Stochastic capture zone delineation within the generalized likelihood uncertainty estimation methodology: Conditioning on head observations

A stochastic methodology to evaluate the predictive uncertainty in well capture zones in heterogeneous aquifers with uncertain parameters is presented. The approach is based on the generalized likelihood uncertainty estimation methodology. The hydraulic conductivity is modeled as a random space function allowing for the uncertainty that stems from the imperfect knowledge of the parameters of the correlation structure. Parameters are sampled from prior distributions and are used for the generation of a large number of hydraulic conductivity fields, which are subsequently used to solve the groundwater flow equation. A likelihood is calculated for every simulation, based on some goodness-of-fit measure between simulated heads and available observations. Using inverse particle tracking, a capture zone is determined which is assigned the likelihood calculated for that particular simulation. Statistical analysis of the ensemble of all simulations enables the predictive uncertainty of the well capture zones to be defined. Results are presented for a hypothetical test case and different likelihood definitions used in the conditioning process. The results show that the delineated capture zones are most sensitive to the mean hydraulic conductivity and the variance, whereas the integral scale of the variogram is the parameter with the smallest influence. For all likelihood measures the prior uncertainty is reduced considerably by introducing the observation heads, but the reduction is most effective for the very selective likelihood definition. The method presented can be used in real applications to quantify the uncertainty in the location and extent of well capture zones when little or no information is available about the hydraulic properties, through the conditioning on head observations.