Quantifying Uncertainty in Complex Groundwater
Flow Models
Chuen-Fa Ni and Shu-Guang Li
Department of Civil and Environmental Engineering, Michigan State
University, East Lansing, MI 48824
http://www.egr.msu.edu/igw/
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 small-scale 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.
Nonstationary Variance Modeling in Complex Trending and composite Media
(a) Complex Trending Media (b) Complex Composite Media- Case 1 (c) Complex Composite Media- Case 2
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Nonstationary and Unsteady Modeling of Velocity Variances in Confined/Unconfined Aquifers in the Presence of Complex Sources and Sinks
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(a) Steady with sources and sinks (b) Transient with sources and sinks
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Hybrid Spectral Method:
With local correction processes applied around the wells, the hybrid spectral method can efficiently and accurately capture the detail dynamic of velocity uncertainty.
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An Integrated Software Environment for Hybrid Spectral Method:
The software environment for the hybrid spectral method is based on object-oriented program (OOP) structure. This software environment allows users to define the local correction areas interactively.
Download the Entire 2005 AGU Fall Meeting Poster (3.69 MB)
References:
Ni, C.F. and S.G. Li, "Modeling Groundwater Velocity Uncertainty in Complex Composite Media". Accepted by Advances in Water Resources.
Ni, C.F. and S.G. Li, "Simple Closed-Form Formulas for Predicting Groundwater Flow Model Uncertainty in Complex, Heterogeneous Trending Media". Water Resources Research, Vol. 41, No. 11, 2005
Li, S.G., H. S. Liao, and C.F. Ni, A computationally practical approach for modeling complex mean flows in mildly heterogeneous media, Water Resources Research, Vol. 40, No. 12, 2004.
Li, S.G., H. S. Liao and C.F. Ni, Stochastic Modeling of Complex Nonstationary Groundwater Systems, Advances in Water Resources. 27(11), pp 1087-1104, 18 pages, 2004.
Li, S.G. and Q. Liu, "A real-time, computational steering environment for integrated groundwater modeling". Recommended for publication, under revision, Ground Water.
Li, S.G., Q. Liu, and S. Afshari, "An Object-Oriented Hierarchical Patch Dynamics Paradigm (HPDP) for Groundwater Modeling". Recommended for publication, under revision, Environmental Modeling and Software.
Ni, C.F. and S.G. Li, "Simple Closed-Form Formulas for Predicting Groundwater Flow Model Uncertainty in Complex, Heterogeneous Trending Media". Recommended for publication, under revision. Water Resources and Research, Download PDF
S.G. Li and Q. Liu, "Interactive Ground Water (IGW)", Environmental Modeling and Software. Vol. 20, No. 12 ( In Press). Download PDF
S.G. Li, Q. Liu, Interactive Ground Water (IGW): An Innovative Digital Laboratory For Groundwater Education and Research, COMPUTER APPLICATIONS IN ENGINEERING EDUCATION. Vol. 11(4):179~202, 2003.