QBO Disruption?

"One of the earth’s most regular climate cycles is disrupted" issued recently by the UK Met office

Plus all these recent papers:

Newman, P. A., L. Coy, S. Pawson, and L. R. Lait (2016), The anomalous change in the QBO in 2015–2016, Geophys. Res. Lett., 43, 8791–8797, doi:10.1002/2016GL070373.

Dunkerton, T. J. (2016), The Quasi-Biennial Oscillation of 2015-16: Hiccup or Death Spiral?, Geophys. Res. Lett., 43, doi:10.1002/2016GL070921.

An unexpected disruption of the atmospheric quasi-biennial oscillation, Scott M. Osprey, Neal Butchart, Jeff R. Knight, Adam A. Scaife, Kevin Hamilton, James A. Anstey, Verena Schenzinger, Chunxi Zhang, Science, 08 Sep 2016, DOI: 10.1126/science.aah4156

Do strong warm ENSO events control the phase of the stratospheric QBO?, Geophysical Research Letters, Sep 2016, Bo Christiansen, Shuting Yang, Marianne S. Madsen, DOI: 10.1002/2016GL070751

At RealClimate.org someone named Nemesis asked:

What might the implications of a disrupted QBO be? Any idea?

Concerning the QBO disruption that Nemesis mentions above. Does anybody really understand the QBO to begin with? The original theory was developed by the contrarian Richard Lindzen and it really is a limited model if you dig into it. For example, he never could derive the rather obvious period (28 months) of the QBO.

Years ago (circa 1998) the observation was about the "continuing difficulties in obtaining a realistic QBO" yet you continue to find references to "obtaining realistic QBOs"


Get a solid theory for QBO in place and only then can you start to reason about anomalies and disruptions that occur. IMO shouldn't make assertions regarding the source of the latest disruption unless we can agree on the nominal QBO behavior.

Compact QBO Derivation

I created a QBO page that is a concise derivation of the theory behind the oscillations:


Four key observations allow this derivation to work

  1. Coriolis effect cancels at the equator and use a small angle (in latitude) approximation to capture any differential effect.
  2. Identification of wind acceleration and not wind speed as the measure of QBO.
  3. Associating a latitudinal displacement with a tidal elevation via a partial derivative expansion to eliminate an otherwise indeterminate parameter.
  4. Applying a seasonal aliasing to the lunar tractive forces which ends up perfectly matching the observed QBO period.

These are obscure premises but all are necessary to derive the equations and match to the observations.

This model should have been derived long ago .... that's what has me stumped. Years ago I spent hours working on transport equations for semiconductor devices so have a good feel for how to handle these kinds of DiffEq's. You literally had to do this otherwise you would never develop the intuition on how a transistor or some other device works. The QBO for some reason reminds me quite a bit of solving the Hall effect. And of course it has geometric resemblance to the physics behind an electric motor or generator. Maybe I am just using a different lens in solving these kinds of problems.

ENSO Model Final Stretch (maybe)

I recently posted a bog article called QBO Model Final Stretch. The idea with that post was to give an indication that the physics and analytical math model explaining the behavior of the QBO was in decent shape. I would like to do the same thing with the ENSO model but retain the context of the QBO model.  Understanding the QBO was a boon to making progress with ENSO as it provided an excellent training ground for time-series analysis and also provided some insight into the underlying forcing functions.  In the literature, there is a clear indication that ENSO and QBO are somehow related, but the causality chain remains unclear.

Continue reading

Geophysical Fluid Dynamics first, and then CFD

A recent perfunctorily-peer-reviewed paper in the Proceedings of the Royal Society

Vallis GK. 2016 "Geophysical fluid dynamics: whence, whither and why?" Proc. R. Soc. A 472: 20160140. http://dx.doi.org/10.1098/rspa.2016.0140 and PDF

explains the distinction between analytical physics models of the climate and purely numerical models — i.e. the field known as computational fluid dynamics (CFD). The lack of an intense review cycle makes for a very readable paper, with a refreshing conversational writing style that the editors apparently allowed. The gist of the piece is that the formulation of analytically-based Geophysical Fluid Dynamics (GFD) models of the atmosphere & ocean are essential to making sure that the CFD's are on the right track.

Continue reading

QBO Model Final Stretch

I had this loose thread in the last QBO post:

One caveat in this derivation is that the QBO may actually be the v(t) term - the horizontal longitudinal velocity of the fluid, the wind in other words - which can be derived from the above by applying the solution to Laplace's third tidal equation in simplified form above.

Following up on this gap, I extended the derivation to formally evaluate the velocity.

So from:

\zeta(t) = \sin( \sqrt{A} \sum_{i=1}^{i=N} k_i \sin(\omega_i t) + \theta_0 )

and the third simplified Laplace equation

\frac {\partial v}{\partial t} =-\frac {1}{a} \frac {\partial }{\partial \varphi } (g\zeta +U)

we can derive

\frac {\partial v}{\partial t} = \cos( \sqrt{A} \sum_{i=1}^{i=N} k_i \sin(\omega_i t) + \theta_0 )

So the acceleration of wind, not the velocity, is what obeys the Sturm-Liouville equation. A derivative preserves the periods of the Fourier components, but not the amplitudes, so what we see is a differently shaped envelope for QBO —  i.e. one that is more spiky due to the time derivative applied.

A single lunar Draconic tidal term of \lambda_d=27.212 days multiplied by a yearly modulation sharply peaked at a specific season is enough to capture the QBO acceleration time-series:

\cos^N(2 \pi t) cos(\frac{2\pi}{\lambda_d} t)

The seasonal sharpness is controlled by the power N. This can be approximated as a Fourier series with the same periods found previously: 2.37 years, 0.7 years, 0.41 years, etc.

Fig. 1: The sesonally modulated lunar cycle can be approximated by a sum of Fourier components

This gives the following fit to the QBO acceleration with a correlation coefficient of 0.35 (good, considering the data waveform has no filtering applied and very little optimization went into the fit):

Fig 2:  Modulation of Draconic lunar with seasonal period captures the acceleration of the QBO wind.

The excellent model fit makes sense as the acceleration of wind is simply a F=ma response to a gravitational forcing.

The bottom-line is that this acceleration version of the QBO is much more spiky than the more smoothly oscillating conventional wind speed description of QBO. Yet this spikiness is more closely representative of the seasonally modulated lunar forcing. So what was a caveat in the previous post is now a fundamental revelation which provides an excellent modeling path going forward.

Furthermore, a simple time integration of the acceleration model will recover the wind speed version of the QBO. And fortunately this will retain the same Fourier components that we used earlier to model the QBO, so a self-consistency with the prior model of the QBO is retained.

That's how a solution should ideally converge — unless one has all the pieces simultaneously, incremental changes to an initial model will provide the process to a solution.

Incidentally, I submitted this research to the AGU meeting for this fall and will find out if the abstract gets accepted in October.

8/28/2016: Additional information pulled from an Azimuth Project forum comment

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:


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


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.


This image has been resized to fit in the page. Click to enlarge.

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.