U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2010–5214

Prepared in cooperation with the Village of Chenequa, the Southeastern Wisconsin Regional 

Planning Commission and the Wisconsin Department of Natural Resources

Application of the Local Grid Refinement Package to an Inset 

Model Simulating the Interaction of Lakes, Wells, and Shallow 

Groundwater, Northwestern Waukesha County, Wisconsin

10 20 30 40 50 60 70 80 90 100

COLUMN

ROW

20

30

40

50

60

70

80

90

100

110

118

10

27,778 feet

32,778 feet

Nagawicka 

Lake

Pine Lake

Bark 

River

Beaver Lake

North Lake

Cornell 

Lake

Okauchee

Lake

Oconomowoc

River

Mason Creek

Nagawicka 

Lake

Pine Lake

Bark 

River

Beaver Lake

North Lake

Cornell 

Lake

Okauchee

Lake

Oconomowoc

River

Mason Creek Constant-head conditions

Streams and lakes from RIV package in MODFLOW

Streams from SFR1 package in MODFLOW

Lakes from LAK3 package in MODFLOW

Approximate location of Maquoketa Shale subcrop

Grid lines for child model

EXPLANATION

Application of the Local Grid Refinement 

Package to an Inset Model Simulating the 

Interaction of Lakes, Wells, and Shallow 

Groundwater, Northwestern Waukesha 

County, Wisconsin

By D.T. Feinstein, C.P. Dunning, P.F. Juckem, and R.J. Hunt

Prepared in cooperation with the Village of Chenequa, the Southeastern 

Wisconsin Regional Planning Commission and the Wisconsin Department 

of Natural Resources

Scientific Investigations Report 2010–5214

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2011

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Feinstein, D.T., Dunning, C.P., Juckem, P.F., and Hunt, R.J., 2010, Application of the Local Grid Refinement package to 

an inset model simulating the interactions of lakes, wells, and shallow groundwater, northwestern Waukesha County, 

Wisconsin: U.S. Geological Survey Scientific Investigations Report 2010–5214, 30 p. 
iii

Acknowledgments 

This report was funded by two Lake Management Planning Grants awarded by the Wisconsin 

Department of Natural Resources under the Chapter NR 190 Lake Management Planning Grant 

Program (LPL–1129–07 Modeling and LPL–1130-07 Water Budget—Village of Chenequa).

The project benefited greatly from the counsel and data provided by

Jeffrey Kante, Forester and Superintendent, Village of Chenequa;

Dr. Jeffrey Thornton, Principal Planner, Southeastern Wisconsin Regional Planning Commission;

Robert Nauta, RJN Environmental Services; and

John Jansen and Ted Powell, Rukert-Mielke Engineering.

Also key to the project were field investigations performed by William Rose, Hydrologist, USGS. 

Generous assistance with the LGR modeling package was provided by Steffen Mehl, Professor 

at California State University, Chico; and Christopher Hoard, Hydrogeologist, USGS.

The preparation of the report depended on timely contributions from USGS colleagues Michelle 

Greenwood, Reports Specialist; Leah Leonard, Science Support; Michael Eberle, Technical Publications Editor, and Rosemary Stenback, Illustrator.

v

Contents

Abstract...........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Southeastern Wisconsin Background Regional Model..........................................................................3

Child Model Embedded in Parent Regional Model .................................................................................3

Inset Model Grid Refinement..............................................................................................................3

Input to the Parent Regional Model...................................................................................................7

Temporal Discretization of the Models .............................................................................................8

River Package Input to the Child Model ...........................................................................................9

Streamflow Routing Package (SFR1) Input to the Child Model.....................................................9

Lake Package Input to the Child Model ............................................................................................9

Recharge Input to the Child Model....................................................................................................9

Hydraulic Conductivity and Storage Input to the Child Model....................................................14

Water Withdrawals from Wells in the Child Model ......................................................................18

Calibration of the Child Model ...................................................................................................................18

Model Results...............................................................................................................................................22

Discussion.....................................................................................................................................................24

Model Limitations.........................................................................................................................................28

Summary and Conclusions.........................................................................................................................28

References Cited..........................................................................................................................................29

Figures

1. Map showing location of study area, near Chenequa, Waukesha County, 

Wisconsin ......................................................................................................................................2

2. Stratigraphic section for southeastern Wisconsin.................................................................4

3. Model layering in example east-west section. A, Layering in background regional 

model. B, Layering in parent regional and child model..........................................................5

4. Map showing location of the child model centered on Beaver, Pine, Cornell and 

North Lakes....................................................................................................................................6

5. Original discretization and boundary conditions in parent regional model for area 

replaced by child model ..............................................................................................................7

6. Grid discretization and boundary conditions for child model ...............................................8

7A. Map showing bathymetry of Beaver Lake..............................................................................10

7B. Map showing bathymetry of Pine Lake...................................................................................11

7C. Map showing bathymetry of North Lake ................................................................................12

8. Recharge distribution in child model.......................................................................................13

9. Map showing location of pumping wells in child model......................................................14

10. Graph showing aquifer-test analysis of drawdowns at three observation wells............16

11. Distribution of horizontal hydraulic conductivity in child model, layers 1 and 2..............17

12. Map showing locations of flow measurements ....................................................................19

13. Child-model domain showing the simulated water-table elevation for the 

calibration run .............................................................................................................................22
vi

Conversion Factors and Datums

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Flow, precipitation, evaporation, and recharge rates

inch per year (in/yr) 25.4 millimeter per year (mm/yr)

cubic foot per day (ft3/d) 0.02832 cubic meter per day (m3/d)

gallon per minute (gal/min) 0.06309 liter per second (L/s)

Hydraulic conductivity

foot per day (ft/d) 0.3048 meter per day (m/d)

Transmissivity

foot squared per day (ft2/d) 0.09290 meter squared per day (m2/d)

Vertical coordinate information is referenced to the insert National Geodetic Vertical Datum of 

1929 (NGVD 29).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83) 

and the Albers projection.

14. Graph showing simulated water budgets of Beaver, Pine, and North Lakes under 

base-case conditions.................................................................................................................24

Tables

1. Summary of flow measurements in Chenequa area, Wisconsin .......................................13

2. Comparison of measured to simulated values for calibration targets for 

base-case simulation.................................................................................................................20

3. Sensitivity analysis. ...................................................................................................................21

4. Lake budgets for base-case simulations................................................................................23

5. Simulated change to stage of Beaver, Pine, Cornell, and North Lakes and change to 

outflow from Beaver and Pine Lakes due to 5 years of dry weather conditions. ............25

6. Simulated change to stage of Beaver, Pine, Cornell, and North Lakes and change 

to outflow from Beaver and Pine Lakes with test well pumped for 5 years at 

47 gallons per minute and at 200 gallons per minute under average weather 

conditions.....................................................................................................................................25

7. Simulated change to stage of Beaver, Pine, Cornell, and North Lakes and change to 

outflow from Beaver and Pine Lakes with test well pumped for 5 years at 

47 gallons per minute under dry weather conditions. ..........................................................26

8. Simulated sources to test well pumped for 5 years at 47 gallons per minute (for 

average and dry weather conditions) and at 200 gallons per minute (for average 

weather conditions). .................................................................................................................26

9. Simulated groundwater inflow to lakes under various pumping and weather 

conditions.....................................................................................................................................27
Application of the Local Grid Refinement Package to an 

Inset Model Simulating the Interaction of Lakes, Wells, 

and Shallow Groundwater, Northwestern Waukesha 

County, Wisconsin

By D.T. Feinstein, C.P. Dunning, P.F. Juckem, and R.J. Hunt

Abstract

Groundwater use from shallow, high-capacity wells is 

expected to increase across southeastern Wisconsin in the 

next decade (2010–2020), owing to residential and business 

growth and the need for shallow water to be blended with 

deeper water of lesser quality, containing, for example, excessive levels of radium. However, this increased pumping has 

the potential to affect surface-water features. A previously 

developed regional groundwater-flow model for southeastern 

Wisconsin was used as the starting point for a new model to 

characterize the hydrology of part of northwestern Waukesha 

County, with a particular focus on the relation between the 

shallow aquifer and several area lakes. An inset MODFLOW 

model was embedded in an updated version of the original 

regional model. Modifications made within the inset model 

domain include finer grid resolution; representation of Beaver, Pine, and North Lakes by use of the LAK3 package in 

MODFLOW; and representation of selected stream reaches 

with the SFR package. Additionally, the inset model is actively 

linked to the regional model by use of the recently released 

Local Grid Refinement package for MODFLOW–2005, which 

allows changes at the regional scale to propagate to the local 

scale and vice versa. 

The calibrated inset model was used to simulate the 

hydrologic system in the Chenequa area under various weather 

and pumping conditions. The simulated model results for base 

conditions show that groundwater is the largest inflow component for Beaver Lake (equal to 59 percent of total inflow). 

For Pine and North Lakes, it is still an important component 

(equal, respectively, to 16 and 5 percent of total inflow), but 

for both lakes it is less than the contribution from precipitation 

and surface water. Severe drought conditions (simulated in a 

rough way by reducing both precipitation and recharge rates 

for 5 years to two-thirds of base values) cause correspondingly severe reductions in lake stage and flows. The addition 

of a test well south of Chenequa at a pumping rate of 47 gal/

min from a horizon approximately 200 feet below land surface 

has little effect on lake stages or flows even after 5 years of 

pumping. In these scenarios, the stage and the surface-water 

outflow from Pine Lake are simulated to decrease by only 

0.03 feet and 3 percent, respectively, relative to base conditions. Likely explanations for these limited effects are the 

modest pumping rate simulated, the depth of the test well, 

and the large transmissivity of the unconsolidated aquifer, 

which allows the well to draw water from upstream along the 

bedrock valley and to capture inflow from the Bark River. 

However, if the pumping rate of the test well is assumed to 

increase to 200 gal/min, the decrease in simulated Pine Lake 

outflow is appreciably larger, dropping by 14 percent relative 

to base-flow conditions. 

Introduction

Shallow high-capacity wells will likely continue to be 

drilled across southeastern Wisconsin in the next decade 

(2010–20) for numerous purposes, including new water 

supplies for residential and business growth and blending 

of shallow water with deeper water of lesser quality—for 

example, water with excessive concentrations of radium—in 

order to improve overall quality of the drinking-water supply. 

Pumping wells, particularly where they intercept substantial 

groundwater flow to surface water, have the potential to affect 

lake levels; the groundwater inflow to wetlands, creeks, and 

rivers; and water temperature. The effect of pumping can be 

pronounced because in many hydrogeologic settings, and particularly in much of southeastern Wisconsin, groundwater is in 

direct hydraulic connection with lakes, wetlands, and streams. 

Quantifying hydrologic changes resulting from groundwater 

pumping and assessing the effect on hydrologic and biologic 

resources is a challenge faced by many communities and lake 

organizations across southeastern Wisconsin.

