QBO Model Sensitivity

I have been concentrating on modeling the quasi-biennial oscillation (QBO) recently because the results I am getting are a sure bet in my opinion, and the ENSO model will mature and follow in due time.

There are no adjustable parameters in my QBO model, as it relies completely on the known lunar tidal periods. So it's actually conceptually difficult to do a real sensitivity analysis. Those are set in stone, so moving them from their nominal values is artificially changing the physical foundation for the model. Still it would be useful to consider how to move the periods in unison away from the nominal values, so that the artificiality is minimized.

One clever way of doing this is to change a common factor used in the aliasing calculation for each of these periods. Obviously the best candidate is the solar year. To get the correct aliasing with respect to each of the periods, the value of the year in days must be set ( see this article ). And because of the aliased signal's period sensitivity to the mixing frequency, any change in the year value will magnify the error in a fit. So if the theoretically predicted aliased lunar months form an optimal fit, then any change in the solar year away from the nominal value will degrade this fit. And it should degrade it rapidly, because of the sensitivity of the aliasing calculation.

In the following chart, the nominal value for the solar year is 365.242 days, and the x-axis shows what happens when the value is modified away from this value, based on the multiple linear regression fit. The upper-right inset is a magnified region about 365 days, and the yellow highlighting points to the most highly correlated regions.


The best fit is 365.23 and is close enough to 365.242 in my book. Both are also right on the plateau of maximum correlation, indicating that this may be within the sampling error.

After some prodding on my part, I got this tweet from a climate science gatekeeper

It's straightforward to argue that Richard Lindzen's model [1] is wrong by an exclusionary principle. If Lindzen neglected to include the gravitational forcing due to the moon's orbit, yet an absolutely trivial model shows a nearly unity correlation with a precise alignment, then Lindzen must be over-fitting. So by excluding lunar forcing, what Lindzen came up with is not the real physics but more likely a biased fit, based on the unlimited number of adjustable factors he could draw from. I would suggest that his "tour de force" paper will need to be completely reconsidered from scratch.

So the most plausible and parsimonious explanation is a model not much different than that used to predict the ocean's tides.

From the NASA site:

"The Ocean Motion website provides resources developed for inquiring minds both in and outside the classroom, for reading level grades 9-12 (Flesch-Kincaid)."
"Observing the changing water levels caused by astronomical tides is relatively simple and has long been important for major ports."

Although simple, this is real science -- no free parameters and nearly perfect agreement with the empirical data.

[1]R. S. Lindzen and J. R. Holton, “A theory of the quasi-biennial oscillation,” Journal of the Atmospheric Sciences, vol. 25, no. 6, pp. 1095–1107, 1968.

Project Loon and QBO

Missed this recent development related to QBO. Google is planning on deploying balloons to the stratosphere which carry transceivers capable of improving global Internet capability.

This is the stratosphere, so remember that the Quasi-Biennial Oscillation (QBO) of winds will likely play an important role in how the balloons get carried aloft around the earth. Google scientists and engineers might want to consider in more detail how the winds alternate in east-west directions, as their image below shows.

Based on a detailed modeling of previous wind data collected by similar high-altitude deployed balloons, the origin of the QBO is becoming less mysterious. From the data collected from these so-called radiosonde measurements, the origin of this alternation is not according to that proposed by the AGW-denier scientist Richard Lindzen, but via the periodic gravitational pull of the moon, aliased by a seasonal modulation. This is described in a short two-page paper worked out both on this site, and at the collaborative Azimuth Project forum.

The model's ability in capturing the dynamics of QBO is amazing:

Fig 1: Modeling the second derivative of QBO to lunar tidal periods allows a highly detailed predictive capability.  Training the data on a known set of lunar tidal periods (red interval), forecasts the "out-of-bad" data remarkably well !

This modeling is actually quite trivial and as straightforward as modeling the cyclic behavior of ocean tides, but one has to understand how aliasing works.  That is what  Lindzen apparently missed during his 50 years worth of hapless research efforts.

Besides the importance for this Google project, the QBO has lots of relevance for climate, including predicting storm activity and occurrence of El Ninos.

More on Project Loon

Project Loon balloon
Loon for All – Project Loon

How Loon Works – Project Loon

Project Loon - Wikipedia


Why is the QBO important?

After making a breakthrough on modeling the Quasi-Biennial Oscillation of atmospheric winds (QBO) and simultaneously debunking the fearsome AGW skeptic Richard Lindzen's original theory for QBO, it might be wise to take a step back and note the potential significance of having a highly predictive model.

From this QBO site

Why the QBO is important?

  1. The phase of the QBO affects hurricanes in the Atlantic and is widely used as a prognostic in hurricane forecasts.
    Increased hurricane activity occurs for westerly (or positive) zonal wind anomalies; reduced hurricane activity for easterly or negative zonal wind anomalies.
  2. The QBO along with sea surface temperatures and El Niño Southern Oscillation are thought to affect the monsoon.
  3. Tropical cyclone frequency in the northwest Pacific increases during the westerly phase of the QBO. Activity in the southwest Indian basin, however, increases with the easterly phase of the QBO.
  4. Major winter stratospheric warmings preferentially occur during the easterly phase of the QBO, Holton and Tan (1980).
  5. Predictions of ENSO use the expected wind anomalies at 30mb and 50mb to forecast the strength and timing of the event.
  6. The QBO is thought to affect the Sahel rainfall pattern and is used in forecasts for the region.
  7. The decay of aerosol loading following volcanic eruptions such as El Chichon and Pinatubo depends on the phase of the QBO.

