Toward Practical Stochastic Groundwater Modeling: 

A New Data Source, Nonstationary Modeling Methodologies, & An Integrated Computational Platform
   
Investigators Shu-Guang Li, Hua-Sheng Liao, Qun Liu
Research Assistants David Ni
Funding Agency: National Science Foundation

  

Despite the intensive research over the past 30 years in the field of stochastic subsurface hydrology, our ability to analyze and model heterogeneous groundwater systems remains limited. Although the "stochastic revolution" has produced an enormous number of theoretical publications and influenced significantly the way we think about heterogeneity, it has had relatively little impact on practical modeling community. The prevalent groundwater simulation paradigm used in practice today is still largely deterministic based on essentially the same classical theories developed decades ago.

A natural question that arises is:  If heterogeneity is so important why is that "nobody" is using stochastic modeling theories in practice (Zhang and Zhang 2004) ?  A number of recent review articles examined this question in some significant detail and provided the following reasons:

Stochastic modeling is probably incompatible with the conventional measurement technologies available today. Standard field data is often too limited to provide the geostatistical parameters needed for stochastic modeling. New measurement technologies, new sources of data of much better resolution, and practically usable data inversion approaches to characterize aquifer heterogeneity are urgently needed.

 
Stochastic analytical theories are very difficult to apply for most problems of realistic complexities. These theories are based on too many restrictive requirements to be practically useful. The assumptions of stationarity, ergodicity, mean uniform flow, gaussian distribution, and small perturbation must be substantially relaxed.

 
Stochastic numerical theories are computationally impractical, not just somewhat inefficient, for most problems of realistic sizes. Contrary to common expectation, many recent first order perturbation techniques are even more unrealistic than the classical Monte Carlo simulation. One must recognize and remove these tough computational bottlenecks before meaningful stochastic modeling applications are possible.

 
Stochastic theories are abstract and complex and difficult to implement even for experts who developed them. There is an urgent need for a general, integrated computational platform before stochastic modeling can be popularized.

Motivated by these critical assessments, we address in this project a number of key conceptual, computational, and implementation issues in stochastic groundwater modeling. This research represents our effort toward minimizing the gap between stochastic theories and applications and ultimately making stochastic groundwater modeling practical.  

2005 AGU Fall Meeting, San Francisco, USA - "Quantifying Uncertainty in Complex Groundwater Flow Models" - by Chuen-Fa Ni and Shu-Guang Li

Publications:

Li, S.G. and Q. Liu, "A real-time, computational steering environment for integrated groundwater modeling". Recommended for publication, under revision, Ground Water.

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, Liao, H. S.; Ni, Chuen-Fa, A computationally practical approach for modeling complex mean flows in mildly heterogeneous media, Water Resour. Res., Vol. 40, No. 12, 2004. Download PDF

S.G. Li, 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. Download PDF

S.G. Li, McLaughlin D., Liao HS. The accuracy of Stochastic Perturbation Solutions to Subsurface Transport Problems, ADVANCES IN WATER RESOURCES, 27(1): 47-56, 10 pages, JAN 2004. 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. Download PDF

S.G. Li, McLaughlin D., Liao HS. A computationally practical method for stochastic groundwater modeling. ADVANCES IN WATER RESOURCES, 26(11): 1137-1148, 12 pages, NOV 2003. Download PDF

S.G. Li and D.B. McLaughlin, "Asymptotic Properties of the Eulerian Truncation Approximation: Analysis of the Perfectly Stratified Transport Problem". Water Resources Research, 38(8), 1143-1149, 7 pages, AUG 2002. Download PDF



Shu-Guang Li, http://www.egr.msu.edu/~lishug

Department of Civil and Environmental Engineering
A133 Engineering Research Complex
Michigan State University
East Lansing, MI 48824-1226

Phone: (517)432-1929
Fax: (517)335-0250
E-mail: lishug@egr.msu.edu