U.S. Department of the Interior

U.S. Geological Survey

Prepared in cooperation with Pierce, Polk, and St. Croix Counties

Simulation of the Groundwater-Flow System in Pierce,

Polk, and St. Croix Counties, Wisconsin

Scientific Investigations Report 2009–5056

Simulation of the Groundwater-Flow 

System in Pierce, Polk, and St. Croix 

Counties, Wisconsin

By Paul F. Juckem

Prepared in cooperation with Pierce, Polk, and St. Croix Counties

Scientific Investigations Report 2009–5056

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2009

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U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested citation:

Juckem, P.F., 2009, Simulation of the groundwater-flow system in Pierce, Polk, and St. Croix Counties, Wisconsin: 

U.S. Geological Survey Scientific Investigations Report 2009–5056, 53 p.

Cover illustration. See figure 7, page 16.

978 1 4113 2429 9
iii

Contents

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

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

Purpose and Scope ..............................................................................................................................5

Physical Setting.....................................................................................................................................5

Study Methods ...............................................................................................................................................7

Conceptual Model of the Groundwater-Flow System ...........................................................................10

Aquifers and Confining Units ............................................................................................................10

Sources and Sinks of Water .............................................................................................................11

Hydrogeologic Boundaries ...............................................................................................................11

Hydraulic Properties of the Groundwater-Flow System .......................................................................11

Hydraulic Conductivity.......................................................................................................................11

Recharge..............................................................................................................................................11

Streambed Leakance .........................................................................................................................14

Groundwater Withdrawals.........................................................................................................................15

Three-Dimensional Simulation of the Regional Groundwater-Flow System .....................................15

Model Construction and Assumptions............................................................................................15

Model Grids..........................................................................................................................................17

Model Calibration................................................................................................................................19

Sensitivity Analysis.............................................................................................................................29

Mass Balances....................................................................................................................................29

Application of the Regional Model ...........................................................................................................30

Groundwater-Flow Directions and Interaction with Surface Water..........................................30

Predevelopment Conditions Compared to Present (1994–2004) Conditions. ............................33

Demonstration Simulations of Local-Scale Groundwater Flow..................................................34

Telescopic Mesh Refinement ..................................................................................................34

Construction and Simulation of the St. Croix County Demonstration Inset Model.........35

Results of Simulating Groundwater/Lake-Water Interaction near Twin Lakes 

near Roberts, St. Croix County ..........................................................................37

Construction and Simulation of the Pierce County Demonstration Inset Model ............38

Results of Simulating Sources of Groundwater to Streams 

in Western Pierce County ..................................................................................39

Construction and Simulation of the Polk County Demonstration Inset Model ................40

Results of Simulating Transient Streamflow in Osceola Creek, Polk County..........40

Model Limitations.........................................................................................................................................42

Suggestions for Future Investigations .....................................................................................................42

Summary and Conclusions.........................................................................................................................44

Acknowledgments.......................................................................................................................................45

References....................................................................................................................................................45

Appendix 1. Groundwater withdrawals from municipal wells in the regional 

groundwater-flow model ..................................................................................................49

Appendix 2. Groundwater withdrawals from agricultural, industrial, and 

commercial wells in the regional groundwater-flow model.......................................51
iv

Figures

1–3. Maps showing:

1. Location of the study area centered on Pierce, Polk, and St. Croix Counties, 

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

2A. Location of municipal wells in and near Pierce, Polk, and St. Croix Counties, 

Wisconsin .............................................................................................................................3

2B. Location of private high-capacity wells in and near Pierce, Polk, and St. Croix 

Counties, Wisconsin............................................................................................................4

3. Generalized bedrock geology of Pierce, Polk, and St. Croix Counties, Wisconsin ..6

4. Geologic and hydrostratigraphic units in Pierce, Polk, and St. Croix Counties, 

Wisconsin ......................................................................................................................................7

5A. Conceptual model of groundwater flow through the central and southern 

study area (St. Croix and Pierce Counties), Wisconsin..........................................................8

5B. Conceptual model of groundwater flow through the northern study area 

(Polk County), Wisconsin.............................................................................................................8

6. Map showing extent of the analytic element model (GFLOW) and MODFLOW 

model grid ......................................................................................................................................9

7. Block diagrams showing the regional MODFLOW model layers 

and hydraulic-conductivity zones and values .......................................................................16

8–9. Maps showing:

8. Interpolated crystalline bedrock elevation used to form the base of the regional 

model (layer 4), inactive cells in layer 4, and the location of faults ..........................18

9. Perimeter and internal boundary conditions, water-level-observation wells, 

and base-flow targets in the regional model of Pierce, Polk, and St. Croix 

Counties, Wisconsin..........................................................................................................22

10. Graph showing measured water levels plotted against simulated water levels 

for the regional model................................................................................................................23

11–14. Maps showing:

11A. Simulated water-table elevation and water-level residuals for observation 

wells in the regional groundwater-flow model, layer 1...............................................24

11B. Simulated water-table elevation and water-level residuals for well-construction 

report wells in the regional groundwater-flow model, layer 1...................................25

12. Simulated potentiometric-surface elevation and water-level residuals for 

observation wells in the regional groundwater-flow model, layer 2 ........................26

13. Simulated potentiometric-surface elevation and water-level residuals for 

observation wells in the regional groundwater-flow model, layer 4 ........................27

14. Simulated water-table elevation and residuals for stream base-flow 

measurements in the regional groundwater-flow model, layer 1 .............................28

15. Graph showing composite sensitivities computed by PEST for parameters of the 

regional MODFLOW model of Pierce, Polk, and St. Croix Counties, Wisconsin..............29

16–22. Maps showing:

16. Simulated water-table elevation, particle flow paths from the water table, 

and groundwater/surface-water interaction in the regional groundwater-flow 

model, layer1 ......................................................................................................................31

17. Simulated vertical flow directions between model layers in Pierce, Polk, and 

St. Croix Counties, Wisconsin..........................................................................................32
v

18. Simulated water-table decline (layer 1) from predevelopment to present 

(1994–2004) water-use conditions in Pierce, Polk, and St. Croix Counties, 

Wisconsin ...........................................................................................................................33

19. Simulated potentiometric-surface decline in the Mount Simon aquifer (layer 4) 

from predevelopment to present (1994–2004) water-use conditions in Pierce, 

Polk, and St. Croix Counties, Wisconsin........................................................................34

20. Simulated water-table elevation and water-level residuals for the St. Croix 

County, Wisconsin, demonstration inset model, layer 2 .............................................37

21. Simulated groundwater/lake-water interaction near Twin Lakes near 

the village of Roberts, Wisconsin, from the St. Croix County demonstration 

model,layer 1 ......................................................................................................................38

22. Simulated areas contributing groundwater recharge to rivers in western 

Pierce County, Wisconsin ................................................................................................39

23. Graph showing simulated base flow in Osceola Creek, Polk County, Wisconsin, 

for predevelopment and present (1994–2004) pumping conditions....................................40

24. Map showing simulated groundwater-flow patterns near Osceola Creek, 

Polk County, Wisconsin .............................................................................................................41

Tables

1A. Previously reported horizontal hydraulic conductivity (Kh) and vertical hydraulic 

conductivity (Kv) values, and calibrated values from the regional model.........................12

1B. Reference or source of horizontal and vertical hydraulic conductivity values 

reported in table 1A....................................................................................................................13

2. Recharge rates from groundwater-flow models or other methods near the 

regional model area ...................................................................................................................14

3A. Mean error, mean absolute difference, and root mean squared difference 

between simulated and measured groundwater levels.......................................................19

3B. Calibration results for stream base-flow targets and associated weights used 

for calibration with the parameter estimation program PEST ............................................20

4. Mass-balance components for Pierce, Polk, and St. Croix Counties, Wisconsin, 

collectively and individually, and the entire model area......................................................30

5. Parameter values used for the demonstration inset models ..............................................36

6. Simulated mass-balance components for Twin Lakes, St. Croix County, Wisconsin .....37
vi

Conversion Factors and Datum

Multiply By To obtain

Length

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

acre 0.4047 hectare (ha)

Flow and precipitation rate

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

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

foot per year (ft/yr) 0.3048 meter per year (m/yr)

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

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

million gallons per year (Mgal/yr) 3,785 cubic meter per year (m3

/yr)

million gallons per day (Mgal/d) 0.04381 cubic meter per second (m3

/s)

acre-foot per year (acre-ft/yr) 0.001233 cubic hectometer per year (hm3

/yr)

Hydraulic conductivity*

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

Leakance

foot per day per foot ([ft/d]/ft) 1 meter per day per meter ([m/d]/m)

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

Elevation, as used in this report, refers to distance above the vertical datum.

*Hydraulic conductivity: The standard unit for hydraulic conductivity is cubic foot per day per 

square foot of aquifer cross-sectional area (ft3/d/ft2). In this report, the mathematically reduced 

form, foot per day (ft/d), is used for convenience.
Abstract

Groundwater is the sole source of residential water 

supply in Pierce, Polk, and St. Croix Counties, Wisconsin. 

A regional three-dimensional groundwater-flow model and 

three associated demonstration inset models were developed 

to simulate the groundwater-flow systems in the three-county 

area. The models were developed by the U.S. Geological 

Survey in cooperation with the three county governments. The 

objectives of the regional model of Pierce, Polk, and St. Croix 

Counties were to improve understanding of the groundwaterflow system and to develop a tool suitable for evaluating the 

effects of potential water-management programs. 

The regional groundwater-flow model described in 

this report simulates the major hydrogeologic features of 

the modeled area, including bedrock and surficial aquifers, 

groundwater/surface-water interactions, and groundwater 

withdrawals from high-capacity wells. Results from the 

regional model indicate that about 82 percent of groundwater 

in the three counties is from recharge within the counties; 

15 percent is from surface-water sources, consisting primarily 

of recirculated groundwater seepage in areas with abrupt 

surface-water-level changes, such as near waterfalls, dams, 

and the downgradient side of reservoirs and lakes; and 4 percent is from inflow across the county boundaries. Groundwater 

flow out of the counties is to streams (85 percent), outflow 

across county boundaries (14 percent), and pumping wells 

(1 percent). These results demonstrate that the primary source 

of groundwater withdrawn by pumping wells is water that 

recharges within the counties and would otherwise discharge 

to local streams and lakes.

Under current conditions, the St. Croix and Mississippi 

Rivers are groundwater discharge locations (gaining reaches) 

and appear to function as “fully penetrating” hydraulic 

boundaries such that groundwater does not cross between 

Wisconsin and Minnesota beneath them. Being hydraulic 

boundaries, however, they can change in response to water 

withdrawals. Tributary rivers act as “partially penetrating” 

hydraulic boundaries such that groundwater can flow underneath them through the deep sandstone aquifers. The model 

also demonstrates the effects of development on groundwater 

in the study area. Water-level declines since predevelopment 

(no withdrawal wells) are most pronounced where pumping 

is greatest and flow between layered aquifers is impeded by 

confining units or faults. The maximum simulated water-level 

decline is about 40 feet in the deep Mount Simon aquifer 

below the city of Hudson, Wisconsin.

Three inset models were extracted from the regional 

model to demonstrate the process and additional capabilities 

of the U.S. Geological Survey MODFLOW code. Although 

the inset models were designed to provide information about 

the groundwater-flow system, results from the inset models 

are presented for demonstration purposes only and are not 

sufficiently detailed or calibrated to be used for decisionmaking purposes without refinement. Simulation of groundwater/lake-water interaction around Twin Lakes near Roberts, 

in St. Croix County, Wisconsin, showed that groundwater 

represents approximately 5 to 20 percent of the overall 

lake-water budget. Groundwater-contributing areas to streams 

in western Pierce County are generally similar in size to the 

surface-water-contributing areas but do not necessarily correspond to the same land area. Transient streamflow simulations 

of Osceola Creek in Polk County demonstrate how stream 

base flow can be influenced not only by seasonal precipitation 

and recharge variability but also by systematic changes to the 

system, such as groundwater withdrawal from wells.

Introduction

Groundwater is the sole source of residential water 

supply in Pierce, Polk, and St. Croix Counties, WI (fig. 1), 

and it also sustains area lakes, streams, and wetlands. There 

are currently 29 municipal water-supply systems with 

65 active wells operating in Pierce, Polk, and St. Croix 

Counties (fig. 2), which withdrew an average of approximately 

8.2 million gallons per day (Mgal/d) from 1994 to 2004 

(Appendix 1). Of the 65 active wells, 9 withdraw water from 

Quaternary sand and gravel aquifers, whereas the remaining 

56 municipal wells withdraw water from bedrock aquifers. 

These aquifers are susceptible to contamination (Juckem, 

2007) as indicated by local areas with high concentrations of 

nitrates in groundwater samples (Masarik and others, 2006). 

In addition, the counties are experiencing population growth 

because of their proximity to the Twin Cities metropolitan area 

in Minnesota. This growth is contributing to the conversion 

Simulation of the Groundwater-Flow System in Pierce, 

Polk, and St. Croix Counties, Wisconsin

By Paul F. Juckem
2 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

Figure 1. Location of the study area centered on Pierce, Polk, and St. Croix Counties, Wisconsin.

0 10 20 MILES

0 10 20 KILOMETERS

EXPLANATION

Cities in Pierce, Polk, 

and St. Croix Counties

County boundary

Streams and lakes

Regional model area

Hudson

River

Falls

Prescott

Ellsworth

New Richmond

Baldwin

Clear

 Lake

St. Croix

Falls

Osceola

Somerset

Amrey

Inset model boundary

Luck

St. Croix River

Mississippi River

Apple River

Willow River

Kinnickinnic

 River

Rush River

Clam River

Chippewa River

ST. CROIX

PIERCE

POLK

BARRON

DUNN

WASHINGTON

PEPIN

BUFFALO

WABASHA

GOODHUE

DAKOTA

CHISAGO

BURNETT

45°

45°45'

44°30'

93° 92°

WISCONSIN

MINNESOTA

MINN ESO TA WISCONSIN

Regional 

model area

(shown at right)

Pierce Co.

Polk Co.

St. Croix Co.

Base map compiled and modified from digital

data sources: U.S. Geological Survey, 1:100,000
Introduction 3

Figure 2A. Location of municipal wells in and near Pierce, Polk, and St. Croix Counties, Wisconsin.

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0 10 20 MILES

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45°

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44°30'

93° 92°

Base map compiled and modified from digital

data sources: U.S. Geological Survey, 1:100,000
4 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

Figure 2B. Location of private high-capacity wells in and near Pierce, Polk, and St. Croix Counties, Wisconsin.

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County:

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1812

12

45

12

12 123

14

14 25

15

12

14

8

187

EXPLANATION

Streams and lakes

County boundary

0 10 20 MILES

0 10 20 KILOMETERS

45°

45°45'

44°30'

93° 92°

12 Private high-capacity well

and average pumping rate 

(million gallons per year) 

from 1978 to 1989

Base map compiled and modified from digital

data sources: U.S. Geological Survey, 1:100,000
Introduction 5

Purpose and Scope

This report presents the results of a regional hydrologic 

investigation in Pierce, Polk, and St. Croix Counties., WI. The 

purpose of the study was to (1) improve understanding of the 

groundwater-flow system and its relation to surface waters, 

(2) develop a groundwater-flow model for use on an ongoing 

basis by water-resource managers, and (3) demonstrate use 

of the regional model as a framework for extracting local 

inset models to simulate groundwater flow and groundwater/

surface-water interactions at local scales. The third objective 

was accomplished by constructing one inset model in each 

of the three counties to demonstrate additional capabilities of 

groundwater-flow models.

The scope of this study is regional, and was a cooperative 

effort that included Pierce, Polk, and St. Croix Counties and 

the USGS. This report describes (1) the conceptualization of 

the groundwater-flow system, (2) the methods used in simulating groundwater flow, (3) the calibrated model parameters and 

sensitivity, (4) interpretation of simulated results, (5) demonstration of inset modeling in each county, and (6) limitations 

of the models. 

The regional model includes the entire area of Pierce, 

Polk, and St. Croix Counties, parts of 6 adjacent counties in 

west-central Wisconsin, and parts of 11 counties in Minnesota 

(fig. 1). The three demonstration-inset models include an area 

near the village of Osceola in Polk County, a large area in 

St. Croix County extending from Hudson to Woodville, and 

the area west of the town of Trimbelle in Pierce County.

Physical Setting

Pierce, Polk, and St. Croix Counties are in the St. Croix 

and Chippewa River watersheds of west-central Wisconsin 

(fig. 1). The area receives about 32 inches (in.) of precipitation 

annually, with temperatures that typically range from lows 

around zero degrees Fahrenheit (°F) in the winter to highs 

around 85 °F in the summer (Natural Resources Conservation 

Service, 2002). Land cover in the three counties is dominated 

by agriculture and grasslands, but substantial forested and 

urban acreage also is included (Wisconsin Department of 

Natural Resources, 1998).

Most of Polk County is in the Central Plain physiographic 

region of Wisconsin (described by Martin, 1965), which has 

generally low topographic relief and thick glacial deposits. 

St. Croix and Pierce Counties are part of the Western Upland 

(Martin, 1965), which is characterized by broad uplands that 

are interrupted by distinct valleys where erosion has removed 

the relatively thin glacial deposits and much of the thick 

sequence of underlying sedimentary rock. Most streams in 

the Central Plain region of Polk County derive base flow (the 

portion of total streamflow that is derived from groundwater 

discharge) from the glacial aquifer that overlies relatively 

thin sedimentary bedrock. The glacial deposits are composed 

primarily of tills and sands of variable thickness (Johnson, 

of some cropland to low- and high-density residential and 

commercial development. Although groundwater is widely 

recognized as an important drinking-water source, it also 

sustains surface-water features such as streams and wetlands. 

Urban and county planners are faced with decisions in which 

the need for increased groundwater withdrawals needs to 

be balanced with maintaining the quantity and quality of 

groundwater-supported surface-water resources, such as 

trout streams. Managing and protecting the ground- and 

surface-water (or “hydrologic”) resources requires a basic 

understanding of hydrologic systems. Information about the 

groundwater system—such as the extent of aquifer units, their 

water-bearing properties, and their recharge and discharge 

areas—is helpful in assessing the susceptibility of water 

supplies to overuse and changes in recharge or contamination. 

The regional groundwater study described in this report 

was conducted by the U.S. Geological Survey (USGS) in 

cooperation with Pierce, Polk, and St. Croix Counties, WI. 

Data from topographic and geologic maps, well-construction 

reports (WCRs; Wisconsin Department of Natural Resources, 

2003), water-level measurements, and surface-water features 

were synthesized to produce a conceptual model of aquifer 

units and the regional groundwater-flow system. Although 

the data and maps produced in a regional study provide basic 

hydrogeologic information for water-resource management, 

this information also is the basis for constructing groundwaterflow models. These models are mathematical representations 

of the natural system that can be used to simulate how water 

flows through the system and how the system will react to 

stress (such as increased pumping from wells or decreased 

recharge below impervious areas). 

Previous work in and around the three-county area 

included regional two-dimensional groundwater-flow models 

(Feinstein and others, 2005; Muldoon and others, 2007) and 

characterization of local groundwater flow at several contamination sites, including one for which a groundwater-flow 

model was constructed (Delta Environmental Consultants, 

written commun., 1997). The modeling described in this 

report differs from the previous work in the following ways. 

