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)
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 and stage information. These two functions each timestep, and to determine the amount of flow to and from the groundwater. The REST package was not designed `A 1992 survey of groundwater professionals found that MODFLOW was by far the most common modeling software package in use (Geraghty & Miller, 1992)
458 are related through the lakebed hydraulic conductance, which the sum of outflows from all stream reaches that are tributary controls the degree of lake-groundwater interaction. to the lake. These outflows are contained in the ARTRIB variable of the Streamflow Routing (STR2) package. Groundwater Flow Boundary Condition When steady-state mode is specified for a lake, the steady- One major function of the Lake Package is to help state stage is computed after each head solution formulate the boundary conditions that control the solution of approximation. In this manner, the stage remains in balance potentiometric head. The formulation is very similar to that with successive approximations of groundwater head until the used in the River (MV) package, which specifies the flux head solution converges. An efficient solution method, based through the lakebed or riverbed as a function of stage, on Newton's method is used to calculate steady-state stage in potentiometric head in the connected cells, and the lakebed or an iterative fashion. The derivative of outflow with respect to riverbed conductance. The lakebed conductance, COND lake stage is calculated, which indicates the direction and [L2/1], at each cell is either specified by the user in the Lake approximate magnitude of stage change necessary to maintain package input file, or calculated from the lakebed geometry a steady-state balance. Modifications to Newton's method and hydraulic conductivity: allow for potential discontinuities in the outflow vs. stage relationship. Iteration stops when the lake stage is within a KL A COND. (2) specified tolerance of the exact solution. The number of cells TOP -- BOT representing the lake may change in this process. where KL is the lakebed conductivity [L/T], A is the area of the cell covered by the lake [LI, and TOP and BOT are the Transient stage. In transient mode, the stage is updated at lakebed top and bottom elevations [L]. every timestep, increasing when inflows exceed outflows and As with the River package, flow from the lake to the decreasing when outflows exceed inflows. For the first goundwater is limited when the head in a cell falls below the timestep, MODFLOW solves for potentiometric head, with the lakebed bottom. Also, if the stage of the lake is below the top lake boundary conditions formulated using the specified initial of the lakebed, the lake cell is dry and seepage into the lake stage. After the head solution is complete, lake inflows goundwater is cut off for that cell. and outflows are summed to determine the volume change for the lake, AV during the timestep of length At: Lake Volumetric Balance Once head values are obtained by MODFLOW, subroutines A V (Qp QR0 QSTR1N QGV QE Q.STROUT ) 2!it (4) in the Lake package sum the inflows and outflows which can be used to update the lake stage. Simple, volumetric equations This volume change is added to the original volume to obtain are applied to update stage in steady-state and transient modes. the volume for the next timestep. If the new volume is less than zero, the lake is dry in the next timestep, and a warning Steady-state stage. To solve for steady-state lake stage, is issued in the output file (the simulation continues, however, the following volumetric-balance equation is applied (all flow because the lake may become rewetted in subsequent terms have units of OT): simulation periods). Otherwise, the stage for the next timestep is computed. The stage is set by an iterative method (similar QE Qp+ QRO Q-S/R/N QGW ( 8 ) (S)-1- Q.srneee(S) (3) to that used for the steady-state stage solver) to a value that gives the appropriate volume. The number of cells In equation (3), which simply states that inflow equals representing the lake may change in this process. outflow, the three terms on the right-hand-side are each a function of the lake stage, S. The total flux to the goundwater Output options. The Lake package has many output (QGw) is the sum of each lake cell's individual flux. The options to aid in the interpretation of results. The status of evaporative flux, QE is computed as the product of the user- each lake can be listed in a table in the main output file at the specified evaporation rate and the "wetted" lake area, which end of each simulation period. These tables include computed includes only those cells with a lakebed top elevation below or specified stage, lake wetted area and water volume, all of the lake stage. The total stream outflow, aThoui, is the sum of the terms of equations (3) and (4), the total of all inflows and any number of individual stream outflows, each computed (as outflows, and the net flow (or steady-state