The U.S. Geological Survey and cooperating organizations, such as the Wisconsin Geological and Natural History 

Survey (WGNHS) and the Southeastern Wisconsin Regional 

Planning Commission (SEWRPC), have previously worked 
2 Application of the Local Grid Refinement Package to an Inset Model, Northwestern Waukesha County, Wisconsin

together to develop a regional understanding of the hydrology 

of southeastern Wisconsin. This work has taken the form of 

geologic mapping, groundwater-flow modeling, quantifying 

and predicting demand on surface and groundwater resources, 

and field investigations. A southeastern Wisconsin regional 

groundwater-flow model was developed as part of this work to 

serve as a framework for hydrologic studies addressing a wide 

range of water-supply concerns. In a recent extension of this 

longstanding research, the USGS joined with the Southeastern 

Wisconsin Regional Planning Commission and the Village of 

Chenequa in work funded by the Wisconsin Department of 

Natural Resources under the Chapter NR 190 Lake Management Planning Grant Program, to characterize the hydrology 

of part of northwestern Waukesha County (fig. 1), with a particular focus on the relation between the shallow aquifer and 

area lakes. The specific objectives of this study were to

1. improve the overall understanding of the dynamics of the 

shallow aquifer in northwestern Waukesha County near 

Chenequa;

2. evaluate the role of groundwater on maintaining lake 

levels in northwestern Waukesha County by using Beaver, 

Cornell, North, and Pine Lakes as examples;

3. develop hydrologic budgets for the area; and

4. develop databases and a refined groundwater-flow model 

that may have future benefit to researchers and waterresource professionals in the northwestern Waukesha 

County area. 

The steps undertaken to achieve the objectives were

• compilation of existing hydrologic data;

• limited collection of surface-water-flow data to support 

model development and calibration;

• development of an inset MODFLOW model originating from the regional groundwater-flow model and 

implementing the recently released Local Grid Refinement package for MODFLOW-2005 (Mehl and Hill, 

2005);

• calibration of the inset model to available head and 

flow targets; 

• analysis of the results of the base-case simulation, 

focusing on the water budgets of the Chenequa-area 

lakes; and

• simulation of selected scenarios involving changes in 

climatic conditions and local pumping rates.

The complexity of the inset model increased compared to 

that of the existing regional model but was commensurate with 

the extent of the dataset in the local area. Changes to model 

layering and zonation of hydrologic parameter values were 

based on interpretation of available data.

This report presents the findings from the above-mentioned study and describes the interrelations within the hydrologic system simulated in this study, which encompasses the 

lakes, streams, and shallow groundwater system. 

Figure 1. Location of study area, near Chenequa, Waukesha County, Wisconsin.

W I S C O N S I N

Waukesha County

Waukesha

Chenequa

Delafield Brookfield

Menomonee

Falls

88°25' 88°10'

42°55'

43°10'

0 5 10 MILES

0 5 10 KILOMETERS
Child Model Embedded in Parent Regional Model 3

Southeastern Wisconsin Background 

Regional Model

The inset model is based on the previously developed 

three-dimensional finite-difference MODFLOW groundwater-flow model of the seven-county region of southeastern 

Wisconsin administered by the SEWRPC. The Southeastern 

Wisconsin background regional model (hereafter called the 

background regional model) was constructed cooperatively 

by the WGNHS and the USGS. Readers are directed to 

Feinstein, Eaton, and others (2005) and Feinstein, Hart, and 

others (2005) for detailed explanation of the development and 

application of the background regional model.

The hydrogeologic setting of the Chenequa area is typical 

of the part of southeastern Wisconsin represented in the background regional model. Crystalline bedrock of Precambrian 

age underlies the region; sandstone and carbonate units of 

Cambrian and Ordovician age overlie the crystalline bedrock 

(fig. 2). These units consist of the Mount Simon Formation, 

Eau Claire Formation, Wonewoc Formation, Tunnel City 

Group, Trempealeau Group, Prairie du Chien Group, and St. 

Peter Formation. Directly overlying the St. Peter Formation 

is the Sinnipee Group and Maquoketa Formation, a sequence 

with generally low vertical hydraulic conductivity, that isolates 

glacial and carbonate aquifers above (Silurian and younger) 

from the sandstone-dominated deep aquifer system below 

(Ordovician and older). The near-surface stratigraphy of southeastern Wisconsin consists of unlithified, glacially derived 

Pleistocene and Holocene deposits. Owing to the eastward dip 

of the consolidated bedrock stratigraphic units in southeastern 

Wisconsin, progressively younger bedrock units pinch out to 

the west. The Maquoketa Formation is present over most of 

Waukesha County but pinches out in areas of the southern and 

northwestern parts of the county; it is present only under part 

of the Chenequa study area. Where the Maquoketa Formation is absent, the shallow, unlithified deposits are in better 

hydraulic connection to the underlying sandstone aquifers, but 

resistive layers in the Sinnipee Group still limit somewhat the 

amount of vertical exchange.

Child Model Embedded in Parent 

Regional Model 

In the field of groundwater modeling, one-way coupling 

from a coarse regional model to a local and refined model grid 

is commonly called telescopic mesh refinement (TMR) and is 

most often accomplished by using some form of interpolation 

of either heads or fluxes, or both, from the coarse grid onto the 

boundaries of the refined grid (for example, Buxton and Reilly, 

1986; Ward and others, 1987; Leake and Claar, 1999; Davison 

and Lerner, 2000; Hunt and others, 2001). This approach is 

fairly straightforward and works well for many problems. The 

one-way coupling, however, does not allow for feedback from 

the refined grid (hereafter called the child grid) to the coarse 

grid (hereafter called the parent grid). Therefore, after running 

both models, the modeler must determine whether heads along 

and fluxes across the interfacing boundaries are consistent for 

both models (Leake and Claar, 1999, p. 5–7). If they do not 

match, then the modeler must make adjustments by trial and 

error: there is no formal mechanism for adjusting the models 

to achieve better agreement. For this reason, TMR methods 

generally lack numerical rigor and sometimes lead to significant, often undetected errors (Mehl and Hill, 2002a,b). 

A numerically more rigorous method that ensures consistency of heads and fluxes between the two grids—local grid 

refinement (LGR)—is an iteratively coupled method that links 

the parent and child grids in a way that provides feedback 

from the child grid to the parent grid, thus allowing two-way 

communication between the grids. Two-way iterative coupling 

is used to ensure that the models have consistent boundary 

conditions along their adjoining interface. Solutions with 

feedback can be achieved either through iteration or through 

simultaneous solution schemes. LGR couples the models by 

means of shared nodes; that is, the grids are constructed such 

that nodes of the parent grid are coincident with selected 

boundary nodes of the child grid. LGR uses the iteratively 

coupled shared-node method of local grid refinement developed and tested by Mehl and Hill (2002 a,b; 2003; 2004) and 

Mehl (2003).

Inset Model Grid Refinement

The first modification in creating the inset model for the 

Chenequa study was made to the entire domain of the southeastern Wisconsin background regional model. The original 

regional model was developed with MODFLOW 96 and was 

modified to run under MODFLOW–2005. The lower 8 layers 

of the initially 18-layer background regional model—those 

constituting the sandstone-dominated deep aquifer system 

(fig. 3)—were combined into a single confined layer with 

representative bulk hydraulic properties. These bulk properties 

preserve the spatial variation of the transmissivity and storage 

capacity of the deep aquifer system. This simplification was 

appropriate because the primary objective of the inset model 

is to simulate the interaction between the shallow groundwater system and area lakes. Given that confining units within 

the Maquoketa Formation and Sinnipee Group hydraulically 

separate the deep aquifer system from the shallow aquifers 

in this area, the shallow modeling results are largely insensitive to a detailed representation of the internal flow dynamics 

of the deep aquifer system. The new refined version of the 

regional model is hereafter referred to as the “parent regional 

model.” Layers 1 through 10 are the same in both versions of 

the regional models, but layer 11 of the parent regional model 

combines layers 11 through 18 of the background model. The 

inset model embedded inside the parent regional model also 

represents the deep aquifer system with the single layer 11 

(fig. 3B). 
4 Application of the Local Grid Refinement Package to an Inset Model, Northwestern Waukesha County, Wisconsin

Figure 2. Stratigraphic section for southeastern Wisconsin (modified from Brown and Eaton, 2002). 

Trempealeau Group

Tunnel City Group

Wonewoc Formation

Eau Claire Formation

Mount Simon Formation

Maquoketa Formation

Sinnipee Group

St. Peter Formation

Prairie du Chien Group

Undifferentiated

Three distinct till units

Fine-, medium- and coarse-grained, 

proglacial-lake sediment

Complex and variable ice margin unit

Soil, estuarine and alluvial deposits

Dolomite

(Pleistocene)

Kewaunee, Oak Creek and 

New Berlin Formations

(Holocene)

sediments

Shale and dolomite

Dolomite with limestone and shale

Orthoquartzite sandstone with

minor limestone

Dolomite with some sandstone 

and shale

Sandstone with some

dolomite and shale

Undifferentiated Crystalline

Precambrian Cambrian 

Period

Ordovician

Period

Silurian and

Devonian Periods

Quaternary 

Period

10,000

20,000

360 million

440 million

490 million

540 million

Geologic

time interval

Years

before

present

Stratigraphic unit Lithology

0
Child Model Embedded in Parent Regional Model 5

Figure 3. Model layering in example east-west section. A, Layering in 

background regional model. B, Layering in parent regional and child model. 

(The comparison of model layering shows that the deep sandstone aquifer 

system is represented by eight model layers in the background regional 

model but is represented by a single layer in the parent regional and child 

models. The east/west section contains the entire east-west extent of 

the child model, which consists of 100 columns, each 277.78 ft wide. The 

section bisects the north-south extent of Beaver Lake and further to the east 

intersects a northeast-southwest-trending bedrock valley. See fig. 4 for the 

trace (A–A ́) of the example section.)

West 

East Beaver 

Lake

Bedrock

valley

Glacial deposits (layers 1–2)

Silurian dolomite (layers 3–6)

Maquoketa Formation (layers 7–8)

Sinnipee Group (layers 9–10)

St. Peter Formation and Prairie du Chien 

Group (layer 11)

Trempealeau/Tunnel City Groups (layer 12)

Wonewoc Formation (layer 13)

Eau Claire Formation (layer 14)

Mount Simon Formation (layers 15–18)

EXPLANATION

5,000 feet Vertical exaggeration x 40 125 feet

West 

East Beaver 

Lake

Bedrock

valley

Glacial deposits (layers 1–2)

Silurian dolomite (layers 3–6)

Maquoketa Formation (layers 7–8)

Sinnipee Group (layers 9–10)

Deep sandstone aquifer system (layer 11)

EXPLANATION

5,000 feet Vertical exaggeration x 40 125 feet

A

B
6 Application of the Local Grid Refinement Package to an Inset Model, Northwestern Waukesha County, Wisconsin

In both the parent regional and child models, Layers 1 

through 10 maintain the hydrostratigraphic sequence used in 

the background regional model (fig. 3B). The top two layers 

represent the unlithified glacial material, layer 3 represents 

Pennsylvanian and Mississippian bedrock (absent in southeastern Wisconsin and therefore this layer is given a negligible 

thickness), layers 4 through 6 represent the Silurian dolomite, 

layers 7 and 8 represent the Maquoketa Formation, and layers 

9 and 10 represent the Sinnipee Group. In general, the glacial 

deposits can act as an unconfined aquifer or a confining unit, 

the Silurian dolomite serves as an unconfined or semi-confined 

aquifer, the Maquoketa Formation is a confining unit, and 

the Sinnipee Group can act as a confining unit or contribute 

transmissivity to the underlying confined, deep aquifer system. 

