Velocity profile  along A-A a  .
			Head profile along B-B  b

The focus of this research is to investigate a new, nature-inspired computational paradigm to analyze, characterize, and model large, complex groundwater systems and their interactions with surface water bodies. In particular, we propose to develop, test, and apply: 1) a biologically-motivated, hierarchical and patch dynamics framework for modeling 3D dynamic groundwater systems across multiple spatial and temporal scales – one that promises to eliminate or significantly alleviate key, longstanding computational bottlenecks and conceptual difficulties and 2) a new modeling paradigm that resolves a new, significant computer science problem - a barrier to the practical implementation of generalized hierarchical patch dynamics modeling. Our novel and interdisciplinary approach to modeling large-scale groundwater systems has the potential to substantially improve our ability to understand, characterize, and predict water and solute pathways and fluxes within soils, alluvial aquifers, and through geological formations and the fluxes across pertinent interfaces, to quantify the complex dynamic scale interactions and the local and regional feedback mechanisms that affect the response of aquifer systems to local and external forcing factors, and to develop model-based tools for integrated water resources planning and management, pollution control, and environmental cleanup.

Despite the dramatic growth of computational capability over the last two decades—one that has allowed computational science and engineering to become a unique, powerful tool for scientific discovery—our ability to model complex, 3D groundwater systems is still severely limited because of the following tough computational and conceptual challenges:  

1.  The machine bottleneck.  The computational cost in large-scale groundwater modeling, analysis, and visualization increases exponentially with the problem size and the level of details simulated and quickly becomes prohibitive for large 3D problems. This is especially the case for 3D multi-scale modeling, coupled processes modeling, inverse modeling, uncertainty analysis, design optimization, iterative hypothesis testing, and data sufficiency evaluation.

2.  The numerical algorithmic bottleneck. Three-dimensional modeling based on a single, large numerical representation of a complex, heterogeneous, and multi-scale system faces an algorithmic bottleneck. The high dimensionality, especially when combined with distorted grids representing heterogeneity, anisotropy, multitudes of scales, complex stratigraphy, and singular stresses, translates into highly “ill-conditioned” systems and causes a host of tough numerical problems.

3.  The scale and data assimilation problem. A fundamental problem in the analysis of complex ground-water systems is the interplay of data and modeling. Improving how data and models are used, especially across a multitude of scales, has proven to be exceedingly difficult [Hill and Tiedeman, 2002; Tiedeman et al, 2003, Vachaud et al 2002]. The following are many unresolved questions of fundamental nature and extreme practical significance facing the groundwater hydrology community: 

Ø  How can we maximally exploit data and information to enhance our ability to understand the complex subsurface processes and to quantify the fluxes across-groundwater/surface water interfaces [e.g., Medina , 2003; Vachaud, 2002; McLaughlin et al., 1993; Li, 1993]?

Ø  How can we systematically incorporate data collected at one scale into a model representing dynamics at another disparate scale [Kolaczy and Huang, 2001; Vachaud, 2002; Hoaglund, et al., 2002]?

Ø  How can we model at any scale of interest in a way that systematically accounts for the influences of regional control as well as subgrid scale processes and local scale measurements [Hoaglund, et al., 2002; Vachaud, 2002; Beckie et al., 1994; Bakker et al., 1999]?

Ø  How can we address today’s pressing integrated water resources and environmental management problems that require regional solutions satisfying potentially large numbers of “scattered”, local constraints [NRC, 1993b, 1999, 2001b; Commission on Geosciences, Environment and Resources, 2000; Rothman, 2000; Martell, 1996; Grasle, 2003; Bakker et al., 1999]?

Ø  How can we model realistically and robustly complex groundwater systems across multiple spatial and temporal scales in a way that is systematic, physically based, and computationally practical [Sposito, 1998; Kirkby et al, 1996; Beckie, 1994; Sahimi, 2001]?  

In this ambitious project, we will address systematically these fundamental difficulties in large-scale, 3D groundwater modeling using an interdisciplinary approach.  In particular, we will utilize hierarchy theory, successfully applied in evolutionary biology and landscape ecology, and develop: 1) a new hierarchical and patch dynamic framework for modeling subsurface flow and transport across multiple spatial scales – one that promises to significantly alleviate the longstanding computational bottlenecks and conceptual difficulties and 2) a new modeling paradigm that resolves a new, significant computer science problem - a barrier to the practical implementation of generalized hierarchical modeling. Specifically, the IT-enabled hierarchical patch dynamic approach will:  

• allow modeling and visualizing large systems in high resolution without having to solve large matrix systems and thus substantially alleviate the infamous “curse of dimensionality” in 3D groundwater modeling;

• allow modeling complex, heterogeneous, and 3D dynamics incrementally (one scale at a time) and thus obviate the need to use highly distorted grids representing multiple scales of variability, and substantially alleviate the stiff matrix problem - the algorithmic bottleneck;

• provide a systematic and efficient “scaling ladder” to link data and models across multiple spatial scales and assimilate information from disparate sources;

• provide on the fly and dynamic integration of hierarchical computations, analyses, and visualizations, free users from having to interact with each subscale modeling “patches”, and eliminate the associated human bottleneck;

• allow a modeler to interactively steer the hierarchical computation, to guide the evolution of the subsurface flow and plume migration dynamics, to control the visual representation of data during processing, and to dynamically modify the computational process during its excecution. A sophisticated navigation process would be an invaluable tool for scientific discovery, for understanding fundamental processes, and for practical site investigation.

The proposed IT enabled, 3D hierarchical and patch dynamic modeling environment may potentially impact the entire groundwater hydrology community and beyond.

Publications: 

• 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.

• 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. 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