volumetric balance a function of stage) with user-specified outflow relationships. error). Additionally, the stage and/or flow terms can be saved The computed stream outflows are also assigned as the inflow to a separate output file after each timestep, for easy loading terms for specified segnents of the Streamflow Routing into post-processing software or spreadsheets. Cell-by-cell (STR2) package. flows between the lake and groundwater can be printed in the The left-hand-side of equation (3) contains inflows that are main output file or saved in MODFLOW's binary format for independent of lake stage. The precipitation inflow, Q,, is the post-processing and linking to other programs (such as particle product of the user-specified precipitation rate and the total tracking and solute transport programs). lake area (when full). The runoff inflow, (1 0, is specified by the user in the input file, and the total stream inflow, Qsfluiv, is
459 Code Testing modeling effort, concentrating on the lakes simulated with the Several tests were performed on the LAK2 package to LAK2 package. ensure that it correctly formulates the groundwater equations and properly calculates lake stage. For two test problems Model Calibration (Cheng and Anderson, 1993 and Cheng, 1994), the results of Before predictive simulations can'be performed, reasonableas the LAK2 package were identical to those of LAK1. The values for model/system parameters (sach as aquifer hydraulic steady-state and transient stage solvers were tested against conductivity, lakebed conductivities, and other boundary hand calculations of volumetric balance for various test conditions) are chosen. The selected parameter values should problems, and simulations were conducted to verify that the result in a model that matches observed heads, lake levels, and groundwater equations were being formulated in a manner streamflows when simulated for the period of time consistent identical to that used by the River (RIV) package. with the observations. This process of calibration to past and current conditions is critical to producing meaningful predictions For this application several calibration time EXAMPLE APPLICATION frames were chosen to eliminate as much parameter uncertainty as, practicable. A flow model using the LAK2 Lake package was used to An average, steady-state, simulation to baseline conditions simulate lake-groundwater interaction near a proposed zinc produced heads and lake stages that were in good agreement and copper mine site in northern Wisconsin (Foth and Van observed baseline conditions. The observed and modeled Dyke, 1995 and GeoTrans, 1996). The model was constructed lake stages are listed in Table 1 (columns 2 and 3). The to simulate past, current and future flow conditions in order to predicted values in this table result from a "Best Engineering assess potential environmental effects of mining Judgement" choice of parameter values (GeoTrans, 1996).
Background The mine site is located approximately 5 miles south of Crandon, Wisconsin. The regional model shown in Figure 2 1 mirli extends over 57 square miles, and is discretized into a finite- 1 1111 1 difference MODFLOW grid with 169 rows and 135 columns. 1111111111 111111111IM Cell widths range from 100 to 1000 feet. Vertically, the I 111111111111111 model is discretized into seven layers that vary in thickness to 1111111 II 111111111111k follow the geologic stratigraphy. The upper four layers 11101 111111111= contain glacial till, glacial outw ash, and lacustrine sediments. 111110 111. The lower three layers represent bedrock with differing 11111111N111 degrees of weathering. The orebody to be mined is located in 1111114111111 ( zwEa 11 the bedrock layers. 1010fill0100111111. 110101 The model is set up to predict what would happen once the Asimamoutairmiiiir mine goes into operation. As a result of mine dewatering, water would be removed from the bedrock system leading to a decrease in head near the mine. A decrease in groundwater head could then lead to a decline in water levels in overlying lakes and streams. The model is used to predict the location and magnitude of groundwater drawdown, and the amount of lake stage decline at the nearest four lakes. Note that these lakes are connected directly to the saturated groundwater, with no significant unsaturated zone beneath them. Extensive field programs were completed in order to determine the physical nature of the aquifer and lakebeds, as well as the natural environmental stresses on the system, such as precipitation and evaporation. Some of the types of tests performed were: time-domain electro-magnetic (TDEM) geophysical investigations, aquifer and lake borings, slug tests, and pump tests. The results of these investigations were used as a starting point for estimating model inputs. A detailed discussion of the entire modeling process is presented in the project's modeling report (GeoTrans, 1996). The discussion in this paper only touches on a small part of the Figure 2. Model grid and site features for the Crandon Mine regional model.
