Stochastic delineation of capture zones: Classical versus Bayesian approach

L. Feyen, P. J. Ribeiro, F. De Smedt, P. J. Diggle

Research output: Contribution to journalArticle

Abstract

A Bayesian approach to characterize the predictive uncertainty in the delineation of time-related well capture zones in heterogeneous formations is presented and compared with the classical or non-Bayesian approach. The transmissivity field is modelled as a random space function and conditioned on distributed measurements of the transmissivity. In conventional geostatistical methods the mean value of the log transmissivity and the functional form of the covariance and its parameters are estimated from the available measurements, and then entered into the prediction equations as if they are the true values. However, this classical approach accounts only for the uncertainty that stems from the lack of ability to exactly predict the transmissivity at unmeasured locations. In reality, the number of measurements used to infer the statistical properties of the transmissvity field is often limited, which introduces error in the estimation of the structural parameters. The method presented accounts for the uncertainty that originates from the imperfect knowledge of the parameters by treating them as random variables. In particular, we use Bayesian methods of inference so as to make proper allowance for the uncertainty associated with estimating the unknown values of the parameters. The classical and Bayesian approach to stochastic capture zone delineation are detailed and applied to a hypothetical flow field. Two different sampling densities on a regular grid are considered to evaluate the effect of data density in both methods. Results indicate that the predictions of the Bayesian approach are more conservative.

Original languageEnglish (US)
Pages (from-to)313-324
Number of pages12
JournalJournal of Hydrology
Volume281
Issue number4
DOIs
StatePublished - Oct 20 2003
Externally publishedYes

Fingerprint

transmissivity
uncertainty
prediction
Bayesian theory
methodology
flow field
stems
method
parameter
sampling

Keywords

  • Bayesian inference
  • Capture zone
  • Groundwater
  • Stochastic modelling

ASJC Scopus subject areas

  • Soil Science
  • Earth-Surface Processes

Cite this

Stochastic delineation of capture zones : Classical versus Bayesian approach. / Feyen, L.; Ribeiro, P. J.; De Smedt, F.; Diggle, P. J.

In: Journal of Hydrology, Vol. 281, No. 4, 20.10.2003, p. 313-324.

Research output: Contribution to journalArticle

Feyen, L. ; Ribeiro, P. J. ; De Smedt, F. ; Diggle, P. J. / Stochastic delineation of capture zones : Classical versus Bayesian approach. In: Journal of Hydrology. 2003 ; Vol. 281, No. 4. pp. 313-324.
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