Forced versus Natural Response, not a secret

This is a concept that is beaten into the head of electrical engineers.

Engineers tend to assume the forced response first, as being pessimists they always assume the worst case.  For example: Why is that annoying 60 Hz hum coming out of that circuit?  hmmm .. probably because the AC power somehow leaked into the input and the hum resulted from the forced response of the internal transfer function?  Issue solved.

Physicists tend to look for a natural response first. Being optimists, a research physicist first and foremost wants to make a discovery. A natural response would tell us something interesting about the behavior … and perhaps a new physical law!  Look and See! The eigenvalues!   Often to them, the forced response is a nuisance that needs to be removed to observe the natural response.

But what happens when the forced response is actually the interesting physical behavior?

A prototypical example of a forced response is the phenomenon of cyclic ocean tides. The periods of tides, though complex in breadth, are merely a reflection of the orbital rates of the moon and sun.

Pictures of (left) high tide (right) low tide, linked from Science Buddies

Obviously the ocean has a natural response to a forcing stimulus, obeying some variation of the wave equation, but the overriding output directly links to the observed orbits. Even the second-order effects such as the 9-day tides are simply beats arising from nonlinear interactions of the fortnightly and monthly long period tides.  Everything from the semi-diurnal periods to the long-period monthly periods are forced responses to the gravitational tug of the lunisolar orbits.  Any resonant frequencies in the ocean’s natural response are over-ridden by the forced response.

And so it likely goes for the quasi-biennial oscillations (QBO) of the equatorial stratospheric winds, as these most definitely are a forced response to the inputs … in spite of what the current literature infers.

When I first observed the time-series behavior of the QBO, I automatically assumed a forced response as a possibility.  The oscillations appeared somewhat jittery, but the overall profile seemed consistent with a forced response.

As I demonstrated last year here, the seasonally aliased long-period luni-solar tides have the precise values necessary to map to the QBO periodicity. And this is across the board, as it applies well to the 70,50,40,30,20,15, & 10 hPa sets over the past 60+ years, see Figure 1 below:

Fig. 1 : Aliased long-period tidal fits to each of the QBO time-series since 1953.  Each profile uses the same set of sinusoidal tidal factors, only adjusted in amplitude and phase.

Having stated that, the most recent studies of modeling QBO still assert that the oscillations are some spontaneous or emergent result of the complex interactions within the atmosphere [1][2].  Although hard to definitively extract from the papers, the broad claim is that the period of the QBO is dependent on the magnitude of the forcing [2].  This is in conflict with the luni-solar forcing theory whereby the period is simply analogous to the idea of the tide going in and out (roughly that one direction of the QBO corresponding to a low tide, and the opposite direction to a high tide). Like the oceanic tides, that match is exact and invariant over any transformation.

If there is blame to be assigned to the wrong track that the consensus QBO model has taken, it rests on the shoulders of Richard Lindzen [3], and many of his colleagues specializing in atmospheric physics including Murry Salby, Judith Curry, Roy Spencer, John Christy, Roger Pielke Sr, and William M. Gray (all who curiously happen to be AGW skeptics also).

Interesting piece of self-serving fluff by Richard Lindzen from 1987 [4] recounting the history of his formulation of the theory behind QBO (abbreviated LH [1]).

Reading through it, you get the impression that Lindzen’s entire theory  is similar to a Rudyard Kipling “just-so story”.  Layer after layer of rationalization or explanation is added to the initial hypothesis until something works.  By working, the system starts oscillating.  He doesn’t say how the exact period comes about, but I guess that isn’t considered important after Lindzen declared an early victory in his historical account.

Yet there is some inspiration to be gained from the concluding paragraph, where Lindzen writes:

I guess that isn’t too far from what we are doing with the scientific research carried on behind the scenes of this blog. Apologies to Lindzen for stealing his final line, but its no longer a secret that the QBO is a forced response due to the luni-solar orbit. He even implied as much when he stated that “it is unlikely that lunar periods could be produced by anything other than the lunar potential.” See [5] and context below.

Gotcha Lindzen!

Q.E.D = QBO erat demonstrandum


[1] W. Yao and C. Jablonowski, “Spontaneous QBO‐like oscillations in an atmospheric model dynamical core,” Geophysical Research Letters, vol. 40, no. 14, pp. 3772–3776, 2013.

[2] J. A. Anstey, J. F. Scinocca, and M. Keller, “Simulating the QBO in an atmospheric general circulation model: sensitivity to resolved and parameterized forcing,” Journal of the Atmospheric Sciences, no. 2016, 2016.

[3] 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.

[4] R. S. Lindzen, “On the development of the theory of the QBO,” Bulletin of the American Meteorological Society, vol. 68, no. 4, pp. 329–337, 1987.

[5] Lindzen, Richard S., and Siu-Shung Hong. “Effects of mean winds and horizontal temperature gradients on solar and lunar semidiurnal tides in the atmosphere.” Journal of the Atmospheric Sciences 31.5 (1974): 1421-1446.

4 thoughts on “Forced versus Natural Response, not a secret

  1. If the moon can cause this:

    what else can it do?

    That’s the overriding question and one that can only be answered by observational data, since we don’t have a controlled experiment at our disposal. .

    Yet when the numbers match up so perfectly, the correlation has to be taken seriously.


  2. Here is another fit over all the QBO time-series, except it uses only data from 1955 to 1985 as the training interval (the yellow shaded region). The model after 1985 is a pure projection, which can be used to validate the goodness of the fit, thus reducing possible over-fitting errors.


  3. This paper by Mayr & Lee has an interesting slant at how seasonal modulation can occur.

    It is clear that a strong and temporally-narrow seasonal modulation against the lunar gravitational forcing is the driving stimulus behind the QBO. Yet actually “seeing” this effect is no easy task, and models such as Mayr’s are promising physical abstractions to start with.


  4. Pingback: Inferring forced response from QBO wave equation | context/Earth

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