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