Descriptions of the properties of these units, including thickness and permeability, can be found in Feinstein, Eaton and 

others, 2005.

The inset (child) model constructed for the Chenequa 

study is derived from the parent regional model. The child 

model was sized to include Beaver, Pine, and North Lakes 

(lakes of primary interest to the study), as well as some distant surface-water boundaries, while keeping the model size 

relatively compact (fig. 4). The child model grid was refined 

by use of a TMR approach similar to one described by Ward 

and others (1987). The TMR routine was run with Groundwater Vistas (Rumbaugh and Rumbaugh, 2007). In the parent 

regional model, grid spacing is 2,500 ft (fig. 5); in the child 

model, the grid is one-ninth the spacing, or 277.8 ft on a side. 

Thus, every parent regional model node is represented by 

81 nodes in the child model. The layering of the child model is 

identical to the layering in the parent model. The child model 

has 118 rows and 100 columns (fig. 6). With 118 rows, 

100 columns, and 11 layers, the child model has 129,800 cells, 

all of which are active. As a result of smaller grid spacing, the 

Figure 4. Location of the child model centered on Beaver, Pine, Cornell, and North Lakes. (The brown line is the westernmost extent 

of the Maquoketa Formation confining unit that separates the shallow and deep systems where it is present. The yellow perimeter

corresponds to the parent regional model cells that are shared with the child model. The child model extends half the distance into the 

yellow perimeter. The A–A ́ trace shows the location of the sections in fig. 3.)

A

Nagawicka 

Lake

Pine Lake

Beaver Lake

North Lake

Lake 

Keesus

Cornell 

Lake

Okauchee

Lake

DODGE COUNTY

Lac Labelle

Oconomowoc Lake

Nashota Lake

A A’

MILWAUKEE 

COUNTY

OZAUKEE COUNTY

WASHINGTON 

COUNTY

JEFFERSON 

COUNTY

Pewaukee Lake

Lakes, ponds and wetlands

Streams

Approximate location of Maquoketa Shale subcrop

EXPLANATION

88°30' 88°20' 88°10'

43°10'

43°05'

0 2.5

0 2.5 5 KILOMETERS

5 MILES

Bark River

Fox River

WAUKESHA 

COUNTY

Pewaukee Creek

Oconomowoc River

Oconomowoc River

Mason 

Creek
Child Model Embedded in Parent Regional Model 7

Figure 5. Original discretization and boundary conditions in parent regional model for area replaced by child model. 

(Cells in parent regional model are 2,500 feet on a side.)

surface-water features, pumping stresses, and the hydraulichead distribution are represented more accurately in the child 

model than in the regional model. Therefore, interactions 

between streams and lakes, as well as three-dimensional flows 

near those features, are also simulated more accurately.

In addition to the greater resolution built into its grid, 

the child model is designed to more actively portray surfacewater features. Selected streams were converted from the 

MODFLOW River Package (McDonald and Harbaugh, 1988), 

shown in figure 5, to the more sophisticated Stream Routing 

(SFR1) Package (Prudic and others, 2004), shown in figure 

6. The latter allows accounting of streamflow and limits the 

amount of water a stream can lose to the aquifer to the amount 

of water captured upstream. In the child model, SFR cells are 

used to represent stream segments connecting the Chenequa 

lakes and streams entering and exiting North Lake, whereas 

the River Package is used to simulate the Bark River and parts 

of Lakes Okauchee and Nagawicka (fig. 6) because neither 

stream routing nor the ability to control infiltration quantities 

was required for these features.

A final refinement in the child model was the conversion of Beaver, Pine, and North Lake from the MODFLOW 

River Package (fig. 5) to the more sophisticated Lake (LAK3) 

Package (Merritt and Konikow, 2000) (fig. 6). This package 

provides for active model grid cells representing the aquifer 

adjacent to and beneath lakes; these active cells can simulate 

exchange of water between an aquifer and a lake at a rate 

determined by relative heads and by conductances that are 

based on grid-cell dimensions, hydraulic conductivities of the 

aquifer material, and user-specified precipitation, evaporation, and leakance distributions that represent the resistance 

to flow through the material of the lakebed (fig. 6). The use 

of the LAK3 package allows the lake stages to be calculated 

(instead of specified) and the complete lake water budget to be 

evaluated.

Input to the Parent Regional Model

The parameterization of the surface-water network, 

hydraulic conductivity of unconsolidated and bedrock units, 

and the distribution of recharge in the parent regional model 

is identical to the input to the background regional model 

described in Feinstein, Eaton, and others (2005). No changes 

were made to the regional input except to assign an average 

hydraulic conductivity to the cells in the single layer that 

represents the units composing the deep sandstone aquifer (in 

order to preserve the combined transmissivity assigned the 

multiple layers in the background regional model).

mowoc Lake

Nashota Lake

Mason Creek

Lakes and streams represented

by the RIV package in MODFLOW

Lakes, ponds and wetlands

Streams

Approximate location of 

Maquoketa Shale subcrop

Nagawicka 

Lake

Pine Lake

Bark River

Beaver Lake

North Lake

Lake Keesus

Cornell 

Lake

Okauchee

Lake

32, 778 feet

27, 778 feet

EXPLANATION

Oconomowoc River
8 Application of the Local Grid Refinement Package to an Inset Model, Northwestern Waukesha County, Wisconsin

Temporal Discretization of the Models

The parent regional and child models incorporate the 

deep pumping which, since the late 19th century, created and 

has gradually enlarged a regional cone of depression under 

southeastern Wisconsin in the deep sandstone aquifer system (Feinstein, Hart, and others, 2005). The effects of shallow pumping in the Silurian dolomite and glacial deposits, 

although less dramatic and more local in terms of drawdown, 

also are simulated by the models. For the purposes of this 

analysis, the historical rates of shallow and deep pumping 

used originally in the 18-layer background regional model to 

simulate conditions for multiple intervals between 1864 and 

1990 were input to the 11-layer parent regional model. As in 

the case of the background regional model, the parent regional 

model was used first to simulate steady-state predevelopment 

conditions, and then transient results were obtained for the 

1864 to 1990 period starting from the simulated steady-state 

condition. Both the steady-state and transient results are 

similar to the original results reported by Feinstein, Hart, and 

others (2005) for the background regional model. The parent 

regional model was then linked to the embedded child model 

by using the LGR procedure enabled by MODFLOW–2005 

(Mehl and Hill, 2005). A 20-year runup period was simulated, 

beginning from 1990 parent regional model results and using 

the same discharge rates originally assigned the background 

regional model for the 1991–2000 interval. This hypothetical transient runup period is needed to allow the model to 

react to the linking of the two models and reach a new set of 

stable conditions (it does not correspond to an actual period 

of time). Finally, an additional 5-year period was added to the 

end of the linked transient simulation in order to investigate 

the interactions of groundwater and the Chenequa-area lakes 

under several pumping, recharge, precipitation, and evaporation scenarios. The 1991–2000 pumping rates were sustained 

for this transient 5-year observation period. 

Figure 6. Grid discretization and boundary conditions for child model. (Cells in child model are 277.8 feet on a side.) 

10 20 30 40 50 60 70 80 90 100

COLUMN

ROW

20

30

40

50

60

70

80

90

100

110

118

10

27,778 feet

32,778 feet

Nagawicka 

Lake

Pine Lake

Bark 

River

Beaver Lake

North Lake

Cornell 

Lake

Okauchee

Lake

Oconomowoc

River

Mason Creek

Nagawicka 

Lake

Pine Lake

Bark 

River

Beaver Lake

North Lake

Cornell 

Lake

Okauchee

Lake

Oconomowoc

River

Mason Creek Constant-head conditions

Streams and lakes from RIV package in MODFLOW

Streams from SFR1 package in MODFLOW

Lakes from LAK3 package in MODFLOW

Approximate location of Maquoketa Shale subcrop

Grid lines for child model

EXPLANATION
Child Model Embedded in Parent Regional Model 9

River Package Input to the Child Model

Within the child model, the Bark River and outlying lakes 

(Nagawicka Lake and Okauchee Lake) were represented by 

means of the MODFLOW RIV package. Stage was specified 

on the basis of elevations recorded on topographic maps. In 

the case of the Bark River, the topographic elevations were 

used to determine the slope of the stream surface within the 

child grid. The hydraulic conductivity of the bed of the Bark 

River was assumed to be 1 ft/d, and the bed thickness was 

assumed to be 1 ft. The hydraulic conductivity and thickness of the lake beds was assumed to be 0.1 ft/d and 1 ft, 

respectively.

Streamflow Routing Package (SFR1) Input to the 

Child Model

The MODFLOW SFR1 package allows stream stage 

to be calculated as part of the model solution. The code also 

routes flow from upgradient to downgradient stream nodes 

along the network, allowing the model to keep track of the 

streamflow and the surface water available to be captured, 

for example, by pumping. The channel connections between 

the Chenequa-area lakes were represented by SFR nodes. 

In addition, the flow in tributaries to North Lake within the 

child model domain (including Mason Creek and stretches of 

the Oconomowoc River) was handled by the SFR1 package. 

In each case the hydraulic conductivity of the lakebed was 

assumed to be 1 ft/d and the bed thickness to be 1 ft.

The slopes of the streambeds input to the SFR1 package 

are based on topographic contours reported on U.S. Geological Survey maps (Stonebank and Merton topographic quadrangles, 1959, scale 1:24,000). The streambed elevations at the 

outlets of Beaver, Pine, Cornell, and North Lakes are estimated to be between 0.1 and 2 ft below the target lake stage 

and are implemented in the child model so that stream depth 

increases downstream. 

Lake Package Input to the Child Model

The geometries of the child-model layers and model cells 

representing Beaver, Pine, and North Lakes are based on information in historical bathymetric maps (fig. 7). The hydrologic 

characteristics of the lake model cells were assigned by using 

existing data and were refined through the calibration process. 