It is larger in extent, incorporating all of Pierce, Polk, and 

St. Croix Counties and parts of 17 surrounding counties in 

Wisconsin and Minnesota. It also includes extensive geologic 

and hydrologic data that facilitate the conceptualization and 

parameterization of the regional groundwater-flow system 

through use of multiple layers to simulate three-dimensional 

flow. Moreover, the regional model was designed to function 

as a framework for evaluating groundwater flow at multiple 

scales by extracting inset models, as demonstrated in this 

report. The resulting regional model can be used to identify 

major areas of groundwater recharge and discharge, and 

estimate the amount of groundwater discharge to surfacewater bodies. The model also can be used in a “what if” 

capacity to simulate effects of groundwater withdrawals, 

both existing and potential, and the effects of proposed 

water-management programs. 
6 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

Johnson (2000), Runkel and others (2003), Kostka and others 

(2004), LePain and others (2005), LePain (2006), Runkel and 

others (2006), Tipping and others (2006), Cobb (2007), and 

Evans and others (2007). A summary of the regional geology 

from these sources follows. For consistency, the stratigraphic 

nomenclature and ages of the units used in this report are 

those of the Wisconsin Geological and Natural History Survey, 

following the nomenclature of Ostrom (1967) and Mickelson 

and others (1984).

Rocks of Cambrian age (490 to 523 million years) 

include, from oldest to youngest (and deepest to shallowest), 

the Mount Simon Formation, Eau Claire Formation, Wonewoc 

Formation, Tunnel City Group, and Trempealeau Group 

(St. Lawrence and Jordan Formations) (fig. 4). The Mount 

Simon Formation is a medium- to coarse-grained sandstone 

with some shale and is about 

250 feet (ft) thick in the threecounty study area. The overlying 

Eau Claire Formation is composed 

of laterally extensive layers of very 

fine- to fine-grained sandstone and 

silty shale with a total thickness 

of about 100 ft. The Wonewoc 

Formation is a clean, well-sorted, 

medium- to coarse-grained 

quartzose sandstone, approximately 

75 ft thick. Above the Wonewoc, 

the approximately 150-ft-thick 

Tunnel City Group is composed 

of interbedded layers of shale and 

poorly sorted, glauconitic, very 

fine- to coarse-grained sandstone. 

The uppermost Cambrian unit is 

the Trempealeau Group (about 

100 ft thick), which consists of very 

fine-grained dolomitic siltstone and 

silty glauconitic dolomite in the 

St. Lawrence Formation and clean, 

fine- to coarse-grained quartzose 

sandstone in the Jordan Formation. 

Rocks of Ordovician age 

(443 to 490 million years) overlie 

the Cambrian rocks and consist of 

the Prairie du Chien Group, the 

Ancell Group, and the Sinnipee 

Group, in order from oldest to 

youngest (fig. 4). The Prairie du 

Chien Group consists of fine- to 

medium- grained sandstone and 

sandy dolomite and is about 200 ft 

thick where it is not eroded below 

glacial deposits. The Prairie du 

Chien Group is susceptible to 

fracturing and weathering, which 

can produce solution cavities and 

conduits associated with karst 

aquifers. The Ancell Group is a 

Figure 3. Generalized bedrock geology of Pierce, Polk, and St. Croix Counties, 

Wisconsin (modified from Cannon and others, 1997).

0 10 20 MILES

0 10 20 KILOMETERS

Geologic units

EXPLANATION

Sinnipee Group

Ancell Group

Prairie du Chien Group

Cambrian units (undivided)

Precambrian units (crystalline)

Faults

County boundary

Cottage Grove

Fault

Hastings Fault

Base map compiled and modified from digital

data sources: U.S. Geological Survey, 1:100,000

2000). In central Polk County, the glacial deposits lie directly 

on a ridge of low-permeability crystalline bedrock (locally 

referred to as Trap Rock). Glacial deposits are similar in St. 

Croix and Pierce Counties (Baker, 1984; Kostka and others, 

2004), yet most of the base flow in streams of the Western 

Upland region in St. Croix and Pierce Counties is derived 

primarily from permeable bedrock consisting of alternating 

layers of dolomite (limestone), sandstone, and shale.

Impermeable, Precambrian crystalline bedrock (primarily 

granite and basalt) underlies all sedimentary rocks in the 

three counties (figs. 3 and 4). Alternating layers of sandstone, 

shale, and dolomite of Cambrian and Ordovician age overlie 

the crystalline rock. Detailed maps and descriptions of the 

geology of the region have been assembled by Mudrey and 

others (1987), Brown (1988), Mossler (1992), Young (1992), 
Study Methods 7

fine- to medium-grained, well-sorted sandstone (about 75 ft 

thick where present) that is overlain by the thin-bedded 

dolomites of the Sinnipee Group (as much as about 20 ft thick 

where present). The Ancell and Sinnipee Groups have been 

extensively eroded in the three counties and occur only in 

upland ridges and mounds in Pierce and St. Croix Counties.

In some locations, the characteristics 

of the sedimentary rocks have been altered. 

Sedimentary rocks are vertically offset by 

hundreds of feet along two regional faults 

(fig. 3) and by tens of feet along smaller 

mapped and unmapped faults throughout 

the study area. The regional Hastings and 

Cottage Grove Faults extend through all 

of the sedimentary rock and place rocks of 

different formations adjacent to one another 

(Mudrey and others, 1987; LePain, 2006). 

The internal structure of faults in the study 

area is not well understood, nor is the effect 

of the faults on groundwater-flow patterns. 

Research outside of the study area suggests 

that faults generally are composed of a thin 

internal fine-grained core and a surrounding 

damage zone in which the native rocks are 

fractured (Caine and others, 1996; Rawling 

and others, 2001). 

Fractures in the Ordovician dolomite 

rocks throughout the study area can increase 

the potential for dissolution of these carbonate rocks and have led to the formation of 

cavities, caves, and sinkholes in the study 

area. These features form a “triple porosity 

system” (Cobb, 2007) more generally 

referred to as a “karst aquifer” through 

which large quantities of groundwater can 

flow rapidly over hundreds to thousands 

of feet (Runkel and others, 2003; Tipping 

and others, 2006; Cobb, 2007). The largest 

conduits generally occur in the uppermost 

sections of the Prairie du Chien Group, and 

flow through these conduits generally is 

controlled by the size and degree of connection among individual conduits or conduit 

zones (Runkel and others, 2003; Tipping and 

others, 2006; Cobb, 2007). 

Study Methods

Before construction of the threedimensional ground-water-flow models, a 

conceptual model of the regional system 

(figs. 5A, B) was developed on the basis 

of previously collected data. Using the 

methodology described by Hunt, Anderson, 

and Kelson (1998) and Hunt, Kelson, and Anderson (1998), 

a two-dimensional analytic-element groundwater-flow model 

(GFLOW code, Haitjema, 1995) developed by Feinstein and 

others (2005) for the St. Croix River Basin was modified 

and used as a simplified screening model to quickly test the 

conceptual model and derive hydrologic boundaries for the 

Figure 4. Geologic and hydrostratigraphic units in Pierce, Polk, and St. Croix 

Counties, Wisconsin. The regional model consolidates all bedrock units above the 

Wonewoc aquifer into one hydrostratigraphic unit (upper bedrock aquifer).

GEOLOGIC

UNITS

(Young, 1992)

Average thickness ≈ 75 feet

(where present)

Average thickness < 20 feet

(where present)

Average thickness ≈ 200 feet

(where present)

Average thickness ≈ 100 feet

Average thickness ≈ 150 feet

Glacial deposits and

unlithified valley fill

Sinnipee Group

Prairie du Chien Group

Trempealeau Group

Tunnel City Group

Average thickness ≈ 75 feet

Average thickness ≈ 100 feet

Average thickness ≈ 250 feet

Wonewoc Formation

Eau Claire Formation

Mount Simon

 Formation

Precambrian basalt and granite

Ancell Group

USGS REGIONAL

MODEL UNITS

(this report)

(layer 1)

(layer 2)

Sand and gravel aquifer

Wonewoc aquifer

(layer 3)

(layer 4)

Eau Claire confining unit

Mount Simon aquifer

Impermeable base

Upper bedrock aquifer

QUAT ER -

NARY O R D O V I C I A N C A M B R I A N
8 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

Figure 5A. Conceptual model of 

groundwater flow through the central 

and southern study area (St. Croix 

and Pierce Counties), Wisconsin 

(modified from Kammerer and others, 

1998). Note: Some groundwater flow 

is perpendicular to the cross section 

(north and south).

Figure 5B. Conceptual model of 

groundwater flow through the northern 

study area (Polk County), Wisconsin 

(modified from Kammerer and others, 

1998). Note: Some groundwater flow 

is perpendicular to the cross section 

(north and south).

FEET

1,800

1,600

1,400

1,200

1,000

800

600

400

200

-200

DATUM

(NAVD 88)

VERTICAL SCALE GREATLY EXAGGERATED

Upper bedrock aquifer

Wonewoc aquifer

Sand and gravel aquifer

Mount Simon aquifer

Eau Claire confining unit

Cottage Grove Fault

Hastings Fault

Crystalline basement

St. Croix River

Red Cedar River

Recharge

Recharge

WEST EAST

2,000

FEET

1,800

1,600

1,400

1,200

1,000

800

600

400

200

DATUM

(NAVD 88) VERTICAL SCALE GREATLY EXAGGERATED

Upper bedrock aquifer

Crystalline basement

Sand and gravel aquifer

Mount Simon aquifer

Eau Claire confining unit

Wonewoc aquifer

Cottage Grove FaultHastings andLake Owen Fault

St. Croix River

Apple River

Recharge Recharge

WEST EAST
Study Methods 9

three-dimensional regional model (fig. 6). A complete description of analytic-element modeling is beyond the scope of this 

report; a brief overview is given below. Strack (1989) and 

Haitjema (1995) provide detailed discussions of the analyticelement method. 

Figure 6. Extent of the analytic element model (GFLOW) and MODFLOW model grid. Uniform grid spacing is 348 columns, 

604 rows (not shown).

EXPLANATION

GFLOW linesinks

GFLOW model extent

County boundary

Regional MODFLOW

model grid extent

93°30'

91°45'

44°

46°30'

0 30 60 MILES

0 30 60 KILOMETERS

WISCONSIN

MINNESOTA

Study area

Base map compiled and modified from digital

data sources: U.S. Geological Survey, 1:100,000

Analytic-element modeling assumes an aquifer of infinite 

extent. The problem domain does not require a grid or involve 

interpolation between cells. To construct an analytic-element 

model, features important to groundwater flow (for example, 

wells) and surface-water bodies are entered as mathematical 
10 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

elements or strings of elements. The amount of detail specified 

for each feature depends on its distance from the area of 

interest. Each element corresponds to an analytic solution, 

and these solutions are superposed or added together in the 

model to arrive at a solution for the groundwater-flow system. 

Because the solution is not confined to a grid, as it is in the 

finite-difference method, groundwater levels and flows can 

be computed anywhere in the model domain without nodal 

averaging. In GFLOW modeling, the analytic elements are 

two-dimensional and are used only to simulate steady-state 

conditions (that is, groundwater levels do not vary with time). 

Comparisons of analytic element to finite-difference numerical 

modeling techniques are given in Hunt and Krohelski (1996); 

Hunt, Anderson, and Kelson (1998); and Hunt, Kelson, and 

Anderson (1998).

MODFLOW–2000 (Harbaugh and others, 2000), a USGS 

block-centered, finite-difference code, was used to simulate 

the three-dimensional flow system in the regional and inset 

models. MODFLOW requires input arrays (gridded data) that 

describe hydraulic parameters such as hydraulic conductivity 

and recharge, top and bottom elevation of aquifers, and 

boundary conditions. Detailed discussions of finite-difference 

methods, MODFLOW input requirements, and theory are 

provided by McDonald and Harbaugh (1988), Anderson 

and Woessner (1992), and Harbaugh and others (2000). 

Three steps were used to create the input arrays required by 

MODFLOW. First, geographic information system (GIS) 

coverages of aquifer top and bottom elevations were developed from data in well logs and published reports (Mossler, 

1983; Mandle and Kontis, 1992; Young, 1992; Wisconsin 

Geological and Natural History Survey, 2003). Second, these 

GIS coverages were intersected with the model grid and 

imported into Groundwater Vistas (Rumbaugh and Rumbaugh, 

2007), a groundwater modeling preprocessor. Third, boundary 

conditions at the model perimeter were extracted directly 

from the analytic-element model. The details of the technique 

are described in more detail by Hunt, Kelson, and Anderson 

(1998).

Calibration of the regional MODFLOW model was aided 

by use of parameter-estimation techniques included in the 

code PEST (Doherty, 2004). The primary benefit of parameter 

estimation is the ability to automatically calculate parameter 

values (for example, hydraulic conductivity and recharge) that 

are a quantified best fit between simulated model output and 

observed data (for example, groundwater levels and streamflows). Other benefits also include quantification of the quality 

of the calibration, parameter correlation (for example, hydraulic conductivity and recharge), and parameter sensitivity. 

Conceptual Model of the GroundwaterFlow System

Before simulating a groundwater system, a conceptualization of the system is essential as a basis for model 

development. The conceptualization is a necessary simplification of the natural system because inclusion of all of the 

complexities of the natural system into a computer model is 

not feasible given the existing knowledge of the subsurface 

and current computer capabilities. Steps in the development 

of the conceptual model include (1) definition of aquifers 

and confining units, (2) identification of sources and sinks 

of water, and (3) identification and delineation of hydrologic 

boundaries encompassing the area of interest. The first two of 

these steps were accomplished by review and interpretation of 

existing and new geologic and hydrogeologic data. The third 

step was accomplished by use of a screening model.

Aquifers and Confining Units

Four regionally extensive aquifers and two regionally 

extensive confining units are present in the three-county 

area, based on the hydrogeologic units (fig. 4) identified for 

west-central Wisconsin (Young, 1992) and south-eastern 

Minnesota (Delin and Woodward, 1984). The conceptual 

model of the groundwater-flow system is shown in figure 5. 

The vertical scale of the conceptual-model diagrams has been 

greatly exaggerated to illustrate the geologic units; regional 

flow through the aquifers is primarily horizontal. 

A sand and gravel aquifer is made up of unconsolidated 

glacial and alluvial materials overlying the bedrock. Except in 

narrow alluvial valleys and the broader St. Croix and Mississippi River Valleys, the sand and gravel aquifer in the model 

is limited to the northern part of the area and is simulated in 

the regional model only where the upper bedrock aquifer is 

absent. The unconsolidated deposits that form this aquifer 

generally are 50 to 200 ft thick in Polk County and less than 

50 ft thick in much of St. Croix and Pierce Counties where the 

deposits commonly are above the regional water table (Trotta 

and Cotter, 1973; Borman, 1976). The upper bedrock aquifer 

underlies the sand and gravel aquifer. The upper bedrock is 

made up of sandstone and dolomite and includes the Sinnipee 

and Ancell Groups, where present, and the Prairie du Chien, 

Trempealeau, and Tunnel City Groups. Several subregional 

confining units are identified within the upper bedrock aquifer, 

including the base of the Tunnel City Group. This confining 

unit is largely absent in the St. Croix and Mississippi River 

Valleys and tributary valleys to the Chippewa River, but it 

forms the first of two confining units where it is present in 

the regional model. The Wonewoc Formation underlies the 

shaly base of the upper aquifer (the base of the Tunnel City 

confining unit) and forms the thin Wonewoc aquifer. Several 

shaly facies within the Eau Claire Formation underlie the 

Wonewoc aquifer and form the Eau Claire confining unit. The 

Mount Simon Formation forms the lower bedrock aquifer that 

overlies Precambrian crystalline basement rock. The Precambrian crystalline basement rock is assumed to be impermeable 

and forms the lower boundary of the groundwater-flow 

system. Most municipal and private water-supply systems use 

the upper bedrock aquifer or the sand and gravel aquifer where 

it is sufficiently thick.
Hydraulic Properties of the Groundwater-Flow System 11

Sources and Sinks of Water

Water enters the groundwater-flow system as recharge 

to the water table. Recharge occurs over the entire regional 

model area, except where groundwater discharges to streams. 

Groundwater-flow paths may be local or regional. As shown 

in figure 5, the upper bedrock aquifer includes both local and 

regional flow paths, whereas flow through the underlying 

Wonewoc and Mount Simon aquifers tends to occur primarily 

along long, regional flow paths. Some recharging water moves 

downward to the sand and gravel or upper bedrock aquifer, 

travels a short horizontal distance, and discharges to a stream 

or wetland. Recharge may also move downward through the 

confining units into the Wonewoc and Mount Simon bedrock 

aquifers. In areas where the confining units are absent, 

recharge may move through the sand and gravel aquifer 

directly to the Wonewoc or Mount Simon bedrock aquifers. 

Because of the conductive nature of the Mount Simon bedrock 

aquifer and the nearly impermeable Precambrian rock forming 

the lower boundary of the system, flow paths in the Mount 

Simon bedrock aquifer are primarily horizontal on the regional 

scale. Pumping wells, a locally important sink of groundwater, 

can be open to the sand and gravel aquifer (for example, in 

municipalities underlain by glacial deposits, such as the cities 

of Frederic and Balsam Lake) or to the bedrock aquifers (for 

example, in municipalities on the bedrock uplands, such as the 

cities of New Richmond, Hudson, and Ellsworth). Pumping 

associated with the wells captures part of the groundwater that 

under predevelopment conditions would have discharged to 

streams and wetlands. In areas of large groundwater withdrawals, especially in surficial aquifers, streams that otherwise 

would capture groundwater may instead locally recharge the 

groundwater system. 

Hydrogeologic Boundaries

The analytic-element screening model developed 

by Feinstein and others (2006), using the code GFLOW 

(Haitjema, 1995), was extended by about 50 mi to the east, 

south, and west of the mouth of the St. Croix River at Prescott, 

WI, so that the simulated area extended well beyond the 

three-county area of interest (fig. 6). The screening model 

is a simplified representation of the natural system because 

(1) the flow system is assumed to be two‐dimensional, for 

which vertical components of flow and the three‐dimensional 

nature of the geologic deposits are ignored, (2) surface-water/

groundwater interactions are simulated by means of coarse 

representations, and (3) the system is at steady state (that 

is, water levels are not changing over time). Although the 

advantage of such simplification is that the model can be 

constructed with minimal time and data, the screening model 

may not generally be suitable for extensive use in land-use 

planning or other applications because of the limitations 

associated with these simplifications. The screening model is 

able to serve, however, as a foundation upon which to build 

the more complex, three-dimensional regional MODFLOW 

model. Flux-specified boundary conditions were extracted 

from the GFLOW model (Haitjema 1995; Hunt, Kelson, 

and Anderson 1998) as input for the well (WEL) package in 

MODFLOW. The extracted extents (fig. 6) were designed such 

that the MODFLOW model boundaries were distant from the 

area of interest (Pierce, Polk, and St. Croix Counties). The 

extracted extents include parts of Minnesota to allow direct 

simulation of potential underflow beneath the St. Croix River, 

as implied by Schoenberg (1984, 1990) and Wuolo (Ray 

Wuolo, Barr Engineering, written commun., 2005). 

Hydraulic Properties of the 

Groundwater-Flow System

Initial estimates of hydraulic conductivity, recharge, and 

streambed leakance for the three-dimensional MODFLOW 

groundwater-flow model were based on existing geologic and 

hydrologic data. The following is a brief 

description of these estimates. 

Hydraulic Conductivity

Horizontal and vertical hydraulic conductivities of the 

geologic units in the area have been estimated by others 

(table 1) through the use of specific-capacity tests, standard 

and discrete-interval aquifer tests, and hydrogeologic modeling. Horizontal hydraulic conductivities of the sand and gravel 

aquifer are reported to range from 7 to 670 feet per day (ft/d). 

Measured horizontal hydraulic conductivities in the bedrock 

aquifers typically are lower than those in the sand and gravel 

aquifer, with reported values ranging from 0.06 to 100 ft/d. 

Vertical hydraulic conductivities in the sand and gravel aquifer 

and the bedrock aquifer generally are 1 to 7 orders of magnitude lower than the corresponding estimates of horizontal 

hydraulic conductivity (table 1). Although these ranges are 

useful for characterizing the system, the model requires 

specific values for the hydraulic-conductivity variation in the 

system. Thus, values associated with zones of locally uniform 

hydraulic conductivity were treated as calibration parameters. 

