Researchers have developed a novel physics-informed deep learning approach that reconstructs Earth’s rotational history with unprecedented precision, revealing that climate change is lengthening days at rates unseen in 3.6 million years.
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Climate change is lengthening Earth’s days by approximately 1.5 milliseconds per century, according to researchers at the University of Vienna and ETH Zurich. Rising sea levels are slowing Earth’s rotation, causing an unprecedented increase in day length over the past 3.6 million years. The scientists published their findings in the Journal of Geophysical Research: Solid Earth.
“In our earlier work, we showed that the accelerated melting of polar ice sheets and mountain glaciers in the 21st century is raising sea levels, which slows Earth’s rotation and therefore lengthens the day — similar to a figure skater who spins more slowly once they stretch their arms, and more rapidly once they keep their hands close to their body,” explains Mostafa Kiani Shahvandi of the University of Vienna’s Department of Meteorology and Geophysics. “What remained unclear was whether there were earlier periods when climate increased day length at a similarly rapid pace.”
In a previous study, the team examined a 1.33 millisecond per century rate of day length increase from 2000 to 2018 and found that it was faster than at any point in the past 100 years. The new study extends the analysis back 3.6 million years using fossil evidence.
Fossil proxies enable deep-time reconstruction
The research team reconstructed ancient day-length fluctuations using the fossil remains of single-celled marine organisms called benthic foraminifera. “From the chemical composition of the foraminifera fossils, we can infer sea-level fluctuations and then mathematically derive the corresponding changes in day length,” says first author Kiani Shahvandi from the University of Vienna.
Researchers developed a novel Physics-Informed Diffusion Model (PIDM), a probabilistic deep learning approach that combines convolutional LSTM neural networks with gravitationally self-consistent physical constraints. The methodology generates 50,000 Monte Carlo samples to quantify uncertainty while maintaining adherence to the Sea Level Equation, a complex algorithm that accounts for gravitational, rotational, and deformational effects of mass redistribution. The results showed that during the Quaternary (the last 2.6 million years), the growth and melting of large ice sheets repeatedly caused significant day-length variations.
The PIDM represents a significant advance over traditional computational approaches. Using a 111-layer Earth rheology model, far more sophisticated than the 4-layer models previously employed, the team achieved 1.5% to 2.1% prediction error compared to 3.4% to 4.4% with conventional methods. The algorithm employs a Markov chain diffusion process that transforms input time series to noise and back, generating probabilistic reconstructions that capture both aleatoric and epistemic uncertainty.
Earth day length variability over the past 3.6 million years.
Current rates rival ice age extremes
However, compared with values from the 21st century, they found that today’s day-length increase is unparalleled in the climate history of the past 3.6 million years. “This rapid increase in day length implies that the rate of modern climate change has been unprecedented at least since the late Pliocene, 3.6 million years ago. The current rapid rise in day length can thus be attributed primarily to human influences,” says Benedikt Soja, Professor of Space Geodesy at ETH Zurich.
Even though changes in day length are only milliseconds, they can cause problems in areas like space navigation, which requires accurate information about the Earth’s rotation. This could also have direct consequences for GPS and satellite navigation systems, atomic clock synchronization and earth rotation monitoring infrastructure used by geodetic research facilities.
