Length of Day (LOD) is a measure of the difference between observed duration of a day and nominal value of 86400 seconds (i.e., 24 hours). LOD variations occur on all timescales, from subdaily to geological, and have magnitude of a few milliseconds (ms). Although the magnitude of these variations is small, they significantly affect the Earth's rotational energy and its centrifugal force. Furthermore, understanding the causes of LOD variations is important because it provides a way to gain insight into the Earth's dynamics and constrain various geophysical models. It is also important to note that since LOD depends on the rotation rate of the Earth, astronomical observations that are related to Earth's rotation could be used to infer LOD variations. Specifically, in the range 720 BC to 2020 lunar occultation and eclipse records exist (observed by ancient civilizations) that can be used for this purpose.

LOD variations derived from lunar occultation and eclipse records contain two main features: (1) a secular trend, and (2) decadal and millennial fluctuations. The secular trend of  ms/cy (milliseconds per century) tends to increase LOD by slowing down the Earth's rotation. The causes of this secular trend were an enigma until Kiani Shahvandi et al. (2024a) explained this secular trend (within the observation and reconstruction uncertainties) based on a combination of lunar tidal friction (which arises due to the gravitational pulling of the Moon on Earth and subsequent energy dissipation in the Earth's oceans, slowing down the Earth's rotation and thereby increasing LOD by  ms/cy) and glacial isostatic adjustment (which is due to the rebound of the solid Earth after the termination of the last ice age, which decreases the Earth's oblateness due to the movement of materials from equatorial to polar regions, thereby accelerating the Earth's rotation and decreasing LOD by a rate of  ms/cy). However, the causes of long-period fluctuations are more ambiguous. These fluctuations have magnitudes of around 3 to 4 ms and occur on decadal and millennial timescales. As such, any mechanism put forth as the cause of these fluctuations must be large-scale, and have oscillatory behavior with periods close to those observed in the LOD record. Several candidates exist that might be able to explain these fluctuations, including climatic oscillations and dynamics of the Earth's core.

In a new study, Kiani Shahvandi et al. (2024b) investigate the causes of aforementioned decadal and millennial fluctuations. They tested two possible sources: climatic effects and core dynamics. They derived climatic effects due to temperature-driven sea-level change in the last 3000 years. These effects exhibit decadal and millennial fluctuations, but their magnitude is too small to be able to account for the totality of the observed LOD record. Furthermore, these climatic effects are out of phase with the observed LOD record. As such, Kiani Shahvandi et al. (2024b) concluded that climatic effects do not have enough power to drive these long-period fluctuations and thus, are not the cause of the mentioned fluctuation. On the other hand, core processes result in azimuthal flows in the Earth's core that could explain these fluctuations. The authors used the methodology of Bayesian Physics-Informed Neural Networks (BPINNs) in the study, which was previously used by Kiani Shahvandi et al. (2024c) to explain the causes of long-period polar motion.

Recently, new geomagnetic datasets have been compiled, both archaeomagnetic—which are based on lavas, lake sediments, and archaeological artifacts—and more modern geomagnetic data—which are mainly based on old surveys, and observatory and satellite data. The authors used state-of-the-art mathematical model of BPINNs, trained on geomagnetic data and constrained to satisfy geophysical models of core dynamics. Using BPINNs, they independently reconstruct LOD variations in the past three millennia and compare them with the observed fluctuations. The authors show—for the first time—the good match between observed and reconstructed values, thus explaining the origin of these fluctuations. Furthermore, they show that LOD reconstructions based on BPINNs with geophysical models of wave propagation in the core do not explain the observed fluctuations.  Therefore, the authors conclude that (multi-) decadal and millennial LOD fluctuations are caused by the fluid motion at the top of the Earth's core (here, fluid being the molten iron).

The results of Kiani Shahvandi et al. (2024b) provide critical constraints on the internal and external geodynamics. Most importantly, they show that their LOD reconstructions do not feature any trend. Using this, they present an alternative solution to the Munk's enigma of 20^th-century sea-level rise, confirming the role of ongoing climate change (Munk's enigma concerns the role of contemporary climate change on the Earth's rotation, which according to previous independent geophysical estimates, did not appear to affect Earth's rotation, raising questions regarding validity of 20th-centry sea-level estimates). In addition, although the authors showed that the climatic effects are not the primary cause of the long-period LOD fluctuations, they demonstrated the existence of decadal and millennial fluctuations in these reconstructions. Since similar periods could also be observed in the reconstructions based on archaeomagnetic data, an interesting conjecture arises: whether the internal and external geodynamics are related at the timescales of a few centuries. Previous research by Kiani Shahvandi et al. (2024c) provided evidence of a similar connection between internal and external geodynamics at a timescale of 30 years, a period at which polar motion exhibit multidecadal oscillations known as Markowitz wobble. With the current research, a new link between internal and external geodynamics is revealed, which might be an incentive for future studies.    

References

Kiani Shahvandi, M., Adhikari, S., Dumberry, M., Mishra, S., Soja, B.  (2024a). The increasingly dominant role of climate change on length of day variations. Proceedings of the National Academy of Sciences, 121: e2406930121, https://doi.org/10.1073/pnas.2406930121

Kiani Shahvandi, M., Noir, J., M., Mishra, S., Soja, B.  (2024b). Length of day variations explained in a Bayesian framework. Geophysical Research Letters, 51: e2024GL111148, https://doi.org/10.1029/2024GL111148

Kiani Shahvandi, M., Adhikari, S., Dumberry, M., Modiri, S., Heinkelmann, R., Schuh, H., Mishra, S., Soja, B. (2024c). Contributions of core, mantle and climatological processes to Earth’s polar motion. Nature Geoscience, 17: 705-710, https://doi.org/10.1038/s41561-024-01478-2