Final values used in the modeling described here were determined by use of PEST (Doherty, 2004) and then compared to 

the range of available measurements and estimates.

Recharge

Rates of recharge are variable because of differing soil 

percolation rates, slope, and relative topographic position, 

among other factors. This spatial variability is difficult 

to estimate and was of limited significance for regional 

groundwater-flow simulations in a similar setting in southwest 

Wisconsin (Hunt and others, 2003); thus, an average recharge 
12 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

Table 1A. Previously reported horizontal hydraulic conductivity (Kh) and vertical hydraulic conductivity (Kv) values, and calibrated 

values from the regional model.—Continued

[ft/d, foot per day; <, less than. Reference and source codes listed in table 1B]

Hydrogeologic unit

Hydraulic conductivity Reference or 

source code

Calibrated 

value 

(ft/d) Type Reference value 

(ft/d)

Horizontal hydraulic conductivity

Sand and gravel aquifer

Simulated value 12.5 A

90

Measured range 7–670 B

Simulated values 40–420 D

Simulated values 40–120 E

Geometric mean of measurements 73.3 L

Measured range 13–272 L

Upper 

bedrock 

aquifer

Ancell–

Prairie du Chien–

Jordan aquifer

Simulated values 4.3–81 A

23

Simulated value 10 E

Measured range 3.3–67 G

Range in average of measurements 15.9–33.5 J

Measured range 0.1–100 K

Measured range 5–26 N

St. Lawrence–

Tunnel City 

confining unit

Simulated values 0.35–4.3 A

Simulated value 2.5 E

Measured range 0.1–2 H

Measured range <0.06–7.7 I

Range in average of measurements 5.9–27.8 J

Measured range 1.3–20 N

Wonewoc aquifer

Simulated value 12.2 A

11

Simulated value 12 E

Measured range 4–83 G

Measured range 1–4 H

Measured range 1.7–8.2 I

Average of measurements 10.8 J

Measured value 11 K

Measured range 7.4–19 N

Eau Claire confining unit

Simulated value 2.0 D

2a Simulated value 2.5 E

Measured value 0.1 H

Mount Simon aquifer

Simulated value 12 D

7

Simulated value 12 E

Measured range 2–23 G

Average of measurements 39.5 J

Measured value 17 K

Measured range 6.3–21 N

Faults Simulated range 0.0056–0.28 C 0.09
Hydraulic Properties of the Groundwater-Flow System 13

Table 1A. Previously reported horizontal hydraulic conductivity (Kh) and vertical hydraulic conductivity (Kv) values, and calibrated 

values from the regional model.—Continued

[ft/d, foot per day; <, less than. Reference and source codes listed in table 1B]

Hydrogeologic unit

Hydraulic conductivity Reference or 

source code

Calibrated 

value 

(ft/d) Type Reference value 

(ft/d)

Vertical hydraulic conductivity

Sand and gravel aquifer

Simulated value 0.15 A

0.9b Simulated values 0.4–4.2 D

Simulated values 4–12 E

Upper 

bedrock 

aquifer

Ancell–Prairie du 

Chien–Jordan aquifer

Simulated values 0.003–6.2 A

0.005a

Simulated value 1 E

St. Lawrence–

Tunnel City 

confining unit

Simulated values 0.3–3.6 A

Simulated values 0.0003–0.003 E

Measured values 0.0005–0.00008 F

Measured range 0.001–0.2 H

Measured range <0.0006–0.77 I

Wonewoc aquifer

Simulated value 3.3 A

0.11b Simulated value 1.2 E

Measured range 0.1–0.4 H

Measured range 0.17–0.82 I

Eau Claire confining unit

Simulated values 0.6–0.006 D

0.00009

Simulated value 0.0003 E

Measured value 0.001 H

Measured value 0.0000002 M

Mount Simon aquifer Simulated value 1.2 D0.07b

Simulated value 1.2 E

Faults Simulated range 0.0056–0.28 C 0.09 

a

 Indicates the value was specified, not calibrated.

b

 Indicates the ratio Kh:Kv was specified as 100:1.

Table 1B. Reference or source of horizontal and vertical hydraulic conductivity values reported in table 1A.

[MN, Minnesota; WI, Wisconsin]

Reference or 

source code Reference

A Barr Engineering Company and Washington County (2005) – simulated values in Washington County, MN.

B Borman (1976) – specific capacity tests from 120 wells in St. Croix County, WI.

C Hart and others (2006) – simulated range derived from Rawling and others (2001) to test sensitivity of a regional model to previously 

unsimulated faulting. 

D Hunt and others (2003) – simulated values in La Crosse County, WI.

E Juckem and others (2006); Juckem (2003) – simulated values in Monroe, La Crosse, and Vernon Counties, WI.

F Kanivetsky and Hoyer (1987) – measurements of vertical hydraulic conductivity.

G Kanivetsky and Walton (1979) – specific-capacity tests in southeastern Minnesota.

H Miller (1984) – lumped estimates of horizontal hydraulic conductivities based on discrete-interval packer tests in St. Paul, MN, and 

lumped estimates of vertical hydraulic conductivities based on laboratory determination from drill cores in St. Paul, MN.

I Miller and Delin (1993) – measurements of horizontal hydraulic conductivity from discrete-interval packer tests and vertical hydraulic 

conductivity from laboratory determination from drill cores in St. Paul, MN.

J Runkel and others (2003) – specific-capacity tests in southeastern Minnesota.

K Runkel and others (2003) – standard aquifer tests in southeastern Minnesota.

L Specific-capacity tests from 19 municipal wells in the sand and gravel aquifer in the northern part of the model domain, including Polk, 

Barron, Burnett, and Washburn Counties, WI.

M Witherspoon and Neuman (1967) – measurement based on gradients across the Eau Claire confining unit after a 137-day aquifer test in 

northern Illinois.

N Young (1992) – standard aquifer tests by the U.S. Geological Survey in southeastern Minnesota and western Wisconsin.
14 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

rate was applied uniformly across the regional model domain. 

The average groundwater-recharge rate was expected to fall 

within the range of values reported for previously calibrated 

groundwater-flow models and recharge-estimation studies 

in the area (table 2). The recharge rate was treated as a 

calibration parameter, with the value determined by use of 

the parameter estimation code PEST to match observed water 

levels and streamflows. 

Streambed Leakance

Estimates of streambed leakance were needed to simulate the interaction between surface water and groundwater. 

Streambed leakance is equal to the vertical hydraulic conductivity of a streambed or lakebed divided by its thickness, and 

in this study was estimated as ranging from 0.035 foot per 

day per foot ([ft/d]/ft) for lakes, the Mississippi River, and 

the St. Croix River downstream from Stillwater, MN, to 

2 (ft/d)/ft for all other rivers and streams. This range is 

between values of 0.02 to 0.1 (ft/d)/ft simulated for lakes 

near Hayward, WI, by Juckem and Hunt (2007) and values 

of 1.6 to 37 (ft/d)/ft measured in streams in Dane County, 

WI, by Krohelski and others (2000). Because of the relative 

insensitivity of the regional flow system to riverbed leakance 

(see “Sensitivity Analysis” section), this parameter was not 

adjusted during calibration. 

Table 2. Recharge rates from groundwater-flow models or other methods near the regional model area. The calibrated recharge 

rate used in the regional model of Pierce, Polk, and St. Croix Counties, Wisconsin, was 8.2 inches per year.

[in/yr, inch per year; MN, Minnesota; WI, Wisconsin; >, greater than; %, percent; <, less than]

Reference Method description Study area Recharge value

(in/yr)

Feinstein and others (2006) Three recharge zones trending roughly north to 

south in a one-layer analytic-element model

St. Croix River basin, MN and WI 5.8–8.9

Juckem (2007) One or more recharge zones for five watersheds 

simulated with refined versions of the model 

by Feinstein and others (2006)

Apple watershed, WI 6.6–9.5

Kettle watershed, MN 3.9

Kinnickinnic watershed, WI 8.1

Snake watershed, MN 3.0

Sunrise watershed, MN 5.0

Juckem and Hunt (2007) One recharge zone for a one-layer analyticelement modelGrindstone Creek and New Post 

Community, 

Lac Courte Oreilles reservation, 

northwest WI

10.1

Barr Engineering Company 

and Washington County 

(2005)

Cell-by-cell estimated recharge from an uncalibrated watershed-modeling component of the 

program MIKE SHE

Washington County, MN Range: 0–>20

Average: 8.7

Lorenz and Delin (2007) Regional regression recharge model for the state 

of Minnesota

Part of Minnesota included in the 

regional model domain

4–10

Gebert and others (2007) Average annual base flow divided by drainage 

area for streamgages in the specified basin

St. Croix River basin, WI Range: 6.7–0.8

Average: 8.8

Lower Chippewa River basin, WI Range: 2.3–9.1

Average: 6.3

Ruhl and others (2002) Five methods were included in this study:

Percent (27%) of precipitation Twin Cities area, MN 7.7–8.3

Median of streamflow-recession 

displacements

Twin Cities area, MN 1.2–12.2

Median groundwater-level fluctuations Twin Cities area, MN 4.5–13.6

Age dating at a nested-well site Twin Cities area, MN 8.8

Minimum from analysis of watershed 

characteristics

Twin Cities area, MN <0.1–5.6

Schoenberg (1990) Estimated groundwater discharge to Mississippi 

and St. Croix Rivers, 1935–87

Twin Cities area, MN Minimum: 1.6

Median: 4.3
Three-Dimensional Simulation of the Regional Groundwater-Flow System 15

Groundwater Withdrawals

Pumping rates represented in the model for individual 

municipal wells in the three counties were computed as the 

average annual rate from 1994 to 2004 (Appendix 1). Nonmunicipal use (irrigation, industrial, and commercial) in the 

three counties was estimated as the average from 1978 to 

1989, the only period for which data were available 

(Appendix 2). Pumping from individual private wells in the 

counties is not included in the model because the discharge 

from these wells is widely distributed, relatively small 

(especially where balanced by return flow from septic 

systems), and negligibly significant on the overall regional 

water balance.

The estimated total high-capacity-well withdrawal 

for Pierce, Polk, and St. Croix Counties is 4,533 million 

gallons per year (Mgal/yr). Municipal water supplies in the 

three counties withdrew an average of about 2,975 Mgal/yr 

of groundwater from 1994 to 2004, or roughly 66 percent 

of the total groundwater withdrawn from all high-capacity 

wells. The largest municipal withdrawals in the individual 

counties were by the communities of River Falls in 

Pierce County (417 Mgal/yr); Clear Lake in Polk County 

(300 Mgal/yr), of which about 90 percent is used by local 

industries; and Hudson in St. Croix County (580 Mgal/yr). 

Generally, municipal withdrawals increased in Pierce, Polk, 

and St. Croix Counties at approximately 1, 1, and 5 percent 

per year, respectively, from 1994 to 2004. Groundwater 

withdrawal rates for irrigation, industrial, and commercial uses 

in the three counties were estimated at roughly 1,558 Mgal/yr 

based on data from 1978 to 1989.

The upper bedrock aquifer is the primary source of 

groundwater in the three counties and is used for most 

municipal and private drinking-water supplies, as well as for 

irrigation and industrial uses. The lower bedrock aquifers 

(Wonewoc and Mount Simon aquifers) are used by a few 

municipal systems, most notably the city of Hudson. The sand 

and gravel aquifer is used where it can supply sufficient quantities of water or where the upper bedrock aquifer is absent or 

thin in Polk and St. Croix Counties and along the St. Croix and 

Mississippi River Valleys in the three counties. Large-diameter 

wells can yield more than 1,000 gallons per minute (gal/min) 

from the bedrock and sand and gravel aquifers where saturated 

thickness is sufficient (Borman, 1976). 

Three-Dimensional Simulation of the 

Regional Groundwater-Flow System

The three-dimensional regional model and the 

demonstration inset models are mathematical representations 

of groundwater flow and use the USGS MODFLOW–2000 

code (Harbaugh and others, 2000). The steps involved in 

developing the regional model were the following: 

1. Input boundary conditions identified by the screening 

model and select appropriate aquifers and confining units 

as identified in the conceptual model.

2. Construct a finite-difference grid.

3. Assemble hydrologic data (for example, aquifer and 

confining-unit geometry and hydraulic conductivities, 

recharge rate, and leakance of streambeds).

4. Input pumping rates and locations of simulated wells.

5. Calibrate the model by use of the parameter estimation 

code PEST. The model is calibrated by adjusting selected 

parameters over realistic ranges until there is a reasonable match between measured and simulated groundwater 

levels and measured and simulated surface-water flows.

6. Ensure that the model is in mass balance; that is, 

the volume of water entering the model approximates the 

volume of water being withdrawn or 

leaving the model. 

The steps involved in developing the inset demonstration 

models were identical to those described above, except for 

step 5; that is, many of the parameter values used in the 

demonstration models were taken directly from the regional 

model, whereas some parameter values were adjusted to 

improve the match to local water levels and streamflows 

where these data were available. Despite these improvements, 

the demonstration inset models are not considered calibrated, 

and their simulated results are intended for illustrative 

purposes only.

Model Construction and Assumptions

As currently implemented, the regional model simulates 

a steady-state groundwater system; that is, groundwater 

levels are not changing with time, and there is no change in 

groundwater storage. The steady-state assumption is appropriate because of the relatively constant rate of pumping over 

time and the close hydraulic connection between aquifers and 

surface water, which dampens the effect of transient stresses 

applied to the groundwater-flow system.

The sand and gravel aquifer was simulated wherever one 

of the four bedrock units was removed by erosion, and it is 

included in the three uppermost model layers (layers 1 to 3; 

fig. 7). This aquifer was divided into two zones representing 

alluvial valley sediments in the Chippewa, Mississippi, and 

St. Croix River Valleys and unlithified glacial deposits in 

northwestern Polk County. The bedrock units were combined 

into four model layers. Layer 1 consists of the unconfined 

upper bedrock aquifer (where present) above the shaly base of 

the Tunnel City Group (fig. 7). The altitude of the water table, 

which is computed during MODFLOW simulations, represents 

the top of an unconfined aquifer; in contrast, a low-permeability layer represents the top of a confined aquifer. Layer 2 in the 

model represents the confined Wonewoc aquifer, except where 
16 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

it is eroded and, therefore, represented by the sand and gravel 

aquifer. Layer 3 represents the shaly Eau Claire confining unit, 

except where it is eroded. In parts of layers 2 and 3 where a 

bedrock unit was eroded away and represented by the sand and 

gravel aquifer, the layer was assigned a thickness of 1 ft, with 

the bulk of the sand and gravel aquifer thickness simulated in 

layer 1. Layer 4 represents the confined Mount Simon aquifer. 

This layer is underlain by relatively impermeable Precambrian 

crystalline bedrock that forms the model base. The four model 

layers are represented mathematically by horizontal and 

Figure 7. The regional MODFLOW model layers and hydraulic-conductivity zones and values. (Kh, horizontal hydraulic conductivity; 

Kv, vertical hydraulic conductivity; ft/d, foot per day)

Layer 1

Sand and gravel aquifer (orange and red)

Kh

 = 90 ft/d

Kv

 = 0.9 ft/d

Upper bedrock aquifer (yellow)

Kh = 23 ft/d

Kv = 0.005 ft/d

Layer 2

Sand and gravel aquifer (orange and red)

Kh

 = 90 ft/d

Kv

 = 0.9 ft/d

Wonewoc bedrock aquifer (green)

Kh

 = 11 ft/d

Kv = 0.11 ft/d

Layer 3

Sand and gravel aquifer (orange and red)

Kh

 = 90 ft/d

Kv = 0.9 ft/d

Eau Claire confining unit (light blue)

Kh

 = 2 ft/d

Kv = 0.00009 ft/d

Layer 4

Mount Simon bedrock aquifer (blue)

Kh = 7 ft/d

Kv

 = 0.7 ft/d

River cells

Sand and gravel 

aquifer (1 ft thick 

where bedrock 

aquifer is absent)

Inactive area 

(no aquifer, white)

Uplift between two 

parallel faults 

(layers 2, 3, and 4)
Three-Dimensional Simulation of the Regional Groundwater-Flow System 17

vertical hydraulic conductivities in the Layer-Property Flow 

Package (Harbaugh and others, 2000). 

Two regional faults, where bedrock layers are vertically 

offset (figs. 3, 5, and 7), were simulated by adjusting the layer 

geometry (refer to “Model Grids” section) and adjusting the 

bedrock hydraulic conductivity in cells immediately adjacent 

to the faults. An area-averaged horizontal and vertical hydraulic conductivity was computed for these cells following the 

method of Hart and others (2006) by incorporating estimated 

properties of the bedrock in each layer and a single value for 

the fault zone; that is, horizontal hydraulic conductivity for 

these cells was computed as the harmonic mean of the bedrock 

conductivity for the layer and the fault-zone conductivity 

(table 1), assuming that the fault zone is 10 ft wide. Similarly, 

vertical hydraulic conductivity for these cells was computed 

as the arithmetic mean of the bedrock vertical conductivity for 

the layer and the fault-zone conductivity. The fault zone was 

assumed to have the same vertical and horizontal conductivity. 

Based on the conceptual model of groundwater flow through 

fault zones proposed by Caine and others (1996), the harmonic 

mean was used to compute the effective horizontal hydraulic 

conductivity, and the arithmetic mean was used to compute 

the effective vertical hydraulic conductivity, because vertical 

faults are expected to decrease the effective horizontal 

conductivity and increase the effective vertical conductivity 

of an area relative to the adjacent bedrock. The influence of 

faulting on the regional flow system appears to be relatively 

minor (refer to “Sensitivity Analysis” section) but may be 

important locally. Finally, vertically uplifted Precambrian 

crystalline bedrock between the Hastings and Cottage Grove 

Faults is adjacent to the entire thickness of the Mount Simon 

aquifer along much of the faults. This effectively impermeable 

horizontal boundary was simulated in layer 4 (the Mount 

Simon aquifer) by incorporating the Horizontal Flow Barrier 

Package (HFB; Hsieh and Freckleton, 1993) for MODFLOW 

and assigning a very low horizontal hydraulic conductivity 

(10–5 ft/d) to the barrier. 

The MODFLOW model has perimeter boundary conditions extracted from the analytic-element screening model, 

which are assigned as specified-flux cells (by means of the 

MODFLOW Well Package). Flux values were determined 

from a single-layer MODFLOW extraction of the corresponding area of the GFLOW model. This area extended beyond 

the county boundaries by about 15 miles (mi), or a distance 

equal to three times the estimated characteristic leakage 

length (Haitjema, 2006, eq. 5) based on initial estimates of 

aquifer transmissivity in the Mount Simon aquifer and vertical 

resistance to flow across the Eau Claire confining unit. The 

characteristic leakage length (Haitjema, 2006, eq. 5) is equal 

to the square root of the product of aquifer transmissivity 

and the resistance of the overlying confining unit, with the 

confining-unit resistance computed as the thickness of the 

unit divided by the vertical hydraulic conductivity of the unit 

(the inverse of leakance). Haitjema (2006) demonstrates that 

95 percent of vertical flow across a confining unit will occur 

within approximately three characteristic leakage lengths. 

Thus, any boundary artifacts are expected to be mitigated over 

the 15 mi between the MODFLOW model boundaries and 

the three counties. The perimeter flux values were distributed 

among multiple layers of the MODFLOW model by means 

of analytic element wells in the MODFLOW preprocessor 

Groundwater Vistas (Rumbaugh and Rumbaugh, 2007). 

This approach allows the constant flux to be automatically 

partitioned among model layers based on the transmissivity of 

individual cells. 

Internal hydrologic boundaries include rivers and 

lakes within the model domain. These boundaries are headdependent flow boundaries; groundwater flow to or from these 

surface-water bodies depends on the difference in surfacewater and groundwater levels, the vertical conductivity and 

thickness of the riverbed (leakance), and the length and width 

of the river or lake in the model cells that encompass 

the surface-water body. The assumed riverbed leakance 

[2 (ft/d)/ft] indicates a close hydraulic connection; that is, the 

hydraulic conductivity of the riverbeds is such that river stages 

have a substantial effect on the local groundwater system. 

