Bayesian methodology to stochastic capture zone determination: Conditioning on transmissivity measurements

[1] 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.