Bayesian model-data synthesis with an application to global Glacio-Isostatic Adjustment

Glacial isostatic adjustment (GIA) is a crucial component in evaluating sea level change. The GIA process has been simulated globally from various physical forward models and it can also be measured locally at some GPS stations. In this paper we combine the physical model simulations and GPS measurements in a Bayesian hierarchical modelling framework to update global GIA. In common with many large-scale spatial modelling applications, there are two major challenges. One is the scale of the update, which is too large for naive Gaussian conditioning. The other is the need to represent non-stationarity in the prior. We address the first challenge with the now well-established stochastic partial differential equations (SPDE) and integrated nested Laplace approximation (INLA) approach. For non-stationary global process, we propose two general models that accommodate commonly-seen geospatial patterns. We present and compare the GIA result for the two models, alongside the default option of assuming stationarity.