River-cell conductance (McDonald and Harbaugh, 1988) in 

the regional model varies on a cell-by-cell basis according to 

the length of the river contained within each cell, as determined by overlapping the MODFLOW grid on a 1:24,000-

scale hydrography map by use of a GIS. The Mississippi 

River, the St. Croix River downstream from Stillwater, MN, 

and all lakes simulated in the regional model also are assumed 

to be head-dependent flow boundaries that, despite their lower 

assumed leakance [0.035 (ft/d)/ft], are also well connected 

to the groundwater-flow system because of their depth, large 

size, and low elevation. 

In addition to boundary conditions, initial input to the 

models included the top and bottom elevations of each model 

layer, hydraulic conductivities, recharge rates, and pumping 

rates and locations of wells. Initial model input represents a 

cell average of the aquifer properties.

Model Grids

The regional three‐dimensional, finite‐difference 

ground‐water-flow model covers a 66- by 114-mi area that is 

subdivided into 840,768 cells (348 columns, 604 rows, and 

4 layers), of which 778,969 (93 percent) are active. The row 

and column dimensions of each cell are uniform throughout 

the model area, with each cell measuring 1,000 ft on a side and 

having an area of about 23 acres. This uniformly spaced grid 

was used to simulate all parts of the flow system.

Layer elevations were estimated from geologic-contact 

information identified from wells (Wisconsin Geological 

and Natural History Survey, 2003) and maps (Mossler, 

1983). Layers were constructed by first interpolating the 

top elevation of the Precambrian crystalline bedrock, which 

forms the base of the model. This was performed separately 

for the area southeast of the Hastings Fault and northwest 

of the Cottage Grove Fault (fig. 8). The top elevation of the 
18 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

Figure 8. Interpolated crystalline bedrock elevation used to form the base of the regional model (layer 4), 

inactive cells in layer 4, and the location of faults (solid where simulated as an impermeable horizontal barrier 

between the Mount Simon aquifer and crystalline bedrock).

EXPLANATION

No-flow boundary condition 

(inactive cell) in layer 4

Layer uplift along faults

Layer uplift and Horizontal 

Flow Barrier (HFB) 

between the Mount Simon 

aquifer and crystalline bedrock

County boundary

Crystalline bedrock elevation 

(in feet above or below NAVD 88)

–300 to –150

–149 to 0

1 to 150

151 to 300

301 to 450

451 to 600

601 to 750

751 to 900

901 to 1,050

1,051 to 1,200

Hastings Fault

Cottage Grove

Fault

0 10 20 MILES

0 10 20 KILOMETERS

crystalline bedrock between the faults was estimated from 

reported uplift (Mudrey and others, 1987) and the interpolated 

elevations along the edge of the faults. The thicknesses of 

aquifers and confining units were interpolated across the entire 

study area. Thickness, rather than contact elevation, was used 

because thickness was expected to be less affected by faulting 

and could therefore be interpolated across the entire model 

domain without consideration of faulting, which occurred after 

deposition of the Cambrian and Ordovician sedimentary rocks. 

The base of layer 3 (contact between the Mount Simon aquifer 

and Eau Claire confining unit) was then computed by adding 

the layer thickness of the Mount Simon to the top elevation 

of the crystalline bedrock. Similarly, the base of layer 2 was 

computed by adding the thickness of the Eau Claire to the 

bottom elevation of layer 3. The base of layer 1 was computed 

by adding the thickness of the Wonewoc aquifer to the bottom 

elevation of layer 2. The top of layer 1 was interpolated from a 

digital elevation model.

A top-of-bedrock surface was interpolated from wellconstruction data (Wisconsin Geological and Natural History 

Survey, 2003; Wisconsin Department of Natural Resources, 

2003). This surface incorporated more data because the type of 
Three-Dimensional Simulation of the Regional Groundwater-Flow System 19

rock was unimportant, making this surface more detailed than 

the previously interpolated top and bottom elevations for the 

layers. Cells in layer 4 were deactivated (no-flow boundary) 

where the crystalline bedrock surface (bottom of layer 4) 

matched or exceeded the top-of-bedrock surface, indicating 

that the Mount Simon aquifer is absent. Cells in layer 3 were 

deactivated where the Mount Simon was absent and the 

bottom of layer 3 matched or exceeded the top-of-bedrock 

surface. Similarly, cells in layer 2 were deactivated where the 

Eau Claire was absent (inactive) and the bottom of layer 2 

matched or exceeded the top-of-bedrock surface; cells in 

layer 1 were deactivated if the Wonewoc was absent and the 

bottom of layer 1 matched or exceeded the top-of-bedrock 

surface. For cells in which the bottom elevation matched or 

exceeded the top of bedrock, but the layer below was not 

inactive (that is, the underlying aquifer or confining unit was 

present), the bottom elevation was adjusted downward to 

produce a layer that was 1 ft thick and represented by the sand 

and gravel aquifer. 

The layer interpolation method included the assumption 

of gradual changes in the crystalline bedrock elevation (except 

at the Hastings and Cottage Grove Faults) and sedimentary 

bedrock thickness over a regional scale. Locally, this assumption may be violated where the crystalline bedrock elevation 

or aquifer thickness changes rapidly, such as in central and 

northern Polk County. In this area, some local crystalline 

bedrock ridges may not be represented in the model, and 

layer thicknesses may locally differ from lithologic contacts 

described from well cuttings. Extraction of inset models, particularly those near crystalline bedrock ridges in Polk County, 

may benefit from local reinterpolation of layer geometries.

Model Calibration

The model was calibrated by use of PEST (Doherty, 

2004). The PEST parameter estimation routine automatically adjusted parameter values and compared simulated 

groundwater levels and stream gains to measured water levels 

and base flows after each model run. The parameter estimation 

continued until simulated water levels and base flow matched 

measured water levels and base flow as closely as possible 

given the model construction and relative importance (weight) 

assigned to each measurement. 

Although a steady-state model was used (in which 

groundwater levels do not change with time), measured water 

levels used during calibration spanned many years, and their 

location is somewhat uncertain. Because of these uncertainties, along with simplifications inherent in constructing a 

regional model, perfect agreement between the simulated and 

measured values was not expected. An approximate evaluation 

of data quality is included in the calibration by way of the 

PEST weight assigned to each target (table 3). The weighted 

residuals between measured and simulated values were 

used by PEST to determine the best fit. Water-level targets 

were arranged into four categories: (1) median values from 

long-term groundwater-observation wells in Pierce, Polk, 

and St. Croix Counties, (2) median values from long-term 

groundwater-observation wells outside of Pierce, Polk, and 

St. Croix Counties, (3) median values from observation 

wells with irregular measurement intervals, and (4) water 

levels from well-construction reports used by the Wisconsin 

Geological and Natural History Survey to compile water-table 

maps for Pierce, Polk, and St. Croix Counties (Lippelt, 

Table 3A. Mean error, mean absolute difference, and root mean squared difference between simulated and measured 

groundwater levels. Associated weights used for calibration with the parameter estimation program PEST (Doherty, 2004) also 

are shown.

[ft, foot; WGNHS, Wisconsin Geological and Natural History Survey; n/a, not applicable]

Well type Number of 

targets

Mean 

error

(ft)

Mean absolute

 difference

(ft)

Root mean 

squared 

difference

(ft)

Weight

Median of time-series values at long-term observation 

wells in Pierce, Polk, and St. Croix Counties 5 6.8 12.8 15.9 1–10a

Median of time-series values at long-term observation 

wells outside of Pierce, Polk, and St. Croix Counties 33 6.9 12.7 15.7 0.5–10b

Median of time-series values at observation wells with 

irregular measurements 22 –13.3 17.8 26.8 0.5–1c

Well-construction-report data used by WGNHS to map 

water tables in Pierce, Polk, and St. Croix Counties 2,831 –8.0 25.7 36.4 0.01

All water-level targets 2,891 –7.9 25.5 36.2 n/a

a

 Assignment based on the length of record, screened interval, and accuracy of measured well elevation.

b

 Assignment based on the length of record, screened interval, accuracy of measured well elevation, and distance to the model boundary.

c

 Assignment based on the length of record and accuracy of measured well elevation.
20 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin Table 3

B. Calibration results for stream base-flow targets and associated weights used for calibration with the parameter estimation program PEST. All streamflow-gaging 

stations are in Wisconsin.[USGS, U.S. Geological Survey; ft3/s, cubic feet per second; %, percent]

Station name and location

USGS station 

identification 

number

Observed 

base flow 

(ft3/s)

Simulated 

base flow 

(ft3/s)

Difference 

(ft3/s) Weight Type

Apple River near Somerset, St. Croix County 05341500 356 354 –1.4 (0%) 2.5e–4 Year-round streamflow-gaging stationHay River at Wheeler, Dunn County 05368000 270 270 +0.4 (0%) 2.5e–4 Year-round streamflow-gaging stationWillow River at Willow River State Park, St. Croix County 05341752 118 133 +15.3 (13%) 2.5e–4 Year-round streamflow-gaging stationKinnickinnic River near River Falls, Pierce County 05342000 107 79 –28.2 (26%) 2.5e–4 Year-round streamflow-gaging stationYellow River at Barron, Barron County 053674464 85.0 77.1 –7.9 (+9%) 2.5e–4 Year-round streamflow-gaging stationTrade River near Trade River, Burnett County 05340390 65.7 73.3 +7.6 (12%) 2.5e–4 Year-round streamflow-gaging stationWood River at North Williams Road near Grantsburg, 

Burnett County 05338955 49.0 52.7 +3.7 (8%) 2.5e–4 Year-round streamflow-gaging station

Eau Galle River at Spring Valley, Pierce County 05370000 19.0 22.8 +3.8 (20%) 2.5e–4 Year-round streamflow-gaging stationEau Galle River at low-water bridge at Spring Valley, 

Pierce County 05369945 13.0 11.4 –1.6 (12%) 2.5e–4 Year-round streamflow-gaging station

Eau Galle River near Woodville, St. Croix County 05369900 6.2 1.6 –4.6 (74%) 2.5e–4 Year-round streamflow-gaging stationKnights Creek near Weston, Dunn County 8.8 7.9 –0.9 (11%) 5.0e–5 Seasonal streamflow-gaging stationCady Creek near Elmwood, Pierce County 6.9 4.7 –2.2 (32%) 5.0e–5 Seasonal streamflow-gaging stationRush River at State Highway 35 near Maiden Rock, 

Pierce County 130 105 –25.1 (19%) 2.5e–5 Synoptic measurement

Kinnickinnic River about 200 feet downstream from 

Lake George, River Falls, Pierce County 82.6 40.2 –42.4 (51%) 2.5e–5 Synoptic measurement

Kinnickinnic River at State Highway 65 near River Falls, 

St. Croix County 65.1 43.5 –21.6 (33%) 2.5e–5 Synoptic measurement

Kinnickinnic River at 120th Street near River Falls, 

St. Croix County 51.5 34.9 –16.6 (32%) 2.5e–5 Synoptic measurement

Kinnickinnic River at Steeple Drive near Roberts, 

St. Croix County 41.8 14.8 –27.0 (65%) 2.5e–5 Synoptic measurement

Kinnickinnic River at 140th Street near I–94 near Roberts, 

St. Croix County 8.5 7.2 –1.3 (15%) 2.5e–5 Synoptic measurement

Parker Creek near the mouth near River Falls, St. Croix County 10.2 11.0 +0.8 (7%) 2.5e–5 Synoptic measurementSouth Fork Kinnickinnic River near the mouth near River Falls, 

Pierce County 9.2 1.3 –7.9 (86%) 2.5e–5 Synoptic measurement

Rocky Branch Creek near the mouth near River Falls, 

Pierce County 5.7 3.6 –2.1 (37%) 2.5e–5 Synoptic measurement
Three-Dimensional Simulation of the Regional Groundwater-Flow System 21

1990a, b; Muldoon, 2000). Higher weights were assigned to 

wells with long records and accurately measured referencepoint elevations; lower weights were assigned to wells with 

just one or a few measurements and less accurately estimated 

elevations. In addition, a long-term observation well in Lake 

City, MN, is on a peninsula in the Mississippi River, where 

the river stage is well known. The difference between the 

Mississippi River stage and the water level in the Lake City 

observation well (Minnesota unique well number 222329) was 

computed and used as a head-gradient target for calibration 

with PEST. Finally, base-flow measurements were assigned 

weights (table 3B) according to three categories: (1) yearround streamflow-gaging stations, (2) seasonal (non-freezeperiod) streamflow-gaging stations, and (3) one-time synoptic 

measurements. The highest weights were assigned to yearround gages; the lowest weights were assigned to synoptic 

measurements. These base-flow measurements were compared 

to simulated stream gains as part of the model calibration. 

Values for hydraulic conductivity used in the final 

calibrated model are shown in table 1 and in figure 7. Only 

a subset of all possible parameters was estimated by PEST. 

Parameters were excluded if they were insufficiently sensitive 

(for example, vertical hydraulic conductivity of aquifers) for 

automated calibration. In these cases, the parameter value 

was either set equal to a value within the range reported in 

table 1 or tied to another parameter at a specified ratio. For 

example, a 100:1 ratio was specified between the horizontal 

and vertical hydraulic conductivities of many aquifers due 

to insensitivity of vertical hydraulic conductivity for these 

units. Similarly, values of other parameters were limited such 

that their value could not exceed that of another parameter. 

For example, horizontal hydraulic conductivity of alluvial 

sediments in the Chippewa, St. Croix, and Mississippi River 

Valleys was allowed to vary but was assigned a lower bound 

equal to the horizontal hydraulic conductivity of the upland 

glacial sediments, which was concurrently calibrated. The 

calibrated horizontal hydraulic conductivity representing the 

glacial sediments is 90 ft/d; alluvial-valley sediments were 

estimated with the same value and are therefore lumped with 

the glacial sediments and referred to collectively as the sand 

and gravel aquifer in this report. Horizontal hydraulic conductivities calibrated for the upper bedrock aquifer, the Wonewoc 

aquifer, and the Mount Simon aquifer are 23, 11, and 7 ft/d, 

respectively. The Eau Claire confining unit was assigned (not 

calibrated, because of low sensitivity) a horizontal hydraulic 

conductivity of 2 ft/d (Hunt and others, 2003) for the entire 

model domain, which represents the ability of the confining 

unit to transmit water laterally through the thin sandstone 

lenses within the unit. The ratio of horizontal to vertical 

hydraulic conductivity (Kh:Kv) was fixed at 100:1 for the 

sand and gravel aquifer, Wonewoc aquifer, and Mount Simon 

aquifer, which corresponds to vertical hydraulic conductivities 

of 0.9, 0.11, and 0.07 ft/d, respectively. The vertical hydraulic 

conductivity for the upper bedrock aquifer was assigned a 

value of 5x10–3 ft/d, which equates to a Kh:Kv ratio of 4,600:1 

and reflects the laterally extensive low-permeability confining 

unit commonly associated with the base of the Tunnel City 

Group (Young, 1992; Miller and Delin, 1993; Juckem, 2003; 

R.G. Tipping, Minnesota Geological Survey, written commun., 

2005). This value was relatively insensitive during model 

calibration (see “Sensitivity Analysis” section). The Eau 

Claire confining unit also contains laterally extensive layers of 

shale, resulting in a calibrated vertical hydraulic conductivity 

of 9x10–5 ft/d (Kh:Kv ratio of about 20,000:1). The hydraulic 

conductivity of faults was estimated to be 0.09 ft/d, which is 

within the range suggested by Hart and others (2006). 

Field-measured groundwater levels were compared 

to model-calculated groundwater levels (fig. 9) at specific 

model cells. Water-level measurements from 2,831 drillers’ 

construction reports in Pierce, Polk, and St. Croix Counties 

that spanned approximately 50 years from 1950 to 2000 were 

compared to model-calculated water levels. These water-level 

targets provide data on the water table in the sand and gravel 

and the upper bedrock aquifers. Water levels from 60 monitoring wells with either continuous or irregular measurements 

also were compared to model-calculated water levels. Median 

water levels measured in these monitoring wells are more 

representative of average conditions for the study period than 

are water levels from well-construction reports and were 

therefore given higher weight during model calibration. Of 

the 60 monitoring wells, 9 are open to the deeper Wonewoc 

aquifer, Eau Claire confining unit, or Mount Simon aquifer. 

Measured water levels in these nine wells represent the 

potentiometric surface of these lower units and were compared 

to model-calculated water levels in the associated layer. Of 

special importance was the calculated gradient between the 

Mississippi River stage and the water level in the observation 

well in Lake City, MN (unique well number 222329), which 

was closely simulated (within 0.2 ft).

The summary statistics for the groundwater-level 

calibration from the regional model (table 3A) are similar 

to what has been observed in other regional models in 

Wisconsin. The mean error of all the groundwater-level targets 

in the regional model (a measure of the model bias) is –7.9 ft 

(fig. 10; a negative value indicates that measured values were 

less than simulated values); the mean errors for the water table 

(layer 1) and all potentiometric heads (layers 2, 3, and 4) are 

–7.9 and 1.5 ft, respectively. The root mean square differences 

(RMSD) between measured and simulated water levels for 

the water table and potentiometric heads are 36.1 and 17.6 ft, 

respectively. The mean absolute difference (MAD) is 25.5 ft 

for the water table and 15.1 ft for potentiometric heads. These 

RMSD and MAD values represent less than 6 percent of the 

total range of observed water levels across the model area. 

In addition to comparing measured and modeled water 

levels by means of summary statistics, spatial comparisons 

between the measured and simulated water table (layer 1) and 

potentiometric surfaces in layers 2 and 4 were made (figs. 11, 

12, and 13). The agreement between simulated water levels 

and measured water levels in observation wells (figs. 11A, 

12, and 13) is generally close and shows little spatial bias. 

The match to well-construction-report water levels (fig. 11B) 
22 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

Figure 9. Perimeter and internal boundary conditions, water-level-observation wells, and base-flow targets in the regional 

model of Pierce, Polk, and St. Croix Counties, Wisconsin.

!(

")

")

")

")

")

")

")

")

")

")

")

")

")

")

")

")

")

")

")")")")")")")

")

")

")

") ")

")")

")

")

") ")

")

")

")

")

")

")

")

")

")

")

")

")

")

")

")

$+

$+

$+

%,

%,

%, %,

%,

*#

*#

*#

*# *#

*#

*#

*#

*# *#

*#

*#

*#

*# *#

*#

*#

*#

*# *#

*#

EXPLANATION

") Observation-well target - layer 1

$+ Observation-well target - layer 2

!( Observation-well target - layer 3

%, Observation-well target - layer 4

*# Base-flow target

No-flow boundary condition 

(inactive cell) in layer 1, estimated 

from interpolated stratigraphic layers

Head-dependent internal boundary

representing a river or lake

Constant-flux well perimeter 

boundary using rate extracted 

from GFLOW model

County boundary

0 10 20 MILES

0 10 20 KILOMETERS

45°

45°45'

44°30'

93° 92°
Three-Dimensional Simulation of the Regional Groundwater-Flow System 23

Figure 10. Measured water levels plotted against simulated water levels for the 

regional model.

600

700

800

900

1,000

1,100

1,200

1,300

1,400

600 700 800 900 1,000 1,100 1,200 1,300 1,400

MEASURED WATER LEVELS, IN FEET

SIMULATED WATER LEVELS, IN FEET

Layer 1

Layer 2

Layer 3

Layer 4

1:1 LINE

shows some banding, with simulated water levels greater than 

observed water levels in northwestern Polk County and central 

St. Croix County. The area of high simulated water levels in 

northwestern Polk County coincides with an area in which 

groundwater levels are commonly 50 to 100 ft below surfacewater levels (Muldoon, 2000) and the system is characterized 

by a local, upper perched water table and a lower regional 

water table. This level of local flow-system complexity 

was not simulated in the regional model, in which stacked 

local systems were simplified into one upper model layer. 

