Amateur Hour

Three science philosophy papers and two recent findings seemed to fit together for this post.

Divergent Perspectives on Expert Disagreement: Preliminary Evidence from Climate Science, Climate Policy, Astrophysics, and Public Opinion :
James R. Beebe (University at Buffalo), Maria Baghramian (University College Dublin), Luke Drury (Dublin Institute for Advanced Studies), Finnur Dellsén (Inland Norway University of Applied Sciences)

“We found that, as compared to educated non-experts, climate experts believe (i) that there is less disagreement within climate science about climate change, (ii) that more of the disagreement that does exist concerns public policy questions rather than the science itself, (iii) that methodological factors play less of a role in generating existing disagreement among experts about climate science, (iv) that fewer personal and institutional biases influence the nature and direction of climate science research, (v) that there is more agreement among scientists about which methods or theoretical perspectives should be used to examine and explain the relevant phenomena, (vi) that disagreements about climate change should not lead people to conclude that the scientific methods being employed today are unreliable or incapable of revealing the truth, and (vii) that climate science is more settled than ideological pundits would have us believe and settled enough to base public policy on it. In addition, we observed that the uniquely American political context predicted participants’ judgments about many of these factors. We also found that, commensurate with the greater inherent uncertainty and data lacunae in their field, astrophysicists working on cosmic rays were generally more willing to acknowledge expert disagreement, more open to the idea that a set of data can have multiple valid interpretations, and generally less quick to dismiss someone articulating a non-standard view as non-expert, than climate scientists. ”

Any scientific discipline that lends itself to verification via controlled experiments is more open to non-standard views. It really is amazing how fast a new idea can be accepted when an experiment can be repeated by others. In climate science, no such control is possible, as the verification process can take years, while the non-standard views continue to proliferate. No wonder climate scientists get hardened to outsider views, as they have no way of immediately dismissing alternate interpretations.

On the other hand, astrophysics has a long history of being open to outsider opinion, with the amateur astronomer often given equal attention to a new finding. Two very recent cases come to mind.

These are two very concrete and objective findings that can be verified easily by others. So kudos to these two amateur sleuths for their persistence.

However, it's not so easy to verify that one is achieving verifiable progress in areas such as hydrology, as an ongoing debate series reveals that "Hydrology is a hard subject" (with a not to Feynman). The following paper tries to argue for a more open interpretation to the scientific process.

Debates—Hypothesis testing in hydrology: Pursuing certainty versus pursuing uberty
Victor R. Baker

Every scientist borrows techniques from each column, but it is certainly true that the lack of being able to devise controlled experiments in climatology and hydrology places those researchers at a disadvantage compared to the lab-based researchers, or to incremental event-based discoveries (such as with astronomy).  Baker is almost suggesting  that a  better qualitative measure of holistic progress (uberty?) should take the place of a complete quantitative understanding.

And even if one could make sense of a hypothesized behavior, one still has to navigate the landmines of prediction versus a probabilistic forecast.

Stigma in science: the case of earthquake prediction
Helene Joffe, Tiziana Rossetto, Caroline Bradley, and Cliodhna O’Connor

Earthquake prediction is at a cross-roads, with a rather obvious debate going on at the USGS (and spilling over to other research groups) on whether lunisolar gravitational forcing can provide a significant trigger to the timing of an earthquake. Again, because of a lack of controlled experimentation, the argument can only take place in statistical  terms, and will take time and more observational data to resolve.

Yet, bottom-line, the question remains, who owns disciplines such as astrophysics, climate science, hydrology, and seismology?  To take as an example, the entire data set for the ENSO climate behavior can be reduced to the monthly time series of barometric pressure measured at only two locations, one in Tahiti and one in Darwin. This is as open to public interpretation as the amateur astronomers that scan the night-time skies for fresh discoveries. The three papers all say that experts disagree on how to solve or model the big geophysics problems.  I'd suggest that we allow the educated non-experts take a crack and listen to what they have to say.

