U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2012–5289

Prepared in cooperation with the Forest County Potawatomi Community 

Simulation of the Shallow Groundwater-Flow System 

in the Forest County Potawatomi Community, 

Forest County, Wisconsin 
Cover. Bug Lake, Forest County, Wisconsin. (Photograph taken by Michael N. Fienen, U.S. Geological Survey.) 
Simulation of the Shallow GroundwaterFlow System in the Forest County 

Potawatomi Community, Forest County, 

Wisconsin 

By Michael N. Fienen, David A. Saad, and Paul F. Juckem 

Prepared in cooperation with the Forest County Potawatomi Community

Scientific Investigations Report 2012–5289 

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: 2013

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Suggested citation:

Fienen, M.N., Saad, D.A., and Juckem, P.F., 2013, Simulation of the shallow groundwater-flow system in the Forest 

County Potawatomi Community, Forest County, Wisconsin: U.S. Geological Survey Scientific Investigations Report 

2012–5289, 24 p.
iii

Contents

Acknowledgments........................................................................................................................................vi

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

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

Purpose and Scope ..............................................................................................................................3

Physical Setting.....................................................................................................................................3

Data Sources.........................................................................................................................................4

Methods...........................................................................................................................................................4

Development of a Conceptual Model of the Shallow Groundwater-Flow System...................5

Description of the Regional GFLOW Model......................................................................................5

Updating Lake Stage Information .............................................................................................6

Partial Recalibration using PEST ..............................................................................................6

Simulation of the Shallow Groundwater-Flow System to Assess Areas Contributing Recharge 

to Existing and Proposed Wells in the Forest County Potawatomi Community.....................7

Assumptions and Limitations.......................................................................................................................9

Summary and Conclusions.........................................................................................................................21

References Cited..........................................................................................................................................21

Figures

1. Map showing location of study area in the Forest County Potawatomi Community, 

Forest County, Wisconsin, and overview of major model elements (modified and 

expanded from Fienen and others, 2011)..................................................................................2

2. Chart showing measured and modeled results for streamflow targets before and 

after partial recalibration of the GFLOW model by using PEST............................................8

3. Map showing simulated areas contributing recharge using the GFLOW model 

for average pumping conditions (North well, 89 gallons per minute; South well, 

70 gallons per minute) at Bug Lake Road, Forest County Potawatomi Community, 

Forest County, Wisconsin..........................................................................................................10

4. Map showing simulated areas contributing recharge using the GFLOW model 

for maximum pumping conditions (North well, 150 gallons per minute; South well, 

80 gallons per minute) at Bug Lake Road, Forest County Potawatomi Community, 

Forest County, Wisconsin..........................................................................................................11

5. Map showing simulated areas contributing recharge using the GFLOW model 

for average pumping conditions (25 gallons per minute from each well) at Lois 

Crow Drive, Forest County Potawatomi Community, Forest County, Wisconsin..............12

6. Map showing simulated areas contributing recharge using the GFLOW model 

for maximum pumping conditions (30 gallons per minute from each well) at Lois 

Crow Drive, Forest County Potawatomi Community, Forest County, Wisconsin..............13
iv

Tables

1. Lake-level measurements (NAVD 88) made during October 25–27, 2010, in the 

Forest County Potawatomi Community, Forest County, Wisconsin......................................3

2. Flow measurements (Q80 ) defined as the flow that is equaled or exceeded 

80 percent of the time, provided by the Forest County Potawatomi Community, 

Forest County, Wisconsin, and used as model-calibration targets......................................3

3. Existing and proposed wells with both average and maximum flow rates, 

provided by the Forest County Potawatomi Community, Forest County, Wisconsin.........9

7. Map showing simulated areas contributing recharge using the GFLOW model 

for average pumping conditions (North well, 11 gallons per minute; South well, 

34 gallons per minute) at Devils Lake Lane, Forest County Potawatomi Community, 

Forest County, Wisconsin..........................................................................................................14

