Distributed-parameter models are increasingly being used to incorporate hydrogeologic uncertainty in predictive analyses of groundwater flow and contaminant transport. Geostatistical techniques have proven to be useful for generating multiple equiprobable realizations of subsurface parameters that are consistent with the available data. However, computational constraints commonly preclude detailed transport calculations with all realizations in a Monte Carlo simulation framework for quantifying the uncertainty in model predictions. As a result, several studies have been performed investigating techniques to rank realizations of a stochastic reservoir or groundwater aquifer model. These techniques share the common goal of trying to develop a surrogate measure that will preserve the quantiles of the desired performance measure. This chapter proposes a technique to both rank and weight realizations through the use of a surrogate traveltime measure and to then accurately reproduce the performance-measure statistics with only a few forward simulations. The methodology is demonstrated using a field example from the Waste Isolation Pilot Plant site in New Mexico that is well documented in the groundwater literature.