> "I wrote Ansatz because the 2.4 Period Appears to me to be a lot for having those rather long strictly 2 year periods before a "flip" of phase."

That's a property of discrete periodic signals. A model of seasonally modulated tidal periods puts an emphasis at the same time each year. As the tidal signal will either constructively or destructively interfere at a specific time, it will look like the cycles will maintain a set period until the lunar periods make it go out-of-phase and therefore "flip" the sign of the interference. A model of analog cycles that reproduces the discrete cycles will generate an *apparent* 2.37 year period, along with the associated higher frequency harmonics to create this particular erratic yet periodic discrete signal. That's just how Fourier series work.

Here is another fit, where I modeled a very sharp seasonal modulation, and then smoothed it with an damped exponential. Again the *acceleration* of QBO defined according to Laplace's tidal equations matches most of the observed delta spikes.

![qbop](http://imageshack.com/a/img923/7199/zqEfww.png)

That is using only one lunar factor, due to the draconic/nodal tide. Adding the other tidal factors will improve this fit even more.

To get back to the QBO *velocity*, all we need to do is integrate this waveform. And this will naturally generate a square-wave like oscillation reminiscent of QBO, because a square-wave will generate +/- delta functions upon differentiation, spaced just as the acceleration waveform shows!

Now, the natural question is: Can the seasonal modulation be this sharp? Certainly. If one looks at a histogram of tropical storms, it has a very narrow distribution, sharply centered on September 10. The width of this peak fits within a single 27 day tidal cycle!

![storm](http://imageshack.com/a/img921/3905/QnqHEU.gif)

I don't know why it's this sharp but that's what the historical data shows.

Another [recent paper](http://contextearth.com/kramer2016/) shows the same sharp anomalies in atmospheric gravity waves over the city of Prague

![gw](http://imageshack.com/a/img922/1163/QwNzzC.png)

> Kramer, Ricarda, Sabine Wüst, and Michael Bittner. "Investigation of gravity wave activity based on operational radiosonde data from 13 years (1997-2009): Climatology and possible induced variability." Journal of Atmospheric and Solar-Terrestrial Physics 140 (2016): 23-33.

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Putting this in some perspective, here are a couple of take-away bullets:

# QBO

- The QBO is arguably the most fundamental global behavior in atmospheric sciences.
- Yet, the *consensus* explanation requires [several paragraphs](http://www.goes-r.gov/users/comet/tropical/textbook_2nd_edition/print_4.htm#page_2.2.0), a [scaled lab model](http://www.goes-r.gov/users/comet/tropical/textbook_2nd_edition/print_4.htm#ch4r159), and numerical simulation to demonstrate.

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# Ocean Tides

- The ocean tide is a fundamental behavior in geophysics.
- An explanation takes a sentence and knowledge of the lunar and solar orbit.

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So what's wrong with this picture? Why is the consensus theory for tides so intuitively simple, yet the QBO so horribly complex?

I think the answer is that the AGW denier Richard Lindzen fell well short in setting up a foundational theory for QBO. The actually model is likely much simpler to explain and to mathematically express than we have been lead to believe. That shouldn't be surprising if one finds out how many times Lindzen's theories have been debunked over the years. I hate to say this but Lindzen may give astronomer Thomas Gold a run for his money in terms of failed theories.

Updated my blog [here](http://contextearth.com/2016/08/23/qbo-model-final-stretch/) as well.