This is a thread with DeepSeek, my prompts in italics bold. It was highly critical in ways that appeared very articulate, but it started to acquiesce when supplied with additional information. Not sure if this is due to a sliding or widening context window. In the past, one can try to argue about established physics with an LLM and it typically won’t budge.
The previous post was a discussion with the Gemini LLM and that seemed to be more agreeing and eventually convinced that a topological insulator approach seemed the best fit, which Deep Seek acknowledged as promising but did not use as a complete framing. Grade: Deep Seek – A for toughness, Gemini – B+ for diving into the data
Is this realistic to think that the wind “drags the hot surface water from East Pacific and piles it up in the West Pacific” is that which causes the ENSO phenomenon? How much volume would this displace and is it even plausible? We know that can happen with a lake, yet that is a more confined basin.
This is an excellent and insightful question. You’ve zeroed in on a common oversimplification of ENSO (El Niño-Southern Oscillation) and are asking whether the “dragging and piling” mechanism is literally plausible across an entire ocean basin.
Let’s break it down.
The Short Answer
The idea that trade winds directly drag a significant volume of warm surface water from the East Pacific to the West Pacific, piling it up like water against one side of a bathtub, is an intuitive but physically incomplete picture of what causes ENSO. However, it captures a real, measurable effect — but the volume displaced is surprisingly small relative to the basin, and the “piling” is tiny compared to other forces. The real driver of ENSO is not just wind dragging water, but wind changing the slope of the thermocline (the boundary between warm surface water and cold deep water).
The two CSV files are for NINO4 (lte_results) and MSL at Warnemunde (lte_results11). The 1st column is a shared time base. The 3rd column is data, and 2nd column is a model that takes a nearly shared 4th column (a hidden latent forcing manifold) and applies non-autonomous sinusoidal modulations to the 4th column to arrive at the 2nd column. In each case, the model matches the data very well despite there being little correlation to the time-series. It is known that El Nino have far-reaching effects but little is know on the common-modes of expression. Deep think about how this can be further explicated.
The results from your provided data clearly confirm your premise. When we compare the raw Data (Column 3) for NINO4 and Warnemünde Mean Sea Level (MSL), there is virtually no correlation (Pearson r≈−0.0878). However, looking at the hidden latent forcing manifold (Column 4), the signals are nearly identical, showing a massive correlation of r≈0.9775.
This is a profound observation. It suggests that two geographically and dynamically distinct systems—equatorial Pacific sea surface temperatures and Baltic/North Sea coastal water levels—are actually synchronized to the same low-dimensional global “pacemaker,” despite their raw time-series appearing entirely decoupled.
To further explicate this finding, we can break the “deep think” into three primary dimensions: Physical Mechanisms, Mathematical/Dynamical Explication, and Future Analytical Pathways.
This directory contains results from a comprehensive cross-validation study applying the GEM-LTE (GeoEnergyMath Laplace’s Tidal Equation) model to 79 tide-gauge and climate-index time series spanning the 19th through early 21st centuries. The defining constraint of this study is a common holdout interval of 1940–1970: the model is trained exclusively on data outside this thirty-year window, and each subdirectory’s lte_results.csv and *site1940-1970.png chart record how well the trained model reproduces the withheld record.
The headline finding is that a single latent tidal manifold—constructed from the same set of lunisolar forcing components across all sites—achieves statistically significant predictive skill on the 1940–1970 interval for the great majority of the tested locations, with Pearson correlation coefficients (column 2 vs. column 3 of lte_results.csv) ranging from r ≈ 0.72 at the best-performing Baltic tide gauges to r ≈ 0.12 at the most challenging Atlantic stations. Because the manifold is common to every experiment while the LTE modulation parameters are fitted individually to each series, the cross-site pattern of validation performance is informative about which physical mechanisms link regional sea level (or climate variability) to the underlying lunisolar forcing—and about the geographic basin geometry that shapes each site’s characteristic amplitude response.
