Ocean

Simpler models … examples

/ Paul Pukite (@whut) / 3 Comments

… continued from last post.

Each fitted model result shows the cross-validation results based on training of held-out data — i.e. training on only the intervals outside of 0.6-0.8 (i.e. training on t<0.6 and t>0.8 of the data, which extends from t=0.0 to t=1.0 normalized). The best results are for time-series that have 100 years or more worth of monthly data, so the held-out data is typically 20 years. There is no selection bias trickery here, as this is a collection of independent sites and nothing in the MLR fitting process is specific to an individual time-series. In the following, the collection of results starts with the Stockholm site in Sweden, keeping in mind that the dashed line in the charts indicates the test or validation interval.

I was recently in Stockholm, and this is a photo pointed toward the location of the measurement station, about 4000 feet away labeled by the marker on the right below:
Stockholm, Sweden
Korsor, Denmark
Klaipeda, Lithuania
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Simpler models can outperform deep learning at climate prediction

/ Paul Pukite (@whut) / 3 Comments

This article in MIT News:

https://news.mit.edu/2025/simpler-models-can-outperform-deep-learning-climate-prediction-0826

“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).

https://pukpr.github.io/results/image_results.html

“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. “

Mathematical GeoEnergy 2018 vs ChatGPT 2025

/ Paul Pukite (@whut) / Leave a comment

On RealClimate.org

Paul Pukite (@whut) says

1 JUL 2025 AT 9:48 PM

Your comment is awaiting moderation.

“If so, do you have an explanation why the diurnal tides do not move the thermocline, whereas tides with longer periods do?”

The character of ENSO is that it shifts by varying amounts on an annual basis. Like any thermocline interface, it reaches the greatest metastability at a specific time of the year. I’m not making anything up here — the frequency spectrum of ENSO (pick any index NINO4, NINO34, NINO3) shows a well-defined mirror symmetry about the value 0.5/yr. Given that Incontrovertible observation, something is mixing with the annual impulse — and the only plausible candidate is a tidal force.
So the average force of the tides at this point is the important factor to consider. Given a very sharp annual impulse, the near daily tides alias against the monthly tides — that’s all part of mathematics of orbital cycles. So just pick the monthly tides as it’s convenient to deal with and is a more plausible match to a longer inertial push.

Sunspots are not a candidate here.

Some say wind is a candidate. Can’t be because wind actually lags the thermocline motion.

So the deal is, I can input the above as a prompt to ChatGPT and see what it responds with

https://chatgpt.com/share/68649088-5c48-8010-a767-4fe75ddfeffc

Chat GPT also produces a short Python script which generates the periodogram of expected spectral peaks.

I placed the results into a GitHub Gist here, with charts:
https://gist.github.com/pukpr/498dba4e518b35d78a8553e5f6ef8114

I made one change to the script (multiplying each tidal factor by its frequency to indicate its inertial potential, see the ## comment)

At the end of the Gist, I placed a representative power spectrum for the actual NINO4 and NINO34 data sets showing where the spectral peaks match. They all match. More positions match if you consider a biennial modulation as well.

Now, you might be saying — yes, but this all ChatGPT and I am likely coercing the output. Nothing of the sort. Like I said, I did the original work years ago and it was formally published as Mathematical Geoenergy (Wiley, 2018). This was long before LLMs such as ChatGPT came into prominence. ChatGPT is simply recreating the logical explanation that I had previously published. It is simply applying known signal processing techniques that are generic across all scientific and engineering domains and presenting what one would expect to observe.

In this case, it carries none of the baggage of climate science in terms of â€śyou can’t do that, because that’s not the way things are done here”. ChatGPT doesn’t care about that prior baggage — it does the analysis the way that the research literature is pointing and how the calculation is statistically done across domains when confronted with the premise of an annual impulse combined with a tidal modulation. And it nailed it in 2025, just as I nailed it in 2018.

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Teleconnection vs Common-Mode

/ Paul Pukite (@whut) / 3 Comments

A climate teleconnection is understood as one behavior impacting another — for example NINOx => AMO, meaning the Pacific ocean ENSO impacting the Atlantic ocean AMO via a remote (i.e. tele) connectiion. On the other hand, a common-mode behavior is a result of a shared underlying cause impacting a response in a uniquely parameterized fashion — for example NINOx = g(F(t), {n1, n2, n3, ...}) and AMO = g(F(t), {a1, a2, a3, ...}), where the n's are a set of constant parameters for NINOx and the a's are for AMO.

