One-Week Module on Stochastic Groundwater Modeling

INTRODUCTION Students of groundwater hydrology enjoy several benefits from an introduction to groundwater modeling software, such as MODFLOW (Harbaugh and McDonald, 1996). From a practical perspective, students gain a skill that is useful in consulting practice. From an educational perspective, students gain insight into the geometry and dynamics of groundwater flow, since results are presented visually. In addition, learning groundwater modeling provides an opportunity to develop higher-level cognitive skills, as students critically evaluate their model in terms of its conceptual basis, assumptions, and intended use. These cognitive skills allow students to appreciate the well -known notion that ―all models are wrong but some are useful‖ (Box, 1979). Perhaps the most important assumption in elementary groundwater models is that of homogeneous hydraulic conductivity. This assumption is a major simplification, meaning that predictions of production rates, power requirements, and water quality may suffer from major errors. Deterministic models lack the ability to quantify these errors. Stochastic groundwater models, in contrast, allow the modeler to calculate the uncertainty of model results, most commonly by modeling the heterogeneous hydraulic conductivity as a spatially-correlated random variable. In academic research, stochastic groundwater modeling is a standard approach, dating back to the 1970s (Freeze, 1975), for which standard textbooks are available (Rubin, 2003; Zhang, 2002). However, stochastic groundwater models are not widely used in consulting practice (Schwartz and Ibaraki, 2001), and several explanations have been proposed (e.g., Pappenberger and Beven, 2006; Zhang and Zhang, 2004). One explanation is the lack of information to quantify the heterogeneity of typical aquifers; this concern has been partially addressed by a published summary of the mean, standard deviation, and spatial correlation length of hydraulic conductivity at numerous sites (Tables 10.7 and 10.8 in Rubin et al., 1999), and by the World Wide Hydrogeological Parameters Database at wwhypda.org (Comunian and Renard, 2009). A second explanation is a lack of software to implement stochastic groundwater models; this concern has been partially addressed by MODFLOW-STO (Liu et al., 2006). A third explanation is that while stochastic groundwater modeling is standard in academic research, it is not yet standard in groundwater education (Neuman, 2004; Renard, 2007; Winter, 2004). The objective of this article is to partially address this third explanation. Li and Liu (2004) present a compelling argument for the need for a constructive approach when teaching groundwater hydrology, in which students first learn specific concepts, then integrate them into a general understanding. Since then, several constructive methods for teaching groundwater have appeared in the geoscience education literature. Neupauer (2008) presents a semesterlong containment design project that integrates various groundwater topics. Neupauer and Dennis (Neupauer and Dennis, 2010) describe an in-class demonstration that allows students to discover Darcy’s law. All of these studies are based on the premise that active learning—in which students manipulate physical objects, build computer models, or participate in classroom discussions—can be more effective than traditional lecturing (e.g., Light, 2001; Lowman, 1995). However, articles on active learning methodology for stochastic groundwater modeling appear to be absent from the geoscience education literature. This article describes a one-week introduction to stochastic groundwater modeling, intended for the end of a first course on groundwater hydrology, or the beginning of a second course on stochastic hydrogeology or groundwater modeling. This brief module is not intended to create expert stochastic modelers. Instead, the goal is for students to learn the qualitative concepts of stochastic groundwater modeling through a guided computer exercise, in order to gain insight into the limitations inherent in deterministic groundwater models. The educational objectives for this one-week module are listed in Table 1. Each objective begins with a verb, indicating an David C. Mays 1