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Bayesian methodology to stochastic capture zone determination : conditioning on transmissivity measurements.

Feyen, L. and Ribeiro Jr, Paulo J. and De Smedt, F. and Diggle, Peter (2002) Bayesian methodology to stochastic capture zone determination : conditioning on transmissivity measurements. Water Resources Research, 38 (9). 1164-. ISSN 0043-1397

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Abstract

A methodology to determine the uncertainty associated with the delineation of well capture zones in heterogeneous aquifers is presented. The log transmissivity field is modeled as a random space function and the Bayesian paradigm accounts for the uncertainty that stems from the imperfect knowledge about the parameters of the stochastic model. Unknown parameters are treated as random quantities and characterized by a prior probability distribution. Log transmissivity measurements are incorporated into Bayes' theorem, updating the prior distribution and yielding posterior estimates of the mean value and the covariance parameters of the log transmissivity. Conditional simulations of the log transmissivity field are generated using samples from the posterior distribution of the parameters, yielding samples from the predictive distribution of the log transmissivity field. The uncertainty in the model parameters is propagated to the predictive uncertainty of the capture zone by solving numerically the groundwater flow equation, followed by a semianalytical particle-tracking algorithm. The method is applied to a set of hypothetical flow fields for various sampling densities and assuming different levels of parameter uncertainty. Simulation results for all the sampling densities show no univocal relation between the predictive uncertainty of the capture zones and the level of parameter uncertainty. However, in general, the predictive uncertainty increases when parameter uncertainty is taken into account.

Item Type: Article
Journal or Publication Title: Water Resources Research
Subjects: Q Science > QA Mathematics
Departments: Faculty of Health and Medicine > Medicine
VC's Office
ID Code: 19263
Deposited By: ep_ss_importer
Deposited On: 19 Nov 2008 13:22
Refereed?: Yes
Published?: Published
Last Modified: 26 Jul 2012 15:27
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/19263

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