A hierarchical Constrained Bayesian (ConBay) approach to jointly estimate water storage and Post-Glacial Rebound from GRACE(-FO) and GNSS data

Gravity Recovery and Climate Experiment (GRACE) its Follow-On mission (GRACE-FO) have become an indispensable tool in monitoring global mass variations. However, separating GRACE(-FO) signals into individual Terrestrial Water Storage Changes (TWSC) surface deformation contributors, i.e. Post-Glacial Rebound (PGR), is desirable for many hydro-climatic geophysical applications. In this study, a hierarchical constrained Bayesian (ConBay) approach formulated to apply fields the uplift rate measurements from Global Navigation Satellite System (GNSS) stations simultaneously estimate contribution of TWSC PGR. The proposed based on Markov Chain Monte Carlo optimisation algorithm within dynamic multivariate state-space model, while accounting uncertainties priori information observations. numerical implementation demonstrated over Great Lakes area, covering 2003–2017, where W3RA water balance ICE-5G(VM2) ICE-6G-D(VM5a) GIA models are merged with GRACE GNSS data. Validations performed against independent measurements, which indicate that average root-mean-squares-of-differences between PGR estimates reduced by 72% after merging observations through ConBay. ConBay updates, introduced long-term trends, as well seasonal inter-annual components, found be realistic.