Of particular importance are the conductance values assigned 

to the lakebeds because they control the flow between the 

groundwater system and the water bodies. Beaver, Pine, and 

North Lakes were assigned higher conductance values under 

the shoreline (littoral zone) than under the interior of the lake 

(profundal zone). The littoral zone was defined to be one cell 

wide, equivalent to 278 ft. 

Also important are the stage-discharge relations assumed 

for each lake. Observed outflows from the lakes vary widely 

in response to season and stage. Measured streamflow out of 

Beaver Lake (table 1) varied from 107,136 ft3/d on June 7, 

2007, to zero on July 17, 2007, to 86,400 ft3/d on September 

27, 2007. Measured streamflow out of Pine Lake (table 1) varied from 254,018 ft3

/d, zero, and 5,357 ft3/d on the same successive dates. Given the scarcity of flow data, it was necessary 

to base an average outflow condition for these lakes on the 

average of the three available measurements. This discharge 

was assumed to correspond to the long-term average elevation of the lakes as shown on the USGS topographic maps 

for the Chenequa area (Stonebank and Merton quadrangles, 

1959, scale 1:24,000): 909 ft elevation for Beaver Lake, 900 ft 

elevation for Pine Lake, and 896 ft elevation for North Lake; 

Cornell Lake elevation was estimated as the average of the 

stages of Pine and North Lakes. These levels were selected 

because they are consistent with stream input also drawn from 

topographic maps. However, data collected for Beaver and 

Pine Lakes in 2006–8 indicated higher levels, averaging 1 ft 

higher in the case of Beaver Lake and between 2 and 3 ft in 

the case of Pine Lakes (Jeffrey Kante, Village of Chenequa, 

written commun., February 9, 2009). These recent data indicate a degree of uncertainty in lake levels, possibly connected 

to climate variability.

Input to the LAK3 package also includes precipitation and evaporation to the lake surfaces. These values were 

assumed to be 32 and 29 in/yr, respectively, on the basis of 

average long-term observations in northwestern Waukesha 

County (Linsley and others, 1982, p. 78 for precipitation rate 

and p. 154 for evaporation rate). The long-term average rate 

of overland flow to the lakes was assumed to be negligible 

because of the generally coarse soils in the area, so it was set 

to zero in the model input.

Recharge Input to the Child Model

Recent research by the Wisconsin Geological and Natural 

History Survey (Hart and others, 2008) involving a GISbased soil-water-balance model (Westenbroek and others, 

2010) produced a detailed recharge distribution over time for 

all of southeastern Wisconsin including the Chenequa area. 

This approach, however, is partially unconstrained in that it 

encompasses only the soil zone and therefore does not track 

or integrate infiltration out of the soil zone to surface-water 

features where flow measurements are made (Westenbroek and 

others, 2010). The groundwater-flow model constructed for 

the Chenequa-area study does integrate upgradient recharge 

at surface-water features, so it was used to constrain a multiplier applied to the spatial recharge distribution of Hart and 

others (2008). The Hart and others pattern for the child-model 

domain was scaled so as to agree with the average recharge 

rate input for the Chenequa area in the background regional 

model (8.5 in/yr). Around this average recharge rate of 8.5 in/

yr, recharge in the child model varies between a low of 3.9 in/

yr and a high of 19.5 in/yr. (fig. 8). The higher values reflect 

the presence of sandy soils over much of the area. No recharge 

was applied to the lakes in the child model.
10 Application of the Local Grid Refinement Package to an Inset Model, Northwestern Waukesha County, Wisconsin

Figure 7A. Bathymetry of Beaver Lake (from Wisconsin Conservation Department, 1941 and 1955).

A. A. Beaver Lake
Child Model Embedded in Parent Regional Model 11

Figure 7B. Bathymetry of Pine Lake (from Wisconsin Conservation Department, 1941 and 1955).

B. B. Pine Lake
12 Application of the Local Grid Refinement Package to an Inset Model, Northwestern Waukesha County, Wisconsin

Figure 7C. Bathymetry of North Lake (from Wisconsin Conservation Department, 1941 and 1955).

C. C. North Lake
Child Model Embedded in Parent Regional Model 13

Table 1. Summary of flow measurements in Chenequa area, Wisconsin.

[Site locations are shown in fig. 12; —, not measured]

Site 

number Site name

Measured streamflow, in cubic feet per day, by date

6/7/2007 7/17/2007 9/27/2007

1 Beaver Lake outlet at Hwy 83 107,136 0 86,400

2 Pine Lake outlet at Cty Hwy K 254,018 0 5,357

3 Bark River at Dorn Road near Merton 1,676,160 1,054,080 1,667,520

4 Bark River at Nagawicka Road at Delafield 2,246,400 1,296,000 2,073,600

5 Lake Keesus outlet at Whitcomb Road 155,520 19,872 117,504

6 Oconomowoc at Funk Road 2,220,480 1,071,360 1,728,000

7 Oconomowoc at North Lake — — 2,039,040

8 Oconomowoc at Westshore Drive — — 3,049,920

9 Oconomowoc at Cty Hwy K at Stonebank — 2,021,760 3,257,280

Figure 8. Recharge distribution in child model.

Groundwater recharge, 

in inches per year

 19.5

 11.7

 7.8

 3.9

 0.0

27,778 feet

32,778 feet

EXPLANATION
14 Application of the Local Grid Refinement Package to an Inset Model, Northwestern Waukesha County, Wisconsin

Hydraulic Conductivity and Storage Input to the 

Child Model

In 2005, investigations were performed by the City of 

Delafield to plan for a new public-supply well to supplement 

the existing set of high-capacity wells in the area (fig. 9). An 

aquifer test conducted in late 2005 near Pine Lake in the City 

of Delafield ( Earth Tech, Inc., 2006), at the location marked 

“Test well” in fig. 9, provided new information on the hydraulic conductivity of the unconsolidated sediments in the vicinity 

of the Chenequa-area lakes, thereby allowing the original 

values from the background regional model to be updated. 

The USGS did not perform the aquifer test; details of the test, 

including 1) a detailed description of the test methods and procedures, 2) a map of the test site, 3) well construction, 4) site 

hydrogeologic characteristics, 5) time-discharge records of the 

pumped well, 6) water-level records, and 7) methods and computations of adjustments to measured drawdowns are included 

in Earth Tech, Inc. (2006). A hard copy of Earth Tech, Inc. 

(2006) is included as part of the physical aquifer-test archive, 

on file in the Wisconsin Water Science Center. 

The purpose of the USGS analysis of the aquifer-test 

data was to evaluate aquifer properties to better characterize the child-model domain. As part of the USGS analysis, 

Earth Tech, Inc. (2006) aquifer-test data were incorporated in 

a special groundwater-flow model designed to reproduce the 

drawdown and recovery patterns observed during the aquifer 

test. The aquifer-test model treated the entire thickness of the 

glacial material near the test well as a single unconfined flow 

system. The model consisted of four layers (used exclusively 

to represent the glacial thickness) and a nonuniform lateral 

grid spacing centered on the pumping well. The row and 

column spacing increased by a factor of 1.2 outward from the 

pumping well, a resolution which allowed the three observation wells surrounding the pumping well to be precisely 

located horizontally as well as vertically. Boundary conditions 

were provisionally inserted to take account of surface-water 

features (Pine Lake and the Bark River); but, likely because 

of the distance to these features relative to the strength and 

duration of the aquifer-test stress, the model results were 

largely insensitive to presence or absence of boundary conditions. Earth Tech, Inc. reported that the pumping well was 

open approximately 200 ft below land surface, corresponding 

Figure 9. Location of pumping wells in child model.

gpm

Test well

Head target

43

43

131

161

196

234

88 

gpm

Constant head

River (RIV package)

Stream (SFR1 package)

Lake (LAK3 package)

Pumping well, with pumping stress in gallons per minute

EXPLANATION

Model cell

Nagawicka 

Lake

Pine Lake

Bark 

River

Beaver Lake

North Lake

Cornell 

Lake

Okauchee

Lake

Oconomowoc

River

27,778 feet

32,778 feet
Child Model Embedded in Parent Regional Model 15

to model layer 4, and was pumped at a rate of 539 gal/min 

for 3 days. These pumping conditions were duplicated by 

the model, and a 3-day recovery phase of the test also was 

simulated. During the test, water levels were recorded at one 

observation well (OW–1) 150 ft east of the pumping-test 

well and a second (OW–3) 300 ft north of the pumping-test 

well. Both observation wells were open to the unconsolidated 

aquifer at the same elevation as the pumping-test well. A third 

observation well 150 ft east of the pumping-test well was open 

at a shallower interval at the water table. This arrangement 

allowed the transient aquifer-test data to be used to calculate 

not only the horizontal but also the vertical hydraulic conductivity of the unconsolidated aquifer by fitting the shallow 

and deep water-level responses simulated by the model to the 

observed responses.

A close fit was achieved between the observed drawdown 

reported by Earth Tech, Inc.1 and the drawdown simulated by 

the aquifer-test model (fig. 10) when the horizontal hydraulic 

conductivity in the east/west direction was assigned a value 

of 55 ft/d, the horizontal hydraulic conductivity in the north/

south direction was assigned a value of 110 ft/d, and the 

vertical hydraulic conductivity was assigned a value of 1 ft/d. 

The horizontal anisotropy of 2:1 between the east-west and 

north-south directions possibly represents a directional fabric 

of the outwash deposited in the bedrock valley, which crosses 

the child-model domain from its northeast corner in a south 

to southwest direction. Although the simulation of the deeper 

wells was good (figs. 10B and 10C), the simulated response in 

the water-table observation well OW–2 (fig. 10A) duplicates 

the slope of the observed response but not the absolute trends. 

The likely reason for this discrepancy is that the groundwaterflow model releases storage immediately by the mechanism 

of pore drainage; however, in the actual test, this source of 

storage is slightly delayed at the beginning of the test, and the 

only actual storage release is due to the elastic response of the 

aquifer, producing a very steep initial drawdown curve. Nevertheless, the close fit to the slope of the drawdown suggests 

that the model is successfully simulating the combined effects 

of pore drainage, vertical resistance to flow, and horizontal 

transmissivity with respect to the shallow observation well. 

The specific yield implied by the slope of the drawdown curve 

for the shallow observation well shown in figure 10A is 0.06, 

1

 The Earth Tech, Inc. report (2006) contains an analysis of the pumping test 

based on analytical solutions for leaky aquifers applied to the two deep observation wells, OW–1 and OW–3. Assumed in the analysis is that the aquifer is 

overlain by a leaky confining unit. These analyses yield an average transmissivity equal to 13,847 ft2

/d and a storativity equal to 1×10-4. For comparison to 

the values derived from the numerical modeling described above, if the aquifer thickness is assumed to be between 150 ft and 200 ft (depending on the 

thickness of the supposed confining unit), the isotropic hydraulic conductivity 

implied by the analytical solution is between 69 and 92 ft/d. The reported storativity, corresponding to the response of a semiconfined aquifer, and implying 

a specific storage of approximately 5×10-7 per ft for a 200-ft-thick aquifer, is 

much lower than the specific yield derived from the numerical model analysis, 

which reflects the dewatering of pores at the water table and the assumption 

that the entire glacial system is unconfined rather than semiconfined.

a value needed for the transient simulations with the child 

model. 