In this formulation F(t) is a forcing and g() is a transformation. Perhaps the best example of a common-mode response to a forcing is in the regional tidal response in local sea-level height (SLH). Obviously, the lunisolar forcing is a common mode in different regions and subtle variations in the parametric responses is required to model SLH uniquely. Once the parameters are known, one can make practical predictions (subject to recalibration as necessary).

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Difference Model Fitting

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By applying an annual impulse sample-and-hold on a common-mode basis set of tidal factors, a wide range of climate indices can be modeled and cross-validated. Whether it is a biennial impulse or annual impulse, the slowly modulating envelope is roughly the same, thus models of multidecadal indices such as AMO and PDO show similar skill — with cross validation results evaluated here for a biennial impulse. Now we will evaluate for annual impulse.

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Google Gemini Deep Research on ENSO

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First evaluation of Gemini Advanced 1.5 Pro with Deep Research. Logged in with trial subscription and gave this as an initial prompt. Saved the results to a Google Docs file, and then created the following PDF. Note the top-level focus on this blog and published citations in the scope of Chapter 12 of Mathematical Geoenergy, even though the chapter was not directly cited — only via an embedded cite in a submitted ESD Ideas article, reference 1. Interesting that the Lin & Qian paper not cited.

Prompt: Explain tidal forcing behind ENSO using derivations based on reduced effective gravity on equatorial thermocline.

Tidal Forcing and ENSO Dynamics_Download

Tidal Gauge Differential

/ Paul Pukite (@whut) / 2 Comments

A climate science breakthrough likely won’t be on some massive computation but on a novel formulation that exposes some fundamental pattern (perhaps discovered by deep mining during a machine learning exercise). Over 10 years ago, I wrote on a blog post on how one can extract the ENSO signal by doing simple signal processing on a sea-level height (SLH) tidal time-series — in this case, at Fort Denison located in Sydney harbor.

The formulation/trick is to take the difference between the SLH reading and that from 2 years (24 months) prior, described here

An ENSO Predictor Based on a Tide Gauge Data Model

Check the recent blog post Lunar Torque Controls All for context of how it fits in to the unified model.

https://geoenergymath.com/wp-content/uploads/2024/11/image-30.png

The rationale for this 24 month difference is likely related to the sloshing of the ocean triggered on an annual basis. I think this is a pattern that any ML exercise would find with very little effort. After all, it didn’t take me that long to find it. But the point is that the ML configuration has to be open and flexible enough to be able to search, generate, and test for the same formulation. IOW, it may not find it if the configuration, perhaps focused on computationally massive PDEs, is too narrow. That was my comment to a RC post on applying machine learning to climate science, see the following link and subsequent quote:

¡AI Caramba!

Nick McGreivy commented on:

“ML-based parameterizations have to work well for thousands of years of simulations, and thus need to be very stable (no random glitches or periodic blow-ups) (harder than you might think). Bias corrections based on historical observations might not generalize correctly in the future.”

This same issue arises when using ML to simulate PDEs. The solution is to analytically calculate what the stability condition(s) is (are), then at each timestep to add some numerical diffusion that nudges the solution towards satisfying the stability condition(s). I imagine this same technique could be used for ML-based parametrizations.

Lunar Torque Controls All

/ Paul Pukite (@whut) / 14 Comments

Mathematical Geoenergy

The truly massive scale in the motion of fluids and solids on Earth arises from orbital interactions with our spinning planet. The most obvious of these, such as the daily and seasonal cycles, are taken for granted. Others, such as ocean tides, have more complicated mechanisms than the ordinary person realizes (e.g. ask someone to explain why there are 2 tidal cycles per day). There are also less well-known motions, such as the variation in the Earth’s rotation rate of nominally 360° per day, which is called the delta in Length of Day (LOD), and in the slight annual wobble in the Earth’s rotation axis. Nevertheless, each one of these is technically well-characterized and models of the motion include a quantitative mapping to the orbital cycles of the Sun, Moon, and Earth. This is represented in the directed graph below, where the BLUE ovals indicate behaviors that are fundamentally understood and modeled via tables of orbital factors.

