Improving a Regional Model Using Reduced Complexity and Parameter Estimation

Abstract

The availability of powerful desktop computers and graphical user interfaces for ground water flow models makes possible the construction of ever more complex models. A proposed copper-zinc sulfide mine in northern Wisconsin offers a unique case in which the same hydrologic system has been modeled using a variety of techniques covering a wide range of sophistication and complexity. Early in the permitting process, simple numerical models were used to evaluate the necessary amount of water to be pumped from the mine, reductions in streamflow, and the drawdowns in the regional aquifer. More complex models have subsequently been used in an attempt to refine the predictions. Even after so much modeling effort, questions regarding the accuracy and reliability of the predictions remain. We have performed a new analysis of the proposed mine using the two-dimensional analytic element code GFLOW coupled with the nonlinear parameter estimation code UCODE. The new model is parsimonious, containing fewer than 10 parameters, and covers a region several times larger in areal extent than any of the previous models. The model demonstrates the suitability of analytic element codes for use with parameter estimation codes. The simplified model results are similar to the more complex models; predicted mine inflows and UCODE-derived 95% confidence intervals are consistent with the previous predictions. More important, the large areal extent of the model allowed us to examine hydrological features not included in the previous models, resulting in new insights about the effects that far-field boundary conditions can have on near-field model calibration and parameterization. In this case, the addition of surface water runoff into a lake in the headwaters of a stream while holding recharge constant moved a regional ground watershed divide and resulted in some of the added water being captured by the adjoining basin. Finally, a simple analytical solution was used to clarify the GFLOW model's prediction that, for a model that is properly calibrated for heads, regional drawdowns are relatively unaffected by the choice of aquifer properties, but that mine inflows are strongly affected. Paradoxically, by reducing model complexity, we have increased the understanding gained from the modeling effort.

Analytic Element Modeling of Cylindrical Drains and Cylindrical Inhomogeneities in Steady Two‐Dimensional Unsaturated Flow

“…Warrick and Knight (2002) applied it to a steady flow problem in the vadose zone where a single cylindrical inhomogeneity was embedded. Analytic element models are used to solve practical saturated flow problems on a regular basis (e.g., Haitjema, 1992; Bakker et al, 1999; Kelson et al, 2002) and to study effective aquifer and transport properties of highly heterogeneous media using tens of thousands of inhomogeneities (e.g., Janković et al, 2003a, 2003b).…”

Estimating Recharge Rates with Analytic Element Models and Parameter Estimation

“…AE models were first introduced by Strack and Haitjema (1981a, 1981b) and further developed and discussed by Strack (1989, 1999), Haitjema (1995), and Mitchell‐Bruker and Haitjema (1996), among others. AE models are increasingly used for regional ground water flow modeling studies (e.g., Hunt et al 1998; Bakker et al 1999; Hunt et al 2000; Kelson et al 2002). The existing, two‐dimensional AE (GFLOW) model of Hunt et al (1998) for the Trout Lake basin was modified for the purposes of this study.…”

Ground Water Modeling Applications Using the Analytic Element Method

“…Rather than abandoning such a model and replacing it with a more complex model as more data and insight become available, the initial model is gradually upgraded to a more complex and realistic representation of the hydrological regime (Wittman et al 1996; Dripps et al 2006; Johnson and Mifflin 2006). The focus on parsimonious designs also made stepwise analytic element models well suited for nonlinear parameter estimation techniques for model calibration (Power and Barnes 1993; Simpkins 2006), prediction (Hunt et al 2000b; Kelson et al 2002), and designing future data collection efforts (Hunt 2002). In some cases, the end result of the stepwise process is an analytic element model sufficient to answer the questions that initiated the modeling.…”

“…In the simplest combination, a regional analytic element model was used to determine the size and shape of the model domain for an interior three‐dimensional MODFLOW model (Olsthoorn 1999; Krohelski et al 2000). Or, an analytic element model can be used to assess the efficacy of more complex MODFLOW models such as that of Kelson et al (2002), who used an analytic element model to assess drawdown and streamflow reduction; this type of analysis was warranted because it was noted that proposed mine dewatering might extend beyond the boundaries thought reasonable when constructing previous finite‐difference models. A more powerful application of joint modeling is to use a simpler regional analytic element model to directly extract the MODFLOW input files (Figure 2) for the development of more complex, local finite‐difference models (Hunt et al 1998a, 1998b; Gotkowitz et al 2002; Feinstein et al 2003; Pint et al 2003; Lenz et al 2003; Hunt et al 2003b; Dunning et al 2004; Gotkowitz et al 2005; Juckem et al 2006).…”