Ex-situ priors: A Bayesian hierarchical framework for defining informative prior distributions in hydrogeology

Abstract Stochastic modelingis a common practice for modeling uncertainty in hydrogeology. In stochastic modeling, aquifer propertiesare characterized by their probability density functions ( PDFs). The Bayesian approach for inverse modeling is often used to assimilate information from field measurements collected at a site into properties’ posterior PDFs. This necessitates the definition of a prior PDF, characterizing the knowledge of hydrological properties before undertaking any investigation at the site, and usually coming from previous studies at similar sites. In this paper, we introduce a Bayesian hierarchical algorithm capable of assimilating various information–like point measurements, bounds and moments–into a single, informative PDFthat we call ex-situ prior . This informative PDFsummarizes the ex-situ information available about a hydrogeologicalparameter at a site of interest, which can then be used as a prior PDFin future studies at the site. We demonstrate the behavior of the algorithm on several synthetic case studies, compare it to other methods described in the literature, and illustrate the approach by applying it to a public open-access hydrogeologicaldataset.