The horizontal anisotropy and associated hydraulic conductivity of the unconsolidated layers in the child model were 

specified by using the aquifer-test results for most of the childmodel domain (fig. 11). However, in the southeastern corner of 

the domain east of the Bark River (an area that is not informed 

by the aquifer test on the west side of the river), lower 

hydraulic conductivities were assigned. The lower values are 

needed to properly simulate the divide between the Bark River 

watershed and the neighboring Pewaukee Lake watershed 

(located in the parent regional model) and to ensure that the 

Bark River is, on balance, a gaining stream where it crosses 

the child model. Evidence from well-drillers’ logs in the 

vicinity indicates that the glacial deposits, in fact, do become 

finer starting from the area of the Chenequa lakes, which is 

dominated by outwash deposits, and moving southeast toward 

Pewaukee Lake and the Fox River, an area characterized by 

mixed clayey till, loamy till, and coarse channel deposits 

(Douglas Cherkauer, University of Wisconsin-Milwaukee, oral 

commun., December 2009). The lower horizontal hydraulic 

conductivity in the southeast corner of the child-model grid 

is paired with a lower value for vertical hydraulic conductivity—0.03 ft/d—as opposed to a vertical conductivity equal to 

1 ft/d over the remainder of the domain.

The abrupt transition between the hydraulic conductivity 

assigned the two unconsolidated layers in the child model and 

the parent regional model produced instability in the coupled 

LGR solution. The instability disappeared when the regional 

values were extended three rows and columns (about 800 ft) 

into the child grid, as shown in figure 11.

The zonation of hydraulic conductivity values assigned 

the bedrock layers of the child model is identical to the values 

input to the background regional model except in the case of 

layer 11, representing the deep sandstone aquifer units, where 

the child-model values are averaged across the multiple deep 

sandstone layers in the background regional model. Accordingly, the Silurian dolomite is assigned a horizontal hydraulic 

conductivity of 4 ft/d and a vertical hydraulic conductivity of 

1×10-2 ft/d; the Maquoketa Formation is assigned a horizontal 

hydraulic conductivity that ranges from 0.3 to 0.0003 ft/d and 

a vertical hydraulic conductivity value that ranges from 1×10-3

to 5×10-6 ft/d; the Sinnipee Group is assigned a horizontal 

hydraulic conductivity that ranges from 0.3 to 0.04 ft/d and 

a vertical hydraulic conductivity that ranges from 1×10-2 to 

5×10-4 ft/d; and the deep sandstone aquifer system layer is 

assigned a horizontal hydraulic conductivity between 2.0 and 

4.0 ft/d and a vertical hydraulic conductivity everywhere in 

the neighborhood of 6×10-4 ft/d. As in the background regional 

model, the specific storage assigned to the bedrock layers in 

the child model is 2.6×10-7 1/ft.
16 Application of the Local Grid Refinement Package to an Inset Model, Northwestern Waukesha County, Wisconsin

Figure 10. Aquifer-test analysis of drawdowns 

at three observation wells. (Note: The vertical 

drawdown scale for the shallow observation 

well is different from the scale for the two deep 

observation wells because much less drawdown 

was registered in the shallow observation well.)

OBSERVED AND SIMULATED DRAWDOWN AT OW–2, SHALLOW (WATERTABLE) OBSERVATION WELL; 150 FEET EAST OF PUMPING WELL

0.60

0.50

0.40

0.30

0.20

0.10

0.00

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

DRAWDOWN, IN FEET

DAYS

OBSERVED AND SIMULATED DRAWDOWN AT OW–1, 200-FOOT-DEEP 

OBSERVATION WELL; 150 FEET EAST OF PUMPING WELL

4.00

3.50

3.00

2.50

2.00

1.50

1.00

0.50

0.00

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

DRAWDOWN, IN FEET

DAYS

OBSERVED AND SIMULATED DRAWDOWN AT OW–3, 200-FOOT-DEEP 

OBSERVATION WELL; 300 FEET NORTH OF PUMPING WELL

4.00

3.50

3.00

2.00

2.50

1.50

1.00

0.50

0.00

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6

DRAWDOWN, IN FEET

DAYS

EXPLANATION

Observed drawdown

Simulated drawdown
Child Model Embedded in Parent Regional Model 17

Figure 11. Distribution of horizontal hydraulic conductivity in child model, layers 1 and 2.

55 east-west and 110 north-south

10

5

EXPLANATION

Layer 1

Horizontal hydraulic conductivity,

in feet per day

55 east-west and 110 north-south

10 

5

1

0.2 

EXPLANATION

Layer 2

Horizontal hydraulic conductivity,

in feet per day
18 Application of the Local Grid Refinement Package to an Inset Model, Northwestern Waukesha County, Wisconsin

Water Withdrawals from Wells in the Child 

Model

Available records from the Wisconsin Department of 

Natural Resources and the Waukesha Public Service Commission provide estimates of average 2008 pumping from six 

high-capacity wells in the Chenequa area (fig. 9). The wells 

include one at the Chenequa Country Club on the shores of 

Beaver Lake, several Hartland public-supply wells located 

east and southeast of Beaver Lake, and a water-supply well 

for the city of Delafield. Each well withdraws water from the 

unconsolidated glacial aquifer; there are no records of active 

bedrock wells. The combined pumping from the six wells in 

the unconsolidated aquifer is 853 gal/min. A seventh well, 

called Delafield2, began to pump in 2007. It is not included in 

the base version of the child model.

Calibration of the Child Model

Calibration of the child model consisted of trial-and-error 

adjustment of parameters to improve the agreement between 

observed and simulated values representative of average conditions for a limited number of targets. Five types of targets 

were used to calibrate the model:

• Stages for Beaver, Pine, and North Lakes, corresponding to elevations recorded on 1:24,000-scale U.S. Geological Survey quadrangle maps (Stonebank, 1959; and 

Merton 1959, revised 1971); the stage of Cornell Lake, 

a very small surface-water feature, was estimated as 

the average of Pine and North.

• A single water-level measurement near Pine Lake, 

collected at the outset of the Delafield pumping test 

from a water-table observation well ( Earth Tech, Inc., 

2006). (See fig. 9 for location of head target.)

• An estimate of groundwater inflow to Beaver Lake, 

computed as the average of the calculated values for 

1983–84 (1.36×106 ft3/d) and for 1987 (3.5×106 ft3/d) 

reported by Carman (1988).

• Stream outflows from Beaver and Pine Lakes (see fig. 

12 for outlet locations), equated with the average of the 

three field measurements reported in table 1.

• Gain in streamflow for stretches of the Oconomowoc 

River and Bark Rivers (see fig. 12 for measurement 

locations), based on streamflow measurements collected at times when base flow (that is, groundwater 

inflow) was likely responsible for most, if not all, of 

the streamflow. The calibration target for the Bark 

River was the average gain in streamflow between sites 

3 and 4 in table 1 for the three measurement dates. The 

two calibration targets for the Oconomoc River were 

equal to the gain between sites 6 and 7 and between 

sites 8 and 9 for the September set of measurements 

only (owing to the availability of fewer than three 

measurements for some of the sites).

The calibration process was restricted to adjusting the 

location and configuration of hydraulic-conductivity zonation 

and values of the unconsolidated deposits (as described in the 

previous section) and the hydraulic conductivity of the beds of 

Beaver, Pine, Cornell, and North Lakes in an effort to improve 

fit. When a 1-ft lakebed thickness was assumed, the following 

lakebed hydraulic conductivities provided reasonably close 

agreement between the observed and simulated targets:

• Littoral value for Bark Lake, 2.5×10-2 ft/d.

• Littoral value for Pine and North Lake, 1.0×10-2 ft/d.

• Profundal value for Bark Lake, 2.5×10-3 ft/d.

• Profundal value for Pine and North Lake, 1.0×10-3 ft/d.

• Cornell Lake (very small), a single value of 1.0×10-3

ft/d.

The agreement across targets is shown in table 2. The 

simulated lake stages are fairly close to the observed values, 

as are the base-flow gains in the Oconomowoc River. The 

simulated outflows from Beaver and Pine Lake and the base 

flow for Beaver Lake show larger discrepancies, but the overall rates of flow are comparable to the observed values given 

the temporal variability in the natural flows. The Bark River 

was not a primary calibration target, owing to its distance from 

the lakes of interest, and it is not well simulated. This poor 

representation of base flow in the Bark River is likely due to 

artifacts related to the model boundary conditions that poorly 

approximate the actual contributing areas to the flow system 

that are outside the child-model domain. 

The calibrated child model corresponds to the base 

version of the child model. It incorporates the surface-water, 

recharge, aquifer hydraulic conductivity, lakebed hydraulic 

conductivity, and pumping inputs described in the previous 

report sections. Because the calibration of the child model 

was performed by trial and error, the calibration is likely not 

optimal in terms of reducing the target residuals (observed 

minus simulated values). In order to evaluate the quality of 

the calibration and its dependence on model inputs in greater 

detail, a sensitivity analysis was done in which the following 

sets of parameters of the child model were perturbed while all 

other inputs to the child and parent regional models were left 

unchanged:

1. The recharge rate applied to the water table.—The 

spatial distribution was left unchanged, but the rates were 

increased and decreased by 10 percent.

2. The horizontal and vertical hydraulic conductivities 

assigned model layers 1 and 2 corresponding to the 

unconsolidated material above bedrock.—The spatial zonation was left unchanged, but the values were 

increased and decreased by 30 percent.
Calibration of the Child Model 19

Figure 12. Locations of flow measurements.

Oconomowoc River

Pine Lake

Beaver Lake

Bark River

Lake Keesus 

North Lake

Nagawicka Lake

Cornell Lake

Okauchee Lake

EXPLANATION

5

8

9

2

1

3

4

6 7

43°10'

88°24' 88°22' 88°20'

43°8'

43°6'

0 0.5 1 MILE

0 0.5 1 KILOMETER

Lakes, ponds and wetlands

Streams

Location of flow measurement

1 Beaver Lake outlet at Hwy 83

2 Pine Lake outlet at Cty Hwy K

3 Bark River at Dorn Road near Merton

4 Bark River at Nagawicka Road at Delafield

5 Lake Keesus outlet at Whitcomb Road

6 Oconomowoc River at Funk Road

7 Oconomowoc River at North Lake

8 Oconomowoc River at Westshore Dr

9 Oconomowoc River at Cty Hwy K at Stonebank
20 Application of the Local Grid Refinement Package to an Inset Model, Northwestern Waukesha County, Wisconsin

3. The hydraulic conductivity assigned the lakebed sediments underneath Beaver, Pine, Cornell, and North 

Lakes.—The littoral and profundal zonation was left 

unchanged, but the values were multiplied by 5 and 

divided by 5.