Likewise, the area of high simulated water levels in central 

St. Croix County may be a result of simulating vertically 

averaged aquifer properties for multiple hydrostratigraphic 

units with a single upper bedrock aquifer layer. The units 

lumped into layer 1 in this area have appreciably different 

hydraulic properties. In addition, these units were simulated 

with one parameter zone in the model. Aquifer simplification 

through large-scale parameter zonation provides parsimony 

in a regional model, but it can also limit calibration (Hunt and 

others, 2007). Shallow groundwater flow in central St. Croix 

County is dominated by the karstic Prairie du Chien aquifer, 

which was lumped in the regional model with underlying 

sandstone aquifers represented by the Trempealeau and Tunnel 

City Groups. Cobb (2007) describes the Prairie du Chien 

Group as having “extreme” horizontal to vertical anisotropy. 

Horizontal transmissivity is large and flow is rapid (several 

measurements of local groundwater-flow velocities exceeded 

150 ft/d), yet the water table is commonly near the top of 

the Prairie du Chien Group and vertical gradients are steep, 

indicating a low vertical hydraulic conductivity (Cobb, 2007). 

Because there is little physical data related to spatial changes 

in hydraulic properties of the Prairie du Chien Group at the 

regional scale, effects of flow through karst features could not 

easily be limited to discrete areas in the model. Rather, karst 

features are observed throughout the extent of the Prairie du 

Chien Group in Pierce and St. Croix Counties (Cobb, 2007, 

fig. 3.8). Including this level of geologic complexity was 

beyond the scope of regional model calibration; thus, the 

area of the banded residuals were investigated by use of the 

demonstration model for the area (described below) rather 

than the regional model described here. 

Measured base flows were compared to simulated base 

flows at 21 locations (fig. 14). Streamflow was measured continuously for several years between 1994 and 2004 at 10 yearround streamflow-gaging stations and during the summers of 

2002 and 2003 at two seasonal streamflow-gaging stations 

(table 3B). These streamflow data were used in conjunction 

with an automated hydrograph separation program, BFI (Wahl 

and Wahl, 1995), to estimate base flow for each streamflowgaging station. Streamflow was measured once at an additional 

nine synoptic measurement locations (table 3B). Simulated 

base flows generally matched measured base flows, with five 

of the year-round streamflow-gaging stations having simulated 

base flows greater than measured base flows; simulated 

base flow was less than measured base flow at the other five 

year-round streamflow-gaging stations. Simulated base flow 

was less than measured base flow at 10 of the 11 seasonal 

gages and synoptic measurement sites, and this discrepancy is 
24 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

Figure 11A. Simulated water-table elevation and water-level residuals for observation wells in the regional groundwater-flow 

model, layer 1.

EXPLANATION

Greater than 50 feet too high

20 to 50 feet too high

19 feet too high to 19 feet too low

20 to 50 feet too low

Greater than 50 feet too low

Simulated water-level contour, 

interval 50 feet

Inactive or dewatered cell in layer 1

Rivers and lakes

County boundary

Simulated water-level residual

1100

900

950

1250

900

1000

950

0 10 20 MILES

0 10 20 KILOMETERS

45°

45°45'

44°30'

93° 92°
Three-Dimensional Simulation of the Regional Groundwater-Flow System 25

Figure 11B. Simulated water-table elevation and water-level residuals for well-construction-report wells in the regional 

groundwater-flow model, layer 1.

EXPLANATION

Greater than 50 feet too high

20 to 50 feet too high

19 feet too high to 19 feet too low

20 to 50 feet too low

Greater than 50 feet too low

Simulated water-level contour,

interval 50 feet

Rivers and lakes

Inactive or dewatered cell in layer 1

County boundary

Simulated water-level residual

0 10 20 MILES

0 10 20 KILOMETERS

45°

45°45'

44°30'

93° 92°

1000

850

850

900

1150

1250

1000
26 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

Figure 12. Simulated potentiometric-surface elevation and water-level residuals for observation wells in the regional 

groundwater-flow model, layer 2.

EXPLANATION

Greater than 50 feet too high

20 to 50 feet too high

19 feet too high to 19 feet too low

20 to 50 feet too low

Greater than 50 feet too low

Simulated potentiometric-surface

contour, interval 50 feet

Inactive cell in layer 2

County boundary

Simulated water-level residual

850

1100

900

1050

750

800

800

1100

950

950

950

1250

900

1000 0 10 20 MILES

0 10 20 KILOMETERS

45°

45°45'

44°30'

93° 92°
Three-Dimensional Simulation of the Regional Groundwater-Flow System 27

Figure 13. Simulated potentiometric-surface elevation and water-level residuals for observation wells in the regional 

groundwater-flow model, layer 4.

EXPLANATION

Greater than 50 feet too high

20 to 50 feet too high

19 feet too high to 19 feet too low

20 to 50 feet too low

Greater than 50 feet too low

Simulated potentiometric-surface 

contour, interval 50 feet

Horizontal flow barrier

Inactive cell in layer 4

County boundary

Simulated water-level residual

1150

1000

800

800

800

1000

750

750

700

700

800

750

0 10 20 MILES

0 10 20 KILOMETERS

45°

45°45'

44°30'

93° 92°
28 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

Figure 14. Simulated water-table elevation and residuals for stream base-flow measurements in the regional groundwaterflow model, layer 1 (ft3

/s, cubic feet per second).

EXPLANATION

Less than 10 ft

3

/s

10 to 49 ft

3

/s

50 to 99 ft

3

/s

100 to 199 ft

3

/s

200 to 400 ft

3

/s

Inactive or dewatered 

cell in layer 1

Rivers and lakes

County boundary

Measured base flow, 

as indicated by circle size

30 to 90 percent too high

Seasonal streamflowgaging station Synoptic measurement

10 to 29 percent too high

9 percent too high to

9 percent too low

10 to 29 percent too low

30 to 90 percent too low

Simulated water-level contour,

interval 50 feet

Simulated base flow, 

as indicated by circle color

0 10 20 MILES

0 10 20 KILOMETERS

45°

45°45'

44°30'

93° 92°

1000

950

900

1250

900

900

1100
Three-Dimensional Simulation of the Regional Groundwater-Flow System 29

Figure 15. Composite sensitivities computed by PEST for parameters of the regional MODFLOW model of Pierce, Polk, and St. Croix 

Counties, Wisconsin. Sensitivities were computed independently for each parameter; no parameters were fixed or tied to other 

parameters for the final sensitivity calculations. (* indicates the value was specified during the calibration process; ** indicates the 

ratio Kh:Kv was specified as 100:1 during the calibration process; parameters without an asterisk were estimated during the calibration 

process; Kh, horizontal hydraulic conductivity; Kv, vertical hydraulic conductivity)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Kh

 - glacial

** Kh

 - river valley alluvium

Kh

 - upper bedrock aquifer

Kh

 - Wonewoc

* Kh

 - Eau Claire

Kh

 - Mount Simon

** Kv

 - glacial

** Kv

 - river valley alluvium

* Kv

 - upper bedrock aquifer

** Kv

-Wonewoc

Kv

 - Eau Claire

** Kv

 - Mount Simon

Kh

 and Kv

 - faults

Recharge

* Riverbed leakance

PARAMETER NAME

COMPOSITE PARAMETER SENSITIVITY

likely related to difficulty in matching simulated groundwater 

divides in the headwater area of the Kinnickinnic and Rush 

Rivers with mapped divides (Lippelt, 1990b). The base-flow 

targets simulated within the MODFLOW model domain were 

sufficient to constrain the recharge rate in the MODFLOW 

model. Recharge was applied uniformly to the uppermost 

active layer and calibrated at a rate of 8.2 inches per year 

(in/yr), which is similar to rates estimated by others in 

southeastern Minnesota and western Wisconsin (table 2).

Sensitivity Analysis

Some uncertainty always exists about the accuracy of 

models because the model parameter values are never exactly 

known. However, the importance of each input parameter and 

its effect on simulation results can be evaluated through sensitivity tests in which the value of a parameter, such as hydraulic 

conductivity, is adjusted above or below the calibrated value 

and the magnitude of changes in simulated groundwater levels 

and base flows are quantified. In this study, PEST was used 

to calculate the sensitivity of all water-level and streamflow 

observations to changes in each parameter value during the 

calibration process. For the final calibrated parameter values, 

composite sensitivities computed by PEST (fig. 15) indicate 

that water levels and streamflows were most sensitive to the 

horizontal hydraulic conductivity of the upper bedrock aquifer, 

glacial sediments, and recharge. Less sensitive parameters 

included vertical hydraulic conductivity of aquifers, horizontal 

hydraulic conductivity of confining units, and riverbed leakance. Initial sensitivity analyses showed similar results and 

were used to guide selection of parameters for estimation; that 

is, high sensitivity to a parameter indicates that the calibration 

data (water levels and flows) provide sufficient information 

for constraining values for the parameter, and low sensitivity 

to a parameter indicates that the calibration data lack sufficient 

information to constrain the parameter. Therefore, parameters 

with low sensitivity were specified at reasonable values at the 

outset of parameter estimation or were directly tied to more 

sensitive parameters during the parameter-estimation process 

(fig. 15). 

Mass Balances

Simulated model results indicate that recharge is the 

primary source of inflow to the groundwater-flow system in 

Pierce, Polk, and St. Croix Counties. Recharge accounted for 

82 percent (1,346 cubic feet per second [ft3/s]) of all groundwater inflow to the three counties. The remainder consists 

of recirculated groundwater seepage from internal rivers 

and lakes (244 ft3/s, or about 15 percent of total inflow) and 
30 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

horizontal flow through aquifers across the county boundaries 

(61 ft3/s, or about 4 percent of total inflow). Recirculated 

groundwater seepage from rivers and lakes is groundwater that 

previously entered a river or lake at an upstream location. In 

the three counties, seepage from rivers and lakes commonly 

occurs near waterfalls and dams where water levels change 

abruptly, and it also occurs on the downgradient (downstream) 

end of a lake or reservoir. These sources of groundwater 

were balanced by flow from the aquifers to rivers inside the 

three counties (85 percent or 1,397 ft3/s), to pumping wells 

(1 percent or 19 ft3/s), and outward flow across the county 

boundaries (14 percent or 235 ft3/s). Table 4 summarizes the 

mass-balance sources and sinks for the entire model domain 

and the individual counties. The mass-balance analysis 

indicates that the primary source of groundwater withdrawn 

by pumping wells in each county is water recharged within the 

county and is water that otherwise would have discharged to 

local rivers and lakes.

Application of the Regional Model 

Simulations designed to address specific hydrologic questions can be run after models are calibrated. These simulations 

can include past and present conditions or future scenarios. 

Past and present conditions (1994–2004) are discussed in this 

section. Local refinements through the construction of inset 

models are also described for demonstration purposes.

Groundwater-Flow Directions and Interaction 

with Surface Water

Results from the regional model include simulated water 

levels, flow directions, and mass-balance interactions with 

surface-water features. Contours of simulated water levels 

are similar to water-table maps produced previously for the 

counties in that groundwater flow is perpendicular to the 

Table 4. Mass-balance components for Pierce, Polk, and St. Croix Counties, Wisconsin, collectively and individually, and 

the entire model area.

[ft3/s, cubic foot per second. Percentages may not add to 100 because of rounding]

Area Type of source or sink

Groundwater inflow Groundwater outflow

(ft3/s) (Percent of total) (ft3/s) (Percent of total)

Combined Pierce, Polk, 

and St. Croix Counties

Recharge 1,346 82 0 0

Streams and lakes 244 15 1,397 85

Flow across county borders 61 4 235 14

Well pumping 0 0 19 1

Pierce County

Recharge 352 74 0 0

Streams and lakes 71 15 443 93

Flow across county borders 54 11 31 7

Well pumping 0 0 3 1

Polk County

Recharge 559 75 0 0

Streams and lakes 117 16 655 88

Flow across county borders 68 9 84 11

Well pumping 0 0 5 1

St. Croix County

Recharge 447 81 0 0

Streams and lakes 61 11 461 83

Flow across county borders 47 8 83 15

Well pumping 0 0 11 2

Entire model area

Recharge 4,527 81 0 0

Streams and lakes 882 16 5,184 93

Flow across county borders 147 3 154 3

Well pumping 0 0 219 4
Application of the Regional Model 31

Figure 16. Simulated water-table elevation, particle flow paths from the water table, 

and groundwater/surface-water interaction in the regional groundwater-flow model, 

layer 1.

contours. However, simulated water levels from the regional 

model are further constrained in that the model must also 

account for all water that enters and exits the model, which 

is not a consideration for drawn water-table maps. Numerical 

particles of water can also be traced along flow paths in 

the model to illustrate differences in flow directions among 

vertically stacked aquifers. Figure 16 shows the path of several 

mathematical particles of water flowing downgradient, starting 

at the water table and flowing to discharge locations such as 

wells and rivers. Much of the water that recharges at the water 

table flows through the upper bedrock or sand and gravel 

aquifers and discharges to nearby rivers. Water that recharges 

in areas with steep vertical gradients moves into deep aquifers 

before returning to shallow aquifers near major groundwater 

sinks, such as the St. Croix and Mississippi Rivers. Groundwater flow velocities in the upper bedrock aquifer are expected 

to be variable because of the nature of flow 

through fractures and conduits in the Prairie 

du Chien Group and, to a lesser extent, in 

the Trempealeau and Tunnel City Groups. 

For example, Cobb (2007) measured a range 

of local velocities from about 12 to 340 ft/d 

through fractures in the Prairie du Chien 

Group at one location in St. Croix County. 

Groundwater in the upper aquifers is also 

younger than water in the deep aquifers. 

Flow paths through the deep sandstone 

aquifers are relatively longer, and velocities 

tend to be relatively slower because of the 

lower hydraulic conductivity and hydraulic 

gradients in the deep units. 

Groundwater/surface-water interaction 

was evaluated by use of output from the 

calibrated regional model. Modeled discharge into each river cell was color-coded 

to show gaining and losing reaches (fig. 16). 

Groundwater discharges into all areas of 

the St. Croix and Mississippi Rivers, except 

immediately upstream from lock and dam 

3 on the Mississippi River. Groundwater 

discharge into pools and lakes of the lower 

St. Croix and Mississippi Rivers generally is 

greatest along the shoreline, with decreasing 

rates of groundwater discharge toward the 

center of the pools; groundwater discharge 

into upland lakes also tends to occur 

primarily along the shoreline. Tributaries to 

the St. Croix and Mississippi Rivers show 

more complex transitions between gaining 

and losing reaches. Most river reaches gain 

water from the groundwater-flow system. 

Losing reaches tend to occur upstream from 

impoundments (the downstream shoreline 

of reservoirs) and along the downgradient 

shoreline of lakes.

The model was also used to evaluate vertical groundwater 

flow between layers in the model and to identify factors that 

influence vertical flow patterns (fig. 17). Groundwater flows 

downward between layers over much of the area because 

recharge to the water table induces downward pressure. 

Groundwater flows upward primarily near faults and large 

rivers. As represented in the model, faults appear to have 

relatively modest influence on regional horizontal and vertical 

flow patterns in all layers (small deflection in contours and 

modest correlation with areas of upward flow; fig. 17). 

Locally, however, faults may have substantial influence on 

groundwater flow, as illustrated by complex water levels in 

a nest of monitoring wells south of Afton, MN, and distant 

from pumping centers (Minnesota unique well numbers 

216161, 216162, and 216163). At this site, the 20-year average 

water level measured in the Wonewoc Formation exceeds 

EXPLANATION

Water particle moving through:

Layer 1

Layer 2

Layer 3

Layer 4

River losing water to groundwater

0 to 2.49

2.5 to 4.9

5.0 to 9.9

10 to 49.9

>50

Simulated water-level contour

for layer 1, interval 50 feet

Inactive or dewatered cell in layer 1

County boundary

Groundwater discharge to river cell (cubic feet

per day divided by 1,000)

900

1100

1200

1200

1000

950

950

44°45'

45°30'

92°45'

92°15'

0 10 20 MILES

0 10 20 KILOMETERS

Lock and dam
32 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

Figure 17. Simulated vertical flow directions between model layers in Pierce, Polk, and St. Croix Counties, Wisconsin. 

A, layers 1 and 2. 

B, layers 2 and 3. 

C, layers 3 and 4.

1250

1050 900

1000

750

800

900

1300

1100 900

1050

750

900

800

44°45'

45°30'

92°45'

92°15'

0 10 20 MILES0 10 20 KILOMETERS

44°45'

45°30'

92°45'

92°15'

0 10 20 MILES0 10 20 KILOMETERS

44°45'

45°30'

92°45'

92°15'

0 10 20 MILES0 10 20 KILOMETERS

EXPLANATION

Simulated vertical flow direction

Simulated upward flowSimulated downward flowHorizontal flow barrierHydraulic conductivity adjustment

Simulated potentiometric-surfacecontour, interval 50 feetInactive cellRivers and lakes in layer 1;shown for reference onlyCounty boundary

Simulated faults using:

A

B

C

1000

1150

800

800

800

900

800

900
Application of the Regional Model 33

the average water levels measured in the underlying Mount 

Simon Formation and the overlying Tunnel City Group by 

about 21 ft and 7 ft, respectively. Moreover, where the Mount 

Simon aquifer is adjacent to crystalline bedrock and simulated 

with the Horizontal Flow Barrier (HFB) Package (Hsieh and 

Freckleton, 1993) in layer 4 of the regional model, hydraulic 

damming occurs, which diverts groundwater upward over the 

crystalline rock and(or) horizontally along the faults as the 

water flows toward the St. Croix River. 

Groundwater does not appear to cross between Wisconsin 

and Minnesota beneath the Mississippi and St. Croix Rivers 

in any of the four model layers. Specifically, simulated 

groundwater flow is upward below nearly the entire length of 

the Mississippi and St. Croix Rivers where the rivers border 

Pierce, Polk, and St. Croix Counties (fig. 17). 

In areas where all the groundwater is captured 

by the Mississippi and St. Croix Rivers, the 

rivers function as fully penetrating hydraulic 

boundaries to groundwater flow. The flowsystem divide underneath these large rivers 

may not be stationary, however. It is important 

to note that groundwater withdrawal can 

change the effectiveness of hydraulic boundaries (for example, Strack and others, 1987; 

Feinstein and others, 2005). Smaller tributary 

rivers, such as the Apple, Willow, Kinnickinnic, and Rush Rivers, have gaining and losing 

reaches and appear to be partially penetrating 

hydraulic boundaries. These tributaries induce 

upward flow from the Wonewoc aquifer and 

Eau Claire confining unit, but have less influence on the Mount Simon aquifer, especially 

in headwater areas (fig. 17). Influence of 

the Apple River (fig. 1) on vertical flow is 

complicated by nearby faulting.

Predevelopment Conditions 

Compared to Present (1994–2004) 

Conditions

The calibrated regional model can be 

used to address the effects of pumping (past, 

present, and future) on the groundwater 

resource. In this study, predevelopment 

conditions were compared to present pumping 

conditions. The predevelopment conditions 

were simulated by using the calibrated 

model input and excluding pumping wells. 

Changes in groundwater levels between 

predevelopment and present conditions due 

to the construction or removal of dams and 

reservoirs were not evaluated; that is, no 

river or lake elevations were changed 

from the calibrated model for the predevelopment simulation.

Figure 18. Simulated water-table decline (layer 1) from predevelopment to present 

(1994–2004) water-use conditions in Pierce, Polk, and St. Croix Counties, Wisconsin.

