SIMULATING LAKE-GROUNDWATER INTE CTION WITH MODFLOW Gregory W. Council AUTHOR: Project Engineer, HSI GeoTrans, 1080 Holcomb Bridge Rd, Building 200 Suite 305, Roswell, GA 30076. REFERENCE Proceedings of the 1997 Georgia Water Resources Conference, held March 20-22, at The University of Georgia, Kathryn J. Hatcher, Editor, Institute of Ecology, The University of Georgia, Athens, Georgia Abstract. Simulating the interaction between groundwater A Lake Package for MODFLOW and surface water can help in assessing the impacts of The Lake Package for MODFLOW (LAK2 Version 2.2) development on water resources. A new computer modeling handles the lake-groundwater and lake-stream interactions package (LAK2) was developed for simulating lake- including allowances for lake expansion and contraction, groundwater iteraction with the popular MODFLOW multiple inflow and outflow streams, and user-specified stage- (Modular Three-Dimensional Finite-Difference Ground-Water outflow relationships. The user can choose to have the model Flow Model) program, including lake-steam interaction using calculate the steady-state or transient lake stage, or the stage MODFLOW's steamflow routing (STR2) package. The new can be specified as a linear function of time. The modular package solves for steady-state or transientsient lake stage, or the design of the LAK2 package allows almost seamless stage canc be specified by the user. The new lake package integration with the standard Modular Three-Dimensional builds on the capabilities of previously-documented packages Finite-Difference Ground-Water Flow Model, or MODFLOW, (LAK1 by Cheng and Anderson and RES1 by Fenske and program (McDonald and Harbaugh, 1988), which in its latest others). The utility of the LAK2 package is demonstrated with versions includes the Streamflovv Routing package STR2 a real-world example in which modeling is used to predict lake (Prudic, 1989). Robust solution techniques are used to solve level decline at four lakes in response to groundwater the nonliner equations for lake stage. drawdown resulting from the operation of a proposed The LAK2 Lake Package was developed as part of a broad underground mine. study of the environmental effects of a proposed mine in Northern Wisconsin (Foth & Van Dyke, 1995). As part of the regulatory permitting process, a MODFLOW model was INTRODUCTION developed to determine the effect of proposed mining on groundwater and surface water in the vicinity of the mine. Numerical models of groundwater andan surface water flow Using the LAK2 package, the model predicts the amount of help us understand environmental systems, identify the decline in lake stage at four lakes of interest at the site. That important parameters affecting flow, and predict responses to study provides a good example of the package's utility and is various types of development (e.g. drilling a well to remove discussed in greater detail later in this paper. groundwater from an aquifer, installing a control structure on a lake, or dewatering the underground workings of a mine). Relevance to Georgia Water Resources Traditionally, separate models have been used to analyze Both groundwater and surface water resources are important surface water and groundwater resources. However, it is often in the state of Georgia. Georgians obtain about 51 percent of important to recognize that the interaction between surface their water from surface water sources, and about 49 percent water and groundwater requires a model that incorporates both from groundwater (Dorman, 1992). Georgia contains more components. A change in the level of groundwater (i.e. than 400,000 acres of lakes and reservoirs (Dorman, 1992) potentiometic head) can c affect the water level in overlying andd vice-versa, because of flow through permeable lakebeds. The surface water andan groundwater systems are thus Evaporation coupled, and a model that analyzes both systems Direct Surface Runoff w simultaneously is often desirable. PrecipitationT Figure 1 depicts a lake and its volumetric budget components. The various inflows and outflows are used to determine the stage (water elevation) of the lake In order to properly model the lake, all of the volumetric components must be accounted for While precipitation, evaporation, and surface water runoff may be fairly well-known for a given application, the streamflows and groundwater flow will Groundwater inflow/Outflow generally vary as the (potentially unknown) lake stage Figure 1. Cross-sectional view of a lake showing its changes. volumetric budget components. which serve many ecological, recreational, and industrial to calculate the stage in response to environmental stresses. It purposes. Together, lakes, streams and groundwater (and is not connected to the Streamflow Routing