8. Map showing simulated areas contributing recharge using the GFLOW model 

for maximum pumping conditions (North well, 17 gallons per minute; South well, 

40 gallons per minute) at Devils Lake Lane, Forest County Potawatomi Community, 

Forest County, Wisconsin..........................................................................................................15

9. Map showing simulated areas contributing recharge using the GFLOW model for 

average pumping conditions (60 gallons per minute from each well) at the town 

of Blackwell, Forest County Potawatomi Community, Forest County, Wisconsin ...........16

10. Map showing simulated areas contributing recharge using the GFLOW model 

for average pumping conditions (North well, 60 gallons per minute; South well, 

88 gallons per minute) at the town of Carter, Forest County Potawatomi Community, 

Forest County, Wisconsin..........................................................................................................17

11. Map showing simulated areas contributing recharge using the GFLOW model 

for maximum pumping conditions (North well, 105 gallons per minute; South well, 

88 gallons per minute) at the town of Carter, Forest County Potawatomi Community, 

Forest County, Wisconsin..........................................................................................................18

12. Map showing simulated areas contributing recharge using the GFLOW model 

for average pumping conditions with an additional proposed well (additional 

North well, 80 gallons per minute; North well, 60 gallons per minute; South well, 

88 gallons per minute) at the town of Carter, Forest County Potawatomi Community, 

Forest County, Wisconsin..........................................................................................................19

13. Map showing simulated areas contributing recharge using the GFLOW model 

for maximum pumping with an additional proposed well (additional North well, 

100 gallons per minute; North well, 105 gallons per minute; South well, 88 gallons 

per minute) at the town of Carter, Forest County Potawatomi Community, 

Forest County, Wisconsin..........................................................................................................20

1–1. Map showing location of study area near Mole Lake, Forest County, Wisconsin, 

and overview of major model elements (reproduced from Fienen and others, 2011; 

modified from Kelson and others, 2002)..................................................................................24
v

Conversion Factors, Datums, Abbreviated Water-Quality 

Units, and Abbreviations 

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

Area

square mile (mi2

) 259.0 hectare (ha)

Flow rate

cubic foot per day (ft3

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

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

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

Hydraulic conductivity*

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

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

(NAVD 88).

Horizontal coordinate information is referenced to the North American Datum of 1983, or 

NAD 83, and the datum as adjusted via the Wisconsin High Accuracy Reference Network 

(HARN) survey of 1997, or NAD 83 (1997).

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.

Abbreviations used in this report: 

AEM analytic element method

FCPC Forest County Potawatomi Community 

GPS global-positioning system

RTK real-time kinematic

USGS U.S. Geological Survey
vi

Acknowledgments

The authors acknowledge Nate Guldan of the Forest County Potawatomi Community, Natural 

Resources Department for originating and supporting this study. The authors also acknowledge 

Michael Parsen of the Wisconsin State Geological and Natural History Survey and Maksym 

Gusyev of the Geological and Nuclear Sciences (GNS Science), New Zealand, for their technical 

review comments, which improved the technical accuracy and readability of this report. 
Simulation of the Shallow Groundwater-Flow System 

in the Forest County Potawatomi Community, 

Forest County, Wisconsin 

By Michael N. Fienen, David A. Saad, and Paul F. Juckem 

Abstract

The shallow groundwater system in the Forest County 

Potawatomi Comminity, Forest County, Wisconsin, was simulated by expanding and recalibrating a previously calibrated 

regional model. The existing model was updated using newly 

collected water-level measurements, inclusion of surfacewater features beyond the previous near-field boundary, and 

refinements to surface-water features. The updated model 

then was used to calculate the area contributing recharge for 

seven existing and three proposed pumping locations on lands 

of the Forest County Potawatomi Community. The existing 

wells were the subject of a 2004 source-water evaluation in 

which areas contributing recharge were calculated using the 

fixed-radius method. The motivation for the present (2012) 

project was to improve the level of detail of areas contributing 

recharge for the existing wells and to provide similar analysis 

for the proposed wells. 

