Climate Index and monthly SLH modeling GitHub

[pukpr]

I created a new site for modeling of natural climate change a la various climate indices (ENSO, AMO, QBO, etc) and monthly sea-level height (SLH) at: https://pukpr.github.io/results/image_results.html

This is more dedicated to showing results and using the tools at github to organize and maintain modeling output artifacts, including tables and charts. The source control repo is at https://pukpr.github.io/pukpr.github.io

More info of the motivation at https://geoenergymath.com/2025/09/03/simpler-models-can-outperform-deep-learning-at-climate-prediction/

Could create a github.io site for the Azimuth Project as well, where according to the site https://docs.github.com/en/pages/getting-started-with-github-pages/creating-a-github-pages-site, this is free feature for organizations (I pay for my github subscription)

"Who can use this feature? GitHub Pages is available in public repositories with GitHub Free and GitHub Free for organizations, and in public and private repositories with GitHub Pro, GitHub Team, GitHub Enterprise Cloud, and GitHub Enterprise Server. For more information, see GitHub’s plans."

[pukpr]

Another important recent paper is “Evaluation and prediction of the Effects of Planetary Orbital Variations to Earth’s Temperature Changes” https://www.tandfonline.com/doi/epdf/10.1080/17538947.2025.2487058?needAccess=true

“The influence of planetary orbital changes on Earth’s temperature has been poorly quantified and subject to speculation. Here, we delineated the effects of greenhouse gases and planetary orbital changes on Earth’s temperature and forecasted the latter. Our results indicate that Earth’s revolution around the Sun and its rotation explain ∼75.36% and 15.91% of Earth’s temperature variations in one year, while the Moon’s revolution around the Earth and other planet motions account for 8.26% and 0.26%, respectively. Orbital forcings contributed ∼11.5% global warming since 1837 and will continue to warm the Earth by ∼0.13 °C from 2020 to 2027. However, orbital forcings may contribute to ∼0.25 °C cooling of Earth from 2027 to 2050, but this effect remains insufficient to offset the warming caused by CO₂”

So

• 75.36% is seasonal
• 15.91% is daily
• 8.26% is lunar cycles
• 0.26% is planetary cycles
• (I calculate 0.21% unaccounted for)

How they come up with the 8.26% for the lunar orbit is fascinating. I think they are finding a pattern match in day-to-day measurements separated by fairly long time spans but it appears to be pinned to vernal equinoxes. The common sense (perhaps overly naive) idea would be to attribute this simply to weather variability, yet they specifically state it’s a lunar cause.

”This regular rising and falling pattern in temperature is accompanied by slight irregular fluctuations. We believe that these slight irregular fluctuations are mainly due to changes in lunar forcing exerted on Earth”

The way they substantiate this is :

“f1(t) quantifies the influence of Earth’s rotation on its temperature variation in a year. Building on Section 2.2.1 above, the quasi-sinusoidal diurnal variation in Earth’s temperature is mainly due to its rotation. We calculated the temperature difference (D1) of two consecutive hours for each day from 1979 to 2020. A remarkable agreement is found between the D1 values of two consecutive days. For example, the D1 values for January 1 and 2 from 1979 to 2020 are shown in Figure 6. These results indicate that the variation in D1 is mainly determined by the rotation of the Earth. Therefore, the changes in D1 can be used to quantify the impact of Earth’s rotation on the global temperature in consecutive hours, which can be inferred by taking the derivative of the function f1(t). The derivative of f1(t) is fitted to the time series of D1 by using the Levenberg – Marquardt scheme to determine its unknown parameters. f2(t) quantifies the influence of the lunar revolution on Earth’s temperature variations in a year.The changes in CO2 concentration for two consecutive days have almost no effect on Earth’s temperature. Thus, we can determine the change in Earth’s temperature over two consecutive days (due to the motion of the Moon) by using Equations (16) − (18). To eliminate the impact of large variations in CO2 concentration in two successive days on temperature, we utilized only D2 values for days in which the CO2 concentration was relatively stable.”

Need to take this paper seriously. 7 co-authors from universities in China and affiliations with U. of Toronto, U. of Hawaii (at Manoa - ENSO modeling hotspot), USC, NASA JPL, U. of Wisconsin at Milwaukee, and Pohang Univ in Korea.

[pukpr]

What the jagged variations depending on time of day are, I don't understand, except for the 24 hour cycle, Why would it be the same a day later?

"In this study, vernal equinoxes during the study period (1979−2020) were chosen for analyzing global hourly temperatures (UTC time). We found large variations in global temperature from 4 am to 5 am, 7 am to 8 am, 4 pm to 5 pm and 9 pm to 10 pm Figure 2 shows the global distribution of the temperature difference between 4 am and 5 am, 7 am and 8 am, 4 pm and 5 pm, and 9 pm and 10 pm The Earth’s rotation highly affects the land surface temperature, while the near-surface ocean temperature barely changes in the two consecutive hours. "

Must be some geospatial change that gets triggered -- mountain ranges?

