Glenn Brier is on my list of essential climate science researchers. I am sure he has since retired but his status as both a fellow of the American Meteorological Society and a fellow of the American Statistical Association indicated he knew his stuff. One of his research topics was exploring periodicities in climate data. He was eminently qualified for this kind of analysis as his statistics background provided him with the knowledge and skill in being able to distinguish between stochastic versus deterministic behaviors.
One paper Brier co-authored in 1989 is an obscure gem in terms of understanding the determinism of El Nino and ENSO [1]. He essentially analyzed a 463-year historical chronology of strong El Nino events and was able to find significant periodicities of 6.75 and 14 years in the data.
This compares very well with what I have been able to decipher as the strongest ENSO periodicities (taken from the instrumental record since 1880) of 6.5 and 14 years.
As a bottom-line for the paper, Brier et al were claiming that there was significant determinism which extended backward in time from the more recent instrumental record. He referenced another article (by someone named Anita Baker-Blocker [2]) who essentially found the same periods (6.6 and 13.9 years) using only more recent instrumental data, but — from the title of her paper alone — asserted that this indicated non-determinism.
Yet, what Brier demonstrated was that of another 300+ years of historical data was able to reproduce the same strong periodicities as that of the recent instrumental record; and that there is a strong deterministic component to ENSO that is likely baked into the behavior and isn’t going away. I have also seen this with ENSO coral proxy data.
Further, based on the sloshing model I have developed for ENSO, the periods of 6.5 and 14 years match the predicted wobble frequencies of the Earth’s rotation. The former period is known from the Chandler wobble, and when the angular momentum is deconstructed, shown below in Figure 1, a clear period of 6.5 years is observed:
Fig. 1: Chandler wobble 6.5 year period in angular momentum variation
From Wang’s arguments in [3], the 14 year period is derived by considering that the Earth is actually a tri-axial system, shaped more like a pear (in contrast, the Chandler wobble alone is derived from a bi-axial apple-shaped spheroid), and that asymmetry introduces a longer cycle via the second ellipse, as shown in Figure 2 below.
Brier also has argued for a biennial modulation, which is vital to the sloshing model fit :
Fig 3: From H.H. Lamb, “Climate: Present, Past, and Future”, 1972 and 2013.
The result of applying the strong 6.5 year and 14 year cyclic factors to the biennial sloshing model is shown below. Incidentally, the 2.33 year cycle is incorporated into the 14 year group since it is a beat frequency result of a two-year cycle modulating a 14 year cycle.
Fig. 4: The sloshing model applied to a biennial-modulated transform of the ENSO data.
What puzzles me is why the Brier paper (and even the Baker-Blocker paper before it) has been largely ignored in subsequent research. I independently duplicated the 6.5 year and 14 year periods in the ENSO behavior before I stumbled across the Brier reference yesterday. I was actually concerned that no one else had observed that these were such strong factors, not realizing that Brier’s paper was essentially uncited.
It’s possible that the climate shift of 1980 and the subsequent temporary phase inversion of the biennial cycle threw everyone’s time-series analysis for a loop. That may have been enough of a negative finding to motivate ENSO scientists to focus on newer and more recent research and ignore the results of Brier (and Baker-Blocker).
References
[1] K. Hanson, G. W. Brier, and G. A. Maul, “Evidence of significant nonrandom behavior in the recurrence of strong El Niño between 1525 and 1988,” Geophysical Research Letters, vol. 16, no. 10, pp. 1181–1184, 1989.
[2] A. Baker-Blocker and S. Bouwer, “El Niño: Evidence for climatic nondeterminism?,” Archives for meteorology, geophysics, and bioclimatology, Series B, vol. 34, no. 1–2, pp. 65–73, 1984.
[3] Wang, Wen-Jun, W.-B. Shen, and H.-W. Zhang, “Verifications for Multiple Solutions of Triaxial Earth Rotation,” IERS Workshop on Conventions Bureau International des Poids et Mesures (BIPM), Sep. 2007.
Below is Brier’s paper (right click to enlarge)
K. Hanson, G. W. Brier, and G. A. Maul, “Evidence of significant nonrandom behavior in the recurrence of strong El Niño between 1525 and 1988,” Geophysical Research Letters, vol. 16, no. 10, pp. 1181–1184, 1989.
K. Hanson, G. W. Brier, and G. A. Maul, “Evidence of significant nonrandom behavior in the recurrence of strong El Niño between 1525 and 1988,” Geophysical Research Letters, vol. 16, no. 10, pp. 1181–1184, 1989.
GeoEnergy Math 
Glenn Brier also did early work on QBO, challenging the questionable model of Richard Lindzen. His pointing toward a seasonal forcing is important.
And that a periodic forcing could be involved/
In this paper, he also offered up the idea of applying a Mathieu equation formulation, which I have used on ENSO to great effect.
[1] G. W. Brier, “The quasi-biennial oscillation and feedback processes in the atmosphere-ocean-earth system,” Monthly Weather Review, vol. 106, no. 7, pp. 938–946, 1978.
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Many consider ENSO to be sensitive to initial conditions, following the ideas set forth by chaos theory and the outcome of a “butterfly flapping its wings” as an initial condition.
Most people don’t understand the distinction between initial conditions and boundary conditions. In fact boundary conditions can act much like a recurring set of initial conditions, where the boundary condition acts like a guide to synchronize a behavioral state over time. A good example of a boundary condition is the daily cycle and the seasonal cycle.
What causes the problem is that people immediately think a boundary condition can only have something to do with spatial dimensions, which is understandable since a boundary is typically considered a physical location.
A good example is the ocean tide, which is primarily set by boundary conditions. Tides will never go out of sync with the moon and the sun since they will forever nudge the response of the ocean to keep in sync with the defined orbit. However, they also behave following spatial boundary conditions, especially noticed in certain geophysical locations where the tides are most pronounced.
A huge instability such as a tsunami will have no impact on the tide, and it will readjust and keep going where it left off after the tsunami subsided.
Now think about how that applies to ENSO and QBO. Nothing about either of these two phenomena suggests that they are primarily driven by initial conditions. External forces are obviously maintaining a stationary behavior for each of them.
What is interesting is that there is a current flurry of media activity surrounding a measured perturbation of the QBO. There is speculation that this perturbation signals a change in the behavior of the QBO — some say possibly due to AGW or a strong ENSO effect. Now, all we have to do is watch the QBO in the next few years and find out whether is synchronizes back to the behavior it has exhibited over the last 60 years.
Of course no one really understands QBO, since it is based on a half-backed theory of Lindzen, but say that that it is stimulated by lunar tidal forces, it should re-align with that cycle within the next few years. That will demonstrate a solid boundary condition.
A forcing caused by a growing CO2 imbalance is also a boundary condition, just that this is a boundary condition that is not stable over time. That’s what makes it a bit more tricky.
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