Delineated 5- and 10-year areas contributing recharge for 

existing and proposed wells extend from the areas of pumping 

to delineate the area at the surface contributing recharge to the 

wells. Steady-state pumping was simulated for two scenarios: 

a base-pumping scenario using pumping rates that reflect what

the Community currently (2012) pumps (or plans to in the case

of proposed wells), and a high-pumping scenario in which the

rate was set to the maximum expected from wells installed in

this area, according to the Forest County Potawatomi Community Natural Resources Department. In general, the 10-year

areas contributing recharge did not intersect surface-water

bodies. The 5- and 10-year areas contributing recharge simulated at the maximum pumping rate at Bug Lake Road may

intersect Bug Lake. At the casino near the Town of Carter, 

Wisconsin, the 10-year areas contributing recharge intersect 

infiltration ponds. At the Devils Lake and Lois Crow Drive 

wells, areas contributing recharge are near cultural features, 

including residences.

Introduction

A new groundwater-pumping regime has been proposed 

by the Forest County Potawatomi Community (FCPC), which 

includes ongoing pumping from seven existing wells and 

additional pumping from three proposed wells at five locations 

in the Forest County Potawatomi Community, Forest County, 

Wisconsin (fig. 1). A study was performed by the U.S. Geological Survey (USGS), in cooperation with the FCPC, to 

delineate the area contributing recharge of each of the wells in 

the proposed pumping regime. The area contributing recharge 

is the two-dimensional projection, or footprint on the land 

surface, of the water entering the aquifer system that will be 

captured by a well. Contributing recharge areas are useful for 

identifying the parts of the aquifer system that supply water 

to wells and have utility for assessing a well’s vulnerability to 

contamination. 

The FCPC existing and proposed wells reside in an area 

largely encompassed by and adjacent to a previously published model area of the regional, shallow groundwater system 

developed using GFLOW (Kelson and others, 2002) (fig. 1). 

To improve understanding of shallow groundwater flow in the 

local FCPC area, additional field data collection, model expansion, and model simulations were completed by the USGS, 

in cooperation with the FCPC. The existing model (Kelson 

and others, 2002) was spatially expanded to encompass the 

FCPC wells. The updated model then was recalibrated using 

new field observations of both lake levels and Q80 streamflows, 

defined as the flow that is equaled or exceeded 80 percent of 

the time, (fig. 1 and tables 1 and 2) and then used to delineate 

areas contributing recharge to wells under an expected pumping regime (average pumping rates) and a maximum expected 

pumping scenario (maximum pumping rates). The recharge 

and hydraulic conductivity values chosen for the updated 

model reflected low-recharge and low-streamflow conditions. 
2 Simulation of the Shallow Groundwater-Flow System in the Forest County Potawatomi Community, Wisconsin

45°45'

89° 88°45' 88°30'

45°30'

45°15'

EXPLANATION

LANGLADE COUNTY

Base map compiled and modified from digital data sources: 

Wisconsin Department of Natural Resources, 1:100,000;

U.S. Census Bureau, 2010 TIGER line file 

>

#

#

#

#*

#

#

"

"

Lake head target

Pumping well location

# Stream target

"

Near-field linesink, routed stream

Near-field linesink, 

routed lake

Near-field linesink, 

nonrouted stream

County boundary

Road

0 5 10 MILES

0 5 10 KILOMETERS

Outline of recharge boundary

Hydraulic conductivity inhomogeneity 

(southeast inhomogeneity)

Hydraulic conductivity inhomogeneity 

(Mole Lake area)

Forest County Potawatomi

Community lands

Near-field lake

ONEIDA COUNTY

OCONTO COUNTY

FOREST COUNTY

FLORENCE COUNTY

MARINETTE COUNTY

Near-field linesink, nonrouted lake

Far-field analytic element

Bug Lake

Road

Lois Crow Drive

Devils Lake Drive

Town of Carter

Blackwell

Lake Lucerne

Trump Lake

Swan Creek

North Branch

Oconto River

Otter Creek

Torpee

Creek

Colburn

Creek

Lake

Metonga

Swamp Creek

Mole Lake

Lake Wabikon

Location of study

WISCONSIN

Figure 1. Map showing location of study area in the Forest County Potawatomi Community, Forest County, 

Wisconsin, and overview of major model elements (modified and expanded from Fienen and others, 2011). 
Introduction 3

Table 1. Lake-level measurements (NAVD 88) made during October 25–27, 2010, in the Forest 

County Potawatomi Community, Forest County, Wisconsin.

