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 cap ture zones in heterogeneous aquifers with uncertain parameters is presented . The approach is based on the generalized likelihood uncertainty estimatio n methodology. The hydraulic conductivity is modeled as a random space func tion allowing for the uncertainty that stems from the imperfect knowledge o f the parameters of the correlation structure. Parameters are sampled from prior distributions and are used for the generation of a large number of hy draulic conductivity fields, which are subsequently used to solve the groun dwater flow equation. A likelihood is calculated for every simulation, base d on some goodness-of-fit measure between simulated heads and available obs ervations. Using inverse particle tracking, a capture zone is determined wh ich is assigned the likelihood calculated for that particular simulation. S tatistical analysis of the ensemble of all simulations enables the predicti ve uncertainty of the well capture zones to be defined. Results are present ed for a hypothetical test case and different likelihood definitions used i n the conditioning process. The results show that the delineated capture zo nes are most sensitive to the mean hydraulic conductivity and the variance, whereas the integral scale of the variogram is the parameter with the smal lest influence. For all likelihood measures the prior uncertainty is reduce d considerably by introducing the observation heads, but the reduction is m ost effective for the very selective likelihood definition. The method pres ented can be used in real applications to quantify the uncertainty in the l ocation and extent of well capture zones when little or no information is a vailable about the hydraulic properties, through the conditioning on head o bservations.