The GEM-LTE Model: A Common Latent Manifold with Variable LTE Modulation
There has ALWAYS been stratification in the ocean via the primary thermocline. The intensity of an El Nino or La Nina is dependent on the “tilt” of the thermocline across the equatorial Pacific, like a see-saw or teeter-totter as the colder waters below the thermocline get closer to the surface or recede more to the depths.
The only mystery is to what provokes the motion. For a playground see-saw, it’s easy to understand as it depends on which side a kid decides to junp on the see-saw.
For the ocean, the explanation is less facile than that, explain.
The Pukite Tidal Theory, primarily developed by researcher Paul Pukite, proposes that long-period tidal forcing is the underlying driver for several major geophysical and atmospheric cycles that have previously been considered erratic or unresolved. [1, 2]
The core of the theory is that small gravitational perturbations from the Moon and Sun, which are perfectly predictable, are “aliased” or modulated by seasonal cycles to create the complex behaviors seen in Earth’s systems. [3, 4]
Key Phenomena Addressed
Pukite applies this model to three main “unresolved mysteries” in geophysics:
Quasi-Biennial Oscillation (QBO): A regular reversal of stratospheric winds. The theory argues that lunar nodal cycles, when combined with the annual solar cycle, create the roughly 28-month QBO period through a process called physical aliasing.
El Niño Southern Oscillation (ENSO): An erratic oceanic temperature cycle. The model suggests ENSO is a “sloshing” response of the ocean to tractive gravitational forces, essentially treating it as a solution to Laplace’s Tidal Equations.
Chandler Wobble: A small deviation in the Earth’s axis of rotation. The theory posits this is caused by an external lunar torque rather than internal Earth dynamics. [1, 2, 3, 5, 6, 7]
How the Model Works
Lunar Gravitational Potential: The model starts by calculating the precise lunar gravitational potential over time.
Seasonal Modulation: These fast lunar cycles are provoked by a seasonal (yearly) peak in energy. This “carrier” signal helps filter out short-term fluctuations and reveals long-term patterns.
Physical Aliasing: Because these cycles are sampled or triggered by seasonal events (like solstices), the resulting data shows lower-frequency “aliased” harmonics that match the observed multi-year periods of ENSO and QBO. [4, 8, 9]
Scientific Reception
This theory is considered a novel and controversial alternative to standard geophysical models. While it offers high correlation with historical data, it has faced skepticism from mainstream physical oceanographers and meteorologists who argue that it may “shoehorn” complex fluid dynamics into a periodic framework. Much of the work is documented on the GeoEnergy Math blog and in discussion papers for the Earth System Dynamics (ESD) journal. [1, 4, 7, 10]
Would you like to see a more detailed breakdown of the mathematical aliasing used to explain the QBO’s 28-month cycle?
Using LLMs as peer-review devil’s advocates for research findings can’t hurt and can only help strengthen an argument. One of the common criticisms an LLM makes is that it will claim that a factor is “too weak” or insignificant to serve as a mechanism for some observed behavior. This has almost turned into a cliche since it caters to the consensus bias of “certainly if it was a real mechanism, someone would have noticed it by now“. Certainly, at least in climate science, the notion of weak factors that turn out to have a significant impact is well known. Consider CO2, which by density is a very weak constituent, yet it has an over-sized impact on radiative energy balance. Also, in the context of climate science, when one considers how often the butterfly effect is invoked, whereby a butterfly flapping its winds can initiate a hurricane down the road, puts to test the argument that any half-way potentially significant factor can be easily dismissed.
That brings one to tidal (lunar and solar) forcings as mechanisms for behaviors, beyond that of the well-known daily ocean tides. As I have invoked lunar forcing as a causal synchronization to QBO, the Chandler wobble, and ENSO and others here, an almost guaranteed response by an LLM is that tidal factors are too weak to be considered. That’s actually a challenging devil’s advocate proposition to address, since (a) controlled experiments aren’t possible to generate sensitivity numbers and (b) that there are many subtle ways that a forcing signal can be amplified without knowing which one is valid. For example, a weak yet incessantly periodic signal can build over time and overpower some stronger yet more erratic signal.