Name Northing Easting

Water 

elevation 

(meters)

Water 

elevation 

(feet)

Calibration 

target

Constant head 

model input

Lake Lucerne 5046209.761 355664.195 499.80 1639.76 x

Trump Lake 5037797.132 371077.640 477.20 1565.62 x

Lake Wabikon 5047649.023 360574.630 483.09 1584.95 x

Devils Lake 5045592.429 356850.421 527.88 1731.88 x

Lake Metonga 5046805.969 351932.085 486.94 1597.55 x

Table 2. Flow measurements (Q80 ) defined 

as the flow that is equaled or exceeded 

80 percent of the time, provided by the 

Forest County Potawatomi Community, 

Forest County, Wisconsin, and used as 

model-calibration targets.

Surface-water site Q80 

(cubic feet per day)

Colburn Creek 325,728

North Branch Oconto 925,344

Otter Creek (headwater) 199,584

Swan Creek 45,792

Torpee Creek 304,128

Swamp Creek1 1,709,000

1

Swamp Creek value taken from Kelson and others 

(2002). 

In order to simulate thinning of the aquifer to the southeast, an 

additional hydraulic conductivity inhomogeneity was added 

(fig. 1). Using expanded streamflow data and updated lake 

levels, the recharge rate for the entire model and hydraulic 

conductivity in the newly added inhomogeneity were estimated using the general parameter estimation software package, PEST (Doherty, 2010).

In a simple aquifer system, the ultimate source of water 

to a well is recharge to the water table and the size of a well’s 

area contributing recharge is inversely related to the recharge 

rate and aquifer porosity for a given pumping rate (Reilly 

and Pollock, 1993). In this relatively simple aquifer system, 

low-recharge conditions represent the largest expected areas of 

contribution, thus forming a conservative endmember of well 

vulnerability. This motivates the choice for using hydraulic 

conductivity and recharge values from the “Q80 without Lake 

Lucerne” scenario of Kelson and others (2002) as a starting 

point for values in this model. The hydraulic conductivity 

values in the model area covered by Kelson and others 

(2002) were originally estimated using a large number of data 

points. As a result, the hydraulic conductivity values were 

not updated in the model described in this report. Recharge, 

on the other hand, was updated to inform the water balance 

with current (2012) streamflow data. This was done using the 

Kelson and others (2002) values as a starting point and using 

the Q80 statistic of expanded streamflow data provided by the 

FCPC.

Purpose and Scope

This report describes changes to the regional groundwater 

model of Kelson and others (2002) used for simulation of the 

shallow groundwater-flow system near the FCPC in Forest 

County, Wisconsin, and the surrounding areas. Simulations 

were performed using the model to delineate the areas contributing recharge to seven existing and three proposed pumping 

wells corresponding to two pumping scenarios selected by the 

FCPC. The model and collection of new data focused on the 

shallow groundwater-flow system in the vicinity of several 

existing and proposed wells because of the locations of the 

wells, an emphasis on groundwater and surface-water interactions, and the absence of confining units in the modeled area.

Physical Setting

The study area (fig. 1) is located in southern Forest 

County, Wisconsin. The regional groundwater system in 

the FCPC area is a relatively thin (ranging from about 15 to 

150 feet (ft) in thickness) glacial aquifer overlying comparatively impermeable Precambrian igneous and metamorphic 

rocks (Soller and Packard, 1998). Wells are completed in this 

thin glacial aquifer. Seepage and drainage lakes are common 

in the area and affect the groundwater-flow system. Seepage 

lakes have neither an inlet nor an outlet with water supplied 

by precipitation, runoff, and groundwater. Drainage lakes have 

both an inlet and an outlet and, while they may be in contact 

with the groundwater-flow system, the main source of water is 

stream drainage (Wisconsin Department of Natural Resources, 

1995). The seven existing and three proposed wells are located 

at five locations (fig. 1). Several of the wells are located near 

surface-water features. The regional hydrology is discussed in 

more detail by Kelson and others (2002). In the 1990s, a mine 

was proposed in the study area, which was the motivation for 

the Kelson and others (2002) model.
4 Simulation of the Shallow Groundwater-Flow System in the Forest County Potawatomi Community, Wisconsin

