The ENSO Challenge

It's been quite a challenge decoding the physics of ENSO. Anything that makes the model more complex and with more degrees of freedom needs to be treated carefully. The period doubling bifurcation properties of wave sloshing has been an eye-opener for me. I experimented with adding a sub-harmonic period of 4 years to the 2-year Mathieu modulation and see if that improves the fit. By simply masking the odd behavior around 1981-1983, I came up with this breakdown of the RHS/LHS comparison.

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Lindzen doth protest too much

Incredible that Richard Lindzen was quoted as saying this:

Richard Lindzen, the Alfred P. Sloan Professor of Meteorology at MIT and a member of the National Academy of Sciences who has long questioned climate change orthodoxy, is skeptical that a sunnier outlook is upon us.

“I actually doubt that,” he said. Even if some of the roughly $2.5 billion in taxpayer dollars currently spent on climate research across 13 different federal agencies now shifts to scientists less invested in the calamitous narrative, Lindzen believes groupthink has so corrupted the field that funding should be sharply curtailed rather than redirected.

“They should probably cut the funding by 80 to 90 percent until the field cleans up,” he said. “Climate science has been set back two generations, and they have destroyed its intellectual foundations.”

Consider the psychological projection aspect of what Lindzen is asserting. The particularly galling part is this:

“Climate science has been set back two generations, and they have destroyed its intellectual foundations.”

It may actually be Lindzen that has set back generations of atmospheric science research with his deeply flawed model of the quasi-biennial oscillation of equatorial stratospheric winds — see my recent QBO presentation for this month's AGU meeting.   He missed a very simple derivation that he easily could have derived back in the 1960’s, and that could have set a nice “intellectual foundation” for the next 40+ years. Instead he has essentially "corrupted the field" of atmospheric sciences that could have been solved with the right application of Laplace's tidal equations — equations known since 1776 !

The "groupthink" that Lindzen set in motion on the causes behind QBO is still present in the current research papers, with many scientists trying to explain the main QBO cycle of 28 months via a relationship to an average pressure. See for example this paper I reviewed earlier this year.

To top it all off, he was probably within an eyelash of figuring out the nature of the forcing, given that he actually considered the real physics momentarily:

Alas, all those millions of taxpayer funds that Lindzen presumably received over the years didn't help, and he has been reduced to whining over what other climate scientists may receive in funding as he enters into retirement.

Methinks it's usually the case that the one that "doth protest too much" is the guilty party.

Added: here is a weird graphic of Lindzen I found on the cliscep blog. The guy missed the simple while focussing on the complex.

richardlindzen

From climate scientist Dessler

From climate scientist Dessler

 

QBO Split Training

As with ENSO, we can train QBO on separate intervals and compare the fit on each interval.  The QBO 30 hPa data runs from 1953 to the present.  So we take a pair of intervals — one from 1953-1983 (i.e. lower) and one from 1983-2013 (i.e. higher) — and compare the two.

The primary forcing factor is the seasonally aliased nodal or Draconic tide which is shown in the upper left on the figure.  The lower interval fit in BLUE matches extremely well to the higher interval fit in RED, with a correlation coefficient above 0.8.

These two intervals have no inherent correlation other than what can be deduced from the physical behavior generating the time-series.  The other factors are the most common long-period tidal cycles, along with the seasonal factor.  All have good correlations — even the aliased anomalistic tide (lower left), which features a pair of closely separated harmonics, clearly shows strong phase coherence over the two intervals.

That's what my AGU presentation was about — demonstrating how QBO and ENSO are simply derived from known geophysical forcing mechanisms applied to the fundamental mathematical geophysical fluid dynamics models. Anybody can reproduce the model fit with nothing more than an Excel spreadsheet and a Solver plugin.

Here are the PowerPoint slides from the presentation.

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.

fit

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."

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] 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.