The comparison of model simulations shows declines 

in groundwater levels where high-capacity wells are grouped 

in discrete clusters, but few effects were observed in other 

areas of the counties where pumping wells are much more 

dispersed and discharge at lower rates (figs. 18 and 19). With 

current pumping conditions, the simulated water table in the 

upper unconfined aquifer (model layer 1) has declined by less 

than 2 ft from predevelopment levels throughout most of the 

three-county area except near local pumping centers, such as 

one near Clear Lake in Polk County with a maximum decline 

of about 8 ft (fig. 18). 

EXPLANATION

Area with simulated water-table

decline from predevelopment 

conditions (zero withdrawal)

2.1 to 4 feet

4.1 to 6 feet

6.1 to 8 feet

Inactive or dewatered cell in layer 1

Rivers and lakes

County boundary 44°45'

45°30'

92°45'

92°15'

0 10 20 MILES

0 10 20 KILOMETERS
34 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

overlying aquifers is impeded, thus enhancing 

the potential for drawdown in the Mount Simon 

aquifer regardless of proximity to large rivers. 

Demonstration Simulations of LocalScale Groundwater Flow 

The regional model is useful for understanding groundwater flow at a regional scale and also 

for use as a framework from which local-scale 

investigations can be initiated. The process of 

using the regional model as a framework is 

demonstrated for one location in each of the three 

counties. These inset models were developed 

to demonstrate the utility of this approach 

and additional model capabilities rather than 

to answer a specific question. Moreover, the 

demonstration inset models were not explicitly 

calibrated to data that are commensurate with the 

type of simulated results produced by the models. 

Thus, results from the demonstration models, as 

presented in this report, incur greater uncertainty 

than results shown for the regional model and 

are not suited for decisionmaking. Nonetheless, 

the demonstration models could be refined in 

the future to address specific questions, provided 

that data pertinent to the refined objectives 

are included.

Telescopic Mesh Refinement

Three demonstration inset models were 

extracted from the regional MODFLOW model 

(fig. 1) by use of a telescopic mesh refinement 

(TMR) approach, following the methods of Ward 

and others (1987) and implemented in Groundwater Vistas (Rumbaugh and Rumbaugh, 2007). 

Results from the regional model were used to 

assign constant-flux boundary conditions along 

the perimeter of each inset model. Eventual 

changes to parameter values in the inset models 

subsequently were incorporated into copies of the regional 

model that were dedicated to the TMR process for each inset 

model, and constant-flux boundary conditions were reextracted. This manual coupling was performed to improve the 

perimeter boundary fluxes for the demonstration inset models; 

future inset models would benefit from automated coupling of 

the boundary conditions with the regional model through the 

new Local Grid Refinement (LGR) method for MODFLOW 

(Mehl and Hill, 2005, 2007). In addition, some distance 

between the boundaries of the inset models and the area of 

interest was desired to ensure minimal influence of boundary 

conditions on simulated results. This distance was estimated 

by means of a characteristic leakage length (Haitjema, 2006) 

Figure 19. Simulated potentiometric-surface decline in the Mount Simon 

aquifer (layer 4) from predevelopment to present (1994–2004) water-use 

conditions in Pierce, Polk, and St. Croix Counties, Wisconsin.

The simulated potentiometric surface for the Mount 

Simon aquifer (model layer 4) has declined by more than 10 ft 

from predevelopment levels in western Pierce and St. Croix 

Counties (fig. 19), with a maximum decline of about 40 ft 

near the city of Hudson, WI. The decline in the potentiometric 

surface appears to be associated with pumping from the deep 

aquifer below Hudson, combined with pumping from nearby 

communities in Minnesota. Near Hudson, the simulated 

decline may be exacerbated by the representation of large 

regional faults, which tend to isolate the aquifer to some extent 

from the surrounding flow system. Further, where the overlying shale-rich Eau Claire confining unit has not been removed 

by erosion (most of the study area; fig. 7), leakage from 

10.1 to 20 feet

20.1 to 30 feet

30.1 to 40 feet

Horizontal flow barrier

Area with simulated potentiometricsurface decline from predevelopment

conditions (zero withdrawal)

EXPLANATION

Inactive cell in layer 4

County boundary

44°45'

45°30'

92°45'

92°15'

0 10 20 MILES

0 10 20 KILOMETERS
Application of the Regional Model 35

estimated from properties of aquifers and confining units 

originally combined into layer 1 of the 

regional model.

The grid spacing of 1,000 ft by 1,000 ft for the regional 

model was refined to about 200 ft by 200 ft for the Pierce 

and Polk County inset models and to 250 ft by 250 ft for 

the St. Croix County inset model. Thus, every cell from the 

regional model is represented by about 25 cells in the Pierce 

and Polk County inset models and by 16 cells in the St. Croix 

County inset model. As a result of the smaller grid spacing, 

surface-water features and the hydraulic-head distribution 

were simulated with more detail in the inset models. A second 

refinement was the conversion of some streams from the 

MODFLOW River Package (McDonald and Harbaugh, 1988) 

to more sophisticated Streamflow Routing Packages (Prudic, 

1989; Niswonger and Prudic, 2005). The Streamflow Routing 

Packages track base-flow gains and losses along the stream 

length and also limit the amount of water a stream can lose 

to the aquifer by the amount of water captured in upstream 

reaches. The simpler River Package was used to simulate 

streams outside of the area of interest. The river and stream 

geometries also were refined for each inset model. Hydraulic 

properties of streambed and lakebed sediments (leakance) 

were retained from the regional model, whereas grid-specific 

values were adjusted to match the smaller cell size.

Another important change to the construction of the 

demonstration inset models was refinement of the top layer 

of the regional model. The top layer of the regional model 

was split at the estimated elevation of the contact between 

the Jordan Sandstone and the Prairie du Chien Group in all 

three inset models. A georeferenced grid (Michael Cobb, 

University of Wisconsin, written commun., 2006) representing 

an interpolated elevation of this geologic contact was used 

for the St. Croix and Pierce County inset models. No similar 

grid was available for the Polk County inset model; instead, 

the top layer was split into two equal halves, which roughly 

correspond with the location of this contact in the Pierce and 

St. Croix County inset models. 

In addition to changes in model construction, some 

model parameter values were adjusted during the TMR model 

refinement (table 5). As part of the TMR routine, properties of 

the regional model were directly translated for the Wonewoc, 

Eau Claire, and Mount Simon units. Properties of the new 

upper layers were adjusted to improve simulation of local 

heads and base flows. Parameters were adjusted first for the 

St. Croix County inset model because there was relatively 

more available data than for the Pierce and Polk County 

demonstration models. All parameter values from the St. Croix 

County model were used for the Pierce County inset model 

except the value for recharge, which was specified from the 

regional model, and horizontal hydraulic conductivity of 

the uppermost bedrock layer, which was refined by use of 

local water-level and streamflow data. Parameter values in 

the Polk County inset model were assigned directly from the 

Pierce County model. Additional refinements specific to the 

individual demonstration inset models are described below.

Construction and Simulation of the St. Croix 

County Demonstration Inset Model

The purpose of the St. Croix County inset model was to 

demonstrate simulation of groundwater/lake-water interaction 

for Twin Lakes near Roberts. This was done by means of the 

MODFLOW Lake Package (LAK; Merritt and Konikow, 

2000), which computes lake stage on the basis of a hydrologic 

budget that includes surface processes as well as groundwater 

inflow and outflow. In addition to the refinements described 

above, the St. Croix County model grid was further refined 

above the Prairie du Chien–Jordan contact. Use of the Lake 

Package required that the lakes occupy and replace an aquifer, 

thereby removing the aquifer from the model solution at the 

lake location. Because the lakes are not regional features and 

their connection to the groundwater-flow system was unclear, 

it was preferable that the regional Prairie du Chien Group 

remain intact in the model. Thus, a 45-ft-thick sequence of 

local glacial material (based on well-construction-report 

(WCR) data near the village of Roberts) was split from the top 

of the Prairie du Chien layer. Further, water-level data from 

WCRs indicate that the regional water table is in the Prairie 

du Chien Group near Twin Lakes. As a consequence, the local 

glacial aquifer was simulated only in the immediate vicinity of 

Twin Lakes, as guided by topographic ridges. Thus, East and 

West Twin Lakes were simulated together as a groundwater 

seepage lake (no surface inlet or outlet) in a local glacial 

aquifer above the regional water table in the Prairie du Chien 

Group. All streams were simulated at the surface of the Prairie 

du Chien Group (layer 2) to ensure proper connection with the 

regional water table. 

Simulated sources of water to Twin Lakes included 

average annual precipitation (33.14 in/yr from 1993 to 

2002; Kenneth Schreiber, Wisconsin Department of Natural 

Resources, written commun., 2006), augmentation from 

a wastewater-treatment plant (72 acre-feet per year or 

23.5 Mgal/yr; Schreiber, 1995), and computed groundwater 

inflow. Overland flow was assumed to be negligible given 

the lack of surface streams in the area. Water leaves the lakes 

through direct evaporation and leakage into the groundwaterflow system, which was computed by the model. There are no 

surface-water outlets from the lakes.

Hydraulic conductivity, recharge, and direct evaporation 

from the lakes were adjusted in the St. Croix County inset 

model to improve simulation of the stage of Twin Lakes and 

local water levels (table 5). Horizontal and vertical hydraulic 

conductivities for the Mount Simon, Eau Claire, and Wonewoc 

Formations were specified from the regional model. Horizontal hydraulic conductivities for a new layer representing the 

Jordan Formation, St. Lawrence Formation, and Tunnel City 

Group (lower part of the upper bedrock aquifer in the regional 

model) were estimated from average thicknesses (Mudrey 

and others, 1987) and reasonable conductivities (table 1; 

Ray Wuolo, Barr Engineering Company, written commun., 

May 2007). Horizontal and vertical hydraulic conductivity 
36 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

of the karst Prairie du Chien Group and horizontal hydraulic 

conductivity of the local glacial aquifer were adjusted by 

use of PEST to improve the match to target water levels and 

flows; the Kh:Kv ratio of the local glacial aquifer was specified 

at 100:1. In addition, evaporation from the lake surface, 

recharge, and lakebed leakance were adjusted by use of PEST 

(table 5). Observation data used to constrain parameter values 

included the average combined stage of East and West Twin 

Lakes from May to October 2006 (966.41 ft; Keith Solimar, 

Town of Warren Groundwater Citizens Advisory Committee, 

written commun., October 2006), a synoptic base-flow 

measurement on the Kinnickinnic River at 140th Street near 

Roberts, water-table elevation estimates in WCR wells from 

the regional model (assigned to the Prairie du Chien Group, 

layer 2), water levels from minipiezometers around the lakes 

installed and measured in October 2003 (Kenneth Schreiber, 

Wisconsin Department of Natural Resources, written commun., July 2006), and water levels of local ponds surveyed in 

October 2006 with a differential global positioning system. 

Base-flow and water-level residuals for the local WCR 

targets were improved over those in the regional model 

(average error of WCR targets in the inset model is –9.9 ft; 

average error of the same targets in the regional model is 

–26.8 ft; figs. 20 and 11B). An increase in the simulated 

hydraulic conductivity of the Prairie du Chien Group (table 5) 

lowered simulated water levels compared with the regional 

model (figs. 20 and 11B). An increase in the simulated 

recharge (within the range simulated in karst-prone areas of 

Washington County, MN; Barr Engineering Company and 

Washington County, 2005) improved simulated base flow in 

the Kinnickinnic River at 140th Street (measured, 8.5 ft3/s; 

simulated, 8.2 ft3/s) compared with the regional model 

(simulated, 7.2 ft3/s; table 3B). Although detailed calibration 

was outside the scope of the demonstration modeling, it 

appears that the simulated water table for the demonstration 

model is appreciably improved by the use of more detailed 

hydrostratigraphy and that future models in or near areas with 

banded residuals in the regional model would also likely be 

improved by refined layering. 

Table 5. Parameter values used for the demonstration inset models. 

[ft/d, foot per day; n/a, not applicable or not simulated; in/yr, inch per year; [ft/d]/ft, foot per day per foot; Mgal/yr, million gallons per year]

Hydrogeologic unit St. Croix County model Pierce County model Polk County model

Horizontal hydraulic conductivity (ft/d)

Local sand and gravel aquifer 12 n/a n/a

Regional alluvial aquifer 90a 90a 90a

Prairie du Chien aquifer 207 19 19a

Jordan–St. Lawrence–Tunnel City unit 10a 20a 10a

Wonewoc aquifer 11a 11a 11a

Eau Claire confining unit 2a 2a 2a

Mount Simon aquifer 7a 7a 7a

Faults .09a n/a n/a

Vertical hydraulic conductivity (ft/d)

Local sand and gravel aquifer 0.12b n/a n/a

Regional alluvial aquifer .9a 0.9a 0.9a

Prairie du Chien aquifer .017 .017a .017a

Jordan–St. Lawrence–Tunnel City unit .005a .005a .005a

Wonewoc aquifer .11a .11a .11a

Eau Claire confining unit .00009a .00009a .00009a

Mount Simon aquifer .07a .07a .07a

Faults .09a n/a n/a

Other parameters

Recharge (in/yr) 16.8 8.2a 8.2a

Direct precipitation on lake (in/yr) 33.14a n/a n/a

Direct evaporation from lake (in/yr) 32.12 n/a n/a

Lakebed leakance ([ft/d]/ft) 1.9e–2 n/a n/a

Lake augmentation (Mgal/yr) 23.5a n/a n/a

a

 Indicates the value was specified.

b

 Indicates the ratio Kh:Kv was specified as 100:1. (Kh, horizontal hydraulic conductivity; Kv, vertical hydraulic conductivity).
Application of the Regional Model 37

Results of Simulating Groundwater/

Lake-Water Interaction near Twin Lakes 

near Roberts, St. Croix County

Simulation of groundwater/lake-water 

interaction for Twin Lakes indicates that 

groundwater inflow and outflow represent 

about 5 and 20 percent, respectively, 

of the total lake-water budget (table 6). 

Precipitation and evaporation, representing 

about 85 and 80 percent, respectively, of 

the total lake-water budget, dominate the 

lake budget and are likely to be important 

factors controlling the lake stage. Augmentation from a wastewater-treatment plant 

accounts for the remaining 10 percent of 

water entering the lake. Overland runoff 

was assumed to be negligible and therefore 

was not simulated. Similar to regional 

groundwater-flow directions, groundwater 

in the local glacial aquifer near Twin 

Lakes flows from the northeast to the 

southwest (fig. 21). Likewise, groundwater 

inflow to the lakes is simulated along the 

eastern shoreline of East Twin Lake; flow 

is simulated out of the lakes and into the 

aquifer across the remainder of the lake 

area, but predominantly along the western 

shoreline of West Twin Lake. 

Application of the demonstration 

model of groundwater/lake-water interaction near Twin Lakes near Roberts, WI, 

could be enhanced through a focused field 

investigation of local hydraulic gradients 

and water-budget components for the lake. 

Calibrating the model to these new data 

would decrease uncertainty in simulated 

results. Calibrated results could be used to 

(1) evaluate influences from climatic variability (seasonal to decadal) and augmentation on lake-water 

levels, and (2) estimate individual components of a nutrient 

budget for the lakes when combined with water-quality data.

Figure 20. Simulated water-table elevation and water-level residuals for the St. Croix 

County, Wisconsin, demonstration inset model, layer 2.

Table 6. Simulated mass-balance components for Twin Lakes, St. Croix County, Wisconsin.

[≈, approximately. Percentages have been rounded to indicate level of confidence]

Type of source or sink Inflow to Twin Lakes 

(percent of total)

Outflow from 

Twin Lakes

(percent of total)

Direct precipitation on the lakes ≈85 0

Direct evaporation from the lakes 0 ≈80

Surface-water runoff or streamflow 0 0

Augmentation (effluent from a wastewater-treatment plant) ≈10 0

Groundwater flow ≈5 ≈20

92°40'

92°15'

44°55'

45°5'

EXPLANATION

Simulated water-level residuals

Greater than 50 feet too high

20 to 50 feet too high

19 feet too high to 19 feet too low

20 to 50 feet too low

Greater than 50 feet too low

Simulated water-level contour

(above NAVD 88), interval 50 feet

Streams

Cities and villages

1050

1000

900

900

0 3 6 MILES

0 3 6 KILOMETERS
38 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

Construction and Simulation of the Pierce County 

Demonstration Inset Model

The purpose of the Pierce County inset model was to 

demonstrate the delineation of areas contributing groundwater 

to streams in western Pierce County by means of a groundwater-flow model. The model grid was refined as described in 

the “Telescopic Mesh Refinement” section. River geometries 

from the regional model were refined, and the Kinnickinnic 

and Big Rivers were simulated by use of a Streamflow 

Routing Package (Niswonger and Prudic, 2005). Hydraulic 

conductivities for the Pierce County inset model were derived 

from the regional model and the St. Croix County inset model 

(table 5), with two exceptions (1) the local glacial aquifer 

Figure 21. Simulated groundwater/lake-water interaction near Twin Lakes near the village of Roberts, Wisconsin, from the 

St. Croix County demonstration model, layer 1. Topographic map background shown for reference.

EXPLANATION

Groundwater inflow

Moderate lake-water outflow

Strong lake-water outflow

Simulated water-level contour

for layer 1 (above NAVD 88), interval 10 feet 

Outline of Twin Lakes

Roads

Village of Roberts

Inactive or dewatered cell in layer 1

0 .5 1 MILE

0 .5 1 KILOMETER

Base map compiled from digital data sources: 

U.S. Geological Survey, 1:24,000, 

Roberts quadrangle, 1974

980

970

990

960

980

92 ̊36' 92 ̊32'

45 ̊57'

45 ̊59'

980
Application of the Regional Model 39

used to encompass Twin Lakes was not simulated because 

it represented a local perched aquifer of limited extent, 

and (2) horizontal hydraulic conductivity for the Prairie du 

Chien Group was adjusted with PEST, using local WCR and 

base-flow data along the Kinnickinnic River. Recharge was 

specified at the rate calibrated for the regional model. 

Areas contributing recharge to streams were estimated by 

tracing mathematical particles of water from the water table to 

a discharge location (stream or well) by means of the USGS 

code MODPATH (Pollock, 1994). All particles were set to 

discharge to weak sinks (particles are considered captured as 

soon as they enter a cell containing a sink such as a stream). 

The tracking procedure was used to identify the starting 

location of all particles that ultimately discharged to individual 

stream segments.

Results of Simulating Sources of Groundwater to 

Streams in Western Pierce County

Areas simulated as contributing recharge to 

streams (fig. 22) locally surround individual streams 

and extend upgradient from the stream toward local 

and regional groundwater divides. The contributing 

area for the Big River is entirely within the local 

demonstration area; contributing areas for all other 

simulated streams extend beyond the inset-model 

domain. The contributing area for the Big River may 

be affected by dry-cell artifacts near its confluence 

with the Mississippi River, yet it shows a narrowing 

pattern near the mouth of the river that is similar to 

the contributing area for the Kinnickinnic River at the 

confluence with the St. Croix River. 

Contributing areas illustrate the area over 

which recharge to the water table sustains base flow 

in the receiving stream. The area is proportional to 

the amount of simulated groundwater discharge to 

the stream given uniform areal recharge over the 

model domain; that is, stream reaches that discharge 

large quantities of base flow have large contributing 

areas; stream reaches with little base flow have small 

contributing areas. In addition, the water level of 

the St. Croix and Mississippi Rivers are the lowest 

levels in the area, so these regionally significant rivers 

capture all groundwater that is not captured upgradient by tributary streams, such as the Kinnickinnic and 

Big Rivers. 