Data Sources

With the few exceptions noted in this report, this study 

is based on the previously published model of Kelson and 

others (2002). Surface-water elevations for Lucerne, Trump, 

Wabikon, Devils, and Metonga Lakes were collected during 

October 25–27, 2010, and the measurements are presented in 

table 1. Lake stage at two locations—Trump Lake and Lake 

Wabikon—were used as calibration targets. The other lake 

stages were entered into the model as boundary conditions 

representing updated conditions. All surface-water level measurements are reported as feet and are referenced to the North 

American Vertical Datum of 1988 (NAVD 88). The locations 

of the existing and proposed groundwater wells were provided 

by the FCPC. The FCPC also provided streamflow measurements that were used, in conjunction with the USGS Swamp 

Creek streamgage, as water balance calibration targets pertaining to both the original and expanded domains (table 2). Table 

2 reports the Q80 flow values, in cubic feet per day, based on 

the FCPC measurements that span 2 years (2010–11). The Q80

flow value for Swamp Creek, however, is based on Kelson and 

others (2002).

Methods

The two-dimensional model used for this study is an 

Analytic Element Method (AEM) groundwater-flow model 

(GFLOW, Haitjema, 1995) that was developed for the region 

by Kelson and others (2002). Hunt (2006) gives a review of 

applications of the analytic element method, and Haitjema 

(1995) discusses the underlying concepts and mathematics of 

the method in detail. A complete description of the AEM is 

beyond the scope of this report, but a brief description follows. 

In AEM, the model domain (model area) is represented 

by a gridless, infinite aquifer, and the solution accuracy is 

independent of the grid size. The AEM and comparisons of 

analytic element to finite-difference numerical-model techniques have been extensively discussed in peer-reviewed 

literature (Haitjema, 1995; Hunt and Krohelski, 1996; Hunt 

and others 1998; Hunt and others, 2003; and Hunt, 2006). 

To construct an analytic element model, features important for controlling groundwater flow (for example, wells and 

surface-water features) are entered as mathematical elements 

or strings of elements. The amount of detail specified for the 

features depends on distance from the area of interest. Each 

element is represented by an analytic solution to the groundwater-flow equation. The effects of these individual solutions 

are added together to form a solution for any location in the 

simulated groundwater-flow system. Heads and flows can 

be computed anywhere in the model domain without nodal 

averaging, because the solution is not confined to a grid. In 

the GFLOW model used here, the analytic elements are two 

dimensional and are used only to simulate steady-state conditions—that is, water levels and streamflows that do not vary 

with time. 

The regional GFLOW model of Kelson and others (2002) 

was originally calibrated with the parameter estimation code, 

UCODE (Poeter and Hill, 1998) and in this current effort was 

partially recalibrated to new data using PEST (Doherty, 2010). 

Details about the original calibration and data are provided 

in Kelson and others (2002). The partial recalibration using 

PEST was motivated both by the expanded spatial domain of 

the original GFLOW model to accommodate the well locations of interest and updated streamflow information that 

reflects potential changes in recharge rate. These issues and 

the decisions guiding the use of PEST for partial recalibration 

are discussed the next section, and details of the recalibration 

are discussed in a subsequent section.

