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Multimodel B ayesian analysis of groundwater data worth
Author(s) -
Xue Liang,
Zhang Dongxiao,
Guadagnini Alberto,
Neuman Shlomo P.
Publication year - 2014
Publication title -
water resources research
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.863
H-Index - 217
eISSN - 1944-7973
pISSN - 0043-1397
DOI - 10.1002/2014wr015503
Subject(s) - hydraulic conductivity , groundwater flow , monte carlo method , moment (physics) , linearization , groundwater model , estimation theory , groundwater recharge , groundwater flow equation , bayesian probability , flow (mathematics) , heteroscedasticity , mathematics , aquifer , mathematical optimization , computer science , groundwater , statistics , soil science , geology , nonlinear system , geotechnical engineering , soil water , physics , geometry , classical mechanics , quantum mechanics
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.