lacustrine deposits underlie the first three lakes, and beaver Table 1. Steady-State Lake Stage Calibration and dams on the outgoing streams of these lakes play an important Steady-State Predictions for Lake Stage Decline and part in controlling lake stage. Outflow Stream Reduction. In transient mode, the model predicts the time needed to reach steady-state conditions, and the time required for Pre-Mine Model Prediction complete recovery after the cessation of mining (the proposed Baseline Conditions During Mining mine life is 30 years). Transient simulations show that the Stream time for the lakes to fully respond to the mine operation is Modeled Stage Observed Outflow Lake Stage Decline about 6 years, and the time to full recovery after cessation of Stage Reduction (ft-msl) (ft) mining is also roughly 6 years (GeoTrans, 1996). (feet-msl) (cfs)
Little Sand 1592.13 1592.09 0.07 0.138 Lake CONCLUSION AND DISCUSSION Duck 1611.94 1611.63 0.01 0.006 Lake The LAK2 Lake package provides for the simulation of lakes with MODFLOW, effectively simulating lake- Deep Hole 1605.74 1605.72 0.02 0.023 Lake groundwater interaction. The package provides methods for computing the steady-state or transient lake stage, and Skunk 1597.60 1596.67 0.53 0* Lake integrates seamlessly with the Streamflow Routing package (STR2). LAK2 provides a broad range of features and "Skunk Lake has no stream outflow. capabilities that builds on those offered by the previously- documented packages RES1 and LAK1.
Note that calibration is better at the larger lakes than at Skunk Lake, which, unlike the other lakes, has no stream outflow and 1595 (1.) is underlain by a more conductive soil type. Also note that 1594 1593
this model was not the only tool used to predict lakebed and 1592 1 outfall characteristics. Various field studies and analytical 1591 mass-balance models were used to narrow the range of 1590 s 4 4 444 4 s s a a s2 possible parameter values. A nine-year transient simulation was performed to aid the calibration and help reduce uncertainty in parameter values. 1614 (b) Again using "Best Engineering Judgement" parameter values, 1613 1612
the modeled lake stage hydrographs were compared to 1611
observed hydrographs, as shown in Figure 3. 1610 Transient simulations for other time periods were conducted 1609 4 4 4 a a along with many sensitivity simulations to determine how a a a important individual model parameters were in the calibration process. 1608 1607
1606
Model Predictions 1805
Once calibration quality was within the project's pre- 1604 defined goals, steady-state and transient predictive simulations 1803 a a a a were performed to estimate the hydrological effects of the 1 a 1 a a proposed mine. Dewatering in the mine was simulated using 91) ...,, MODFLOW's Drain (DRN) package. 1699 111.1 1=111• M•11.....11111•111.1=1. 1599 11•111iM111•111111111111•■■11111111111 WINIMA=MPIONIII In steady-state, the rate of mine inflow is replaced by 1599 MMT_Nr11111Mr-110■1111111111MNII 191EZMAIII•111.11=1 1597 1•991MMIIMICYIEFW•1•EWAVIIIMMI=IMMlii•la. 7.7:1•NAIRM increased inflow from, or decreased outflow to, the various 1596 M 1111•1■1•511111311111k44:11111.1111M oikrz.gIIIIIIIIIMEIWIIINIULIIMIIIIIIII 1595 • MINIIIIIINIMI■111111111riaL114111111111111m11111111i1=MI 1594 NV IMENIMM11.1111101111111M■WIIIIIIIIIII ■MIIIIIIIIIMIIIIIIIMANININ water bodies comprising the groundwater model's boundary 1593 ■■•11111•11111■■=1111•111UMMQ111 •MMI■INNI=11111•=1M 1592 Ill••=MM•NMII•B•••IMI II••IMIIIIII•1MMII. conditions. The groundwater levels decrease in the vicinity of 1591 NNNNNNNM111/1 1111 the mine which in turn affects the surface water components: / 4 1 4 4 4 4 4$ 4; 41a; s ; 4; af 1 f f 1 f f 1 1= al wetlands, streams, and lakes. The predicted amounts of steady-state lake stage decline and stream outflow decline are listed in Table 1 (columns 4 and 5). The stage decline is Figure 3. Observed (points) and modeled (lines) markedly less at Little Sand Lake, Duck Lake, and Deep Hole hydrographs for (a) Little Sand Lake, (b) Duck Lake, (c) Lake, than at Skunk Lake because lower-conductivity Deep Hole Lake, and (d) Skunk Lake. The y-axes show lake stage in feet-msl.
