BaHaMAs: a method for uncertainty quantification in geodetic time series and its application in short-term prediction of length of day

Some of the important geodetic time series used in various Earth science disciplines are provided without uncertainty estimates. This can affect the validity of conclusions based on such data. However, an efficient uncertainty quantification algorithm to tackle this problem is currently not available. Here we present a methodology to approximate the aleatoric uncertainty in time series, called Bayesian Hamiltonian Monte Carlo Autoencoders (BaHaMAs). BaHaMAs is based on three elements: (1) self-supervised autoencoders that learn the underlying structure of the time series, (2) Bayesian machine learning that accurately quantifies the data uncertainty, and (3) Monte Carlo sampling that follows the Hamiltonian dynamics. The method can be applied in various fields in the Earth sciences. As an example, we focus on Atmospheric and Oceanic Angular Momentum time series (AAM and OAM, respectively), which are typically provided without uncertainty information. We apply our methodology to 3-hourly AAM and OAM time series and quantify the uncertainty in the data from 1976 up to the end of 2022. Furthermore, since Length of Day (LOD) is a geodetic time series that is closely connected to AAM and OAM and its short-term prediction is important for various space-geodetic applications, we show that the use of the derived uncertainties alongside the time series of AAM and OAM improves the prediction performance of LOD on average by 17% for different time spans. Finally, a comparison with alternative uncertainty quantification baseline methods, i.e., variational autoencoders and deep ensembles, reveals that BaHaMAs is more accurate in quantifying uncertainty.