Last post on ENSO

The last of the ENSO charts.

This is how conventional tidal prediction is done:

Note how well it does in extrapolating a projection from a training interval.

This is an ENSO model fit to SOI data using an analytical solution to Navier-Stokes. The same algorithm is used to solve for the optimal forcing as in the tidal analysis solution above, but applying the annual solar cycle and monthly/fortnightly lunar cycles instead of the diurnal and semi-diurnal cycle.

The time scale transitions from a daily modulation to a much longer modulation due to the long-period tidal factors being invoked.

Next is an expanded view, with the correlation coefficient of 0.73:

This is a fit trained on the 1880-1950 interval (CC=0.76) and cross-validated on the post-1950 data

This is a fit trained on the post-1950 interval (CC=0.77) and cross-validated on the 1880-1950 data

Like conventional tidal prediction, very little over-fitting is observed. Most of what is considered noise in the SOI data is actually the tidal forcing signal. Not much more to say, except for others to refine.

Thanks to Kevin and Keith for all their help, which will be remembered.

Correlation Coefficient of ENSO Power Spectra

The model fit to ENSO takes place in the time domain. However, the correlation coefficient between model and data of the corresponding power spectra is higher than in the time series. Below in Figure 1 the CC is 0.92, while the CC in the time series is 0.82.

Fig.1 : Power spectra of ENSO data against model

The model allows only 3 fundamental lunar frequencies along with the annual cycle, plus the harmonics caused by the non-linear orbital path and the seasonally impulsed modulation.

What this implies is that almost all the peaks in the power spectra shown above are caused by interactions of these 4 fundamental frequencies. Figure 2 shows a satellite view of peak splitting (also shown here).

Fig 2: Frequency sideband plot identifying components created by modulation of a biennial cycle with the lunar cycles (originally described here).

One of the reasons that the power spectrum gives a higher correlation coefficient — despite the fact that the spectrum wasn't used in the fit — is that the lunar tides are precisely determined and thus all the harmonics should align well in the frequency domain. And that's what is observed with the multiple-peak alignment.

Furthermore, according to Ref [1], this result is definitely not a characteristic of noise-driven system, and it also possesses a very low dimension of chaotic content. The same frequency content is observed largely independent of the prediction time profile, i.e. training interval.


1. Bhattacharya, Joydeep, and Partha P. Kanjilal. "Revisiting the role of correlation coefficient to distinguish chaos from noise." The European Physical Journal B-Condensed Matter and Complex Systems 13.2 (2000): 399-403.


Experiment to compare training runs from 1880 to 1980 of the ENSO model against both the NINO34 time-series data and the SOI data. The solid red-curves are the extrapolated cross-validation interval..



Many interesting inferences one can potentially draw from these comparisons. The SOI signal appears more noisy, but that could actually be signal. For example, the NINO34 extrapolation pulls out a split peak near 2013-2014, which does show up in the SOI data. And a discrepancy in the NINO34 data near 1934-1935 which predicts a minor peak, is essentially noise in the SOI data.  The 1984-1986 flat valley region is much lower in NINO34 than in SOI, where it hovers around 0. The model splits the difference in that interval, doing a bit of both. And the 1991-1992 valley predicted in the model is not clear in the NINO34 data, but does show up in the SOI data.

Of course these are subjectively picked samples, yet there may be some better combination of SOI and NINO34 that one can conceive of to get a better handle on the true ENSO signal.

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AGU 2017 posters

ED23D-0326: Knowledge-Based Environmental Context Modeling

click to enlarge

GC41B-1022: Biennial-Aligned Lunisolar-Forcing of ENSO: Implications for Simplified Climate Models

In the last month, two of the great citizen scientists that I will be forever personally grateful for have passed away. If anyone has followed climate science discussions on blogs and social media, you probably have seen their contributions.

