What happened to simple models?

It’s been over 10 years since a thread on simplifying climate models was posted on the Azimuth Project forum => https://forum.azimuthproject.org/discussion/981/the-fruit-fly-of-climate-models

A highly esteemed climate scientist, Isaac Held, even participated and voiced his opinion on how feasible that would be. Eventually the forum decided to concentrate on the topic of modeling El Nino cycles, starting out with a burst of enthusiasm. The independent track I took on the forum was relatively idiosyncratic, yet I thought it held promise and eventually published the model in the monograph Mathematical Geoenergy (AGU/Wiley) in late 2018. The forum is nearly dead now, but there is recent thread on “Physicists predict Earth will become a chaotic world”. Have we learned nothing after 10 years?

My model assumes that El Nino/La Nina cycles are not chaotic or random, which is still probably considered blasphemous. In contrast to what’s in the monograph, the model has simplified, and a feasible solution can be mapped to data within minutes. The basic idea remains the same, explained in 3 parts.

(click images to expand)
  • Tidal Forcing. A long-period tidal forcing is generated, best done by fitting the strongest tidal factors (mapped by R.D.Ray) to the dLOD (delta Length-of-Day) data from the Paris Observatory IERS. With a multiple linear regression (MLR) algorithm, that takes less than a second and fits a sine-wave series model to the data with a correlation coefficient higher than 0.99.

Integrated Response Forcing
  • Annual Trigger Barrier. A semi-annual (+/-) excursion impulse train is constructed, which acts as a sample-and-hold input driver when multiplied by the tidal forcing above. A single parameter controls the slight decay of the sampled value, i.e. the hold or integrated response. Another parameter allows for a slight asymmetry in the + excursions, and the – excursions that occur 6 months later. This creates the erratic pseudo-square wave structure shown above. A monthly time-series is sufficient, with the chosen impulse month the most critical parameter.

  • Fluid Dynamics Modulation. The Laplace’s Tidal Equations are solved along the equator via an ansatz, which essentially creates a non-linear sin(F(t)) mapping corresponding to standing-wave modes spanning the Pacific Ocean basin. A slow-mode mode(s) is used to characterize the main ENSO dipole, and a faster mode(s) to characterize the tropical instability waves. For each mode, a wavenumber, amplitude, and phase is required to calculate the modulation.

The fitting process is to let all the parameters to vary slightly and so I use the equivalent of a gradient descent algorithm to guide the solution. The impulse month is seeded along with starting guesses for the two slowest wavenumbers. Another MLR algorithm is embedded to estimate the amplitude and phases required.

The multi-processing software is at https://github.com/pukpr/GeoEnergyMath/wiki

Recently it has taken mere minutes to arrive at a viable model fit to the ENSO data (the ENS ONI monthly data (1850 – Jul 2022)), starting with the initially calibrated dLOD factors. Each of the tidal factors is modified slightly but the correlation coefficient is still at 0.99 of the starting dLOD.

Even with that, the only way to make a convincing argument is to apply cross-validation during the fitting process. A training interval is used during the fitting and the model is extrapolated as a check once the training error is minimized. Even though the model is structurally sensitive, it does not show wild over-fitting errors. This is explainable as only a handful of degrees of freedom are available.

LTE modulation (low)
LTE modulation (high)

So this demonstrates that the behavior is stationary and definitely not chaotic, only obscured by the non-linear modulation applied to tidally forced waveform.

Notes on Sloshing

Informative article on development of cusped waveforms and Kelvin-Helmholtz instabilities

An experimental study of two-layer liquid sloshing under pitch excitations, Physics of Fluids · May 2022
DOI: 10.1063/5.0093716

Amazing number of harmonics

Related to Tropical Instability Waves along the equator


The most important mechanism for turbulence production in equatorial parallel shear flows is the inflectional instability, which operates at local maxima of the mean shear profile (Smyth and Carpenter, 2019). In the presence of stable stratification, inflectional instability is damped, but it may yet grow, provided that the minimum value of Ri is less than critical. In this case, the process is termed Kelvin–Helmholtz (KH) instability. 

Model Ontology

In Chapter 10 of the book we touch on organization of environmental models.

“Furthermore, by applying ontology‐based approaches for organizing models and techniques, we can set the stage for broader collections of such models discoverable by a general community of designers and analysts. Together with standard access protocols for context modeling,
these innovations provide the promise of making environmental context models generally available and reusable, significantly assisting the energy analyst.”

Energy Transition : Applying Probabilities and Physics

Although we didn’t elaborate on this topic, it is an open area for future development, as our 2017 AGU presentation advocates. The complete research report is available as https://doi.org/10.13140/RG.2.1.4956.3604.

