Bayesian methodology for stochastic capture zone delineation incorporating transmissivity measurements and hydraulic head observations.

Feyen, L. and Ribeiro, P. J. and Gomez-Hernadez, J. J. and Beven, Keith J. and de Smedt, F. (2003) Bayesian methodology for stochastic capture zone delineation incorporating transmissivity measurements and hydraulic head observations. Journal of Hydrology, 271 (1-4). pp. 156-170.

Abstract

The paper presents a methodology to estimate the uncertainty in the prediction of capture zones using transmissivity measurements and hydraulic head observations. We use a stochastic approach to parameterise the transmissivity field. By treating the parameters of the stochastic model as random variables we account for the fact that they are unknown and that a simple deterministic process cannot model their genesis. The method requires the definition of a prior probability density function for the mean value and for the covariance parameters of the log transmissivity field. In a first phase, log transmissivity measurements are incorporated into Bayes' theorem updating the prior densities to yield the posterior densities for the model parameters. Conditional realisations of the log transmissivity field are generated using parameter sets obtained by Monte Carlo sampling from the posterior parameter distributions. The second phase consists of updating the posterior probabilities of the conditional log transmissivity fields using the hydraulic head observations through a second application of Bayes' theorem. Then, for each realisation of the log transmissivity field, the capture zone is determined using particle tracking, which is weighted by the posterior probabilities of the respective log transmissivity field. The set of weighted capture zones results in a capture zone probability distribution. We show an application to a hypothetical flow system consisting of a single abstraction well in a confined aquifer under a regional background gradient and compare the worth of log transmissivity measurements and head observations by incorporating the different data types into the procedure sequentially. Results show that head observations are more effective in reducing the spread of the predictive capture zone distribution, whereas the transmissivity measurements are more valuable in predicting the actual location of the true capture zone.