package. often wetlands as well) form a highly interconnected The original Lake package (LAKI) developed by Xiangxue hydrologic system. In cases where lakes are directly Cheng and Mary Anderson (Cheng, 1994, Cheng and connected to the saturated groundwater (prevalent throughout Anderson, 1993) includes many of the functions in the newer Georgia), the LAK2_ package can be a useful tool for LAK2 package. In providing boundary conditions for estimating the interrelated environmental impacts of surface equation (1), LAK1 also behaves like the River package water or groundwater development. (RIV). Additionally, it calculates lake stage as a transient The mine permitting process in Georgia will likely lead to response to evaporation, precipitation, streamflovv, and analyses similar to the one presented later in this paper. For goundwater flux. The LAKI package_handles lake-stream instance, DuPont is currently planning to apply for permits for interaction with a modified version of the original Streamflow a potential strip mine site at the edge of the Okefenokee Routing package (STR1). The package does not provide for Swamp near Folkston. steady-state solution of lake stage, and requires the use of Manning's equation to calculate flow from a lake to an adjoining stream, based on the stage in the lake. DEVELOPMENT HISTORY The new Lake package (LAK2) described here includes all of the capabilities of the RES1 and LAK1 packages, and MODFLOW and Standard Packages includes new features that were desired for modeling the The Modular Finite-Difference Ground-Water Flow Model proposed mine site in northern Wisconsin. First, computation (MODFLOW) was developed by McDonald and Harbaugh of of steady-state lake stage is possible, using a modified version the USES in 1988. The code solves < (via iterative of Newton's Method. The steady-state lake stage represents approximations in discretized space and time) the groundwater the stage at which lake inflow (from precipitation on the lake, flow equation. which is a combination of the continuity overland runoff, stream inflow, and groundwater flux) <is equation and Darcy's Law: balanced by lake outflow (to streams, groundwater, and the atmosphere via evaporation). Also, the relationship describing g 677 g + f s stream outflow has been made very general, to accommodate ax ac 41i a a a a wide variety of stage-outfall relationships. The LAK2 In equation (1) the dependent variable, h, is potentiometric package is a completely new code, which improves the input head [L], a function of space and time. The independent file structure, output options, and memory requirements of the variables are the spatially variable hydraulic conductivity (Ic, LAK1 package. It is easy to connect to MODFLOW, Ky and Kz) [LIT] and specific storage (S,) [L4] fields. seamlessly connecting with the current Streamflow Routing Together with initial conditions for potenfiometric head and package (STR2) for stream-lake interaction. various boundary conditions, MODFLOW uses a discretized, The LAK2 package provides a variety of lake-groundwater algebraic form of equation (1) to solve for the potentiometric simulation features, within the structured MODFLOW head at every model cell at timesteps within each simulated framework. The widespread acceptance of MODFLOW for period. analyzing water-resources problems makes the code practical Boundary conditions allowed by MODFLOW include the for many applications'. specified-head, specified-flux, and head-dependent flux types. Boundary conditions are specified in MODFLOW through its Other Lake-Groundwater Models various packages, or modules, including: Recharge (RCH), Lake packages for other groundwater flow models have Well (WEL), River (RIV), Drain (DRN), and previously been developed, as documented in Cheng and Evapotranspiration (EVT). Another package was later added Anderson, 1993 Additionally, fully integrated surface- for streamflovv routing (STR1, revised to STR2, Prudic, water/goundwater models have been and are being developed 1989). that vary in terms of capabilities and complexity (see Yan and Smith, 1994 for example). Packages to Simulate Lake -Groundwater Interaction Two previously-documented packages, have been written to simulate lakes with MODFLOW: the Reservoir package LAK2 PACKAGE DESIGN (RES1), and the original Lake package (LAK1). The Reservoir package (REST, Fenske et al., 1996) works like the The LAK2 Lake package provides two major functions: 1) River (RIV) package, but allows for a specified, linearly- it formulates boundary conditions for the system of equations varying (in time) lake stage. The known stage is used to MODFLOW uses to solve equation (1), and 2) it computes determine the number of cells that are covered by the lake at lake-wide budget