What we missed on the first pass was an ontology for citations titled CiTO (Citation Typing Ontology) which enables better classification and keeping track of research lineage. The idea again is to organize and maintain scientific knowledge for engineering and scientific modeling applications. As an example, one can readily see how the Citation Typing Ontology could be applied, with the is_extended_by object property representing much of how science and technology advances — in other words, one finding leading to another.

Mathematical Geoenergy

Our book Mathematical Geoenergy presents a number of novel approaches that each deserve a research paper on their own. Here is the list, ordered roughly by importance (IMHO):

  1. Laplace’s Tidal Equation Analytic Solution.
    (Ch 1112) A solution of a Navier-Stokes variant along the equator. Laplace’s Tidal Equations are a simplified version of Navier-Stokes and the equatorial topology allows an exact closed-form analytic solution. This could classify for the Clay Institute Millenium Prize if the practical implications are considered, but it’s a lower-dimensional solution than a complete 3-D Navier-Stokes formulation requires.
  2. Model of El Nino/Southern Oscillation (ENSO).
    (Ch 12) A tidally forced model of the equatorial Pacific’s thermocline sloshing (the ENSO dipole) which assumes a strong annual interaction. Not surprisingly this uses the Laplace’s Tidal Equation solution described above, otherwise the tidal pattern connection would have been discovered long ago.
  3. Model of Quasi-Biennial Oscillation (QBO).
    (Ch 11) A model of the equatorial stratospheric winds which cycle by reversing direction ~28 months. This incorporates the idea of amplified cycling of the sun and moon nodal declination pattern on the atmosphere’s tidal response.
  4. Origin of the Chandler Wobble.
    (Ch 13) An explanation for the ~433 day cycle of the Earth’s Chandler wobble. Finding this is a fairly obvious consequence of modeling the QBO.
  5. The Oil Shock Model.
    (Ch 5) A data flow model of oil extraction and production which allows for perturbations. We are seeing this in action with the recession caused by oil supply perturbations due to the Corona Virus pandemic.
  6. The Dispersive Discovery Model.
    (Ch 4) A probabilistic model of resource discovery which accounts for technological advancement and a finite search volume.
  7. Ornstein-Uhlenbeck Diffusion Model
    (Ch 6) Applying Ornstein-Uhlenbeck diffusion to describe the decline and asymptotic limiting flow from volumes such as occur in fracked shale oil reservoirs.
  8. The Reservoir Size Dispersive Aggregation Model.
    (Ch 4) A first-principles model that explains and describes the size distribution of oil reservoirs and fields around the world.
  9. Origin of Tropical Instability Waves (TIW).
    (Ch 12) As the ENSO model was developed, a higher harmonic component was found which matches TIW
  10. Characterization of Battery Charging and Discharging.
    (Ch 18) Simplified expressions for modeling Li-ion battery charging and discharging profiles by applying dispersion on the diffusion equation, which reflects the disorder within the ion matrix.
  11. Anomalous Behavior in Dispersive Transport explained.
    (Ch 18) Photovoltaic (PV) material made from disordered and amorphous semiconductor material shows poor photoresponse characteristics. Solution to simple entropic dispersion relations or the more general Fokker-Planck leads to good agreement with the data over orders of magnitude in current and response times.
  12. Framework for understanding Breakthrough Curves and Solute Transport in Porous Materials.
    (Ch 20) The same disordered Fokker-Planck construction explains the dispersive transport of solute in groundwater or liquids flowing in porous materials.
  13. Wind Energy Analysis.
    (Ch 11) Universality of wind energy probability distribution by applying maximum entropy to the mean energy observed. Data from Canada and Germany. Found a universal BesselK distribution which improves on the conventional Rayleigh distribution.
  14. Terrain Slope Distribution Analysis.
    (Ch 16) Explanation and derivation of the topographic slope distribution across the USA. This uses mean energy and maximum entropy principle.
  15. Thermal Entropic Dispersion Analysis.
    (Ch 14) Solving the Fokker-Planck equation or Fourier’s Law for thermal diffusion in a disordered environment. A subtle effect but the result is a simplified expression not involving complex errf transcendental functions. Useful in ocean heat content (OHC) studies.