And that site does not even list the connection between QBO and El Nino that has been observed [1], and definitely by my own eyes as well, and not to forget Eureqa's machine learning eyes.

That last bit is intriguing, a I am still making progress on ENSO modeling, with this QBO effort providing a foundation for lots of ideas on how to go forward. The connection between QBO, lunar forcing, and ENSO is much too compelling to think otherwise. As far as AGW, I will continue to report on what I can discover from models of the data. This is important when you realize that Lindzen had over 50 years to contribute to the field, and essentially left with the sad fact of contributing nothing, and perhaps even stalling progress in the field of atmospheric sciences for a generation.

[1] Liess, Stefan, and Marvin A. Geller. "On the relationship between QBO and distribution of tropical deep convection." Journal of Geophysical Research: Atmospheres (1984–2012) 117.D3 (2012).

Pulling a signal out of the noise

This is an older chart I made that was part of a thread at the Azimuth Forum.

If you were to take a cursory look at the unfiltered signals on the right, you would never imagine that the correlation on the left would be that good. The ENSO signal is the difference between the Tahiti and Darwin signals, and that correlates with the tidal gauge in Sydney, Australia.  The key is to apply the right kind of filtering to the signals; in this case removing the noisy sub-year fluctuations.


Pukite's Model of the Quasi-Biennial Oscillation

I decided to name this model after myself because there are no free parameters and so is locked into place. There's nowhere to hide if it is invalidated, but it is so concise and precise that it's likely worth the risk of attaching my name to it.

The idea is as described earlier : Find the lunar forcing on the earth and then alias the forcing to a seasonal (yearly) period. This becomes the forcing for the QBO. The rationale is that the faster lunar cycles will not cause the stratospheric winds to change direction, but if these cycles are provoked with a seasonal peak in energy, then a longer-term multiyear period will emerge. This is a well-known mechanism that occurs in many different natural phenomena.

There are two steps to the model. (1) Determine the lunar gravitational potential as a function of time, and (2) plot the potential in units of 1 month or 1 year. The last part is critical, as that emulates the aliasing required to remove the sub-monthly cycles in the lunar forcing.

If one then matches this plot against the QBO time-series, you will find a high correlation coefficient. If the lunar potential is tweaked away from its stationary set of parameters, the fit degrades rapidly. So it becomes essentially a binary match. If it didn't fit, then the lunar gravitational potential hypothesis would be invalidated. But since it does fit precisely, then it remains a highly plausible model.

Figure 1 shows the mean-square potential of the lunar gravitational pull, also known as the tidal generating potential (applied in the context of predicting tides). On the left, the scale is expanded.

Fig. 1 : Mean-square potential of the lunar gravitational pull (from [1]). On the left, the scale is expanded.

As background, I originally discovered the connection of QBO to the lunar potential via machine learning (Eureqa), see Figure 2.

Fig 2: The original connection from QBO to a tide generating potential was discovered by machine learning -- upper right, panel A. The fitted signal was unaliased, squared and shown to align in panel B. Panel C shows the details with the fully unaliased signal at a finer scale.

This fit worked remarkably well considering that it is very difficult to dig out the aliased periods. Letting the machine learning run for a day helped considerably.

Yet it is also useful to reverse the direction of the fitting process. Instead of deducing the model from a sinusoidal decomposition, let us estimate the tidal generating potential as shown in Figure 1 and described by Ray [1]. We then inductively proceed  forward and see how well it fits to the QBO time-series.

Fig 3 : Empirical fit to the tidal generating potential of Figure 1.

This empirical fit uses only three factors -- the lunar cycles corresponding to the Draconic month, the Anomalistic month, and the Tropical month. Those are known to a high precision, along with a value for the Tropical year. The composition of these factors is then squared to generate the empirical model of the potential.

If we lay the empirical model on top of Ray's diagram, it looks like Figure 4.

Fig 4 : Alignment of empirical model with Ray chart. Note the long-term 18.6 year (diurnal) beat period and the shorter 4.425 year (semidiurnal) beat period. Also a rapid bi-annual component.

On the expanded scale, the sub-monthly periods appear, as shown in Figure 5.

Fig 5 : Expanded scale showing the sub-monthly variations in the tidal generating potential.

These higher frequency components disappear when the alias is introduced.

I did not do a complete ephemeris-based empirical model for the tidal generating potential as Ray did, since the basic pattern is fairly easy to deduce from the three lunar cycles.

The final step is to un-square and then alias the tidal generating potential and compare to the QBO time-series. This is shown in Figure 6.

Fig 6: Fit of the unaliased tidal generating potential to the QBO

There is nothing at all complicated about the recipe for fitting the tidal generating potential to the QBO. It is a mechanical process since none of the lunar cycles parameters can be changed.

As a next step I will submit this finding to Physical Review Letters.  From what I have seen in the literature search, there is no consideration of applying a straightforward forcing of the lunar gravitational pull to model QBO.  It appears that most QBO models derive from what Richard Lindzen originally proposed some 40+ years ago -- but since many mainstream climate scientists do not consider Lindzen (an AGW denier) very trustworthy or even competent (e.g. a trail of retracted papers and debunked theories), it's likely that his original model was simply wrong, or at best, incomplete. What the new model does is provide a concise recipe and a highly plausible geophysical context for understanding the origin of QBO.

The further significance of all this is that the same lunar forcing that applies to QBO also likely applies to the phenomena of El Nino and modeling the ENSO time-series, see the ENSO sloshing paper and some more recent work.


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

QBO is a lunar-solar forced system

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.

Continue reading