Should you trust climate science? Maybe the eclipse is a clue

An example of a prediction:

"Looks like we're heading for La Nina going into Winter. That means I expect 2018 will not average much different from 2017, both close to 2015 level. Then a probable new record in 2019."

How does anyone know which way the ENSO behavior is heading if there is not a clear understanding of the underlying mechanism? [1]

For the prediction quoted above, the closer one gets to an peak or valley, the safer it is to make a dead reckoning guess. For example, I can say a low tide is coming if it is coming off a high tide — even if I have no idea what causes tides.

Yet, if we understand the mechanism behind ocean tides — that it is due to the gravitational pull of the sun and the moon  —  we can do a much better job of prediction.

The New York Times climate change reporter Justin Gillis suggests that climate science can make predictions as well as geophysicists can predict eclipses:
https://www.nytimes.com/2017/08/18/climate/should-you-trust-climate-science-maybe-the-eclipse-is-a-clue.html.  And there is this:

Yet, if climate scientists can't figure out the mechanism behind a behavior such as ENSO, everyone is essentially in the same boat, fishing for a basic understanding.

So what happens if we can formulate the messy ENSO behavior into a basic geophysics problem, something on the complexity of tides?  We are nowhere near that according to the current research literature, unless this finding — which has been a frequent topic here — turns out to be true.

In this case, the recent solar eclipse is in fact a clue. The precise orbit of the moon is vital to determining the cycles of ENSO. If this assertion is true, one day we will likely be able to predict when the next El Nino occurs, with the accuracy of predicting the next eclipse.

Footnote:

[1] Consider one common explanation invoking winds. In fact, shifts in the prevailing winds is not a mechanism because any shift or reversal requires a mechanism itself, see for example the QBO.

 

ENSO model for predicting El Nino and La Nina events

Applying the ENSO model to predict El Nino and La Nina events is automatic. There are no adjustable parameters apart from the calibrated tidal forcing amplitudes and phases used in the process of fitting over the training interval. Therefore the cross-validated interval from 1950 to present is untainted during the fitting process and so can be used as a completely independent and unbiased test.

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Millennium Prize Problem: Navier-Stokes

Watched the hokey movie Gifted on a plane ride. Turns out that the Millennium Prize for mathematically solving the Navier-Stokes problem plays into the plot.

I am interested in variations of the Navier–Stokes equations that describe hydrodynamical flow on the surface of a sphere.  The premise is that such a formulation can be used to perhaps model ENSO and QBO.

The so-called primitive equations are the starting point, as these create constraints for the volume geometry (i.e. vertical motion much smaller than horizontal motion and fluid layer depth small compared to Earth's radius). From that, we go to Laplace's tidal equations, which are a linearization of the primitive equations.

I give a solution here, which was originally motivated by QBO.

Of course the equations are under-determined, so the only hope I had of solving them is to provide this simplifying assumption:

{\frac{\partial\zeta}{\partial\varphi} = \frac{\partial\zeta}{\partial t}\frac{\partial t}{\partial\varphi}}

If you don't believe that this partial differential coupling of a latitudinal forcing to a tidal response occurs, then don't go further. But if you do, then:

 

 

 

 

Solar Eclipse 2017 : What else?

The reason we can so accurately predict the solar eclipse of 2017 is because we have accurate knowledge of the moon's orbit around the earth and the earth's orbit around the sun.

Likewise, the reason that we could potentially understand the behavior of the El Nino Southern Oscillation (ENSO) is that we have knowledge of these same orbits. As we have shown and will report at this year's American Geophysical Union (AGU) meeting, the cyclic gravitational pull of the moon (lower panel in Figure 1 below) interacting seasonally precisely controls the ENSO cycles (upper panel Figure 1).

Fig 1: Training interval 1880-1950 leads to extrapolated fit post-1950

Figure 2 is how sensitive the fit is to the precise value of the lunar cycle periods. Compare the best ft values to the known lunar values here. This is an example of the science of metrology.