Keith Pickering was an expert on computer science, astrophysics, energy, and history from my neck of the woods in Minnesota. He helped me so much in working out orbital calculations when I was first looking at lunar correlations. He provided source code that he developed and it was a great help to get up to speed. He was always there to tweet any progress made. Thanks Keith

Kevin O'Neill was a metrologist and an analysis whiz from Wisconsin. In the weeks before he passed, he told me that he had extra free time to help out with ENSO analysis. He wanted to use his remaining time to help out with the solver computations. I could not believe the effort he put in to his spreadsheet, and it really motivated me to spending more time in validating the model. He was up all the time working on it because he was unable to lay down. Kevin was also there to promote the research on other blogs, right to the end. Thanks Kevin.

There really aren't too many people willing to spend time working analysis on a scientific forum, and these two exemplified what it takes to really contribute to the advancement of ideas. Like us, they were not climate science insiders and so will only get credit if we remember them.

High Resolution ENSO Modeling

An intriguing discovery is that the higher-resolution aspects of the SOI time-series (as illustrated by the Australian BOM 30-day SOI moving average) may also have a tidal influence.  Note the fast noisy envelope that rides on top of the deep El Nino of 2015-2016 shown below:

For the standard monthly SOI as reported by NCAR and NOAA, this finer detail disappears.  BOM provides the daily SOI value for about the past ~ 3 years here.

Yet if we retain this in the 1880-present monthly ENSO model, by simultaneously isolating [1] the higher frequency fine structure from 2015-2017, the fine structure also emerges in the model. This is shown in the lower panel below.

This indicates that the differential equation being used currently can possibly be modified to include faster-responding derivative terms which will simultaneously show the multi-year fluctuations as well as what was thought to be a weekly-to-monthly-scale noise envelope. In fact, I had been convinced that this term was due to localized weather but a recent post suggested that this may indeed be a deterministic signal.

Lunisolar tidal effects likely do impact the ocean behavior at every known time-scale, from the well-characterized diurnal and semi-diurnal SLH tides to the long-term deep-ocean mixing proposed by Munk and Wunsch.  It's not surprising that tidal forces would have an impact on the intermediate time-scale ENSO dynamics, both at the conventional low resolution (used for El Nino predictions) and at the higher-resolution that emerges from SOI measurements (the 30-day moving average shown above).  Obviously, monthly and fortnightly oscillations observed in the SOI are commensurate with the standard lunar tides of periods 13-14 days and 27-28 days. And non-linear interactions may result in the 40-60 day oscillations observed in LOD.

from Earth Rotational Variations Excited by Geophysical Fluids, B.F. Chao,

It's entirely possible that removing the 30-day moving average on the SOI measurements can reveal even more detail/


[1] Isolation is accomplished by subtracting a 24-day average about the moving average value, which suppresses the longer-term SOI variation.


The ENSO Forcing Potential - Cheaper, Faster, and Better

Following up on the last post on the ENSO forcing, this note elaborates on the math.  The tidal gravitational forcing function used follows an inverse power-law dependence, where a(t) is the anomalistic lunar distance and d(t) is the draconic or nodal perturbation to the distance.

F(t) \propto \frac{1}{(R_0 + a(t) + d(t))^2}'

Note the prime indicating that the forcing applied is the derivative of the conventional inverse squared Newtonian attraction. This generates an inverse cubic formulation corresponding to the consensus analysis describing a differential tidal force:

F(t) \propto -\frac{a'(t)+d'(t)}{(R_0 + a(t) + d(t))^3}

For a combination of monthly and fortnightly sinusoidal terms for a(t) and d(t) (suitably modified for nonlinear nodal and perigean corrections due to the synodic/tropical cycle)   the search routine rapidly converges to an optimal ENSO fit.  It does this more quickly than the harmonic analysis, which requires at least double the unknowns for the additional higher-order factors needed to capture the tidally forced response waveform. One of the keys is to collect the chain rule terms a'(t) and d'(t) in the numerator; without these, the necessary mixed terms which multiply the anomalistic and draconic signals do not emerge strongly.