  16. The Maximum Entropy Principle and the Entropic Dispersion Framework.
    (Ch 10) The generalized math framework applied to many models of disorder, natural or man-made. Explains the origin of the entroplet.
  17. Solving the Reserve Growth “enigma”.
    (Ch 6) An application of dispersive discovery on a localized level which models the hyperbolic reserve growth characteristics observed.
  18. Shocklets.
    (Ch 7) A kernel approach to characterizing production from individual oil fields.
  19. Reserve Growth, Creaming Curve, and Size Distribution Linearization.
    (Ch 6) An obvious linearization of this family of curves, related to Hubbert Linearization but more useful since it stems from first principles.
  20. The Hubbert Peak Logistic Curve explained.
    (Ch 7) The Logistic curve is trivially explained by dispersive discovery with exponential technology advancement.
  21. Laplace Transform Analysis of Dispersive Discovery.
    (Ch 7) Dispersion curves are solved by looking up the Laplace transform of the spatial uncertainty profile.
  22. Gompertz Decline Model.
    (Ch 7) Exponentially increasing extraction rates lead to steep production decline.
  23. The Dynamics of Atmospheric CO2 buildup and Extrapolation.
    (Ch 9) Convolving a fat-tailed CO2 residence time impulse response function with a fossil-fuel emissions stimulus. This shows the long latency of CO2 buildup very straightforwardly.
  24. Reliability Analysis and Understanding the “Bathtub Curve”.
    (Ch 19) Using a dispersion in failure rates to generate the characteristic bathtub curves of failure occurrences in parts and components.
  25. The Overshoot Point (TOP) and the Oil Production Plateau.
    (Ch 8) How increases in extraction rate can maintain production levels.
  26. Lake Size Distribution.
    (Ch 15) Analogous to explaining reservoir size distribution, uses similar arguments to derive the distribution of freshwater lake sizes. This provides a good feel for how often super-giant reservoirs and Great Lakes occur (by comparison).
  27. The Quandary of Infinite Reserves due to Fat-Tail Statistics.
    (Ch 9) Demonstrated that even infinite reserves can lead to limited resource production in the face of maximum extraction constraints.
  28. Oil Recovery Factor Model.
    (Ch 6) A model of oil recovery which takes into account reservoir size.
  29. Network Transit Time Statistics.
    (Ch 21) Dispersion in TCP/IP transport rates leads to the measured fat-tails in round-trip time statistics on loaded networks.
  30. Particle and Crystal Growth Statistics.
    (Ch 20) Detailed model of ice crystal size distribution in high-altitude cirrus clouds.
  31. Rainfall Amount Dispersion.
    (Ch 15) Explanation of rainfall variation based on dispersion in rate of cloud build-up along with dispersion in critical size.
  32. Earthquake Magnitude Distribution.
    (Ch 13) Distribution of earthquake magnitudes based on dispersion of energy buildup and critical threshold.
  33. IceBox Earth Setpoint Calculation.
    (Ch 17) Simple model for determining the earth’s setpoint temperature extremes — current and low-CO2 icebox earth.
  34. Global Temperature Multiple Linear Regression Model
    (Ch 17) The global surface temperature records show variability that is largely due to the GHG rise along with fluctuating changes due to ocean dipoles such as ENSO (via the SOI measure and also AAM) and sporadic volcanic eruptions impacting the atmospheric aerosol concentrations.
  35. GPS Acquisition Time Analysis.
    (Ch 21) Engineering analysis of GPS cold-start acquisition times. Using Maximum Entropy in EMI clutter statistics.
  36. 1/f Noise Model
    (Ch 21) Deriving a random noise spectrum from maximum entropy statistics.
  37. Stochastic Aquatic Waves
    (Ch 12) Maximum Entropy Analysis of wave height distribution of surface gravity waves.
  38. The Stochastic Model of Popcorn Popping.
    (Appx C) The novel explanation of why popcorn popping follows the same bell-shaped curve of the Hubbert Peak in oil production. Can use this to model epidemics, etc.
  39. Dispersion Analysis of Human Transportation Statistics.
    (Appx C) Alternate take on the empirical distribution of travel times between geographical points. This uses a maximum entropy approximation to the mean speed and mean distance across all the data points.

