National Research Program

Application of Stochastic Processes in Hydrogeology

Many aspects of ground-water flow and transport resist standard, deterministic modeling techniques: either there exist elements which are overly complex or which are simply unpredictable. These elements may have either a spatial character, as heterogeneity in porous media, or a temporal character, as recharge events to an aquifer. Provided that an adequate representation can be found, then these aspects of flow and transport frequently are better modeled by taking the complex or unpredictable element to be a stochastic process. Given an adequate representation, then the following questions may be addressed: (1) What is the implication of these elements for flow and transport in porous media? (2) Given observations of the physical process (hydraulic heads, concentrations, discharges), can the stochastic element be characterized (variances, length scales)? (3) Can an adequate monitoring program be designed when the physical process incorporates complex or unpredictable elements? The principal objective of this research is a better understanding of flow and transport phenomena when the underlying physical process contains one or more stochastic elements. A subsidiary objective is the development of a network model to evaluate sampling schemes when the physical process contains a stochastic element. An inverse procedure whereby the statistical properties of the stochastic element can be determined from the outputs of the physical process will be a necessity if these models are to be utilized. Where practicable, investigation will include development of usable computer codes. For additional information, see project's home page.


Naff, R.L., 2012 (web publication 10/12/11), Application of the control volume mixed finite element method to a triangular discretization: International Journal for Numerical Methods in Engineering, v. 89, no. 7, p.s 846–868. (on-line abstract of journal article)

Naff, R.L., 2010, A control volume mixed finite element formulation for triangular elements, Proceedings of XVIII International Conference on Computational Methods in Water Resources, Barcelona, Spain, June 21-24, 2010.

Wilson, J.D., and Naff, R.L., 2010, Multigrid preconditioned conjugate-gradient solver for mixed finite-element method: Computational Geosciences, v. 14, no. 2, p. 289-299. (on-line abstract or on-line article in pdf format, 398 KB, published by Springer with open-access)

Naff, R.L., and Banta, E.R., 2008, The U.S. Geological Survey modular ground-water model - PCGN: A preconditioned conjugate gradient solver with improved nonlinear control: U.S. Geological Survey Open-File Report 2008-1331, 35 p. (on-line abstract or on-line report in pdf format, 776 KB)

Naff, R.L., and J.D. Wilson, 2006, A comparison of preconditioning techniques for parallelized PCG solvers for the cell-centered finite-difference problem: XVI International Conference on Computational Methods in Water Resources, Copenhagen, Denmark, 18-22 June, 9 p. (on-line paper)

Wilson, J.D., and Naff, R.L., 2004, MODFLOW-2000, the U.S. Geological Survey modular ground-water model; GMG linear equation solver package documentation: U.S. Geological Survey Open-File Report 2004-1261, 47 p. (on-line abstract or on-line report in pdf format, 4.09MB)

Naff, R.L., Banta, E.R., and McCord, J., 2003, Obtaining a steady-state solution with elliptic and parabolic ground-water flow equations under dewatering conditions - Experience with a basin model, in Poeter, E.P, Zheng, C., Hill, M.C. and Doherty, J., eds. MODFLOW and more 2003, Understanding through Modeling [Proceedings]: Golden, CO, Colorado School of Mines, September 16-19, 2003, p. 330-335.

Richard L. Naff
U.S. Geological Survey, P.O. Box 25046, ms413, Denver Federal Center, Lakewood, CO
Telephone: 303-236-4986

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