The spatial domain of the current GFLOW model represents an expansion of the original model. In the southeastern 

part of the expanded domain, the thickness of the aquifer 

decreases is evidenced both by field observations of bedrock 

outcrops and by the depth to bedrock map by Trotta and 

Cotter (1973). Moreover, an initial trial-and-error calibration 

produced a better fit to groundwater-head data in that area by 

effectively decreasing transmissivity. Transmissivity is the 

product of hydraulic conductivity and aquifer thickness and, in 

two-dimensional modeling such as in this case, transmissivity 

governs groundwater flow through the aquifer. As a result, by 

enforcing a uniform thickness for the entire model domain, 

adjusting hydraulic conductivity is an effective way to account 

for an anomaly of transmissivity. 

The techniques described in this report take into account 

more of the aquifer dynamics than the fixed-radius method 

used by Watkins (2004). In the fixed-radius method, the equation used is

r Qt

nH = π

(1)

where 

r is the radius, 

Q is the pumping rate, 

t is the time of pumping, 

π is the mathematical constant, 

n is the porosity, and 

H is the aquifer thickness. 

For comparison to the Watkins (2004) results, in the figures showing areas contributing recharge, the radii calculated 

using the fixed-radius method are depicted as yellow circles.
Methods 5

Development of a Conceptual Model of the 

Shallow Groundwater-Flow System

Before simulating the groundwater system using a flowmodeling code, a conceptualization of the hydrologic system 

is essential because it forms the framework for model development and reduces the groundwater system into important component parts that can be implemented in the flow model. This 

reduction is a necessary simplification of the hydrologic system because inclusion of all of the complexities into a model 

is not feasible. Steps in the development of the conceptual 

model include (1) characterization of the aquifer(s), (2) identification of sources and sinks of water, and (3) identification 

and delineation of hydrologic features in the area of interest. 

In the aquifer, groundwater enters through recharge 

and moves from areas of higher groundwater levels to areas 

of lower groundwater levels and generally discharges to 

surface-water features or pumping wells. Accurate locations 

of surface-water features and pumping wells are, therefore, 

critical to simulating the local groundwater-flow system in the 

vicinity of the FCPC.

Description of the Regional GFLOW Model 

The existing regional GFLOW model used in this report 

was developed by Kelson and others (2002) to investigate 

potential impacts to streamflow and groundwater head owing 

to a proposed mining site. The mining site described by Kelson and others (2002) was proposed to target an ore body in 

the area generally indicated by hydraulic conductivity inhomogeneities east of a streamgage on Swamp Creek, as identified 

in figure 1. The 1,400-square-mile (mi2) regional model, outlined in figure 1 by the recharge-area boundary, encompasses 

most of the southern half of Forest County and the area of the 

existing and proposed wells.

Initial model development by Kelson and others (2002) 

included estimating the elevation of the base of the groundwater system, horizontal hydraulic conductivity, and recharge 

rate. The base of the model (1,200 ft above NAVD 88) roughly 

corresponds with the top of the crystalline bedrock in the eastern portion of the model. In a single-layer GFLOW model, it 

is common to maintain constant aquifer base elevation and to 

adjust hydraulic conductivity values during the model calibration. As a result, aquifer base elevation was held constant 

and not varied during model calibration. Horizontal hydraulic 

conductivity was assigned one of three values corresponding 

to different inhomogeneities identified in figure 1. To account 

for aquifer thinning (and therefore lower transmissivity) in the 

expanded model domain, a fourth hydraulic conductivity zone, 

implemented as an inhomogeneity zone, was outlined in the 

southeastern part of the model domain. Hydraulic conductivity values for the newly added inhomogeneity value and the 

regional groundwater-recharge value were considered calibration parameters and were varied during model calibration. 

The parameters were estimated using calibration targets that 

included head values in wells and stream discharge at six locations during “low-flow” periods—referred to as the Q80 flow 

and defined as the flow that is equaled or exceeded 80 percent 

of the time—as discussed by Kelson and others (2002). The 

size of areas contributing recharge to wells is approximately 

inversely related to recharge value: higher values of recharge 

results in smaller areas contributing recharge for a given 

pumping rate (Bhatt, 1993). Therefore, estimating recharge 

corresponding to Q80 flow conditions results in a relatively 

lower estimated value of recharge and correspondingly larger 

areas contributing recharge. This can be considered a conservative estimate of the well’s capture, because its larger size 

provides a larger margin of safety when evaluating potential 

source areas to the well for a given time horizon.

