Can GPS and GRACE data be used to separate past and present-day surface loading in a data-driven approach?

Glacial isostatic adjustment (GIA) and the hydrological cycle are both associated with mass changes and vertical land motion (VLM), which are observed by GRACE and GPS, respectively. Hydrology-related VLM results from the instantaneous response of the elastic solid Earth to surface loading by freshwater, whereas GIA-related VLM reveals the long-term response of the viscoelastic Earth mantle to past ice loading history. Thus, observations of mass changes and VLM are interrelated, making GIA and hydrology difficult to quantify and study independently. In this work, we investigate the feasibility of separating these processes based on GRACE and GPS observations, in a fully data-driven and physically consistent approach. We take advantage of the differences in the spatio-temporal characteristics of the GIA and hydrology fields to estimate the respective contributions of each component using a Bayesian hierarchical modelling framework. A closed-loop synthetic test confirms that our method successfully solves this source separation problem. However, there are significant challenges when applying the same approach with actual observations and the answer to the main question of this study is more nuanced. In particular, in regions where GPS station coverage is sparse, the lack of informative data becomes a limiting factor.