Fig 2: Sensitivity to selection of lunar periods.

The implications of this research are far-ranging. Like knowing when a solar eclipse occurs helps engineers and scientists prepare power utilities and controlled climate experiments for the event, the same considerations apply to ENSO.  Every future El Nino-induced heat-wave or monsoon could conceivably be predicted in advance, giving nations and organizations time to prepare for accompanying droughts, flooding, and temperature extremes.

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ENSO Split Training for Cross-Validation

If we split the modern ENSO data into two training intervals — one from 1880 to 1950 and one from 1950 to 2016, we get roughly equal-length time series for model evaluation.

As Figure 1 shows, a forcing stimulus due to monthly-range LOD variations calibrated to the interval between 2000 to 2003 (lower panel) is used to train the ENSO model in the interval from 1880 to 1950. The extrapolated model fit in RED does a good job in capturing the ENSO data in the period beyond 1950.

Fig. 1: Training 1880 to 1950

Next, we reverse the training and verification fit, using the period from 1950 to 2016 as the training interval and then back extrapolating. Figure 2 shows this works about as well.

Fig. 2: Training interval 1950 to 2016

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Deterministic and Stochastic Applied Physics

Pierre-Simon Laplace was one of the first mathematicians who took an interest in problems of probability and determinism.  It's surprising how much of the math and applied physics that Laplace developed gets used in day-to-day analysis. For example, while working on the ENSO and QBO analysis, I have invoked the following topics at some point:

  1. Laplace's tidal equations
  2. Laplace's equation
  3. Laplacian differential operator
  4. Laplace transform
  5. Difference equation
  6. Planetary and lunar orbital perturbations
  7. Probability methods and problems
    1. Inductive probability
    2. Bayesian analysis, e.g. the Sunrise problem
  8. Statistical methods and applications
    1. Central limit theorem
    2. Least squares
  9. Filling in holes of Newton's differential calculus
  10. Others here

Apparently he did so much and was so comprehensive that in some of his longer treatises he often didn't cite the work of others, making it difficult to pin down everything he was responsible for (evidently he did have character flaws).

In any case, I recall applying each of the above in working out some aspect of a problem. Missing was that Laplace didn't invent Fourier analysis but the Laplace transform is close in approach and utility.

When Laplace did all this research, he must have possessed insight into what constituted deterministic processes:

We may regard the present state of the universe as the effect of its past and the cause of its future. An intellect which at a certain moment would know all forces that set nature in motion, and all positions of all items of which nature is composed, if this intellect were also vast enough to submit these data to analysis, it would embrace in a single formula the movements of the greatest bodies of the universe and those of the tiniest atom; for such an intellect nothing would be uncertain and the future just like the past would be present before its eyes.

— Pierre Simon Laplace,
A Philosophical Essay on Probabilities[wikipedia]
This is summed up as:

He also seemed to be a very applied mathematician, as per a quote I have used before  “Probability theory is nothing but common sense reduced to calculation.”  Really nothing the least bit esoteric about any of Laplace's math, as it seemed always motivated by solving some physics problem or scientific observation. It appears that he wanted to explain all these astronomic and tidal problems in as simple a form as possible. Back then it may have been esoteric, but not today as his techniques have become part of the essential engineering toolbox. I have to wonder if Laplace were alive now whether he would agree that geophysical processes such as ENSO and QBO were equally as deterministic as the sun rising every morning or of the steady cyclic nature of the planetary and lunar orbits. And it wasn't as if Laplace possessed confirmation bias that behaviors were immediately deterministic; as otherwise he wouldn't have spent so much effort in devising the rules of probability and statistics that are still in use today, such as the central limit theorem and least squares.

Perhaps he would have glanced at the ENSO problem for a few moments, noticed that in no way that it was random, and then casually remarked with one his frequent idiomatic phrases:

"Il est aisé à voir que..."  ... or ..  ("It is easy to see that...").

It may have been so obvious that it wasn't important to give the details at the moment, only to fill in the chain of reasoning later.  Much like the contextEarth model for QBO, deriving from Laplace's tidal equations.

