Quantifying Uncertainty in Complex Groundwater Flow Models
A Poster Presentation(H11D-1307) Delivered at the 2005 AGU Fall Meeting, San Francisco, California, 5-9 December 2005 Despite the intensive research over the past decades in the field of stochastic subsurface hydrology, our ability to analyze and model heterogeneous groundwater systems remains limited. Most existing theories are either too restrictive to handle practical complexity or too expensive to be applied to realistic problem sizes. In this study we present a hybrid nonstationary spectral method for predicting uncertainties (e.g., head and velocity variances caused by unmodeled smallscale conductivity variability) in complex groundwater flow models. This method, based on solving stochastic perturbation equations, involves two major computational steps after the deterministic mean flow equation is solved. We first apply a set of closed form formulas to predict the nonstationary variances for the entire modeling area. We then employ first-order numerical spectral method to correct the “regional solution” in localized areas where the variance distribution is highly nonstationary (e.g., around inner boundaries and strong sources/sinks). The boundary conditions for the local numerical solutions are based on the closed form formulas and are implemented on an as-needed basis in a real-time visual software system called Interactive Ground Water (IGW). Since the "regional" closed form solution is instantaneous and the more expensive first-order numerical analysis is only applied locally, the overall hybrid approach can be very efficient, making it possible to model strongly nonstationary variance dynamics in complex flow situations in the presence of general trends and sources and sinks. We demonstrate the accuracy and effectiveness of the hybrid nonstationary spectral method with a number of examples and, when feasible, systematically compare the results with the corresponding single model, nonstationary numerical analysis and Monte Carlo solutions.