This is their schematic for changes -- note the lunar is on a 27 day cycle

The closest they get to making a connection is the chart of D2 matching lunar ephemeris ( such as daily lunar declination (𝛿),) qualitatively

[pukpr]

The other paper mentioned at GeoEnergyMath.com is "Observing ENSO-modulated tides from space"

All the tidal cycles are impacted by ENSO. The site they use is in the Solomon Islands

(a) Oceanic Niño Index (ONI) from 1995 to 2021. (b) Mean sea levels at Honiara. (c) M2 amplitudes at Honiara. (d) O1 amplitudes at Honiara. The correlation coefficient between ONI and mean sea levels/M2 amplitudes/O1 amplitudes at Honiara is -0.66±0.06/-0.72±0.05/0.64±0.07. Correlation coefficients and their 95% confidence intervals are calculated using corrcoef function in MATLAB.

Each of the daily/diurnal tidal factors has a direct representation as a long-period tidal factor (fortnightly or monthly), so my idea is that the long-period factors interact with the annual to modulate these daily factors. It is also manifested as ENSO, in places close to the heart of ENSO, such as the Solomon Islands.

[pukpr]

re: https://www.realclimate.org/index.php/archives/2025/09/time-and-tide-gauges-wait-for-no-voortman

In regard to determining sea-level shifts, the first analysis should be in a comprehensive understanding of the natural SLH variation. To take an example, consider locations in the Baltic Sea and then northerly into the Gulf of Bothnia separating Norway and Finland. Begin by detrending the data and fitting the erratic cycles to tidal periods, concurrently cross-validating the results in the dashed test interval — the graphs shown below demonstrate high significance across the sets and over the interval.

On the brink of overfitting

Yet, look at the long-term trends — the northernmost spot Furuogrund shows a decreasing trend, while the southernmost spot Aarhus in Denmark is trending up. This is commonly understood to be due to glacial rebound, with the effect intuitively being historically stronger the more north (i.e. colder) the measurement siting.

To fully discriminate the climate change acceleration from the glacial rebound deceleration is not the easiest challenge in the world, but being able to precisely isolate the natural tidal cycles will obviously help. To make it even more challenging is that the tidal cycles can show periods in the multidecadal range.

As far as I can tell, no one is doing the long-period tidal analysis correctly, if at all, even though the results shown above demonstrate predictive capability. The challenge to anyone out there is to duplicate the results. Fortunately, it doesn’t take a lot of computing power.

From https://www.researchgate.net/publication/272065019_Baltic_sea_level_low-frequency_variability

The authors claim that the variation is linked to NAO, yet the peaks shown above are all aliased to tidal periods modulated by annual cycles.

[pukpr]

A skeptical science comment : https://skepticalscience.com/argument.php?p=13&t=324&&a=68#comments

[pukpr]

Near-Term Future Sea-Level Projections Supported by Extrapolation of Tide-Gauge Observations
https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2024GL112940

Tide-Gauge Observations
We use monthly tide gauge records from the Permanent Service for Mean Sea Level (PSMSL; Holgate et al., 2013) globally, except the polar oceans (65°S–65°N). Tide-gauge records along the Australia coastline from the Australian National Collection of Homogenized Observations of Relative Sea Level (ANCHORS; Hague et al., 2022) are also included. We removed stations that show apparent data problems like jumps and spikes. Only tide-gauge stations with records covering at least 70% of the 1970–2023 period (54 years) are selected. Since the estimation of a quadratic term is sensitive to the beginning and ending of time series, we remove stations with missing data for more than 10 years at beginning and ending of tide gauge records. Tide gauges located near great earthquakes (≥8 Mw) within a 500 km radius of the epicenters are excluded (Wöppelmann & Marcos, 2016), as the coseismic steps followed by sustained post-seismic land deformation cannot be reasonably represented by either linear or linear-plus-quadratic fits from 1970 to 2023 (Text S1 and Figure S1 in Supporting Information S1). The tide-gauge records remaining after above selection criteria are then assigned to the nearest location on the 1° grid of the AR6 sea-level projection. If there are multiple tide-gauge records near a single grid point, the records are averaged. There are 286 stations available at 222 locations (Figure S2 and Table S1 in Supporting Information S1).

This is a good set of criteria for exclusion.

[pukpr]

continued from https://gist.github.com/pukpr/0b7ac85fad1ea36f65a9b50d6c30958b#file-lte_mlr-py

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[pukpr]

Wismar #8

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fewer extra lp cycles

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[pukpr]

Standard Regression outperforms PySINDy.

https://www.researchgate.net/publication/384040354_Comparison_of_SINDy_against_standard_regression_for_inverse_problems_in_chaotic_dynamical_systems

https://x.com/chenna1985