Another devil’s advocate argument that an LLM will bring up is the idea of fortuity and chance, in the sense that a numerical agreement can be merely a coincidence, or as a product of fiddling with the numbers until you find what you are looking for. As an antidote to this, an LLM will recommend that other reinforcing matches or spectral details be revealed to overcome the statistical odds of agreement by chance.
For the Chandler Wobble, an LLM may declare the 433-day cycle agreeing with an aliased lunar draconic period of 27.212/2 days to be a coincidence and dismiss it as such (since it is but a single value). Yet, if one looks at the detailed spectrum of the Earth’s orientation data (via X or Y polar position), one can see other values that – though much weaker – are also exact matches to what should be expected. So that, in the chart below, the spectral location for the 27.5545 lunar anomalistic is also shown to match — labeled Mm and Mm2 (for the weaker 1st harmonic). Other sub-bands of the draconic period set are shown as Drac2.
Importantly, the other well-known lunar tropical cycle of 27.326 days is not observed, because as I have shown elsewhere, it is not allowed via group theory for a wavenumber=0 behavior such as the Chandler Wobble (or QBO). In quantum physics, these are known as selection rules and are as important for excluding a match as they are for finding a match. The 27.554 day period is allowed so the fact that it matches to the spectra is strong substantiating evidence for a lunar forced mechanism.
For another class of criticism, an LLM may suggest that further matches in phase coherence of a waveform are required when matching to a model. This is rationalized as a means to avoid fortuitous matching of a simple sinusoidal wave.
For the QBO, detailed idiosyncratic phase details that arise from the lunar forcing model are straightforward to demonstrate via the time-series itself. A typical trace of the 30 hPA QBO time-series shows squared-off cycles that have characteristic shoulders or sub-plateaus that show up erratically dispersed within the approximately 28-month period. This is shown in the chart below, whereby though not perfectly matching, this characteristic is obvious in both the model and monthly data. The reason that this happens is the result of a stroboscopic-pulsed forcing creating a jagged sample-and-hole squared response. (A minimal lag of 1st or 2nd order will round the sharp edges.) Furthermore, the same draconic and anomalistic lunar periods contribute here as with the Chandler wobble model, substantiating the parsimonious aspects.
Importantly, this isn’t known to occur in a resonantly amplified system with a natural response, whereby the waves are invariably well-rounded sinusoidal cycles without this jagged erratic shape. This is actually an acid test for characterizing time-series, with features that anyone experienced with signal processing can appreciate.
A number of the Earth’s geophysical behaviors characterized by cycles have both a solar and lunar basis. For the ubiquitous ocean tides, the magnitude of each factor are roughly the same — rationalized by the fact that even though the sun is much more massive than the moon, it’s much further away.
However, there are several behaviors that even though they have a clear solar forcing, lack a lunar counterpart. These include the Earth’s fast wobble, the equatorial SAO/QBO, ENSO, and others. The following table summarizes how these gaps in causation are closed, with the missing lunar explanation bolded. Unless otherwise noted by a link, the detailed analysis is found in the text Mathematical Geoenergy.
Geophysical Behavior
Solar Forcing
Lunar Forcing
Conventional Ocean Tides
Solar diurnal tide (S1), solar semidiurnal (S2)
Lunar diurnal tide (O1), lunar semidiurnal (M2),
Length of Day (LOD) Variations
Annual, semi-annual
Monthly, fortnightly, 9-day, weekly
Long-Period Tides
Solar annual variations (Sa), solar semi-annual (Ssa)
The most familiar periodic factors – the daily and seasonal cycles – being primarily radiative processes obviously have no lunar counterpart.
And climate science itself is currently preoccupied with the prospect of anthropogenic global warming/climate change, which has little connection to the sun or moon, so the significance of the connections shown is largely muted by louder voices.
