“New research shows the natural variability in climate data can cause AI models to struggle at predicting local temperature and rainfall.” … “While deep learning has become increasingly popular for emulation, few studies have explored whether these models perform better than tried-and-true approaches. The MIT researchers performed such a study. They compared a traditional technique called linear pattern scaling (LPS) with a deep-learning model using a common benchmark dataset for evaluating climate emulators. Their results showed that LPS outperformed deep-learning models on predicting nearly all parameters they tested, including temperature and precipitation.“
Machine learning and other AI approaches such as symbolic regression will figure out that natural climate variability can be done using multiple linear regression (MLR) with cross-validation (CV), which is an outgrowth or extension of linear pattern scaling (LPS).
“When this was initially created on 9/1/2025, there were 3000 CV results on time-series that averaged around 100 years (~1200 monthly readings/set) so over 3 million data points“
In this NINO34 (ENSO) model, the test CV interval is shown as a dashed region
I developed this github model repository to make it easy to compare many different data sets, much better than using an image repository such as ImageShack.
There are about 130 sea-level height monitoring stations in the sites, which is relevant considering how much natural climate variation a la ENSO has an impact on monthly mean SLH measurements. See this paper Observing ENSO-modulated tides from space
“In this paper, we successfully quantify the influences of ENSO on tides from multi-satellite altimeters through a revised harmonic analysis (RHA) model which directly builds ENSO forcing into the basic functions of CHA. To eliminate mathematical artifacts caused by over-fitting, Lasso regularization is applied in the RHA model to replace widely-used ordinary least squares. “
TANSTAAFL: there ain’t no such thing as a free lunch … but there’s always crumbs for the taking.
Machine learning won’t necessarily make a complete discovery by uncovering some ground-breaking pattern in isolation, but more likely a fragment or clue or signature that could lead somewhere. I always remind myself that there are infinitely many more non-linear formulations than linear ones potentially lurking in nature, yet humans are poorly-equipped to solve most non-linear relationships. ML has started to look at the tip of the non-linear iceberg and humans have to be alert when it uncovers a crumb. Recall that pattern recognition and signal processing are well-established disciplines in their own right, yet consider the situation of searching for patterns in signals hiding in the data but unknown in structure. That’s often all we are looking for — some foot-hold to start from.
In addition to the standard correlation coefficient (CC) and RMS error, non-standard metrics that have beneficial cross-validation properties include dynamic time warp (DTW), complexity invariant-distance (CID) see [2], and a CID-modified DTW. The link above describes my implementation of the DTW metric but I have yet to describe the CID metric. It’s essentially the CC multiplied by a factor that empirically adjusts the embedded summed distance between data points (i.e. the stretched length) of the time-series so that the signature or look of two time-series visually match in complexity.
CID = CC * min(Length(Model, Data))/ max(Length(Model, Data))
The authors of the CID suggest that it’s a metric based on “an invariance that the community seems to have missed”.
These have similar tidal factor compositions and differ mainly in the LTE modulation and phase delay. As discussed earlier, any anomalies in the QBO behavior are likely the outcome of an erratic periodicity caused by incommensurate annual and draconic cycles and exaggerated by LTE.
In formal mathematical terms of geometry/topology/homotopy/homology, let’s try proving that a wavenumber=0 cycle of east/west direction inside an equatorial toroidal-shaped waveguide, can only be forced by the Z-component of a (x,y,z) vector where x,y lies in the equatorial plane.
To address this question, let’s dissect the components involved and prove within the constraints of geometry, topology, homotopy, and homology, focusing on valid mathematical principles.
Based on the previous post on applying Dynamic Time Warping as a metric for LTE modeling of oceanic indices, it makes sense to apply the metric to the QBO model of atmospheric winds. A characteristic of QBO data is the sharp transitions of wind reversals. As described previously, DTW allows a fit to adjust the alignment between model and data without incurring a potential over-fitting penalty that a conventional correlation coefficient will often lead to.
The ocean is stunning at the moment. Many hotspots. This viz puts the recent global SST anomalies into the context of the last 4 decades. Look closely. Some regions are "on trend," some are short-term spikes, and some are combinations.#GlobalWarming#ClimateEmergencypic.twitter.com/0xf188RPgJ
These correspond to the geographically defined climate indices
Overall I’m confident with the status of the published analysis of Laplace’s Tidal Equations in Mathematical Geoenergy, as I can model each of these climate indices with precisely the same (save one ***) tidal forcing, all calibrated by LOD. The following Threads allow interested people to contribute thoughts
Sorry to have to point this out, but it’s not my fault that geophysicists and climatologists can’t perform controlled experiments to test out various hypotheses. It’s not their fault either. It’s all nature’s decision to make gravitational forces so weak and planetary objects so massive to prevent anyone from scaling the effect to laboratory size to enable a carefully controlled experiment. One can always create roughly-equivalent emulations, such as a magnetic field experiment (described in the previous blog post) and validate a hypothesized behavior as a controlled lab experiment. Yet, I suspect that this would not get sufficient buy-in, as it’s not considered the actual real thing.