4. The net precipitation assigned Beaver, Pine, Cornell, and 

North Lakes.—The evaporation rate was changed so that 

the difference between precipitation and evaporation on 

the lakes was raised from the base value of 3 in/yr to 

55 in/yr and reduced to 55 in/yr.

The results for the eight sensitivity runs are presented in 

table 3 in terms of the change in residuals for each calibration 

target relative to the residuals in the base child simulation. 

Two overall conclusions can be drawn. First, the base simulation yields lake levels that are somewhat too high, so reducing 

the recharge to the water table or reducing the net precipitation 

to the lakes has a favorable effect insofar as it results in lower 

lake levels. Second, none of the sensitivity changes produces 

consistent improvements across the remaining targets—the 

test-well water level, groundwater flows into Beaver Lake, 

surface-water outflows from Beaver and Pine Lakes, or baseflow rates to stretches of the Bark and Oconomowoc Rivers—

suggesting that the parameters in the base child simulation 

produce a reasonable overall fit with respect to these targets. 

The recharge and net precipitation rates in the base child 

model were maintained despite the overestimated lake levels 

because, as mentioned earlier, Village of Chenequa measurements from 2006 to 2008 indicated levels in Beaver and Pine 

Lakes 1 or 2 ft higher than the values reported on topographic 

maps. Indeed, such variation is often expected in Wisconsin 

lakes (House, 1985). Given this evidence, it was judged counterproductive to lower recharge and net precipitation values 

linked to previous studies in order to reproduce target lake 

levels that are lower than recently recorded levels.

Table 2. Comparison of measured to simulated values for calibration targets for base-case simulation.

[Base case omits test well and incorporates average weather conditions (32 inches per year (in/yr) precipitation to lakes, 29 in/yr evaporation from lakes, 

and 8.5 in/yr average recharge to water table within local model area); ft3/d, cubic feet per day]

Stream or lake characteristic Measured Simulated Difference

Lake stage, feet above NGVD 29:

Beaver Lake 909.00 909.62 −0.62

Pine Lake 900.00 900.27 −0.27

Cornell Lake 898.00 898.33 −0.33 

North Lake 896.00 896.18 −0.18

Lake outflow, ft3/d:

Beaver Lake 64,512 107,082 −42,570

Pine Lake 86,458 59,122 27,336

Streamflow gain, ft3/d:

Bark River 406,080 188,374 217,706

Oconomowoc River,

Funk Road to North Lake 311,040 284,754 26,286

Oconomowoc River,

Westshore to Stonebank 207,360 231,131 −23,771

Groundwater:

Groundwater level in test well, 

feet above NGVD 29 898.80 900.11 .31

Base flow to Beaver Lake, ft3/d 232,039 154,999 77,040
Calibration of the Child Model 21

Table 3. Sensitivity analysis. [Residuals for model targets are defined as the observed target value minus the simulated target value. Target residuals have been computed for the BASE (calibrated) simulation and a series of sensitivity simulations for which the values of one set of parameters is increased or decreased by a fixed amount or proportion. The RATIO of sensitivity residual to BASE residual by target is a measure of changes to model fit in terms of improvement (values less than 1) or deterioration (values greater than 1).Ratios between 0.95 and 1.05 are considered to indicate no change in model fit and are colored gray. Ratios less than 0.95 are considered to indicate improvement and are colored blue; ratios less than 0.67 indicate large improvement and are underlined. Ratios greater than 1.05 are considered to indicate deterioration and are colored red; ratios greater than 1.50 indicate large deterioration and are underlined. K is hydraulic conductivity, horizontal and vertical; Kv is vertical hydraulic conductivity; Net Precip. is the precipitation minus evaporation; in/yr, inches per year; ft3/d, cubic feet per day]

Ratio of sensitivity residual to base residual

Target Target value Base residual

Increased

recharge

by 10

percent

Decreased

recharge

by 10

percent

Increased

glacial K

by 30

percent

Decreased

glacial K

by 30

percent

Increased

lakebed K

v

multiplied

by 5

Decreased

lakebed K

v

divided

by 5

Increased 

net precip.

 to lakes 

from 3 in/yr 

to 4.55 in/yr

Decreased 

net precip. 

to lakes 

from 3 in/yr 

to 1.55 in/yr

Beaver Lake stage (ft) 909.00 −0.62 1.24 0.79 0.87 1.16 1.11 0.49 1.08 0.92Pine Lake stage (ft) 900.00 −0.27 2.33 0.22 0.22 3.81 0.37 1.64 1.56 0.52Cornell Lake stage (ft) 898.00 −0.33 2.61 0.79 1.61 3.27 0.36 1.68 1.73 0.27North Lake stage (ft) 896.00 −0.18 1.22 0.72 1.06 0.89 1.00 0.92 1.06 0.89Test-well water level (ft) 898.80 −1.31 1.26 0.76 0.77 1.44 1.01 0.98 1.02 0.97Beaver Lake base flow 

(ft3/d) 232,039 77,040 0.91 1.09 0.89 1.14 0.06 2.01 1.01 0.99

Beaver Lake outflow 

(ft3/d) 64,512 −42,570 1.27 0.74 0.86 1.20 1.13 0.23 1.09 0.91

Pine Lake outflow (ft3/d) 86,458 27,336 0.32 1.86 2.34 0.23 1.49 0.62 0.69 1.34Bark River gain (ft3/d) 406,080 217,706 0.87 1.12 0.92 1.09 1.05 0.95 0.99 1.01Oconomowoc gain (ft3/d):Funk Road to North Lake 311,040 26,286 0.68 1.32 0.91 3.16 1.54 0.35 0.99 1.01Westshore to Stonebank 207,360 −23,771 1.47 0.54 2.54 0.72 1.15 0.96 1.02 0.99
22 Application of the Local Grid Refinement Package to an Inset Model, Northwestern Waukesha County, Wisconsin

Model Results

The calibrated child model was used to simulate the 

hydrologic system in the Chenequa area under various weather 

and pumping conditions. The base-case condition is average 

weather (32 in/yr precipitation to lakes, 29 in/yr evaporation from lakes, and 8.5 in/yr average recharge to water table 

within child model area) and existing pumping from the 

shallow system within the child model—a total of 854 gal/min 

or 1.6×105 ft3/d (fig. 9). The calibrated child model was used 

to simulate the water-table configuration for the study area 

(fig. 13). The model simulates the surface-water and groundwater fluxes under these conditions for each of the lakes 

(table 4); the terms of the water balance are precipitation, 

evaporation, groundwater inflow and outflow, and surfacewater inflow and outflow. This water balance is also depicted 

graphically for Beaver, Pine, and North Lakes (fig. 14). The 

comparison of the summed inflow and outflow terms of this 

balance for any lake is an indication of how well the model 

has succeeded in balancing inflows and outflows; this comparison is expressed as an error (as a percent of inflow). The 

balance in water fluxes also determines the stage of each lake 

under average weather conditions (table 5). 

Dry weather conditions were simulated in child model 

by reducing the groundwater recharge and lake precipitation 

by one-third for a period of 5 years (lake evaporation was 

kept constant). This scenario was not intended to be a realistic simulation of a historical event (in which recharge and 

lake precipitation would not likely change in the exact same 

proportion and evaporation rates would probably not remain 

constant); rather, it was meant to be a heuristic treatment in 

the sense of showing possible effects of a severe, prolonged 

drought on the Chenequa-area lakes. For the same basecase pumping conditions (854 gal/min), the surface-water 

and groundwater fluxes under dry weather conditions were 

Figure 13. Child-model domain showing the simulated water-table elevation for the calibration run. (Steep contours along part of the 

child-model perimeter reflect the effect of the hydraulic-conductivity transition zone between the parent regional and child models used 

for numerical stability, as discussed in text.) 890

900

910

910

890

920

900

890

930

gpm

909.62

909.62

900.27

898.33

896.18

27,778 feet

32,778 feet

Constant head

River (RIV package)

Stream (SFR1 package)

Lake (LAK3 package)

 Simulated water-table contour with

 elevation, in feet above NGVD of 1929

 Pumping wells

 Simulated lake level

EXPLANATION

Model cell
Model Results 23

Table 4. Lake budgets for base-case simulations.

[Base model omits test well and incorporates average weather conditions (32 inches per year (in/yr) precipitation to lakes, 29 in/yr evaporation from 

lakes, and 8.5 in/yr average recharge to water table within local model area); ft3/d, cubic feet per day]

Lake Precipitation

(ft3/d)

Evaporation

(ft3/d)

Groundwater Surface Water

Inflow 

(ft3/d)

Outflow 

(ft3/d)

Inflow 

(ft3/d)

Outflow 

(ft3/d)

Beaver 1.06x105 -9.60x104 1.55x105 -5.52x104 0 -1.10x105

Pine 2.18x105 -1.97x105 6.34x104 -1.37x105 1.10x105 -5.78x104

Cornell 5.64x103 -5.11x103 3.65x103 -3.48x101 5.91x104 -6.33x104

North 1.42x105 -1.29x105 1.23x105 -1.53x104 2.01x106 -2.13x106

Lake

Inflow 

terms 

(ft3/d)

Outflow 

terms 

(ft3/d)

Difference

 (ft3/d

Error 

(percentage of 

inflow)

Beaver 1.06x105 -1.06x105 1.06x100 -

0.003%

Pine 1.06x105 -1.06x105 1.06x101 -0.018%

Cornell 5.64x104 -5.11x104 3.65x100 -0.006%

North 1.42x106 -1.29x106 1.23x102 -0.006%

simulated and compared to the average weather conditions 

(table 5). The comparison is expressed in terms of lake stage 

(Beaver, Pine, Cornell, and North Lakes) and lake outflow 

(Beaver and Pine Lakes).

Different pumping conditions were simulated in the child 

model by adding a test well in row 91, column 62, layer 2. 

Two different rates were applied to this test well—47 gal/min 

and 200 gal/min. The magnitude of these rates can be scaled 

relative to the combined groundwater inflow to nearby Beaver 

and Pine Lakes: they represent 4 and 18 percent, respectively, 

of the lake groundwater inflow. For the two pumping scenarios, amounting to 901 gal/min (854 + 47 gal/min) and 1,054 

gal/min (854 + 200 gal/min) total discharge, the surface-water 

and groundwater fluxes were simulated and compared to the 

base-case pumping conditions amounting to 854 gal/min total 

discharge (table 6). The comparison is expressed in lake stage 

(Beaver, Pine, Cornell, and North Lakes) and lake outflow 

(Beaver and Pine Lakes). In addition, a simulation was done 

that compared surface-water and groundwater fluxes at base 

pumping conditions (854 gal/min) under average weather 

conditions to a model pumping condition of 901 gal/min under 

dry weather conditions (table 7). This comparison is likewise 

expressed in terms of lake stage (Beaver, Pine, Cornell, and 

North Lakes) and lake outflow (Beaver and Pine Lakes).