Published values of horizontal hydraulic conductivity 

for the original model included 33 ft/d for the regional glacial 

and sandstone aquifer and 11 and 19 ft/d for two local inhomogeneity inclusions located to the east of Mole Lake (fig. 1). 

Groundwater recharge in the original model was 7.2 in/yr 

(Kelson and others, 2002). All of these values were estimated 

assuming Q80 flow conditions.

In the updated calibration performed for this report, the 

three hydraulic conductivity zones present in the original 

model were held at their previously calibrated values while 

the hydraulic conductivity in the southeastern inhomogeneity zone was estimated as 2.5 ft/d. Recharge, calibrated with 

the expanded streamflow dataset covering the entire model 

domain, was estimated to be 6.4 in/yr. This value is lower than 

the value from Kelson and others (2002) and reflects drier 

conditions, which have been experienced in the area since the 

Kelson and others (2002) study.

The groundwater-flow model consists of far-field and 

near-field elements where the latter reflect the area of interest 

and are characterized by more sophisticated representation 

of surface-water features and focused field data collection. 

The main changes to the original Kelson and others (2002) 

model are (1) refinement of channel geometry for Swamp 

Creek and the shoreline of Rice Lake, performed by Fienen 

and others (2011) and based on USGS topographic 7.5-minute 

quadrangle data; (2) refinement of the surface-water features 

near the northern well locations; and (3) expansion of the 

model domain, incorporating new surface-water features to the 

southeast. On the basis of the conceptual model, the location 

and elevation of far-field surface-water features were included 

from the Kelson and others (2002) model (fig. 1). These 

features are rivers and lakes distant from the well locations 

and are simulated with coarse linesink networks and little 

or no resistance between the surface-water features and the 

groundwater system. Some features that were in the far field 

in the Kelson and others (2002) model were refined and turned 

into near-field elements in the expansion of the model, and 

new far-field elements were added to the model. Because an 

infinite aquifer extent is assumed in the AEM, the purpose of 

simulating the far-field features is to have the model explicitly 
6 Simulation of the Shallow Groundwater-Flow System in the Forest County Potawatomi Community, Wisconsin

simulate the general groundwater flow in the region and to 

buffer the near-field area of interest from boundary effects. 

The near-field area is focused around the FCPC lands and 

encompasses the locations of all the existing and proposed 

wells.

Streambed resistance in the near field was set to 0.3 day 

by Kelson and others (2002). Resistance is defined as the 

streambed-sediment thickness divided by the vertical hydraulic conductivity. For example, the model value of 0.3 day corresponds to a 1 ft sediment thickness and a vertical hydraulic 

conductivity of 3 ft/d. Parameter sensitivity assessments 

(Kelson and others, 2002) demonstrated that the model results 

were not sensitive to changes in streambed resistance when 

varied over reasonable ranges; therefore, the values for all 

streams were fixed in all model runs. The width of each stream 

was assigned according to stream order and field observations 

and ranged from 10 to 100 ft. 

Lakes, except Trump Lake and Lake Wabikon (discussed 

below), were simulated using linesinks with resistance and 

streamflow routing in the near field. Drainage lakes (lakes 

that have a stream outlet) in the near field were linked to the 

stream network by stream elements, based on the methods of 

Hunt and others (1998). Within the perimeter of each lake, the 

recharge rate applied to the lake represents net precipitation 

rather than groundwater recharge; therefore, the water added 

to the lakes differs from that of the regional aquifer. (This can 

be expressed by the equation Rlake = P-Elake; where Rlake is the 

net precipitation recharged inside the lake, P is the annual 

precipitation, and Elake is the evaporation rate from the lake.) 

The net precipitation recharged inside all near-field lakes in 

the model was set equal to 2.3 in/yr. The value of lake linesink 

resistance was set to 0.3 day for all near-field lakes. The width 

assigned to linesinks representing lakes was one-half the 

length of the shortest axis of the lake represented by the linesink. The stage of lakes was assigned either from map values 

or specific measurements made using site-specific measurements discussed in the next section.

