Multimodel Bayesian analysis of groundwater data worth

Liang Xue, Dongxiao Zhang, Alberto Guadagnini, Shlomo P. Neuman

Research output: Contribution to journalArticle

22 Scopus citations

Abstract

We explore the way in which uncertain descriptions of aquifer heterogeneity and groundwater flow impact one's ability to assess the worth of collecting additional data. We do so on the basis of Maximum Likelihood Bayesian Model Averaging (MLBMA) by accounting jointly for uncertainties in geostatistical and flow model structures and parameter (hydraulic conductivity) as well as system state (hydraulic head) estimates, given uncertain measurements of one or both variables. Previous description of our approach was limited to geostatistical models based solely on hydraulic conductivity data. Here we implement the approach on a synthetic example of steady state flow in a two-dimensional random log hydraulic conductivity field with and without recharge by embedding an inverse stochastic moment solution of groundwater flow in MLBMA. A moment-equations-based geostatistical inversion method is utilized to circumvent the need for computationally expensive numerical Monte Carlo simulations. The approach is compatible with either deterministic or stochastic flow models and consistent with modern statistical methods of parameter estimation, admitting but not requiring prior information about the parameters. It allows but does not require approximating lead predictive statistical moments of system states by linearization while updating model posterior probabilities and parameter estimates on the basis of potential new data both before and after such data are actually collected. Key Points Joint consideration of geostatistical and flow model uncertainties Combined assessment of added hydraulic conductivity and head data worth Inverse solution of stochastic moment equations combined with MLBMA

Original languageEnglish (US)
Pages (from-to)8481-8496
Number of pages16
JournalWater Resources Research
Volume50
Issue number11
DOIs
StatePublished - Nov 2014

Keywords

  • data worth
  • inverse stochastic moment solution
  • maximum likelihood Bayesian model averaging
  • model uncertainty

ASJC Scopus subject areas

  • Water Science and Technology

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