This report provides the necessary documentation of the numerical models developed for the Central Sands Lake study in central Wisconsin and will be included as a technical appendix in the report to the Wisconsin State Legislature by the Wisconsin Department of Natural Resources (WDNR) in response to 2017 Wisconsin Act 10. This legislation directed WDNR to determine whether existing and potential groundwater withdrawals are causing or are likely to cause significant reduction of mean seasonal water levels at Pleasant Lake, Long Lake, and Plainfield Lake (s. 281.34(7m)(2)(b), Wis. Stats.) in Waushara County, Wisconsin. To evaluate the potential hydrologic connection between groundwater withdrawals and the nearby study lakes, hydrologic models were created that focused on the lakes of interest and yet were large enough to cover a broad enough region to extend to the major hydrologic boundaries of the natural flow system. The areas near the lakes require finer-scale grid discretization (or spacing) to better represent the lakes and streams in the model, but also need to cover a large enough area to include the groundwater withdrawal locations that have the potential to cause reduction in water levels in the lakes. To accomplish these goals, three groundwater models were created: a regional model extending to major hydrologic boundaries; and two inset models, inheriting boundaries from the regional model but focused near the lakes. Each of the inset models, in turn, included a detailed area close to the lakes surrounded by an area at the same spatial scale as the regional model (Figure 1).

To support WDNR in evaluating the connection between groundwater withdrawals and lake levels, a representative time period was required over which to compare land use with and without irrigated agriculture and for WDNR to evaluate potential lake stage and flux changes related to irrigated agriculture. WDNR chose the climate period of 1981-2018 to be representative of a typical period and provided two land use scenarios—one with no irrigated agriculture and one with assumed crop rotations similar to current conditions—to simulate with groundwater models to, then, compare lake responses with. As a result, simulations over this climate record are not intended to recreate the history of 1981-2018 because land use changed over that time. These runs are, instead, intended to provide a basis on which to compare land use with and without irrigation-related groundwater withdrawals based on the current arrangement of land use and a varied climatic record. Groundwater withdrawals focused on irrigated-agriculture-related water use because greater than 95% of groundwater withdrawal in the two inset models around the study lakes is for irrigated agriculture water use.

The period of 2012-2018 was used for parameter estimation (synonymously referred to as “history matching”) for the groundwater models. This time period was chosen because it includes the most complete water use records to simulate groundwater withdrawals. History matching was performed using groundwater elevations, lake stages, and streamflow observations over the 2012-2018 time period and processed observations derived from those raw data.

Climatic data were incorporated into the model using a soil-water balance approach. A soil water balance model was constructed at the scale of the regional groundwater model to both calculate recharge based on land use and climate, and in the long-term climate-period runs, to estimate water use required by irrigated agriculture to apply as well boundary conditions in the groundwater model in the absence of reported water use values over that period.