Simulation of the source of water to wells lends insight 

into changes in the surface-water and groundwater fluxes 

resulting from different stresses due to pumping and weather. 

In table 8, a comparison is made between base-case conditions (average weather and 854 gal/min pumping) and total 

pumping of 901 and 1,054 gal/min under average weather 

conditions, as well as between base-case conditions and 

901 gal/min total pumping under dry weather conditions (table 

8). The comparison in each case considers increased induced 

flow to groundwater from surface water, reduced base flow to 

surface water, increased net storage release, and decreased lateral net outflow. The comparison of these different simulations 

is expressed as the percentage of the total additional water 

that is coming from those four categories. The categories 

“increased induced flow to groundwater” and “reduced base 

flow to surface water” are both subdivided into the percentage of the total for that category coming from the Bark River 

and far-field lakes on the one hand and internal lakes (Beaver, 

Pine, Cornell, and North Lakes) on the other.

The groundwater inflow to the four lakes simulated under 

the range of weather and pumping conditions (average and dry 

weather and total pumping of 854, 901, or 1,054 gal/min) is 

compiled in table 9, which provides a comparison of groundwater inflow for each lake under various conditions and 

between lakes for the same conditions.

One aspect of the model results that merits discussion is 

the role of storage release. Given that the simulation is transient, storage is a source and sink of groundwater. The smaller 

the contribution of storage relative to other sources and sinks 

of water, the closer the model is to a long-term steady-state 

condition and to stable water levels. By design, the base model 

simulation is very close to steady-state conditions throughout the 5-year observation period inserted subsequent to the 

20-year runup period. Storage release represents only 0.05 
24 Application of the Local Grid Refinement Package to an Inset Model, Northwestern Waukesha County, Wisconsin

Figure 14. Simulated water budgets of Beaver, Pine, and North 

Lakes under base-case conditions. (North Lake is shown twice, 

at two scales.)

-250,000

-200,000

-150,000

-100,000

-50,000

0

50,000

100,000

150,000

200,000

250,000

FLOW, IN CUBIC FEET PER DAY FLOW, IN CUBIC FEET PER DAY

Precip

GW in

SW in

Evap

GW out

SW out

-250,000

-200,000

-150,000

-100,000

-50,000

0

50,000

100,000

150,000

200,000

250,000

Precip

Precip

GW in

SW in

Evap

GW out

SW out

-250,000

-200,000

-150,000

-100,000

-50,000

0

50,000

100,000

150,000

200,000

250,000

-2,500,000

-2,000,000

-1,500,000

-1,000,000

-500,000

0

500,000

1,000,000

1,500,000

2,000,000

2,500,000

Precip

GW in

SW in

Evap

GW out

SW out

Precip

GW in

SW in

Evap

GW out

SW out

BEAVER LAKE

PINE LAKE

NORTH LAKE

NORTH LAKE

FLOW, IN CUBIC FEET PER DAY FLOW, IN CUBIC FEET PER DAY

percent of the total inflow to the child domain (dominated by 

recharge) after 6 months into the observation period and only 

0.006 percent after 5 years, whereas storage uptake represents 

only 0.008 percent of the total outflow of groundwater (dominated by base flow to surface water) after 6 months into the 

observation period and only 0.0008 percent of total outflow 

after 5 years.

More careful analysis would be needed to quantify the 

approach to steady state in response to a simulated stress such 

as pumping or drought conditions. Both these types of stresses 

tend to lower the water table and release water from storage 

by draining pores at the water table. Starting from the same 

starting conditions after the 20-year runup period as does the 

base model simulation, the two pumping scenarios show a 

decreasing contribution from storage over the 5-year observation period within the child domain. For the case where 

the simulated test well pumps 47 gal/min (9,126 ft3/d), the 

storage inflow is 47 percent of the pumping stress 6 months 

into the observation period but only 2.5 percent of the stress 

after 5 years. For the higher simulated pumping rate equal to 

200 gal/min (38,506 ft3/d), storage release is also appreciable 

after 6 months (34 percent of the pumping stress) but again 

quite small after 5 years (1 percent of the pumping stress). 

The drought case shows a similar approach to steady-state 

conditions over the observation period. The difference in the 

recharge rate over the child domain between the base and 

drought simulations is 560,545 ft3/d. Storage release contributes 38 percent of this amount after 6 months of simulation 

but only 2.4 percent after 5 years. In general, the simulated 

groundwater-flow system shifts almost all the response to the 

simulated pumping and drought stresses away from storage release (proportional to declines in the water table) and 

replaces it, under stable water-table conditions, with water 

drawn from diverted base flow to surface water and from flow 

induced into the subsurface from surface water.

Discussion

The Chenequa-area lakes (Beaver, Pine, Cornell, and 

North) are explicitly represented within the child-model 

domain. Within this area, properties inherited from the background regional model have been changed to incorporate additional information and enhanced model capabilities. First, the 

child grid spacing, set at 278 ft on a side, is much finer than 

that for the surrounding parent regional model, which inherited a spacing of 2,500 ft from the background regional model. 

The finer discretization permits a more accurate solution of 

water levels and flows in the vicinity of the lakes. Second, the 

LGR coupling allows stresses in the child model to propagate 

to the parent regional model (and vice versa), ensuring that the 

flows into and out of the child model are properly simulated. 

Third, the lakes and connecting waterways in the child model 

are represented by advanced modeling packages that allow 

for lake stages to be simulated instead of specified and for the 
Discussion 25

Table 6. Simulated change to stage of Beaver, Pine, Cornell, and North Lakes and change to outflow from Beaver and Pine Lakes with 

test well pumped for 5 years at 47 gallons per minute and at 200 gallons per minute under average weather conditions.

[gal/min, gallons per minute; ft, feet; %, percent]

Location

Total pumping in child model

 in average weather conditions 1

Difference

in lake stage

Total pumping in child model

 in average weather conditions 1

Difference

Base run, in lake stage

854 gal/min

Base run + 47 gal/min = 

901 gal/min

Base run,

854 gal/min

Base run + 200 gal/min =

1,054 gal/min

Lake stage, feet above NGVD 29:

Beaver Lake 909.62 909.60 - 0.02 ft 909.62 909.56 - 0.06 ft

Pine Lake 900.27 900.24 - 0.03 ft 900.27 900.15 - 0.12 ft

Cornell Lake 898.33 898.28 - 0.05 ft 898.33 898.12 - 0.21 ft

North Lake 896.18 896.18 - 0.00 ft 896.18 896.17 - 0.01 ft

Lake outflow, cubic feet per day:

Beaver Lake 107,081 105,935 - 1 % 107,081 102,251 - 5 %

Pine Lake 59,122 57,198 - 3 % 59,122 50,744 - 14 %

1

 Average weather conditions correspond to 32 inches per year (in/yr) precipitation to lakes, 29 in/yr evaporation from lakes, and 8.5 in/yr average recharge to 

water table within local model area.

Table 5. Simulated change to stage of Beaver, Pine, Cornell, and North Lakes and change to outflow from Beaver and Pine Lakes 

due to 5 years of dry weather conditions.

[gal/min, gallons per minute]

Location

Total pumping in child model Difference 

Average weather conditions in lake stage 1,

base run (854 gal/min)

Dry weather conditions 2,

base run (854 gal/min)

Lake stage, feet above NGVD 29:

Beaver Lake 909.62 908.97 - 0.65 ft

Pine Lake 900.27 896.62 - 3.65 ft

Cornell Lake 898.33 897.66 - 0.67 ft

North Lake 896.18 895.97 - 0.21 ft

Lake outflow, cubic feet per day:

Beaver Lake 107,081 21,367 - 80 %

Pine Lake 59,122 ≈ 0 - 100 %

1

 Average weather conditions correspond to 32 inches per year (in/yr) precipitation to lakes, 29 in/yr evaporation from lakes, and 8.5 in/yr average recharge 

to water table within local model area.

2

 Dry weather conditions last 5 years; recharge and lake precipitation reduced by one-third, lake evaporation kept constant.
26 Application of the Local Grid Refinement Package to an Inset Model, Northwestern Waukesha County, Wisconsin

Table 8. Simulated sources to test well pumped for 5 years at 47 gallons per minute (for average and dry weather conditions) and at 

200 gallons per minute (for average weather conditions). 

[gal/min, gallons per minute; —, no percentages shown because the base run is the basis of comparison; values in bold type indicate totals]

Total pumping in child model in 

average weather conditions 1

Total pumping in child model in 

dry weather conditions 2

Base run,

854 gal/min

Base run + 

47 gal/min 

= 901 gal/min

Base run + 

200 gal/min

= 1,054 gal/min

Base run, 854 

gal/min

Base run + 

47 gal/min

= 901 gal/min

Source of additional water Percentage of 

total

Percentage of 

total

Percentage of 

total

Increased induced flow to groundwater — 11.9 15.6 — 15.8

 Bark River and far-field lakes — 7.1 5.6 — 12.2

 Internal lakes — 4.8 10.0 — 3.6

Reduced base flow to surface water — 74.3 78.6 — 75.6

 Bark River and far-field lakes — 56.4 61.5 — 62.6

 Internal lakes — 17.9 17.1 — 13.0

Increased net storage release — 0.6 0.6 — 1.5

Decreased lateral net outflow — 13.2 5.2 — 7.1

TOTAL 100.0 100.0 — 100.0

1

 Average weather conditions correspond to 32 inches per year (in/yr) precipitation to lakes, 29 in/yr evaporation from lakes, and 8.5 in/yr average recharge to 

water table within local model area.

2

 Dry weather conditions last 5 years; recharge and lake precipitation reduced by one-third, lake evaporation kept constant.

Table 7. Simulated change to stage of Beaver, Pine, Cornell, and North Lakes and change to outflow from Beaver and Pine Lakes with 

test well pumped for 5 years at 47 gallons per minute under dry weather conditions.

[gal/min, gallons per minute; ft, feet]

Location

Total pumping in child model

Difference

in lake stage

Average weather conditions 1

Base run,

854 gal/min

Dry weather conditions 2

Base run + 47 gal/min =

901 gal/min

Lake stage, feet above NGVD 29:

Beaver Lake 909.62 908.96 −0.66 ft

Pine Lake 900.27 896.54 −3.73 ft

Cornell Lake 898.33 897.64 −0.69 ft

North Lake 896.18 895.97 −0.21 ft

Lake outflow, cubic feet per day:

Beaver Lake 107,081 19,657 82 %

Pine Lake 59,122 ≈ 0 100 %

1

 Average weather conditions correspond to 32 inches per year (in/yr) precipitation to lakes, 29 in/yr evaporation from lakes, and 8.5 in/yr average recharge to 

water table within local model area.

