Someone on Twitter suggested that tidal models are not understood “The tides connection to the moon should be revised.”. Unrolled thread after the “Read more” break
What’s totally screwed up is long-period tides (>=2 weeks). These impact large scale SLH cycles via fluid dynamics. Start with long record (>100 year) sites, such as Ft Denison in Sydney harbor.
Look at SLH at Brest in France — same tidal forcing (middle panel) but different response. Using a cross-validated interval for testing
Go to Honolulu SLH measurements, still the same tidal forcing. Unique response, starting to look like a machine learning candidate.
Now it gets weird. Start modeling large oceanic cycles. Obvious first candidate is ENSO, using the NINO4 index of SST. Promising cross-validation, same tidal forcing in middle panel
Flip over to Atlantic with AMO. The multidecadal tidal forcing is latent but emerges after training. Despite the reference curve in the middle panel, the tidal forcing is still identical.
Try the NAO in the North Atlantic. Tis requires some averaging since the raw NAO is noisy. Same tidal forcing.
The Tropical North Atlantic (TNA) index. Has a clear warming trend, which is modeled separately from the variability
The Tropical South Atlantic (TSA). Captures part of the strong spike in 2023-2024. Same tidal forcing, unique response captured by Laplace’s Tidal Equation (LTE) fluid dynamics solution, lower panels.
Head back to the Pacific for the PDO in the north. Similar to ENSO in some ways, but more decadal behavior. Same forcing
A very interesting but lesser known index, the North Pacific Gyre Oscillation (NPGO) aka M4. Crazy the amount of detail that the LTE response modulation picks up. Slight variation in the tidal forcing
The EMI or Modoki index, related to ENSO but some character of the NPGO. Again, decent cross-validation in the test interval. Without CV, could be over-fitting but not likely given all the success so far.
On to the Indian ocean, the East part of the Indian Ocean Dipole (IOD). Trend appears here as well, still with good CV and maintaining the same tidal forcing in the middle panel.
The western dipole of the IOD, has a stronger trend, but still good CV with same tidal forcing.
Last index is the Darwin measure of atmospheric pressure, related to ENSO and half of the SOI dipole Same tidal forcing, response with subtle details differing from NINO4.
What does this all mean? SLH measurements would imply that tidal forcing should be an obvious candidate. But for the ocean indices, the ocean’s thermocline also is subject to tidal forcing especially in such a reduced gravity environment. The 2 interact via inverse barometer.
The machine learning community needs to be let loose on this data. The tidal forcing is a latent or hidden layer that ML models such a SINDy, KAN, and others could easily handle. I don’t use ML other than to fit the models with known tidal factors – ManMachineLearning so far.
@WHUT
whut’s happening? → Earth Sciences 🌏 Mathematical GeoEnergy (Wiley/AGU, 2019) 🌊 https://t.co/IGGOHc2YC1 https://t.co/v9iiFNoYzq
Compare to this paper which uses periodograms to investigate the variation:
“Spatio-Temporal Changes in Interannual Sea Level Along the World Coastlines”
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=5139270
Don’t have access to this so bookmarked:
“Multi-Step ENSO Forecasting Using Kolmogorove Arnold Networks”
https://ieeexplore.ieee.org/abstract/document/10924997
In this paper, lead sentence: “The influence of intrinsic ocean variability on coastal sea level remains largely unexplored but is of potential importance for emerging forecasting efforts” —
“Spatiotemporal properties of intrinsic sea level variability along the Southeast United States coastline”
https://egusphere.copernicus.org/preprints/2025/egusphere-2025-1571/egusphere-2025-1571.pdf
On Brest SLH “Table 1 lists the number of stations which manifest a semi-annual and annual cycle, quasi-biennial oscillation, 4-5 year ENSO signal, and secular trend in the first 10 eigenmodes. The annual cycle dominates the sea-level data, and is most often captured by the eigenmode pairs 1-2 or 2-3. The semi-annual cycle is mostly associated with the eigenmodes 4-6 or higher. The ENSO low-frequency signal appears in eigenmodes 5-7, while the quasi-biennial signal is weakest in the RSLH data and only shows up in eigenmodes 8-10 ” — “Interannual and interdecadal oscillation patterns in sea level ”
https://dept.atmos.ucla.edu/sites/default/files/tcd/files/unalghil-rslh-clim_dyn95.pdf
Mention of reduced gravity =>
“We used a nonlinear, reduced gravity model in spherical coordinates to model the California Current system. The model consists of one dynamically active layer of density p and depth H on top of an infinitely deep layer of slightly higher density p + Ap, the interface between these two layers being a proxy of the ocean pycnocline. The equations were used in the transport mode to facilitate some of the numerical implementation.” —
“The Seasonal and Interannual Variability of the California Current System’ A
Numerical Model ”
https://sci-hub.box/https://agupubs.onlinelibrary.wiley.com/doi/epdf/10.1029/JC094iC03p03159
https://twitter-thread.com/t/1927627050212262330
KAN references
“iTFKAN: Interpretable Time Series Forecasting with Kolmogorov–Arnold Network”
https://arxiv.org/pdf/2504.16432
“Symbolic Regression with Multimodal Large Language Models and Kolmogorov–Arnold Networks”
https://arxiv.org/html/2505.07956
“Reduced Order Modeling with Shallow Recurrent Decoder Networks”
https://arxiv.org/abs/2502.10930
“Deep_learning_in_fluid_dynamics”
https://www.researchgate.net/publication/313231782_Deep_learning_in_fluid_dynamics
“GINN-KAN: Interpretability pipelining with applications in Physics Informed
Neural Networks”
https://arxiv.org/pdf/2408.14780
cited here: https://github.com/orgs/azimuth-project/discussions/22#discussioncomment-13284317
“Data-driven identification of parametric partial differential equations”
https://arxiv.org/pdf/1806.00732