And that’s the dilemma. By the same token that analog emulators will not be trusted by geophysicists and climatologists, so too scientists from other disciplines will remain skeptical of untestable claims made by earth scientists. If nothing definitive comes out of a thought experiment that can’t be reproduced by others in a lab, they remain suspicious, as per their education and training.
It should therefore work both ways. As featured in the previous blog post, the model of the Chandler wobble forced by lunar torque needs to be treated fairly — either clearly debunked or considered as an alternative to the hazy consensus. ChatGPT remains open about the model, not the least bit swayed by colleagues or tribal bias. As the value of the Chandler wobble predicted by the lunar nodal model (432.7 days) is so close to the cited value of 433 days, as a bottom-line it should be difficult to ignore.
There are other indicators in the observational data to further substantiate this, see Chandler Wobble Forcing. It also makes sense in the context of the annual wobble.
As it stands, the lack of an experiment means a more equal footing for the alternatives, as they are all under equal amounts of suspicion.
Same goes for QBO. No controlled experiment is possible to test out the consensus QBO models, despite the fact that the Plumb and McEwan experiment is claimed to do just that. Sorry, but that experiment is not even close to the topology of a rotating sphere with a radial gravitational force operating on a gas. It also never predicted the QBO period. In contrast, the value of the QBO predicted by the lunar nodal model (28.4 months) is also too close to the cited value of 28 to 29 months to ignore. This also makes sense in the context of the semi-annual oscillation (SAO) located above the QBO .
Both the Chandler wobble and the QBO have the symmetry of a global wavenumber=0 phenomena so therefore only nodal cycles allowed — both for lunar and solar.
Next to ENSO. As with LOD modeling, this is not wavenumber=0 symmetry, as it must correspond to the longitude of a specific region. No controlled experiment is possible to test out the currently accepted models, premised as being triggered by wind shifts (an iffy cause vs. effect in any case). The mean value of the ENSO predicted by the tidal LOD-caibrated model (3.80 years modulated by 18.6 years) is too close to the cited value of 3.8 years with ~200 years of paleo and direct measurement to ignore.
In BLUE below is the LOD-calibrated tidal forcing, with linear amplification
In BLUE again below is a non-linear modulation of the tidal forcing according to the Laplace’s Tidal Equation solution, and trained on an early historical interval. This is something that a neural network should be able to do, as it excels at fitting to non-linear mappings that have a simple (i.e. low complexity) encoding — in this case it may be able to construct a Taylor series expansion of a sinusoidal modulating function.
The neural network’s ability to accurately represent a behavior is explained as a simplicity bias — a confounding aspect of machine learning tools such as ChatGPT and neural networks. The YouTube video below explains the counter-intuitive notion of how a NN with a deep set of possibilities tends to find the simplest solution and doing this without over-fitting the final mapping.
So that deep neural networks are claimed to have a built-in Occam’s Razor propensity, finding the most parsimonious input-output mappings when applied to training data. This is spot on with what I am doing with the LTE mapping, but bypassing the NN with a nonlinear sinusoidal modulation optimally fit on training data by a random search function.
I am tempted to try a NN on the ENSO training set as an experiment and see what it finds.
April 2, 2023
“I am tempted to try a NN on the ENSO training set as an experiment and see what it finds.”
I don’t immediately trust the research published by highly cited atmospheric scientists. By my count many of them seem more keen on presenting their personal views rather than advancing the field. Off the top of my head, Richard Lindzen, Murry Salby, Roy Spencer, Tim Dunkerton, Roger Pielke, Cliff Mass, Judith Curry are all highly cited but come across as political and/or religious zealots. One guy on the list, Dunkerton, is also a racist, who happened to make the Washington Post twice : “Physicist ousted from research post after sending offensive tweet to Hispanic meteorologist” and “Atmospheric scientist loses honor, membership over ethics violation“. Awful stuff and he hasn’t stopped spouting off on Twitter.
