Short Training Intervals for ENSO

Given the fact that very short training intervals will reveal the underlying fundamental frequencies of QBO, could we do the same for ENSO? Not nearly as short, but about 40 years is the interval required to uncover the fundamental frequencies. Again none of this is possible unless we make the assumption of a phase reversal for ENSO between the years 1980 and 1996.

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Solver vs Multiple Linear Regression for ENSO

In the previous ENSO post I referenced the Rajchenbach article on Faraday waves.

There is a telling assertion within that article:

"For instance, to the best of our knowledge, the dispersion relation (relating angular frequency ω and wavenumber k) of parametrically forced water waves has astonishingly not been explicitly established hitherto. Indeed, this relation is often improperly identified with that of free unforced surface waves, despite experimental evidence showing significant deviations"

What they are suggesting is that too much focus has been placed on natural resonances and the dispersion relationships within a free fluid volume. Whereas the forced response is clearly as important — if not more — and that the forcing will show through in the solution of the equations. I have been pursuing this strategy for a while, having started down the Mathieu equation right away and then eventually realizing the importance of the forced response, yet the Rajchenbach article is the first case that I have found made of what I always thought should be a rather obvious assumption. The fact that the peer-reviewers allowed the "astonishingly" adjective in the paper is what makes it telling. It's astonishing in the equivalent sense that Rajchenbach & Clamond are pointing out that a pendulum's motion will be impacted by a periodic push. In other words, astonishing in the sense that this premise should be obvious!

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Is ENSO predominantly tidal?

The model of ENSO is split into two groups of forcing factors, unified by a biennial modulation. The predominant factors have cycles of 6.4 and 14 years, which extends back through historical proxy data.  Other strong factors track the same lunar cycles that appear as QBO forcing factors.

What's somewhat interesting is that after a multiple linear regression, the optimal values are 6.476 and 13.98 years -- with the mean frequency of these two values at 8.852 years, which is very close to the anomalistic tidal long-period of 8.85 years.

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Modeling Red Noise versus ENSO

With respect to the ENSO model I have been thinking about ways of evaluating the statistical significance of the fit to the data. If we train on one 70 year interval and then test on the following 70 year interval, we get the interesting effect of finding a higher correlation coefficient on the test interval. The training interval is just below 0.85 while the test is above 0.86.


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

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ENSO model maps to LOD cycles

Elaborating on this comment attached to an LOD post,  noting this recent paper:

Shen, Wenbin, and Cunchao Peng. 2016. “Detection of Different-Time-Scale Signals in the Length of Day Variation Based on EEMD Analysis Technique.” Special Issue: Geodetic and Geophysical Observations and Applications and Implications 7 (3): 180–86.  doi:10.1016/j.geog.2016.05.002.

Because of the law of conservation of momentum sloshing can change the velocity of a container full of liquid, momentarily speeding it up or slowing it down as the liquid sloshes back and forth.  By the same token, suddenly slowing or speeding of that container can also cause the sloshing.   So there is a chicken and egg quality to the analysis of sloshing, making it difficult to ascertain the origin of the effect.

If ENSO is a manifestation of a liquid sloshing in a container and if the length-of-day (LOD) is a measurement of the angular momentum changes of the Earth's rotation, then it is perhaps useful to compare the fundamental time-varying signals in each measurement.

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ENSO Proxy Revisited

Although the historical coral proxy measurements are not high resolution (1 year resolution available), they can provide substantiation for models of the modern day instrumental record. This post is a revisit of a previous analysis of the Universal ENSO Proxy (UEP).

The interval from 1881 to 1950 of the ENSO data was used to train the DiffEq ENSO model. This gives a higher correlation coefficient (~0.85) on the test interval (from 1950 to 2014) than the training interval (1881-1950) as shown below:

Fig. 1: ENSO model fit over the modern instrumental record

Since ENSO data shows stationarity and coherence over the interval of 70 years, this fit was re-applied to the UEP data over 4 different ranges 1650-1720, 1720-1790, 1790-1860, and 1860-1930. High correlation coefficients were found for each of these intervals (> 0.70) and compared against fits to a red noise model shown below:

Fig 2: Proxy fits over various ranges as compared to a red noise model (added for clarification: essentially a synthetic data set to evaluate the ENSO model against). The significance is at least at 0.95 for each proxy interval.

Each of the ENSO fits lies within the 0.95 significance level, and only 1 out of 500 red noise simulations obtained a 0.8 correlation coefficient, which is what the 1720-1790 interval achieved.

Interval CC
1650-1720 0.772
1720-1790 0.807
1790-1860 0.710
1860-1930 0.763

The significance of having each of these intervals at least 0.95 is 1-(1-0.95)^4 if these are all independent. That is a small number less than about (1/20)^4 in likelihood.

The caveat is that the ENSO is also not likely to be coherent over intervals much greater than 70 years, as the shift around 1980 in phase for the model demonstrates.

This substatntiates the finding of Hanson, Brier, Maul [1] that ENSO and El Nino frequencies may be relatively constant back to the year 1525.

Astudillo et al [2] also confirmed the ENSO shift after 1980 stating that "the amplitude of the 1982-1983 event is unique".  Further they concisely describe the ENSO behavior as being highly deterministic by stating:

"This is of crucial importance since if a system is deterministic, the vector field at every period of the state space is uniquely defined by a set of ordinary differential equations."


[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] H. Astudillo, R. Abarca-del-Río, and F. Borotto, “Long-term potential nonlinear predictability of El Niño–La Niña events,” Climate Dynamics, pp. 1–11, 2016.

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 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.