Rating of Climate Change blogs

Scientific blogging is on a decline and that is especially evident with respect to climate change blogs. Nothing really good left apart from forums such as https://forum.azimuthproject.org/discussions (which allows equation markup, image posting, and freedom to create threaded discussions).

Here is a grading of blogs that I have on my RSS feed:

  • WUWT :  F-
    A horrible AGW denier blog that pretends to be fair & balanced. RSS feed does not work with Owl.
  • Tallbloke’s Talkshop : F-
    A horrible AGW denier blog that specializes in numerology
  • Real Climate : C
    Sparse postings and comment moderation has long latencies so the discussion is glacially paced
  • Open Mind : C
    Not very interesting, mostly from a statistical angle, which is not where progress in analysis occurs
  • Science of Doom : D
    I don’t understand this site, seems to be run by a thinly veiled skeptic. Might as well read books by Pierrehumbert to gain an understanding of the physics instead of struggling along with the topics.
  • And Then There’s Physics : D+
    The moderators are control freaks, and the discussions are safe as milk
  • Peak Oil Barrel : A
    A very good blog that allows both fossil fuel discussion and climate change discussion, separated in distinct threads.  Moderated slightly and images allowed, along with short-term editing.
  • The Blackboard : F-
    An awful blog run by a mechanical engineer which at one point had climate science discussion but now consists of pro-Trump cheerleading.
  • Clive Best : D+
    The moderator tries hard but then stumbles as he desperately tries to debunk the AGW consensus. Marginally better than Science of Doom because at least the scientific ideas are creative.
  • Climate Audit : F-
    Awful conspiracy-laden blog run by a former Canadian mining executive.
  • Climate Etc : F-
    Pointless blog stressing climate science uncertainty run by a now-retired climate science professor J. Curry with a comment section that seems infested with Australian AGW deniers. 
  • Moyhu : B
    Halfway-decent posts by a retired fluid dynamics researcher but an ugly and unstable comment-entry system. 
  • Hotwhopper : C+
    Well-thought out counter-attacks to nonsense at sites such as WUWT, but nothing really about discussions of science
  • Robert Scribbler : C
    The American version of HotWhopper, with probably too much doom & gloom.
  • Skeptical Science: D
    Nothing interesting here as they never seem to veer from the consensus.  The comments seem to be overly moderated and at one time the RSS feed was broken, but that has recently been fixed.
  • Roy Spencer, PhD : F-
    Horrible blog by a religious zealot with comments infested by AGW deniers
  • Rabbet Run : B-
    Below Moyhu because nothing really innovative but occasional insight
  • More Grumbine Science : B
    By a NASA guy,  posts very rarely

This is a previous summary I had written two years ago (I had forgotten I had saved it in a draft folder, and so you can see how little has changed)

Blog Grade Rationale
Real Climate C Too long turnaround for comments
And Then There’s Physics D Too much ClimateBall
Skeptical Science D Too insular, won’t discuss cutting edge
Science of Doom D- Inflitrated by deniers
Open Mind C Too much on statistics, which does a disservice to unlocking deterministic aspects such as ENSO
Moyhu B Worst comment entry, but the research is quality
This Week in Science: DailyKos C+ Nothing in depth
Watt’s Up With That F Garbage
Tallbloke’s Talkshop F Loony bin
The Blackboard F Nasty people
Climate Etc F Clueless (mainly Aussies) lead by a clueless
Roy Spencer F Zero real science
Rabbet Run C Too much inside posturing
Hot Whopper C Good if you want to see deniers get debunked
Robert Scribbler C Verges on hysterical but who knows
Azimuth Project A A true forum. Allows everyone to create markup and add charts

Commenting at PubPeer

For our Mathematical GeoEnergy book, there is an entry at PubPeer.com for comments (one can also comment at Amazon.com, but you need to be a verified purchaser of the book to be able to comment there)

PubPeer provides a good way to debunk poorly researched work as shown in the recent comments pertaining to the Zharkova paper published in Nature’s Scientific Reports journal.

An issue with the comment policy at Amazon is that one can easily evaluate the contents of a book via the “Look Inside” feature or through the Table of Contents. Often there is enough evidence to provide a critical book review just through this feature — in a sense, a statistical sampling of the contents — yet Amazon requires a full purchase before a review is possible. Even if one can check the book out at a university library this is not allowable. Therefore it favors profiting by the potential fraudster because they will get royalties in spite of damaging reviews by critics that are willing to sink money into a purchase.

In the good old days at Amazon, one could actually warn people about pseudo-scientific research. This is exemplified by Curry’s Bose-Einstein statistics debacle, where unfortunately political cronies and acolytes of Curry’s have since purchased her book and have used the comments to do damage control. No further negative comments are possible since smart people have not bought her book and therefore can no longer comment.

PubPeer does away with this Catch-22 situation.

Mathematical GeoEnergy

Book will be out next year published by Wiley


This blog will be ramped up for the book, but ContextEarth.com contains all the research leading up to the book.

Two papers at AGU 2017:



Dynamic Context Server

Tropics, poles and reefs

Diagram Monkey

2014, 2015 and 2016 played a recurring theme of El Nino. A tentative El Nino in late 2014 and early 2015 segued with a stutter into a strong El Nino in 2015/2016 dragging global temperatures in train. Temperatures in the tropical Pacific dropped a bit after that and may or may not have slipped into La Nina depending on which agency you listen to, but now, it looks like El Nino might be coming back: surface water temperatures in the eastern Pacific, off the coast of South America, have risen to four or more degrees above average although they’ve not spread further west and a number of seasonal forecasting centres are suggesting that temperatures might continue to rise. No one’s called it an El Nino, yet, but the effects of the elevated sea-surface temperatures are sadly plain to see. Heavy rain in Peru has already led to flooding and all the…

View original post 261 more words


Please refer to my new WordPress blog Context/Earth for future posts.

WordPress has better commenting options such as provisions for pictures and charts.

The scope of the blog is also more comprehensive, as it will include all environmental and energy topics tied together in a semantic web framework. 

Onward and upward as they say.