The cyan background represents behaviors that have a longitudinal dependence
(rendered by GraphViz)

However, those ovals highlighted in GRAY are nowhere near being well-understood in spite of being at least empirically well-characterized via years of measurements. Further, what is (IMO) astonishing is the lack of research interest in modeling these massive behaviors as a result of the same orbital mechanisms as that which causes tides, seasons, and the variations in LOD. In fact, everything tagged in the chart is essentially a behavior relating to an inertial response to something. That something, as reported in the Earth sciences literature, is only vaguely described — and never as a tidal or tidal/annual interaction.

I don’t see how it’s possible to overlook such an obvious causal connection. Why would the forcing that causes a massive behavior such as tides suddenly stop having a connection to other related inertial behaviors? The answers I find in the research literature are essentially that “someone looked in the past and found no correlation” [1].

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AMO and the Mt tide

/ Paul Pukite (@whut) / 1 Comment

Geophysics is a challenging endeavor — one part geology as historical evidence and the other part current measurements revealing how the forces of nature are continuously shaping the behavior of the Earth. Yet, how much faith can we place on any one interpretation, or on any past consensus?

"But for geophysics on such a massive scale, nothing can be checked via a lab controlled experiment."Someone has described geology!I prefer my own description (though taken from someone else and modified): Geology is like trying to learn about barley by studying beer.

— Compton Scatterbrained (@stommepoes.bsky.social) 2024-09-18T15:13:20.671Z

This goes double for the study of geophysical fluid dynamics — volumes and forces so large that controlled experiments are impossible. So that when a semi-controlled impulse comes about, say from the calving of a glacier, the empirical results may be surprising:

The subsequent mega-tsunami — one of the highest in recent history — set off a wave which became trapped in the bendy, narrow fjord for more than a week, sloshing back and forth every 90 seconds.

The phenomenon, called a “seiche,” refers to the rhythmic movement of a wave in an enclosed space, similar to water splashing backwards and forwards in a bathtub or cup. One of the scientists even tried (and failed) to recreate the impact in their own bathtub.

While seiches are well-known, scientists previously had no idea they could last so long.

“Had I suggested a year ago that a seiche could persist for nine days, people would shake their heads and say that’s impossible,” said Svennevig, who likened the discovery to suddenly finding a new colour in a rainbow. — http://www.msn.com/en-in/news/techandscience/what-caused-the-mysterious-9-day-earth-vibration-scientists-point-to-650-ft-mega-tsunami-that-rocked-greenland/ar-AA1qwIqk

This took place in a large Greenland fjord — massive but not as massive as the ocean. And that’s where massive geophysical forces also take place, such as from tidal pull.

So what about the Atlantic Multidecadal Oscillation (AMO)? The Mt long-period tide is an interference between the Mf nodal tidal cycle (13.66 days) and the Mm anomalistic tidal cycle (27.55 days). When this is synchronized to an annual impulse, a multidecadal response results.

It is much too easy to model the 50-60 year AMO cycle via nonlinear triad frequency-doubling mechanisms, and also simulate the faster cycling from the predominate Mf and Mm interactions with the annual cycle. This is essentially a sloshing behavior operating on the ocean’s thermocline as described in Chapter 12 of Mathematical Geoenergy, applying the nonlinear geophysical dynamics embedded within Laplace’s Tidal Equations.

New colors of the rainbow are waiting to be revealed. No excuse for others to reproduce the tidal forcing models as described and perform cross-validated model fits to replicate the results above. Work smart not hard.

NAO and the Median Filter

/ Paul Pukite (@whut) / Leave a comment

a random quote

“LLMs run a median filter on the corpus”

The North Atlantic Oscillation (NAO) time-series has always been intimidating to analyze. It appears outwardly like white-noise, but enough scientists refer to long periods of positive or negative-leaning intervals that there must be more of an underlying autocorrelation embedded in it. To reduce the white noise and to extract the signal requires a clever filtering trick. The desire is that the filter preserve or retain the edges of the waveform while reducing the noise level. The 5-point median filter does exactly that at a minimal complexity level, as the algorithm is simply expressed. It will leave edges and steep slopes alone as the median will naturally occur on the slope. That’s just what we want to retain the underlying signal.

Once applied, the NAO time-series still appears erratic, yet the problematic monthly extremes are reduced with the median filter suppressing many of them completely. If we then use the LTE model to fit the NAO time-series (with a starting point the annual-impulsed tidal forcing used for the AMO), a clear correlation emerges. The standing-wave modes of course are all high, in contrast to the one low mode for the AMO, so the higher frequency cycling is expected yet the fit is surprisingly good for the number of peaks and valleys it must traverse in the 140+ year historical interval.