2

 Dry weather conditions last 5 years; recharge and lake precipitation reduced by one-third, lake evaporation kept constant.
Discussion 27

Table 9. Simulated groundwater inflow to lakes under various pumping and weather conditions.

[gal/min, gallons per minute]

Condition Beaver Lake Pine Lake Cornell Lake North Lake

Base-case simulation 1.55×105 6.34×105 3.65×103 1.23×105

Test well pumped 47 gal/min1 1.54×105 6.30×105 3.71×103 1.23×105

Test well pumped 200 gal/min1 1.53×105 6.13×105 3.92×103 1.23×105

Dry weather conditions2 1.28×105 8.82×104 1.59×103 9.16×104

Dry weather conditions with test 

well pumped 47 gal/min1,2 1.27×105 8.85×104 1.58×103 9.13×104

1

Test well pumps for 5 years.

2

 Dry weather conditions last 5 years; recharge and lake precipitation reduced by one-third, lake evaporation kept constant.

entire budget of each lake to be explicitly evaluated. Finally, 

the zonation of properties—notably, hydraulic conductivity and recharge—was updated in the child model by use of 

results from a recent aquifer test and new estimates of how 

recharge varies over space.

The simulated model results for base conditions show the 

relative importance of groundwater flow in the lake budgets 

(table 4 and fig. 14). Groundwater is the largest inflow component for Beaver Lake (equal to 59 percent of total inflow). For 

Pine and North Lakes, it is an important component (equal, 

respectively, to 16 and 5 percent of total inflow) but less than 

the contribution from precipitation and surface-water inflow. 

Effects of changes to base conditions on the lake budgets 

range from negligible to substantial. The addition of a test 

well south of Chenequa at the reported 2008 pumping rate of 

47 gal/min of the new Delafield well has little effect on lake 

stages or flows after 5 years of simulated pumping (table 6), 

by which time the low rate of storage release indicates that 

the groundwater-flow system in the child domain is very close 

to steady-state conditions. The stage and the surface-water 

outflow from Pine Lake are simulated to decrease by only 

0.03 ft and 3 percent, respectively, relative to base conditions. 

The chief explanations for these modest effects are the low 

pumping rate, the depth of the test well (which, like the new 

Delafield well, is assumed to pump from a horizon approximately 200 ft below land surface), and the high transmissivity of the unconsolidated aquifer, which allows the well to 

draw water from upstream along the bedrock valley and to 

capture inflow from the Bark River. However, if the pumping rate of the test well is assumed to increase to 200 gal/min, 

the decrease in Pine Lake outflow is appreciably larger: the 

simulated drop in outflow is 14 percent relative to base-flow 

conditions, although the drop in stage is only 0.12 ft. 

Severe drought (represented by 5 years of precipitation 

and recharge rates reduced by one-third relative to base values) would cause correspondingly severe reductions in lake 

stage and flows (table 5). For example, the model indicates 

that, under the simulated dry condition, the level of Pine Lake 

would decline by 3.7 ft and that surface-water outflow would 

cease because the lake level would be well below its outlet 

sill elevation. The simulated conditions are so severe that the 

small feature corresponding Cornell Lake, which is assumed 

to be underlain by relatively tight lakebed material, maintains 

a higher level than the upgradient Pine Lake (table 5). The 

addition of pumping at the 47-gal/min rate to dry weather 

conditions has little effect on the simulated outcome because 

the effect of the drought is so dominant (comparison of tables 

5 and 7). 

Pumping wells can affect lakes by reducing stage and 

flows; lakes can affect pumping wells (and the drawdown 

around them) by acting as a source of the water withdrawn. 

The lakes act as a source in two ways: lake water is transferred 

to the groundwater system (that is, increased induced flow) 

and groundwater that would otherwise discharge to lakes is 

diverted to the well (that is, reduced base flow). The model 

results (table 8) indicate that the lakes are a source of water 

for the test well: increased induced flow and reduced base 

flow from the Chenequa-area lakes together account for 23 

percent of the water flowing toward the well at a pumping 

rate of 47 gal/min. At a test rate of 200 gal/min, the Chenequa 

lakes account for 27 percent of the well supply. By way of 

comparison, the contribution of other water bodies—the Bark 

River and outlying lakes—is about 65 percent of the test-well 

discharge for both the 47- and 200-gal/min rates.
28 Application of the Local Grid Refinement Package to an Inset Model, Northwestern Waukesha County, Wisconsin

Model Limitations

The child and parent models are simplifications of reality. Both discretize properties of the subsurface into a limited 

number of zones that only approximate heterogeneous natural 

conditions. The degree of connection between the shallow 

aquifer and surface-water features, both rivers and lakes, is not 

well known. Although stresses such as recharge and pumping 

change not only across space but also through time, they are 

represented in the child and parent models by time-constant 

values. 

The application of advanced modeling techniques to the 

Chenequa study adds assumptions and limitations to the modeling process. The use of the LAK3 package to simulate stages 

and water budgets for Beaver, Pine, and North Lakes requires 

the specification of additional inputs, some of which are based 

on available data (for example, the bathymetry of the lake 

bottom) and some of which are only partly constrained by 

field observations (for example, the elevation of the outlets 

controlling surface-water flow draining the lakes and the 

assumption that overland flow to the lakes is a negligible part 

of their water budgets). More precise measurements of these 

elevations and flows could serve to update and improve the 

existing child model. Although changes were made to the 

unconsolidated hydraulic-conductivity fields within the childmodel domain on the basis of aquifer-test analysis, the parent 

regional model inherited all its parameter values from the 

background regional model, resulting in an abrupt shift in permeability at the child/parent boundary. The effect of this shift 

was mitigated by extending the regional hydraulic-conductivity values a short distance into the child-model grid (fig. 7). 

The calibration process for the coupled child and parent regional model was done by trial and error. Although the 

quality of the calibration is acceptable, a more sophisticated 

automated approach to calibration applying a parameter-estimation code might improve the agreement between measured 

and simulated targets by further minor adjustment of parameter values. The calibration targets used to characterize flow 

through the lakes are associated with considerable uncertainty 

because available measurements show much variability, 

making it difficult to estimate the long-term average. Future 

measurements of these flows could be used to test the performance of the model, and, if necessary, provide justification for 

reevaluating inputs such as lakebed conductance and recharge 

and outputs such as target lake levels.

Summary and Conclusions

In cooperation with the Village of Chenequa, Wis., the 

Southeastern Wisconsin Regional Planning Commission and 

the Wisconsin Department of Natural Resources, the USGS 

characterized the hydrology of part of northwestern Waukesha 

County, with a particular focus on the interaction between the 

shallow aquifer and area lakes. A previous regional groundwater-flow model developed in conjunction with the Southeastern 

Wisconsin Regional Planning Commission was the framework for this effort and the starting point for development 

of an inset model for the project area embedded in a “parent” regional model. The complexity of the input to the inset 

model, or “child” model, is greater than that of the regional 

model and is commensurate with the extent of the existing 

data in the local area. The groundwater/surface-water system 

was simulated by using the combined three-dimensional, transient child and parent regional models. Given the focus of the 

study on shallow groundwater conditions, the computational 

burden could be reduced by modifying the layering inherited 

from the background regional model, reducing the original 

eight layers used to represent the deep sandstone aquifer 

system to a single layer in both the regional parent model and 

the embedded child model. The child model has greater grid 

resolution than the regional parent model: cell area is refined 

from 2,500 ft by 2,500 ft to 278 ft by 278 ft, a factor of 81. 

The increased discretization permits a more accurate solution 

of water levels and flows in the vicinity of the Chenequa-area 

lakes. Beaver, Pine, and North Lakes were simulated within 

the MODFLOW groundwater-flow model by use of the LAK3 

package, which allows for explicit calculation of lake budgets; 

selected stream reaches connecting the lakes were simulated 

with the SFR1 package which allows explicit calculation of 

stream stages. The Local Grid Refinement (LGR) package 

allowed hydrologic stresses in the child model to propagate 

to the parent regional model and vice versa. The zonation of 

properties—notably, hydraulic conductivity and recharge—

were updated in the child model based on the basis of results 

from a recent aquifer test and the availability of new estimates 

of how recharge varies over space.

The simulated model results for base conditions show 

the relative importance of groundwater flow in the lake 

budgets: 59 percent of total inflow for Beaver Lake and 16 

and 5 percent of total inflow, respectively, for Pine and North 

Lakes. Severe drought conditions are represented by 5 years of 

precipitation and recharge rates reduced by one-third relative 

to base value. Simulation of drought conditions shows severe 

reductions in lake stage and flows. For example, the model 

indicates that under the simulated dry weather condition, the 

level of Pine Lake will decline by 3.7 ft and surface-water 

outflow will cease because the lake level is below its outlet 

sill elevation. The addition of a test well south of Chenequa at 

the reported 2008 pumping rate of 47.4 gal/min (9,126 ft3/d, 

equivalent to 4 percent of the combined groundwater inflow 

to nearby Beaver and Pine Lakes in the absence of test-well 

discharge) has little effect on lake stages and fluxes, probably 
References Cited 29

because of the modest pumping rate simulated in conjunction 

with the pumping depth of the test well (approximately 

200 ft below land surface) and the large transmissivity 

assigned the unconsolidated aquifer, which allows the well 

to draw water from upstream along the bedrock valley and to 

capture inflow from the Bark River. The model results indicate 

that although lake levels and fluxes are only modestly affected 

by simulated pumping, the lakes are important sources of 

water from the vantage point of the test well: increased 

induced flow and reduced base flow from the Chenequa-area 

lakes together account for 23 percent of the water flowing 

toward the well at a pumping rate of 47 gal/min. At a simulated test rate of 200 gal/min, they account for 27 percent of 

the well supply. By way of comparison, the contribution of 

other water bodies—the Bark River and outlying lakes—is 

about 65 percent of the test-well discharge for both the 47- and 

200-gal/min rates.

The use of Local Grid Refinement in this study, allowing the boundary conditions of the child model to adjust to 

changing regional conditions, ensures that the flows into and 

out of the child model are properly simulated. This modeling 

approach is an important tool that allows simulated forecasting scenarios to account not only for changes to hydrologic 

stresses in the Chenequa area but also for changes in conditions in surrounding areas outside the child domain. In addition, the effect within the child model of regional trends, such 

as drawdown in the deep sandstone aquifer, can be simulated. 

This approach results in computational efficiency while representing both local and regional hydrogeologic characteristics 

and stresses.

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Director, Wisconsin Water Science Center

U.S. Geological Survey

8505 Research Way

Middleton, Wisconsin 53562

http://wi.water.usgs.gov/
Feinstein and others—Application of the Local Grid Refinement Package to an Inset Model, Northwestern Waukesha County, Wisconsin—Scientific Investigations Report 2010–5214