Where are the Laplace's of today that are willing to push the basic math and physics of climate variability as far as it will take them? It has seemingly jumped from Laplace to Lorenz and then to chaotic uncertainty ala Tsonis or mystifying complexity ala Lindzen. Probably can do much better than to punt like that ... on first down even !

Confirmation Bias

Someone long ago must have stated that the El Nino/Southern Oscillation (ENSO) phenomenon was not related to lunisolar (lunar+solar) tidal forcing. This negative result (or null result) is not documented anywhere (AFAICT) but is likely considered conventional wisdom by climate scientists. The most direct evidence that climate scientists don't consider lunisolar forcing is that it appears nowhere in the parameterization of general circulation model (GCM) source code.

As a general rule, negative findings are rarely reported in research journals:

"As it stands now, researchers are typically rewarded (tenure, grants, better jobs, etc.) for publishing a quantity of publications in prestigious journals. They do this by

  • Running small and statistically weak studies (they are easy to do) that produce only positive results, since journals tend to not publish negative findings.
  • Ignoring negative findings.
  • Publishing only new and exciting findings that journals are looking for.
  • Never checking old findings for accuracy and replicability.
  • Changing methodologies in mid-stream to assure positive results."

I imagine that if a budding graduate student devised a hypothetical ENSO/lunar tidal connection as a potential thesis topic, it would be rejected by his advisor. The advisor would not want to risk his reputation or track record by going down a potential dead end. The same is perhaps true of the recent case of NASA JPL rejecting the proposal of one of their research teams who suggested funding for this actual topic.  Read an excerpt from this footnote:

"None of the peer-reviewers nor collaborators in 2006 had anticipated that the most remarkable large-scale process that we were going to find comes from ocean circulations fueled by Luni-Geo-Solar gravitational energy. We found evidence of the existence of this energy in the data produced by satellites like QuikSCAT and ASCAT. Following the standard
from the 1970’s of using these satellite data as winds in numerical modeling of oceans and climate has created and continues to create significant errors in the simulated ocean temperature, salinity, and currents as well as in the atmosphere. Together with our co-workers, we chose not to publish the errors until a solution to appropriately use

satellite data in numerical modeling was found. However, over the following years, proposed solutions were not considered because of various factors including economic and scientific pressure to publish and continue the standard agenda."


This is a clear example of confirmation bias stalling promising research. Yet, apparently there are no issues with pushing iffy models of ENSO based on nebulous chaos theory by climate change deniers such as Anastasios Tsonis.
Hmmm ... something is not right with this picture.

So if this lunisolar model of ENSO pans out, it is an excellent example of how confirmation bias impeded scientific progress, but with the scientific method eventually winning out.

Fig 1: Top is the ENSO model trained on NINO3.4 data from 1880 to 1920, with the lower curve providing a calibration of the lunar forcing based on sensitive LOD measurements of the earth's rotation. ENSO is not a chaotic process if it can be stimulated directly by the known lunisolar forcing.

And we can do the same confirmation bias exercise with the quasibiennial oscillation (QBO) phenomenon, substituting the climate change denier Richard Lindzen for Tsonis as the impediment to progress.  Lindzen couldn't find the lunar connection (even though there is plenty of evidence he tried), so just assumed it wasn't there.  Everyone that followed Lindzen's original model essentially confirmed his bias and so no progress was made, until the bias was removed and the lunisolar forcing re-evaluated.



The difference here is that I am not preparing a thesis or working for NASA. This is one way of inoculating oneself from historical confirmation biases -- by not being part of an inside consensus, there is no one to suggest to "not go there".  By the same token, I now possess an apparent confirmation bias that a lunisolar forcing plays a primary role in certain climate phenomena.  Yet, it's a weak confirmation bias because I didn't start with this view, but it gathered steam based on all the evidence accrued over the past few years. It is now up to others to use the scientific method to reject this model. And, of course, I will be the first to abandon this model if I come across strong evidence to reject it. After all, I don't have any particular allegiance to the moon gods, only in the learned view that oscillations of this nature do not occur via spontaneous resonance.