Granted that Dunkerton says dumb stuff on Twitter but his highly cited research is also off-base. That’s IMO only because recent papers by others in the field of atmospheric science do continue to cite his ideas as primary, if not authoritative. For example, from a recently published paper “The Gravity Wave Activity during Two Recent QBO Disruptions Revealed by U.S. High-Resolution Radiosonde Data”, citations 1 & 12 both refer to Dunkerton, and specifically to his belief that the QBO period is a property of the atmospheric medium itself
Straight-forward to debunk this Dunkerton theory since the length of the cycle directly above the QBO layer is semi-annual and thus not a property of the medium but of the semi-annual nodal forcing frequency. If we make the obvious connection to the other nodal forcing — that of the moon — then we find the QBO period is fixed to 28 months. I have been highlighting this connection to the authors of new QBO papers under community review, often with some subsequent feedback provided such as here: https://doi.org/10.5194/acp-2022-792-CC1 . Though not visible yet in the comments, I received some personal correspondence that showed that the authors under peer-review are taking the idea seriously and attempting to duplicate the calculations. They seem to be methodical in their approach, asking for clarification and further instructions where they couldn’t follow the formulation. They know about the GitHub software, so hopefully that will be of some help.
In contrast, Dunkerton also knows about my approach but responds in an inscrutable (if not condescending) way. Makes you wonder if scientists such as Dunkerton and Lindzen are bitter and taking out their frustrations via the media. Based on their doggedness, they may in fact be intentionally trying to impede progress in climate science by taking contrarian stances. In my experience, the top scientists in other research disciplines don’t act this way. YMMV
As a review, this was after commenting earlier this year on a Copernicus open-science research article on atmospheric cycles and QBO (with proposed links to sunspots and ENSO) that was undergoing a review, making a suggestion to consider analyses I had presented and published 4 years ago and also prior to that.
Thought that was that and was happy to see that the authors indicated they would revise the manuscript and perhaps advance understanding. But then several days ago, the editor interceded and essentially demanded that the authors not cite my research work. Apparently, the authors were influenced by the editor’s instructions, as they immediately removed my cite and replaced it with a citation to a review article that the editor preferred. The discussion on the article was then closed with no way for me to rebut.
This was all after I spent several hours working with the primary author as they worked to replicate my analysis, sending emails back and forth several times. The editor claimed that my contribution was “a new idea that has not been published in a recognized journal and received peer review”. This is not the case as I said above: Google Scholar citations all ignored.
Trying to understand QBO may lead to madness, if the plights of Richard Lindzen (Macbeth) and Timothy Dunkerton (Hamlet) are any indication. It was first Lindzen — the primary theorist behind QBO — in his quest for scientific notoriety that led to lofty pretentiousness and eventually bad blood with his colleagues. Now it’s the Lindzen-acolyte Dunketon’s turn, avenging his “uncle” with troubling behavior
Regarding the gravity waves concentrically emanating from the Tonga explosion
“It’s really unique. We have never seen anything like this in the data before,” says Lars Hoffmann, an atmospheric scientist at the Jülich Supercomputing Centre in Germany.
“That’s what’s really puzzling us,” says Corwin Wright, an atmospheric physicist at the University of Bath, UK. “It must have something to do with the physics of what’s going on, but we don’t know what yet.”
The discovery was prompted by a tweet sent to Wright on 15 January from Scott Osprey, a climate scientist at the University of Oxford, UK, who asked: “Wow, I wonder how big the atmospheric gravity waves are from this eruption?!” Osprey says that the eruption might have been unique in causing these waves because it happened very quickly relative to other eruptions. “This event seems to have been over in minutes, but it was explosive and it’s that impulse that is likely to kick off some strong gravity waves,” he says. The eruption might have lasted moments, but the impacts could be long-lasting. Gravity waves can interfere with a cyclical reversal of wind direction in the tropics, Osprey says, and this could affect weather patterns as far away as Europe. “We’ll be looking very carefully at how that evolves,” he says.
This (“cyclical reversal of wind direction in the tropics”) is referring to the QBO, and we will see if it has an impact in the coming months. Hint: the QBO from the last post is essentially modeling gravity waves arising from the tidal forcing as driving the cycle. Also, watch the LOD.
Perhaps the lacking is in applying this simple scientific law: for every action there is a reaction. Always start from that, and also consider: an object that is in motion, tends to stay in motion. Is the lack of observed Coriolis effects to first-order part of why the scientists are mystified? Given the variation of this force with latitude, the concentric rings perhaps were expected to be distorted according to spherical harmonics.