461 A demonstration of the usefulness of the LAK2 package is Dorman, D., 1992. Understanding the water system, provided by the proposed mine site example. In predictive University of Georgia Cooperative Extension Service, mode, the LAK2 package predicts the lake level decline that http://vvww.ces.uga.edu/pubed/c819-7w.html. would occur as a result of operating the underground mine. Fenske, J.P., S.A. Leake, and D.E. Prudic, 1996. The lake levels would drop in response to the groundwater Documentation of a computer program (RES 1) to simulate drawdown near the mine. The amount of this decline is leakage from reservoirs using the modular fmite-difference computed in both steady-state and transient simulations. ground-water flow model (MODFLOW), US Geological The flexibilty and capabilities of the LAK2 package with Survey Open-File Report 96-364. MODFLOW make it a practical tool for modeling surface Foth & Van Dyke, 1995. Environmental Impact Report for water and groundwater in a variety of applications. As water the Crandon Project. Submitted to the Wisconsin demands increase (in Georgia and throughout the world), Department of Natural Resources in Madison and the US effective modeling tools such as the LAK2 package will Corps of Engineers in St. Paul, MN. become increasingly important in predicting the environmental GeoTrans, Inc., 1996. Numerical simulation of the effect on impacts of proposed development and management practices. groundwater and surface water of the proposed zinc and copper mine near Crandon, Wisconsin (update to Appendix 4.2-3 of the Environmental Impact Report, Foth & Van ACKNOWLEDGMENTS Dyke, 1995). Geraghty & Miller, 1992. Geraghty & Miller Software The LAK2 package code development and the Crandon Newsletter, Vol. 4, Summer 1992. project modeling study were funded by the Crandon Mining McDonald, M.G. and A.W. Harbaugh, 1988. A Modular Company through their consultant, Foth & Van Dyke. Three-Dimensional Finite-Difference Ground-Water Flow Model. Book 6, Ch. A 1 of Techniques of Water-Resources Investigations of the U.S. Geological Survey. LITERATURE CITED Prudic, D.E., 1989. Documentation of a computer program to simulate stream-aquifer relations using a modular, fmite- Cheng, X. and M.P. Anderson, 1993. Numerical simulation difference, ground-water flow model, US Geological of ground-water interaction with lakes allowing for Survey Open-File Report 88-729. fluctuating lake levels. Ground Water. v. 31:6, pp. 929- Yan, J., and K.R. Smith, 1994. Simulation of integrated 933 . surface water and ground water systems — model Cheng, X., 1994. Numerical Analysis of Groundwater and formulation, Water Resources Bulletin, Vol. 30, No. 5, pp. Lake Systems with Application to the Trout River Basin, 879-890. Vilas County, Wisconsin. Ph.D. Thesis, University of Wisconsin-Madison.
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