As an important footnote to this post, consider the recent admission that lunar forces play a significant role in triggering earthquakes. Up to the last year, the confirmation bias was that the lunar gravitational forcing was too weak to trigger earthquakes, and so the onset was historically described in statistical terms. The earthquake itself triggered by the passage and time and the slow creep of a fault. But the tide turned in 2016 when two independent groups found significant correlations with lunar cycles -- a Japanese group led by Ide [1] and a US Geological Survey group led by van der Elst [2]. These are the same fortnightly lunar cycles (see Figure 2 below) that are used in the ENSO model described above (compare to lower chart in Figure 1).  So the new thinking is that indeed the gravitational pull of the moon will trigger the slipping of a fault, and this happens enough that future predictions of earthquakes (for example along the San Andreas fault [3]) can use tidal tables to aid the analysis.

Fig 2: Lunar forced earthquake analysis by van der Elst et al [2]. Note the fortnightly cycles similar to Fig 1 above.

The bottom-line is that we need to monitor the earth sciences consensus regarding lunar forcing in the next few years, both in terms of ENSO and QBO climate behavior and with regard to earthquake analysis.   Scientific theories are not binding, unlike sporting events -- "World cup matches cannot be replayed, but science can be corrected afterwards.". Thus, the confirmation bias of "no lunar forcing" is not necessarily set in stone.

References

  1. Ide, Satoshi, Suguru Yabe, and Yoshiyuki Tanaka. "Earthquake potential revealed by tidal influence on earthquake size-frequency statistics." Nature Geoscience 9.11 (2016): 834-837.
  2. van der Elst, Nicholas J., et al. "Fortnightly modulation of San Andreas tremor and low-frequency earthquakes." Proceedings of the National Academy of Sciences (2016): 201524316.
  3. Delorey, Andrew A., Nicholas J. van der Elst, and Paul A. Johnson. "Tidal triggering of earthquakes suggests poroelastic behavior on the San Andreas Fault." Earth and Planetary Science Letters 460 (2017): 164-170.

ENSO+QBO Elevator Pitch

Most papers on climate science take pages and pages of exposition before they try to make any kind of point. The excessive verbiage exists to rationalize their limited understanding of the physics, typically by explaining how complex it all is.

Conversely, think how easy it is to explain sunrise and sunset. From a deterministic point of view [1] and from our understanding of a rotating earth and an illuminating sun, it's trivial to explain that a sunrise and sunset will happen once each per day. That and perhaps another sentence would be all that would be necessary to write a research paper on the topic ...  if it wasn't already common knowledge. Any padding to this would be unnecessary to the basic understanding. For example, going further and explaining why the earth rotates amounts to answering the wrong question. Thus the topic is essentially an elevator pitch.

If sunset/sunrise is too elementary an example, one could explain ocean tides. This is a bit more advanced because the causal connection is not visible to the eye. Yet all that is needed here is to explain the pull of gravity and the orbital rate of the moon with respect to the earth, and the earth to the sun. A precise correlation between the lunisolar cycles is then applied to verify causality. One could add another paragraph to explain how mixed tidal effects occur, but that should be enough for an expository paper.

We could also be at such a point in our understanding with respect to ENSO and QBO. Most of the past exposition was lengthy because the causal factors could not be easily isolated or were rationalized as random or chaotic. Yet, if we take as a premise that the behavior was governed by the same orbital factors as what governs the ocean tides, we can make quick work of an explanation.

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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.

Strictly Biennial Cycles in ENSO

Continuing from a previous post describing the historical evolution of ocean dynamics and tidal theory, this paper gives an early history of ENSO [1].