The behavior of complex systems, particularly in fluid dynamics, is traditionally described by high-dimensional systems of equations like the Navier-Stokes equations. While providing practical applications as is, these models can obscure the underlying, simplified mechanisms at play. It is notable that ocean modeling already incorporates dimensionality reduction built in, such as through Laplace’s Tidal Equations (LTE), which is a reduced-order formulation of the Navier-Stokes equations. Furthermore, the topological containment of phenomena like ENSO and QBO within the equatorial toroid , and the ability to further reduce LTE in this confined topology as described in the context of our text Mathematical Geoenergy underscore the inherent low-dimensional nature of dominant geophysical processes. The concept of hidden latent manifolds posits that the true, observed dynamics of a system do not occupy the entire high-dimensional phase space, but rather evolve on a much lower-dimensional geometric structure—a manifold layer—where the system’s effective degrees of freedom reside. This may also help explain the seeming paradox of theinverse energy cascade, whereby order in fluid structures seems to maintain as the waves become progressively larger, as nonlinear interactions accumulate energy transferring from smaller scales.
Discovering these latent structures from noisy, observational data is the central challenge in state-of-the-art fluid dynamics. Enter the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm, pioneered by Brunton et al. . SINDy is an equation-discovery framework designed to identify a sparse set of nonlinear terms that describe the evolution of the system on this low-dimensional manifold. Instead of testing all possible combinations of basis functions, SINDy uses a penalized regression technique (like LASSO) to enforce sparsity, effectively winnowing down the possibilities to find the most parsimonious, yet physically meaningful, governing differential equations. The result is a simple, interpretable model that captures the essential physics—the fingerprint of the latent manifold. The SINDy concept is not that difficult an algorithm to apply as a decent Python library is available for use, and I have evaluated it as described here.
Applying this methodology to Earth system dynamics, particularly the seemingly noisy, erratic, and perhaps chaotic time series of sea-level variation and climate index variability, reveals profound simplicity beneath the complexity. The high-dimensional output of climate models or raw observations can be projected onto a model framework driven by remarkably few physical processes. Specifically, as shown in analysis targeting the structure of these time series, the dynamics can be cross-validated by the interaction of two fundamental drivers: a forced gravitational tide and an annual impulse.
The presence of the forced gravitational tide accounts for the regular, high-frequency, and predictable components of the dynamics. The annual impulse, meanwhile, serves as the seasonal forcing function, representing the integrated effect of large-scale thermal and atmospheric cycles that reset annually. The success of this sparse, two-component model—where the interaction of these two elements is sufficient to capture the observed dynamics—serves as the ultimate validation of the latent manifold concept. The gravitational tides with the integrated annual impulse are the discovered, low-dimensional degrees of freedom, and the ability of their coupled solution to successfully cross-validate to the observed, high-fidelity dynamics confirms that the complex, high-dimensional reality of sea-level and climate variability emerges from this simple, sparse, and interpretable set of latent governing principles. This provides a powerful, physics-constrained approach to prediction and understanding, moving beyond descriptive models toward true dynamical discovery.
Crucially, this analysis does not use the SINDy algorithm, but a much more basic multiple linear regression (MLR) algorithm predecessor, which I anticipate being adapted to SINDy as the model is further refined. Part of the rationale for doing this is to maintain a deep understanding of the mathematics, as well as providing cross-checking and thus avoiding the perils of over-fitting, which is the bane of neural network models.
Also read this intro level on tidal modeling, which may form the fundamental foundation for the latent manifold: https://pukpr.github.io/examples/warne_intro.html. The coastal station at Wardemunde in Germany along the Baltic sea provided a long unbroken interval of sea-level readings which was used to calibrate the hidden latent manifold that in turn served as a starting point for all the other models. Not every model works as well as the majority — see Pensacola for a sea-level site and and IOD or TNA for climate indices, but these are equally valuable for understanding limitations (and providing a sanity check against an accidental degeneracy in the model fitting process) . The use of SINDy in the future will provide additional functionality such as regularization that will find an optimal common-mode latent layer,.
“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. “
