Scaling El Nino

Recently, the rock climber Alex Honnold took a route up El Capitan without ropes.There's no room to fail at that. I prefer a challenge that one can fail at, and then keep trying.  This is the ascent to conquering El Nino:

The Free-thought Route*

Χ  Base camp:  ENSO (El Nino/Southern Oscillation) is a sloshing behavior, mainly in the thermocline where the effective gravity makes it sensitive to angular momentum changes.
Χ  Faster forcing cycles reinforce against the yearly cycle, creating aliased periods. How?
Χ  Monthly lunar tidal cycles provide the aliased factors: Numbers match up perfectly.
This aliasing also works for QBO, an atmospheric analog of ENSO.
Χ  A biennial meta-stability appears to be active. Cycles reinforce on alternating years.
Χ  The well-known Mathieu modulation used for sloshing simulations also shows a biennial character.
Machine learning experiments help ferret out these patterns.
Χ  The delay differential equation formulation matches up with the biennial Mathieu modulation with a delay of one-year.  That's the intuitive yearly see-saw that is often suggested to occur.
  The Chandler wobble also shows a tidal forcing tendency, as does clearly the earth's LOD (length-of-day) variations.
Χ  Integrating the DiffEq model provides a good fit, including long-term coral proxy records
Χ  Solving the Laplace tidal equation via a Sturm-Liouville expression along the equator helps explain details of QBO and ENSO
  Close inspection of sea-level height (SLH) tidal records show evidence of both biennial and ENSO characteristics
Δ Summit: Final validation of the geophysics comparing ENSO forcing against LOD forcing.

Model fits to ENSO using a training interval

The route encountered several dead-ends with no toe-holds or hand-holds along the way (e.g. the slippery biennial phase reversal, the early attempts at applying Mathieu equation). In retrospect many of these excursions were misguided or overly complex, but eventually other observations pointed to the obvious route.

This is a magnification of the fitting contour around the best forcing period values for ENSO. These pair of peak values are each found to be less than a minute apart from the known values of the Draconic cycle (27.2122 days) and Anomalistic cycle (27.5545 days).

The forcing comes directly from the angular momentum variations in the Earth's rotation. The comparison between what the ENSO model uses and what is measured via monitoring the length-of-day (LOD) is shown below:



*  This is not the precise route I took, but how I wish it was in hindsight.

The Lunar Geophysical Connection

The conjecture out of NASA JPL is that the moon has an impact on the climate greater than is currently understood:

Claire Perigaud (Caltech/JPL)
Has this research gone anywhere?  Looks as if has gone to this spin-off.
According to the current consensus, variability in wind is what contributes to forcing for behaviors such as the El Nino/Southern Oscillation (ENSO).
OK, but what forces the wind? No one can answer that apart from saying wind variability is just a part of the dynamic climate system.  And so we are lead to believe that a wind burst will cause an ENSO and then the ENSO event will create a significant disruptive transient to the climate much larger than the original wind stimulus. And that's all due to positive feedback of some sort.
I am only paraphrasing the current consensus.
A much more plausible and parsimonious explanation lies with external lunar forcing reinforced by seasonal cycles.

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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.


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.

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.

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.

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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. 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.

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