Length of Day Variations Explained in a Bayesian Framework

Length of Day (LOD) observations in the range 720 BCE to 2020—derived from lunar occultation and eclipse records—feature a secular trend and various long-period fluctuations. While recent estimates show that the secular trend is caused by the combination of lunar tidal friction and glacial isostatic adjustment, the causes of long-period fluctuations remain ambiguous. We first compute the climatic effects and show that they are anti-correlated with the observed fluctuations and their amplitude is (Formula presented.) 10 smaller. Then, we focus on core dynamics and solve for simplified equations of magnetohydrodynamics, namely tangential geostrophy, using Bayesian Physics-Informed Neural Networks (BPINNs) and independent archeomagnetic and modern geomagnetic observations. Within the observation and reconstruction uncertainty we can reconcile the LOD observations with reconstructions of BPINNs. Furthermore, we demonstrate that LOD variations reconstructed by dynamics of Magneto-Archimedes-Coriolis waves do not explain the observed fluctuations. These results have considerable implications for internal and external geodynamics.