As before, a strictly biennial modulation needs to be applied to this forcing to capture the measured ENSO dynamics — this is a period-doubling pattern observed in hydrodynamic systems with a strong fundamental (in this case annual) and is climatologically explained by a persistent year-to-year regenerative feedback in the SLP and SST anomalies.

Here is the model fit for training from 1880-1980, with the extrapolated test region post-1980 showing a good correlation.

The geophysics is now canonically formulated, providing (1) a simpler and more concise expression, leading to (2) a more efficient computational solution, (3) less possibility of over-fitting, and (4) ultimately generating a much better correlation. Alternatively, stated in modeling terms, the resultant information metric is improved by reducing the complexity and improving the correlation -- the vaunted  cheaper, faster, and better solution. Or, in other words: get the physics right, and all else follows.














Approximating the ENSO Forcing Potential

From the last post, we tried to estimate the lunar tidal forcing potential from the fitted harmonics of the ENSO model. Two observations resulted from that exercise: (1) the possibility of over-fitting to the expanded Taylor series, and (2) the potential of fitting to the ENSO data directly from the inverse power law.

The Taylor's series of the forcing potential is a power-law polynomial corresponding to the lunar harmonic terms. The chief characteristic of the polynomial is the alternating sign for each successive power (see here), which has implications for convergence under certain regimes. What happens with the alternating sign is that each of the added harmonics will highly compensate the previous underlying harmonics, giving the impression that pulling one signal out will scramble the fit. This is conceptually no different than eliminating any one term from a sine or cosine Taylor's series, which are also all compensating with alternating sign.

The specific conditions that we need to be concerned with respect to series convergence is when r (perturbations to the lunar orbit) is a substantial fraction of R (distance from earth to moon) :

F(r) = \frac{1}{(R+r)^3}

Because we need to keep those terms for high precision modeling, we also need to be wary of possible over-fitting of these terms — as the solver does not realize that the values for those terms have the constraint that they derive from the original Taylor's series. It's not really a problem for conventional tidal analysis, as the signals are so clean, but for the noisy ENSO time-series, this is an issue.

Of course the solution to this predicament is not to do the Taylor series harmonic fitting at all, but leave it in the form of the inverse power law. That makes a lot of sense — and the only reason for not doing this until now is probably due to the inertia of conventional wisdom, in that it wasn't necessary for tidal analysis where harmonics work adequately.

So this alternate and more fundamental formulation is what we show here.

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Reverse Engineering the Moon's Orbit from ENSO Behavior

With an ideal tidal analysis, one should be able to apply the gravitational forcing of the lunar orbit1 and use that as input to solve Laplace's tidal equations. This would generate tidal heights directly. But due to aleatory uncertainty with respect to other factors, it becomes much more practical to perform a harmonic analysis on the constituent tidal frequencies. This essentially allows an empirical fit to measured tidal heights over a training interval, which is then used to extrapolate the behavior over other intervals.  This works very well for conventional tidal analysis.

For ENSO, we need to make the same decision: Do we attempt to work the detailed lunar forcing into the formulation or do we resort to an empirical bottoms-up harmonic analysis? What we have being do so far is a variation of a harmonic analysis that we verified here. This is an expansion of the lunar long-period tidal periods into their harmonic factors. So that works well. But could a geophysical model work too?

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Interface-Inflection Geophysics

This paper that a couple of people alerted me to is likely one of the most radical research findings that has been published in the climate science field for quite a while:

Topological origin of equatorial waves
Delplace, Pierre, J. B. Marston, and Antoine Venaille. Science (2017): eaan8819.

An earlier version on ARXIV was titled Topological Origin of Geophysical Waves, which is less targeted to the equator.

The scientific press releases are all interesting

  1. Science Magazine: Waves that drive global weather patterns finally explained, thanks to inspiration from bagel-shaped quantum matter
  2. Science Daily: What Earth's climate system and topological insulators have in common
  3. Physics World: Do topological waves occur in the oceans?

What the science writers make of the research is clearly subjective and filtered through what they understand.

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