Modeling Complex Groundwater Systems Across Multiple Scales: Part 1 - A Hierarchical Patch Dynamic Paradigm

In this paper, we present a hierarchical patch dynamic paradigm for modeling complex groundwater systems across multiple scales – one that has the potential to substantially alleviate the infamous “curse of dimensionality” and the associated computational bottlenecks in large-scale groundwater modeling. The new modeling paradigm is inspired by the observations on how biological systems have been doing a great job coping with complexity, especially on their ability to process far more information than their limited bandwidths allow. Specifically, the new modeling paradigm takes advantage of hierarchy theory, mimics how biological systems “divide and conquer” complexities, and decouples scale-dependent subsurface dynamics hierarchically. The result is a systematic framework that allows converting a large problem into many smaller sub-problems and thus enables modeling complex groundwater systems in high resolution without having to solve large, ill-posed matrix systems. We illustrate the basic concept and the effectiveness of hierarchical modeling with a simple example. In part 2 of this paper series [Li et al., to submit], we address practical implementation issues and present an integrated, object-oriented, computational steering environment to specifically support hierarchical patch dynamic modeling. We demonstrate the power of the hierarchical modeling environment by applying it to solve a large, complex groundwater problem across multiple spatial scales.