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

Regionalization with hierarchical hydrologic similarity and ex situ data in the context of groundwater recharge estimation at ungauged watersheds

“…The more arid US Midwest may have more pronounced localized recharge (de Vries and Simmers, 2002), which cannot be effectively captured by baseflow analysis (Scanlon et al, 2002). This, then, does not fit well with our working assumption.…”

“…Yet the groundwater has increasingly been depleted since the late 20th century (Wada et al, 2010). Therefore, groundwater recharge, here broadly defined as the replenishing of water to a groundwater reservoir, plays a critical role in sustainable water resource management (de Vries and Simmers, 2002). Several studies have reviewed and compared multiple methods for recharge estimation at a wide spectrum of temporal and spatial scales, including lysimeter tests, seepage tests, water table fluctuation, chemical and heat tracers, baseflow analysis, water budget, and numerical modeling (Scanlon et al, 2002;Healy, 2010;Heppner et al, 2007).…”

“…Despite the lack of in situ data, one can still apply Bayesian approaches to establish prior distributions that are informed by data from previous studies or well-established databases (Woodbury and Rubin, 2000;Woodbury, 2011;Hou and Rubin, 2005). More advanced pooling of information from multiple sampled sites has also been demonstrated with the application of Bayesian hierarchical models (Smith et al, 2014;Cucchi et al, 2019), which can account for both intra-and inter-site uncertainty of the parameters. However, the aforementioned Bayesian approaches have several disadvantages, including (1) requiring a system of hydrologic similarity that helps us decide which sampled sites or databases are suitable as "information donors", (2) requiring known or assumed distributional forms of the parameters, and (3) difficulties in accounting for complicated and highly nonlinear dependence on exogenous variables.…”

What We Talk About When We Talk About Uncertainty. Toward a Unified, Data-Driven Framework for Uncertainty Characterization in Hydrogeology

“…One problem that all the above-mentioned uncertainty frameworks share, is the lack of formalized prior derivation. Hydrogeology itself has only produced a small number of studies on this topic (Kitanidis, 2012;Li et al, 2017;Cucchi et al, 2019), which is sadly in line with the situation in many other fields. Since specifying the prior is the first step in any Bayesian analysis, high emphasis should be put on this step.…”

“…Narrowing down the uncertainties could be done by narrowing down the number of used sited by restricting the analysis to similar sites, only. Yet, this would necessitate the existence of a huge database, which we currently do not have (Cucchi et al, 2019).…”