Current Research Projects Investigating groundwater table fluctuations due to changes in precipitation and groundwater withdrawals at the Sheyenne National Grassland, North Dakota. The Sheyenne National Grassland contains the largest, publicly-owned tract of Northern Tallgrass Prairie ecosystem remaining on Earth. Twenty-seven sensitive plants (one-half of all sensitive plant species in the Northern Region of the US Forest Service, which encompasses Idaho, Montana, North Dakota, and South Dakota) occur on the 70,000-acre Sheyenne National Grassland. A shallow aquifer that intersects hummock and swale terrain in many places seasonally is essential to support a diverse plant community. Our groundwater modeling study is aimed at assessing both natural and anthropogenic changes in the groundwater regimes. Specifically, we are interested in groundwater table changes that might adversely affect the sensitive ecological system of the Sheyenne National Grassland. The project is funded for two years by the USDA Forest Service.

Papers Under Development "A Hybrid Finite Difference and Analytic Element Model: An alternative to Local Grid Refinement", Henk Haitjema, Daniel Feinstein, Randy Hunt, and Maksym Gusyev Regional finite difference models tend to have large cell sizes, often on the order of a mile on a side. While the regional flow patterns in deeper formations may be adequately represented by such a model, the intricate surface water and ground water interactions in the shallower layers are not. Several stream reaches and nearby wells may occur in a single cell, precluding any meaningful modeling of the surface water and ground water interactions between them. Additionally, the combination of large cells and a dense surface water network, as is typical for humid areas, will render nearly all cells in the upper model layer as constant head cells or river cells. As a result, there are few cells left to represent ground water flow between these surface waters. This problem has been addressed, in part, by inset models in areas of special interest. More recently, MODFLOW has been equipped with a Local Grid Refinement (LGR) package to locally enhance grid resolution in areas of interest. We propose to replace the upper MODFLOW layer or layers in which the surface water and ground water interactions occur by an analytic element model GFLOW which does not employ a model grid, but represents wells and surface waters directly by use of point-sinks and line-sinks. The analytic element model is provided with a leakage grid at the aquifer bottom which simulates the leakage between the shallow GFLOW model layer and the underlying MODFLOW layers. For many practical cases it suffices to use the leakages calculated in the original complete MODFLOW model, which results in good approximations to the conjunctive surface water ground water flow patterns in the GFLOW model. A lesser approximation occurs when the transmissivity in the deeper (MODFLOW) layers dominate. For those cases an iterative coupling procedure, whereby the leakages between the GFLOW and MODFLOW model are updated, significantly improves the overall solution. The iterative coupling, however, is computationally intensive. The coupled GFLOW-MODFLOW model is applicable to relatively large areas, in many cases to the entire model domain. Even when applied locally, however, it appears an efficient alternative to inset models or LGR. “Truncating cross-sectional groundwater models under wetlands” Henk Haitjema, Maksym Gusyev and Mark Wilsnack Cross-sectional models, which represent two-dimensional flow in the vertical plane, tend to have problematic aspect ratios since the aquifer thickness is often small compared to the lateral extent of the flow domain. For that reason, the model domain is usually limited to the immediate area of interest, for instance the aquifer section underneath a dam. Remote Dirichlet boundaries, such as a constant head boundary formed by a remote canal or other surface water body, can easily be included in such a local, truncated model by use of a Cauchy type boundary condition at the end of the model domain. This is commonly done in MODFLOW models by use of a so-called "general head boundary." It appears possible to use a similar Cauchy boundary condition to represent flow from remote wetlands that are left out of the truncated model. The resistance to flow inherent to such a boundary depends on the aquifer properties and the resistance to flow through the wetland bottom. While the Cauchy boundary condition is based on the Dupuit-Forchheimer approximation to flow underneath the remote wetlands, the error appears to be negligible (less than 0.6%) for most practical cases, including flow in stratified aquifers. For the case of multiple aquifers underneath the wetlands, the total flow in the truncated model can be a few percent in error, which is typically acceptable for most engineering applications. The approach is illustrated with an application near a levee-borrow canal setting in the Florida Everglades. “An exact solution to a line-sink in a leaky aquifer” Maksym Gusyev and Henk Haitjema By use of Wirtinger calculus we obtained an exact solution for a line-sink in a leaky aquifer by integrating the potential for a well in a leaky aquifer. The latter potential is the modified Bessel function of the second kind and zero order K0, which can be represented by an infinite series. Theoretically, this series expansion for the well is exact, although numerical evaluation is only practical within some infinite distance from the well, depending on machine accuracy. For a double precision this distance is about to 18λ, whereby λ is the "leakage factor" or "characteristic leakage length" which depends on the aquifer properties. Earlier solutions, based on an approximation to the function K0, have a limited the domain of validity; from 2 λ to 8 λ away from the well. As a result, earlier (approximate) solutions for the line-sink, could only be applied to line-sinks of length λ. It appears that our use of the infinite series (exact representation of K0), makes it possible to formulate a solution for a line-sink of any length, thus avoiding to need to break up line-sinks into smaller sections as has been done to date. Formulating our solution in terms of the complex variable z and its conjugate ž, using Wirtinger calculus, also allows us to calculate the exact integrated steady- state flow induced by the line-sink across an arbitrarily placed line element. This feature is often necessary in the context of the analytic element method in order to satisfy boundary conditions in terms of integrated fluxes, such as no-flow boundaries or leaky walls. The capability to accurately calculate such integrated fluxes across line elements is also important in order to obtain the integrated leakage over a domain by applying water balance rather than (numerically) integrating the leakage directly. Our exact solution is also useful in the Laplace Transform Analytic Element Method (LT-AEM) for transient groundwater flow.