Deriving the QBO from Laplace's tidal equations, it becomes apparent that the *acceleration* of wind and not the wind *speed* is the fundamental measure to characterize. With that premise, things seem to fall into place much more naturally.

First, multiply the nodal/draconic frequency by a sharply peaked yearly modulation and we get the following as a fit for QBO acceleration:

![qboPrime](http://imageshack.com/a/img922/5399/n5gGWi.png)

The fitting region is 1970 to 1982, and the rest is extrapolated. The correlation coefficient is not extremely high but note the amount of fine detail that gets exposed by the model.

To get back the wind speed QBO, the curves are integrated

![qbo](http://imageshack.com/a/img924/741/KJVfpb.png)

Again the model fitting is only conducted on the interval from 1970 to 1982. Outside of that interval the model doesn't track every peak but enough of the fine detail is captured that it's obvious that the model has predictive power.

The supporting experiment involves running a symbolic regression machine learning trial on this same interval.

![eureqa](http://imageshack.com/a/img922/5362/m1ooXj.png)

Amazingly, the ML finds all the same harmonics caused by multiplying the sharply peaked yearly signal (freq ~ 2π ) with the Draconic tide (aliased ~2.7 year). No other periods are detected.

![Eu2](http://imageshack.com/a/img924/2507/QrnMZH.png)

First, multiply the nodal/draconic frequency by a sharply peaked yearly modulation and we get the following as a fit for QBO acceleration:

![qboPrime](http://imageshack.com/a/img922/5399/n5gGWi.png)

The fitting region is 1970 to 1982, and the rest is extrapolated. The correlation coefficient is not extremely high but note the amount of fine detail that gets exposed by the model.

To get back the wind speed QBO, the curves are integrated

![qbo](http://imageshack.com/a/img924/741/KJVfpb.png)

Again the model fitting is only conducted on the interval from 1970 to 1982. Outside of that interval the model doesn't track every peak but enough of the fine detail is captured that it's obvious that the model has predictive power.

The supporting experiment involves running a symbolic regression machine learning trial on this same interval.

![eureqa](http://imageshack.com/a/img922/5362/m1ooXj.png)

Amazingly, the ML finds all the same harmonics caused by multiplying the sharply peaked yearly signal (freq ~ 2π ) with the Draconic tide (aliased ~2.7 year). No other periods are detected.

![Eu2](http://imageshack.com/a/img924/2507/QrnMZH.png)