The El Niño–Southern Oscillation (ENSO) is among the most pervasive natural climate oscillations on earth, affecting the web of life from plankton to people. During mature El Niño (La Niña) events, the sea surface temperature (SST) in the eastern equatorial Pacific warms (cools), leading to global-scale responses in the terrestrial biosphere transmitted through modifications of large-scale atmospheric circulation. The dynamics of—and global responses to—ENSO have been studied for nearly eight decades (Walker and Bliss 1932; Ropelewski and Halpert 1989; Kiladis and Diaz 1989; Yulaeva and Wallace 1994). Cyclic patterns in climate events have also been connected to something resembling ENSO as early as the mid-nineteenth century. Reminiscing on his 1832 visit to Argentina during his expedition on the H.M.S. Beagle, British naturalist Charles Darwin notes “[t]hese droughts to a certain degree seem to be almost periodical; I was told the dates of several others, and the intervals were about fifteen years” (Darwin 1839). Nearly 60 years later, Darwin enters into his journal “. . . variations in climate sometimes appear to be the effect of the operation of some very general cause” (Darwin 1896). Some believe this “very general cause” was actually an early piecing together of ENSO and its now notorious impact on extreme weather events in South America (Cerveny 2005). It is only a coincidence that Darwin may have been among the first to point out the cyclic nature of ENSO, and the focus of this paper is the association between ENSO and the Galápagos Islands, which also owe their fame to Darwin.

Beyond this history, the purpose of this particular paper is to investigate the mechanics behind ENSO and to isolate the "very general cause" that Darwin first hypothesized (and isn't it always the case how the most intellectually curious are at the root of scientific investigations?). According to this same paper[1], a "strictly biennial" cycle is routinely observed in ENSO when run with an ocean general circulation model (OGCM). Yet they observe correctly as quoted below that "Such strictly biennial regularity is not realistic, as ENSO in nature at present is neither perfectly regular nor significantly biennial."

Note how strong the biennial Fourier factor is in their simulation (along with the perfectly acceptable harmonic at 2/3 year which will shape the biennial into anything from a triangle to a square wave). With our ENSO model, I can easily reproduce a strictly biennial cycle just by changing the forcing from a lunar monthly cycle (incongruent with a yearly cycle) to anything that is a harmonic with the yearly cycle. So it's our claim that it's the lunar cycle that remains the key factor that changes the ENSO cycle into something that is "neither perfectly regular nor significantly biennial" in the words of the cited paper. The biennial factor is still there but it gets modified and split by the lunar cycle to the extent that no biennial factor remains in the Fourier spectra.

Yet if we look into the GCM's that researchers have developed and you will find that none have any capabilities for introducing a lunar tidal factor as a forcing.  Why is that?  Probably because someone long ago simply asserted that the lunar gravitational pull wasn't important for ENSO, contrary to its critical importance for understanding ocean tides.   So is this lunar effect really the "very general cause" that Darwin was thinking of to explain ENSO?

As a result of some intellectual curiosity to actually test the tidal forcing against a biennial modulation, I think the answer is a definitive yes. This is how sensitive the fitting of the model is to selection of the two forcing cycles

By adjusting the values progressively away from the true value for the lunar tidal cycle (27.2122 days for the Draconic cycle and 27.55455 days for the Anomalistic cycle), it will result in a smaller correlation coefficient. This doesn't happen by accident. Fitting this same model to 200 years of ENSO coral proxy data also doesn't happen by accident. And extracting precisely phased and correlated lunar cycles to the actual forcing applied to the earth's rotation also doesn't happen by accident. I think it's time for the GCM's to revisit the role of lunar forcing, just as NASA JPL was about to before they decided to pull the plug on their own lunar research initiative [2].

References

[1] K. B. Karnauskas, R. Murtugudde, and A. J. Busalacchi, “The effect of the Galápagos Islands on ENSO in forced ocean and hybrid coupled models,” Journal of Physical Oceanography, vol. 38, no. 11, pp. 2519–2534, 2008.

[2]  From a post-mortem —  "None of the peer-reviewers nor collaborators in 2006 had anticipated that the most remarkable large-scale process that we were going to find comes from ocean circulations fueled by Luni-Geo-Solar gravitational energy."