past, to create themselves a profession -not being scrutinized.
They say if you give a million monkeys a million typewriters and let them go at it for a million years they’d produce the complete works of Shakespeare. Due to budget cuts we tried the experiment with 12 monkeys, 8 typewriters, a xylophone, two pounds of hashish, and recorded everything they produced over a 3-day weekend. We randomly post the results around the web under the pseudonym stefanthedenier.
What was that other guy’s name from Oz? yes, Girma Orssengo, PhD
For a while there, Girma was non-stop posting gibberish. I can name a lot more from Oz who seem to enjoy doing that.