Finally, the groundwater-contributing areas can 

be compared with surface watersheds (fig. 22). The 

groundwater-contributing areas for the regional-scale 

Kinnickinnic and Trimbelle Rivers are of similar 

size and shape as their surface watersheds within the 

Pierce County demonstration model domain, but they 

do not necessarily coincide locally. For the Big River, 

the groundwater-contributing area is substantially 

smaller than its surface watershed because the river 

is ephemeral throughout much of the headwater 

area; that is, ephemeral streams flow only during flood events 

caused by surface-water runoff. Precipitation that infiltrates 

and recharges the water table in areas with ephemeral streams 

will flow beneath the ephemeral stream channel and discharge 

downstream to perennial segments of the Big River or 

discharge to the Mississippi River. It is also important to note 

that surface watershed boundaries are determined from static 

topographic features. Groundwater-contributing areas, on 

the other hand, are bound by hydraulic divides that can vary 

seasonally or shift systematically with the introduction of a 

hydrologic stress, such as well pumping.

Application of the Pierce County demonstration model 

could be enhanced by calibrating to measurements of base 

flow along the Big River. Such measurements would decrease 

Figure 22. Simulated areas contributing groundwater recharge to rivers in 

western Pierce County, Wisconsin.

850

900

950

800

680

EXPLANATION

the Kinnickinnic River

the Big River

the Trimbelle River

the St. Croix and

Mississippi Rivers

Simulated water-level contour

(above NAVD 88), interval 10 feet 

Dewatered cells in layer 1

Streams

Kinnickinnic River Watershed

Big River Watershed

Trimbelle River Watershed

Area contributing groundwater recharge to :

44°42'

44°52'

92°45' 92°35'

0 3 6 MILES

0 3 6 KILOMETERS

ST. CROIX COUNTY

PIERCE COUNTY

K i n n i c k i n n i c R i v e r

Trimbelle River

B i g

R i v e r

800
40 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

uncertainty pertaining to the river’s contributing area, which 

is proportional to the local distribution of recharge rates. 

The model could also be used to evaluate contributing areas 

to wells. Simulated groundwater traveltimes to wells and 

streams would benefit from local field investigations of aquifer 

and confining unit hydraulic properties, including flow rates 

through fractures and conduits over a range of scales. 

Construction and Simulation of the Polk County 

Demonstration Inset Model

The purpose of the Polk County inset model was to 

demonstrate the influence of seasonal variability and systematic withdrawals on base flow in a small stream near an area 

experiencing rapid urban development. Seasonal variability 

was simulated on a monthly basis by distributing the annual 

recharge rate from the regional model into 12 monthly stress 

periods. Results from a coupled transient groundwater and 

surface-water model of a similarly sized stream in south 

central Wisconsin (Steuer and Hunt, 2001) were used to 

estimate monthly recharge as a percentage of average annual 

recharge over a 5-year simulation period (1994 to 1998). 

These monthly percentages were multiplied by the calibrated 

recharge rate for the regional model to produce 1 year of 

monthly recharge estimates for the Polk County inset model. 

The monthly recharge estimates were repeated 10 times to 

produce a dynamic cyclic simulation of a hypothetical 10-year 

period. Similar to the other county inset models, all stream 

geometries from the regional model were refined, and Osceola 

Creek was simulated by use of a Streamflow Routing Package 

(Prudic, 1989). Hydraulic conductivities for the Polk County 

inset model were derived, without modification, 

from the Pierce County 

inset model (table 5) 

because no local base-flow 

data were available. 

An initial steady-state 

simulation was done with 

a version of the demonstration model that allowed 

cells in the model to 

convert between confined 

and unconfined conditions 

and potentially dewater. 

To facilitate convergence 

of the transient solution, 

dewatered cells from the 

steady-state solution were 

set inactive and all layers 

were specified as confined, 

with the simulated water 

table representing the top 

of layer 1. Specific storage 

(3x10–7) was assigned to 

layers 2 through 5 on the 

basis of work by Feinstein and others (2005) in southeastern 

Wisconsin. This value is within the range of values reported 

by Miller and Delin (1993) for southeastern Minnesota and by 

Young (1992) for the northern Midwest. Specific yield, which 

represents storage properties of unconfined aquifers, was 

used to simulate aquifers in the top layer of the model. Values 

ranging from 10 to 30 percent were used and were based on 

typical values for sedimentary material (Johnson, 1967).

Current and predevelopment pumping conditions were 

also compared for this transient demonstration. Current conditions were simulated by applying the average pumping rates 

used for the regional model to all stress periods. Predevelopment conditions were simulated by removing all withdrawal 

wells from the inset model and the regional model before 

extracting boundary conditions. Thus, a regional predevelopment simulation was the source of boundary conditions for 

the Polk County predevelopment inset model simulation. 

Simulated base flow in Osceola Creek was quantified for 

a downstream reach near State Highway 35 (segment 13, 

reach 8).

Results of Simulating Transient Streamflow in Osceola 

Creek, Polk County

Simulation of seasonal base flow in Osceola Creek is 

shown for five hypothetical years in figure 23. The results 

illustrate how changes in base flow can be influenced by 

seasonal processes, such as recharge, and also by a systematic 

sink to the system, such as a constant rate of well withdrawal; 

that is, the seasonality of simulated base flow is the result of 

simulating recharge as a dynamic cyclic function, whereas 

the difference in base flow between the predevelopment 

scenario and the present conditions simulation is the result 

Figure 23. Simulated base flow in Osceola Creek, Polk County, Wisconsin, for predevelopment and 

present (1994–2004) pumping conditions. Simulated base flow does not include overland runoff, which 

increases annual streamflow variability beyond what is simulated for base flow alone.

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 1 2 3 5

SIMULATED YEARS

SIMULATED BASE FLOW, IN CUBIC FEET PER SECOND

Predevelopment pumping conditions

Current pumping conditions

4
Application of the Regional Model 41

of eliminating wells that withdraw water at a constant rate. 

Although simplifications have been made in the model for 

these seasonal and static functions, natural systems would 

be expected to respond in a similar, albeit somewhat more 

complex, pattern. 

Simulated groundwater-flow patterns near Osceola Creek 

(fig. 24) illustrate that groundwater discharge into Osceola 

Creek is greatest in the headwater area near Osceola Lake. 

Shortly downstream from 248th Street, Osceola Creek begins 

to lose water to the groundwater-flow system, as indicated by 

contour lines that bend in the downstream direction. Increased 

groundwater withdrawal has the potential to decrease water 

levels and potentially increase streamflow leakage out of the 

stream and into the groundwater-flow system near Osceola.

Application of the demonstration model of transient 

groundwater flow near Osceola Creek could be enhanced by 

calibrating to long-term measurements of base flow along 

Osceola Creek. Estimates of local aquifer-storage properties 

and seasonal recharge rates by use of one of the techniques 

described by Scanlon and others (2002) would also improve 

understanding of the system. Calibrating the model against 

these data could reduce uncertainty in simulating the mean 

and variability of base flow in the creek. Projected changes in 

recharge also could be incorporated into the model to evaluate 

potential effects on base flow in the creek. 

Figure 24. Simulated groundwater-flow patterns near Osceola Creek, Polk County, Wisconsin.

!(

!(

!(

!(

!(

!(!(

!(

!(

EXPLANATION

!( Withdrawal wells (all layers)

Simulated water-level contour

(above NAVD 88), interval 10 feet

Inactive cells in layer 1

Streams

Roads

990

950

900

740

92°45'

92°35'

45°15'

45°20'

Osceola Lake

Osceola Creek

248th

street

0 1 2 MILES

0 1 2 KILOMETERS

Base map compiled and modified from digital

data sources: U.S. Geological Survey, 1:100,000

950
42 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

Model Limitations

As is the case with all groundwater-flow models, the 

regional and demonstration inset models are simplifications 

of the physical system and have corresponding limitations 

in model precision and how the models can be used. For 

example, the MODFLOW model discretization (cells) for 

the regional model is 1,000 ft by 1,000 ft. As a result of this 

discretization, the conditions within the cell (groundwater 

level, groundwater flow) are reduced to one average value for 

the entire cell. Therefore, analyses of local and site-specific 

problems would benefit from refinement of the regional 

model in situations for which additional detail is warranted. 

Hydrologic parameter values and aquifer and confining-unit 

geometry in parts of the model area are not well known at 

local scales. For example, aquifer thickness and hydraulic 

conductivity can change vertically at intervals smaller than 

the current model resolution, especially near valley bluffs or 

ridges of crystalline bedrock, such as in west-central Polk 

County. In addition, a modeling artifact (dry cells) affected 

simulated groundwater levels and flows in western and 

northern Polk County. Although simulation of the regional 

flow is representative, modeling local flow near the dry cells 

may require additional refinement to the model.

The model-calibration process focused on long-term 

water-level and base-flow targets to estimate areally averaged 

properties of regional aquifers and confining units in the 

three-county area. Local complexities, such as perched water 

tables and karst aquifers, were not explicitly simulated in 

the regional model. Moreover, although the model simulated 

the upper bedrock aquifer as one layer, the section actually 

contains several layered aquifers and confining units. Thus, 

if simulation of the distribution of groundwater flow among 

individual units in this upper bedrock aquifer is important 

for the modeling objective, layer 1 may need to be divided 

into additional hydrostratigraphic layers, as was done for the 

demonstration models. In addition, water-level and base-flow 

targets are insufficient to estimate groundwater velocities 

and age. Estimation of groundwater-flow velocities was not a 

focus of this study, and future applications of the models for 

such purposes would benefit from field analyses of porosity, 

groundwater age, and traveltimes. Also, little information 

is available on how the two regionally extensive faults 

influence regional and local groundwater flow. These faults 

were simulated with relatively simple changes in hydraulic 

conductivity in cells that are likely about 100 times wider than 

each fault. Where groundwater flow or water-level drawdown 

near these features is an important consideration, additional 

hydraulic information about the faults and more advanced 

methods of simulation may be required. 

The regional model may not perform equally in all 

locations because of local geologic complexities that were not 

incorporated into the model. For example, the regional model 

has limited ability to delineate groundwater-contributing 

areas for headwater streams, which are sensitive to local 

geologic conditions that were not simulated in the regional 

model. This is illustrated in the headwater area of Big River 

in Pierce County, which is simulated as a losing reach in the 

regional model (fig. 16) but is simulated as a gaining reach in 

the Pierce County inset model (fig. 22), in which additional 

geologic layering was simulated. Also, the regional model 

may underestimate the groundwater-contributing areas (and 

associated base flows) for the Kinnickinnic and Rush Rivers 

because the simulated shallow groundwater divide in central 

St. Croix County (fig. 11A) is west of the divide mapped by 

Lippelt (1990b). Moreover, the karst nature of the Prairie du 

Chien Group further complicates interpretation of simulated 

results associated with local flow paths, traveltimes, and 

contaminant transport (Tipping and others, 2006; Cobb, 2007) 

in the upper bedrock aquifer. 

Lastly, the three county inset models were designed for 

demonstration purposes. Although the model construction 

and parameter values were refined to improve the match to 

measured water levels and streamflows, the demonstration 

models were not rigorously tested. Therefore, results from 

these models are provided for illustration purposes only. 

Additional refinement, particularly in response to additional 

data collection, would be needed if simulated results from the 

demonstration models were to be used for informing management decisions.

Suggestions for Future Investigations

The regional and demonstration groundwater-flow 

models could be enhanced with additional hydrologic and 

geologic investigations, data collection and interpretation, 

and the use of additional MODFLOW options and packages. 

As new data become available, the models could be updated 

and recalibrated. The following is a list of investigative tasks, 

data-collection needs, and MODFLOW options that could 

increase the utility of the groundwater-flow models.

1. Within Pierce, Polk, and St. Croix Counties, there are only 

two currently operating observation wells (nonpumping 

wells) in which water levels are monitored. Three of the 

five long-term observation wells in the counties that were 

used to calibrate the regional model (table 3A) are no 

longer in operation. Moreover, the two operating observation wells monitor only the sand and gravel aquifer and do 

not provide information on the deeper flow system or flow 

between the shallow and deep systems. Monitoring of 

water levels, especially with nested wells in which two or 

more wells are open to only one hydrostratigraphic unit, 

would provide insight and valuable calibration points for 

future refinement of the model. Nested monitoring wells 

in the lower bedrock aquifers would aid in understanding 

flow across confining units, thereby improving understanding of how water levels in deep aquifers respond to 

well pumping and associated drawdown.
Suggestions for Future Investigations 43

2. The hydraulic relations between the St. Croix, Mississippi, and Chippewa Rivers and the groundwater system 

are not fully understood. Specifically, the extent of 

“windows” in the shale-rich Eau Claire Formation below 

the rivers is approximated in the regional model by 

interpolation of stratigraphic contacts in well logs and 

geologic mapping in adjacent Minnesota counties. Additional geologic and(or) geophysical mapping within the 

St. Croix, Mississippi, and Chippewa River Valleys could 

improve understanding of groundwater/surface-water 

interaction near these important regional water bodies 

and could improve understanding of groundwater-flow 

patterns and drawdown in the deep aquifers.

3. The hydraulic effects of faulting are not fully understood 

in the three counties. For example, in the present simulation, faults are assumed to enhance vertical permeability and diminish horizontal permeability relative to 

the hydrostratigraphic unit the fault intersects. Although 

hydraulic properties of the faults had only moderate sensitivity (fig. 15) for the regional model calibration, faults 

may have substantial influence on local flow patterns 

and drawdown. Local hydraulic studies of flow through 

areas with faulting (for example, by use of nested wells, 

pumping tests, tracers, or geologic core samples) would 

help to evaluate the degree to which faults influence local 

groundwater flow. 

4. Flow through local karst aquifers, particularly in central 

St. Croix and Pierce Counties, is not well simulated in 

the regional model. Karst aquifers in this study have 

been lumped with porous sedimentary aquifers, and flow 

through karst aquifers has been approximated by use of 

porous-media assumptions. Work by Runkel and others 

(2003), LePain and others (2005), Tipping and others 

(2006), and Cobb (2007) provides a basis for advancing the understanding of local groundwater flow in karst 

aquifers in the counties, and these authors’ publications 

include suggestions for better characterizing these poorly 

understood areas. 

5. Springs in the river valleys are not simulated explicitly because of the regional nature of the model and the 

consolidation of the upper bedrock aquifer into one layer. 

Explicit simulation of springs could be added to the 

model in the future, but doing so may require additional 

geologic and hydrologic information. For example, Cobb 

(2007) identified an apparent relation between springs and 

their topographic position relative to the Prairie du Chien 

Group. An improved understanding of the spatial and 

temporal sources of water to springs could be gained by 

additional field investigation and modeling.

6. The distribution and rate of recharge, along with the 

potential to alter recharge rates, are not well understood 

in the three counties. Recharge is an important source 

of water to aquifers that supply base flow to streams 

(table 4). An understanding of recharge distribution 

would assist water-resource managers in evaluation of the 

effectiveness of mitigation practices designed to protect or 

enhance recharge in local areas. Tools now exist that are 

designed to estimate patterns and rates of recharge on the 

basis of physical processes and the properties and patterns 

of soils, rocks, precipitation, evaporation, and streamflows 

in an area (S.M. Westenbroek, U.S. Geological Survey, 

written commun., 2008).

7. To increase the utility of the regional model, several features could be added. Climatic variations, such as drought 

and significant recharge events, can be simulated if the 

model is run in transient mode, as demonstrated with the 

Polk County inset model. An optimization code, such 

as the MODFLOW module GWM (Ahlfeld and others, 

2005), which helps select the optimum or “best” pumping 

schemes for a given objective (for example, maintaining 

surface-water flows while increasing groundwater withdrawal), could be coupled to the groundwater-flow model 

to enhance the model as a tool to guide location of future 

wells and developments. An optimization model could 

be used to choose well locations so that future pumping 

would have a minimal adverse effect on streamflow and 

wetlands but still meet increased water needs associated 

with population growth in the three counties.

8. The three inset models were constructed for demonstration purposes only. However, these models could be 

enhanced to address specific questions through the collection or compilation of additional hydrologic data and by 

calibration of the models to address the stated purpose. 

Simulation of groundwater flow through karst aquifers 

in the St. Croix County model would most likely be 

improved with data from investigations described in item 

4 above. Simulation of groundwater/lake-water interaction near Twin Lakes would be improved with data from 

a focused field investigation of local hydraulic gradients 

and water-budget components for the lake. Delineation of 

groundwater-contributing areas in Pierce County could 

be improved with measurements of base flow along Big 

River and from evaluations of how uncertainty in model 

parameters and unsimulated seasonal variability could 

influence the distribution of groundwater divides. Evaluations of development near Osceola and the potential 

effects on base flow in Osceola Creek would likely 

require long-term measurements of base flow in the 

creek. Use of the previously described rechargeestimation and groundwater-optimization tools could 

also improve understanding of the system and aid in 

land-use planning decisions.
44 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

Summary and Conclusions

A regional three-dimensional groundwater-flow model 

and three associated demonstration inset models were 

developed to simulate the groundwater-flow systems in Pierce, 

Polk, and St. Croix Counties, WI. The models were developed 

by the USGS in cooperation with the three county governments. Although all four models were designed to provide 

information about the groundwater-flow system, results from 

the three county inset models are presented for demonstration 

purposes only and are not sufficiently detailed or calibrated to 

be used for decisionmaking purposes. The objectives of the 

regional model of Pierce, Polk, and St. Croix Counties were to 

improve understanding of the groundwater-flow system and to 

develop a tool suitable for evaluating the effects of potential 

water-management programs. Simulations made with the 

regional model reproduce groundwater levels and stream base 

flows representative of recent (1994–2004) conditions and 

illustrate groundwater-flow patterns with simulated water-table 

and potentiometric-surface maps. In addition, the regional 

model was designed as a framework from which more detailed 

inset models could be extracted, as was demonstrated by 

incorporating additional capabilities into the inset model for 

each county. 

Four aquifers were simulated in the regional model, 

represented by (1) a shallow unconsolidated sand and gravel 

aquifer; (2) an upper bedrock aquifer, composed of Cambrian 

and Ordovician sandstone and dolomite; (3) an intermediate 

bedrock aquifer, composed of Cambrian sandstone of the 

Wonewoc Formation; and (4) a lower bedrock aquifer, 

composed of Cambrian sandstone of the Mount Simon 

Formation. A shale layer that is part of the Eau Claire Formation was simulated as a confining unit separating the Wonewoc 

and Mount Simon aquifers. Additional confining units within 

the upper bedrock aquifer were not explicitly simulated in the 

regional model. Precambrian crystalline basement rock forms 

the lower base of the groundwater-flow system. 

The USGS MODFLOW groundwater-flow model code 

was used to develop the regional and demonstration inset 

groundwater-flow models. Boundary conditions for the 

regional MODFLOW model were extracted from a USGSdeveloped analytic-element screening model of regional 

groundwater flow in the St. Croix River Basin and adjacent 

basins. Model input was obtained from previously published 

and unpublished geologic and hydrologic data. Pumping rates 

from municipal and non-municipal high-capacity wells also 

were simulated. 

Model calibration included a comparison between 

modeled and field-measured water levels and modeled 

and field-measured base flows in simulated rivers. After 

calibration, most measured water levels compared favorably 

to model-calculated water levels; the mean absolute difference and root mean squared difference between measured 

and simulated water levels were less than 6 percent of the 

total range in measured water levels. Simulated base flows 

were within 10 percent of estimated base flows at 8 of 10 

streamflow-gaging stations where year-round streamflow 

records were available. As currently calibrated, the model is 

suitable for use as a regional water-management tool. Because 

of the regional focus, however, the model may need to be 

refined for local-scale simulations. 

Mass-balance results from the regional model indicated 

that about 82 percent of groundwater in the three counties 

was from recharge within the counties; 15 percent was from 

surface-water sources, consisting primarily of recirculated 

groundwater seepage in areas with abrupt surface-waterlevel changes, such as near waterfalls, dams, and along the 

downgradient side of reservoirs and lakes; and 4 percent 

was from inflow across the county boundaries. Groundwater 

flow out of the counties was to streams (85 percent), outflow 

across county boundaries (14 percent), and pumping wells 

(1 percent). These results demonstrate that the primary source 

of groundwater withdrawn by pumping wells is water that 

recharged within the counties and would have otherwise 

discharged to local streams and lakes.

