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).