Simulated water levels and particle tracking in the 

regional model illustrate groundwater-flow paths through the 

layered aquifer system from recharge areas toward groundwater discharge areas, such as rivers and wells. Groundwater 

discharge to lakes and large rivers (St. Croix and Mississippi) 

is greatest along their shoreline and decreases away from 

shore. Under current conditions, the St. Croix and Mississippi 

Rivers are groundwater discharge locations (gaining reaches) 

and appear to function as “fully penetrating” hydraulic boundaries such that groundwater does not cross between Wisconsin 

and Minnesota beneath them. Being hydraulic boundaries, 

however, they can change in response to water withdrawals. 

The tributary rivers contain both gaining and losing reaches, 

especially near dams and reservoirs. Tributary rivers act as 

“partially penetrating” hydraulic boundaries such that groundwater can flow underneath them. In the conceptualization 

used here, faults have relatively modest influence on regional 

horizontal and vertical flow patterns in all layers, except where 

the Mount Simon aquifer is adjacent to crystalline bedrock and 

hydraulic damming occurs. However, this conceptualization 

is not definitive, and additional study of faults would improve 

the understanding of groundwater flow near them. The model 

also demonstrates the effects of development on groundwater 

in the study area. Water-level declines since predevelopment 

(no withdrawal wells) are most pronounced where pumping 

is greatest and flow between layered aquifers is impeded by 

confining units or faults. The maximum simulated water-level 

decline was about 40 ft in the deep Mount Simon aquifer 

below the city of Hudson, WI.

Three inset models were extracted from the regional 

model to demonstrate the process and additional capabilities of 

the USGS MODFLOW code. Results from these simulations 

were for demonstration purposes only and would need to be 

reevaluated through the addition of data and associated refinements to the models prior to use of any inset-model results to 

support management decisions. Simulation of groundwater/
References 45

lake-water interaction near Twin Lakes near Roberts, in 

St. Croix County, WI, showed that groundwater represents 

approximately 5 to 20 percent of the overall lake-water 

budget. Groundwater contributing areas to streams in western 

Pierce County generally are similar in size to the surfacewater-contributing areas but do not necessarily correspond 

to the same land area. Transient streamflow simulations of 

Osceola Creek in Polk County demonstrate how stream base 

flow can be influenced not only by seasonal precipitation and 

recharge variability but also by systematic changes to the 

system, such as groundwater withdrawal from wells.

For most efficient use, the regional model would require 

periodic updates and improvements as additional field data, 

better assessments of complex hydrologic features (for 

example, faults and karst aquifers), and estimates of future 

hydrologic stressors become available. Additional data collection could improve model characterization of the aquifers, 

springs, lakes, and recharge distribution and magnitude. 

Transient calibration and the use of advanced “packages” of 

the MODFLOW code (for example, the GWM pumping well 

optimization code; Ahlfeld and others, 2005) could improve 

the calibration and utility of the model as a water-resources 

management tool.

Acknowledgments 

Thanks are expressed to David Fodroczi, St. Croix 

County, for arranging multiple meetings at which groundwater-flow concepts and project results were discussed with 

the cooperating agencies and the interested public. Kenneth 

Bradbury, Wisconsin Geological and Natural History Survey, 

provided valuable feedback on the report, as well as on model 

parameters for the regional and inset models. Ray Wuolo, Barr 

Engineering, is thanked for reviewing the report and providing 

advice and information on groundwater flow in Washington 

County, MN. James Boettcher, Wisconsin Department of 

Natural Resources, supplied water-level data used to calibrate 

the model. Maureen Muldoon, University of WisconsinOshkosh, and Peter Schoephoester, Wisconsin Geological and 

Natural History Survey, provided well-construction report 

data that were originally used to produce the Pierce, Polk, and 

St. Croix County water-table maps that are now incorporated 

into the regional model as water-level targets. David LePain, 

formerly with the Wisconsin Geologic and Natural History 

Survey, organized a geologic field trip to the study area 

and provided valuable insight into the geologic properties 

of Pierce and St. Croix Counties. Randall Hunt, Charles 

Dunning, and Daniel Feinstein, all of the USGS Wisconsin 

Water Science Center, provided valuable feedback on model 

design, construction, and calibration throughout the project. 

Cheryl Buchwald, USGS Wisconsin Water Science Center, 

compiled water-use information for high-capacity wells in 

the model area. Keith Solimar, Town of Warren, Groundwater 

Citizens Advisory Committee, provided lake-stage data for 

Twin Lakes that were used in the demonstration model for 

St. Croix County. Kenneth Schreiber, Wisconsin Department 

of Natural Resources, provided data from a hydrologic study 

of Twin Lakes. Michael Cobb, formerly with the University 

of Wisconsin, Geology and Geophysics Department, provided 

a georeferenced grid of the estimated contact elevation 

between the Prairie du Chien Group and Jordan Formation 

that was used in constructing the St. Croix and Pierce County 

demonstration models. 

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Appendixes 49

Appendix 1. Groundwater withdrawals from municipal wells in the regional groundwater-flow 

model.—Continued

[DNR, Wisconsin Department of Natural Resources]

Location in model Average pumping rate, 

1994–2004 Wisconsin 

unique 

well number

DNR 

permit

 number

County

Layer Row Column

Million 

gallons 

per year

Million 

gallons 

per day

1 500 184 18.2 0.050 HW379 01742 Pierce 

1 436 99 30.8 .080 EP394 02336 Pierce 

1,2,3 438 96 41.9 .11 BG679 84046 Pierce 

1 436 95 85.4 .23 BG680 84047 Pierce 

1,2,3 448 176 41.4 .11 AY376 84041 Pierce 

1 448 178 59.1 .16 BG675 84042 Pierce 

3,4 430 265 9.03 .025 KQ651 01743 Pierce 

1,2,3,4 435 263 10.8 .029 BG676 84043 Pierce 

1 432 263 9.27 .025 BG677 84044 Pierce 

1 402 141 83.0 .23 BG681 84048 Pierce 

1 399 140 87.2 .24 BG682 84049 Pierce 

1 404 140 123 .34 BG683 84050 Pierce 

1 399 136 124 .34 BG684 84051 Pierce 

1,2,3 409 242 39.8 .11 BG686 84053 Pierce 

2,3,4 512 220 3.52 .010 BG678 84045 Pierce 

1 257 141 2.54 .007 BG395 82516 Polk 

1,2,3 237 214 12.3 .034 BG371 82442 Polk 

1,2,3 239 216 102 .28 BG372 82443 Polk 

1 186 189 11.6 .032 DV389 00879 Polk 

1 186 191 11.3 .031 BG373 82444 Polk 

1 186 191 14.7 .040 BG374 82445 Polk 

4 184 166 4.10 .011 BG376 82447 Polk 

4 184 166 27.0 .074 BG402 82523 Polk 

1,2,3 232 260 13.7 .038 CO065 00716 Polk 

1 234 263 15.9 .044 BG378 82449 Polk 

1 260 237 187 .51 BG379 82500 Polk 

1 259 237 113 .31 BG381 82502 Polk 

1,2 220 144 20.9 .057 BG383 82504 Polk 

1,2,3,4 221 145 29.2 .080 BG384 82505 Polk 

1 110 191 13.4 .037 BG385 82506 Polk 

1 108 189 10.3 .028 BG386 82507 Polk 

1 109 190 21.9 .060 BG387 82508 Polk 

1 109 190 23.9 .066 BG388 82509 Polk 

1 140 185 35.9 .098 BG389 82510 Polk 

1 139 185 7.28 .020 BG390 82511 Polk 

4 231 127 4.97 .014 BG394 82515 Polk 

2,3 232 132 98.2 .27 BG401 82522 Polk 

4 200 144 46.1 .13 CG779 01775 Polk 

4 196 146 16.8 .046 BG398 82519 Polk 
50 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

Appendix 1. Groundwater withdrawals from municipal wells in the regional groundwater-flow 

model.—Continued

[DNR, Wisconsin Department of Natural Resources]

Location in model Average pumping rate, 

1994–2004 Wisconsin 

unique 

well number

DNR 

permit

 number

County

Layer Row Column

Million 

gallons 

per year

Million 

gallons 

per day

4 201 147 16.1 0.044 BG399 82520 Polk 

4 196 145 18.5 .051 BG400 82521 Polk 

1 158 179 30.5 .084 AV681 00590 Polk 

1 362 206 51.5 .14 BG846 85671 St. Croix

1 367 208 51.1 .14 BG847 85672 St. Croix

1 331 263 35.1 .098 BG870 85696 St. Croix

1 358 191 12.2 .033 BG850 85676 St. Croix

1 360 191 26.5 .073 BG851 85677 St. Croix

1 366 119 27.7 .076 NV213 2915 St. Croix

1 366 119 35.5 .097 RY274 2916 St. Croix

4 360 112 115 .32 BG853 85679 St. Croix

2,3,4 357 110 117 .32 BG854 85680 St. Croix

2,3,4 348 110 56.9 .16 BG855 85681 St. Croix

3,4 364 113 196 .54 BG856 85682 St. Croix

4 346 108 31.3 .086 CG778 85697 St. Croix

1,2,3,4 305 167 11.04 .030 BG857 85683 St. Croix

1,2,3,4 303 166 88.9 .24 BG858 85684 St. Croix

1 306 164 84.9 .23 BG859 85685 St. Croix

1 309 169 197 .54 BG869 85695 St. Croix

1 278 170 28.1 .077 BG864 85690 St. Croix

1 354 161 22.7 .062 BG860 85686 St. Croix

1 355 162 7.01 .019 BG861 85687 St. Croix

1 304 130 30.3 .083 BG863 85689 St. Croix

1,2,3,4 300 133 37.8 .10 ET539 85694 St. Croix

1 369 259 4.90 .013 BG865 85961 St. Croix

1 370 230 31.6 .087 BG867 85963 St. Croix
Appendixes 51

Appendix 2. Groundwater withdrawals from agricultural, commercial, and industrial wells in the regional groundwaterflow model.—Continued

[DNR, Wisconsin Department of Natural Resources]

Location in model Estimated average 

pumping rate, 1978–89 Wisconsin 

unique 

well number

DNR 

permit

number

County Well type

Layer Row Column

Million 

gallons 

per year

Million 

gallons 

per day

1 458 123 11.8 0.032 -- 2183 Pierce Agricultural

1 460 126 11.8 .032 -- 2184 Pierce Agricultural

1 424 108 11.8 .032 BC644 23001 Pierce Agricultural

1 475 183 11.8 .032 BC646 23004 Pierce Agricultural

1 401 115 6.26 .017 BC647 23005 Pierce Agricultural

1 400 150 12.2 .033 BC649 23007 Pierce Agricultural

1,2,3,4 498 169 26.3 .072 BC650 23008 Pierce Agricultural

1 491 152 13.7 .037 -- 23009 Pierce Agricultural

1 429 103 11.8 .032 CG740 23011 Pierce Agricultural

1 407 110 11.8 .032 GV421 23012 Pierce Agricultural

4 512 217 9.40 .026 KQ768 2942 Pierce Industrial

1 494 161 27.1 .074 BE783 57603 Pierce Commercial or industrial

1,2 499 189 27.8 .076 BE790 57610 Pierce Commercial or industrial

1,2,3 407 110 11.8 .032 AK760 794 Pierce Agricultural

1,2,3 440 175 2.57 .077 BP847 -- Pierce Commercial or industrial

1 431 97 0.53 .001 BP849 -- Pierce Commercial or industrial

1 431 95 6.07 .017 KQ771 -- Pierce Commercial or industrial

1,2,3,4 104 189 9.40 .026 MJ324 2075 Polk Commercial or industrial

1 197 259 9.40 .026 -- 2119 Polk Commercial or industrial

1 195 259 9.40 .026 -- 2120 Polk Commercial or industrial

1 195 259 9.40 .026 MJ302 2120 Polk Commercial or industrial

1 272 237 4.90 .013 BC652 23302 Polk Agricultural

1 224 241 11.8 .032 BC653 23303 Polk Agricultural

1,2,3,4 233 139 9.67 .026 BC654 23305 Polk Agricultural

1 269 189 11.8 .032 BC655 23306 Polk Agricultural

1,2,3,4 227 151 6.21 .017 BC656 23307 Polk Agricultural

1,2,3,4 265 148 11.6 .032 BC657 23308 Polk Agricultural

1,2,3,4 225 138 15.1 .041 BC659 23310 Polk Agricultural

1 230 238 11.8 .032 BC660 23313 Polk Agricultural

1 183 233 11.8 .032 BC661 23314 Polk Agricultural

1,2 259 201 21.6 .059 BC662 23315 Polk Agricultural

1 241 211 11.8 .032 -- 23316 Polk Agricultural

1,2,3,4 178 190 11.8 .032 JB268 23317 Polk Agricultural

1,2,3,4 225 171 9.40 .026 RI534 3918 Polk Commercial or industrial

1,2,3,4 224 139 0.40 .001 BE791 58001 Polk Commercial or industrial

1 231 264 100 .27 BE794 58004 Polk Commercial or industrial

1,2,3,4 104 189 9.71 .027 BE795 58005 Polk Commercial or industrial

1 208 226 10.7 .029 BE796 58006 Polk Commercial or industrial
52 Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin

Appendix 2. Groundwater withdrawals from agricultural, commercial, and industrial wells in the regional groundwaterflow model.—Continued

[DNR, Wisconsin Department of Natural Resources]

Location in model Estimated average 

pumping rate, 1978–89 Wisconsin 

unique 

well number

DNR 

permit

number

County Well type

Layer Row Column

Million 

gallons 

per year

Million 

gallons 

per day

1,2,3,4 224 173 56.0 0.153 EL386 738 Polk Commercial or industrial

1,2 329 151 11.8 .032 -- 1036 St. Croix Agricultural

4 295 141 11.8 .032 GL670 1168 St. Croix Agricultural

1 305 157 11.8 .032 -- 1845 St. Croix Agricultural

1 352 129 10.0 .027 NV202 2234 St. Croix Commercial or industrial

1 300 211 11.8 .032 MP038 2550 St. Croix Commercial or industrial

4 331 114 11.8 .032 NB168 2584 St. Croix Agricultural

1 320 162 9.40 .026 RQ528 2713 St. Croix Commercial or industrial

1 324 227 10.0 .027 LB894 2758 St. Croix Commercial or industrial

1 324 227 10.0 .027 LB895 2759 St. Croix Commercial or industrial

1 295 144 1.92 .005 BD453 29201 St. Croix Agricultural

1,2 315 164 15.2 .042 BD454 29202 St. Croix Agricultural

1,2 304 162 5.25 .014 BD455 29203 St. Croix Agricultural

1 333 148 45.0 .12 BD456 29204 St. Croix Agricultural

1 294 170 13.5 .037 BD457 29205 St. Croix Agricultural

1 293 148 11.8 .032 BD458 29206 St. Croix Agricultural

1 294 146 11.8 .032 BD459 29207 St. Croix Agricultural

1 361 115 11.9 .032 BD459 29208 St. Croix Agricultural

1 292 149 4.04 .011 BD461 29209 St. Croix Agricultural

1 395 226 1.45 .004 BD462 29210 St. Croix Agricultural

1 391 133 9.36 .026 -- 29211 St. Croix Agricultural

1 352 259 11.8 .032 -- 29212 St. Croix Agricultural

1,2,3,4 326 132 18.1 .049 BD466 29214 St. Croix Agricultural

1 392 146 6.28 .017 BD468 29216 St. Croix Agricultural

1 384 144 18.2 .050 BD469 29217 St. Croix Agricultural

1 396 120 4.50 .012 BD471 29219 St. Croix Agricultural

1 385 152 0.48 .001 BD472 29220 St. Croix Agricultural

1,2 296 192 13.5 .037 BD477 29226 St. Croix Agricultural

1 352 182 19.5 .053 BD478 29228 St. Croix Agricultural

1,2,3 283 172 25.2 .069 BD479 29230 St. Croix Agricultural

1 322 181 2.80 .008 BD481 29232 St. Croix Agricultural

1,2,3 324 181 10.3 .028 BD482 29233 St. Croix Agricultural

1 363 167 6.13 .017 BD483 29234 St. Croix Agricultural

1,2 321 206 8.45 .023 BD485 29237 St. Croix Agricultural

1,2 324 206 8.20 .022 BD486 29238 St. Croix Agricultural

1 299 183 20.4 .056 BD487 29239 St. Croix Agricultural

1 383 175 5.40 .015 BD488 29240 St. Croix Agricultural

1 349 158 18.0 .049 BD489 29241 St. Croix Agricultural
Appendixes 53

Appendix 2. Groundwater withdrawals from agricultural, commercial, and industrial wells in the regional groundwaterflow model.—Continued

[DNR, Wisconsin Department of Natural Resources]

Location in model Estimated average 

pumping rate, 1978–89 Wisconsin 

unique 

well number

DNR 

permit

number

County Well type

Layer Row Column

Million 

gallons 

per year

Million 

gallons 

per day

1 336 166 8.14 0.022 BD490 29242 St. Croix Agricultural

1,2 284 169 14.2 .039 BD491 29243 St. Croix Agricultural

1 365 205 16.7 .046 BD492 29244 St. Croix Agricultural

1 384 202 16.3 .045 BD493 29245 St. Croix Agricultural

1 374 169 8.43 .023 BD494 29247 St. Croix Agricultural

1 370 163 5.03 .014 BD496 29251 St. Croix Agricultural

1 342 173 10.5 .029 BD499 29259 St. Croix Agricultural

1 350 171 13.3 .036 BD500 29260 St. Croix Agricultural

1 323 143 18.6 .051 BD501 29261 St. Croix Agricultural

1,2,3 323 131 10.0 .027 BD503 29267 St. Croix Agricultural

1 319 173 17.3 .047 BD504 29269 St. Croix Agricultural

1 320 166 3.67 .010 BD505 29270 St. Croix Agricultural

1,2 312 166 26.8 .073 BD507 29272 St. Croix Agricultural

1 315 162 20.9 .057 BD508 29273 St. Croix Agricultural

1,2 312 176 10.3 .028 BD509 29274 St. Croix Agricultural

1 291 163 11.8 .032 BD511 29277 St. Croix Agricultural

1 328 187 5.76 .016 BD512 29278 St. Croix Agricultural

1 344 166 11.8 .032 BD513 29279 St. Croix Agricultural

1 340 165 11.8 .032 BD514 29280 St. Croix Agricultural

1,2 285 174 10.5 .029 BD515 29281 St. Croix Agricultural

1 363 160 9.40 .026 NA628 3307 St. Croix Commercial or industrial

1 346 188 11.8 .032 -- 3764 St. Croix Agricultural

1 379 253 14.0 .038 CG786 381 St. Croix Commercial or industrial

1 325 227 10.0 .027 LE637 3892 St. Croix Commercial or industrial

1 364 209 12.4 .034 BE889 60801 St. Croix Agricultural

1 364 209 93.0 .26 BE890 60802 St. Croix Commercial or industrial

1 378 253 24.4 .067 BE891 60804 St. Croix Commercial or industrial

1 354 159 13.7 .038 BE892 60805 St. Croix Commercial or industrial

1,2,3,4 350 121 1.09 .003 BE893 60806 St. Croix Commercial or industrial

1 352 129 63.0 .17 BE896 60809 St. Croix Commercial or industrial

1 364 113 10.0 .027 -- 60812 St. Croix Commercial or industrial

1,2 280 193 9.40 .026 QW432 67281 St. Croix Commercial or industrial

1 365 161 9.40 .026 -- 67827 St. Croix Commercial or industrial

1 311 164 10.0 .027 -- 85616 St. Croix Commercial or industrial

1 311 165 10.0 .027 -- 85617 St. Croix Commercial or industrial
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Juckem—Simulation of the Groundwater-Flow System in Pierce, Polk, and St. Croix Counties, Wisconsin—Scientific Investigations Report 2009–5056