The stage for Trump Lake and Lake Wabikon was calculated by GFLOW and used as a calibration target, rather than 

assigning the stage from field measurements. Trump Lake is 

a seepage lake so the only additional information necessary 

to explicitly calculate stage is a stage-volume relation that is 

obtained from bathymetry on USGS 7.5-minute topographic 

maps. As a result, Trump Lake was simulated using explicit 

calculation in GFLOW. Lake Wabikon, on the other hand, is a 

drainage lake. To simulate lake stage in Lake Wabikon, explicitly using the lake package of GFLOW in addition to the readily available stage-volume relation, a stage-discharge relation 

for the outlet stream also would be required. This information, 

however, exceeded the scope of this report, so instead, stage 

was calculated by simulating a piezometer in a high hydraulic 

conductivity (10,000 ft/d greater than the background value of 

33 ft/d) zone representing the lake. This approximate method 

(Hunt and Krohelski, 1996) is not as accurate as the full water 

balance calculated by including stage-discharge information, 

but absent that extra information, it is the most appropriate 

option.

The only pumping simulated in the model during calibration was from the existing wells identified later in figures 3–11. To calculate areas contributing recharge, pumping 

from proposed wells was added to subsequent scenario runs.

Updating Lake Stage Information 

The regional groundwater-flow model was expanded to 

encompass the areas to the east and south of the original model 

by Kelson and others (2002), where the FCPC has existing 

and proposed wells. Surface-water features were added by 

digitizing linesinks based on USGS topographic 7.5-minute 

quadrangle maps. In the areas near wells, previously 

constructed linesinks by Kelson and others (2002) also were 

refined by redigitizing with greater detail based on the same 

quadrangle maps. Updated lake stages were measured during 

October 25–27, 2010, as discussed previously, using a realtime kinematic (RTK) global-positioning system (GPS). This 

RTK-GPS system is capable of providing sub-inch level 

accuracy, both vertically and horizontally, by differentially 

correcting GPS signals recorded at two separate GPS receivers 

(Wolf and Ghilani, 2002). The field survey was horizontally 

referenced to the Universal Transverse Mercator coordinate 

system and the North American Datum of 1983 (NAD 83), 

as well as the 1997 adjustment of NAD 83 via the Wisconsin 

High Accuracy Reference Network; it was vertically 

referenced to NAVD 88. Table 1 reports the measurements 

of lake stage used in the model either as updated stages or, in 

the case of Trump Lake and Lake Wabikon, as recalibration 

targets.

Partial Recalibration using PEST

The general parameter estimation software package, 

PEST (Doherty, 2010) was used to determine optimal values of recharge over the entire model domain and hydraulic 

conductivity in the inhomogeneity representing the thinning of 

the aquifer in the southeastern part of the model. To use PEST, 

calibration targets are selected representing model outputs for 

which field observations are available collocated in time and 

space. For this model, the targets were streamflow in several 

stream reaches and two lake-stage values. PEST uses a mathematical algorithm (Gauss-Levenberg-Marquardt) to adjust 

parameters systematically, resulting in close correspondence 

between model outputs and the corresponding field measurements. This correspondence, for mathematical reasons, is 

calculated as the sum of the squared differences between 

modeled and measured values, each divided by a weight. The 

user controls how closely the algorithm will make this correspondence (called “fit”) based on the weights assigned to the 

targets. Perfect correspondence is neither possible nor desired 

because uncertainty owing both to measurement techniques 
Simulation of the Shallow Groundwater-Flow System 7

and imperfection of the model is always present. For this 

application, the relative quality of the lake-stage targets was 

deemed to be greater than that of the streamflow targets. As a 

result, the weight of the lake-stage targets was set at 1.0 while 

the weights of the streamflow targets were set at the inverse 

of the target value. While more robust weighting practices 

are possible in theory (for example, using quantified standard 

deviation of target values), the uncertainty depends on factors 

(especially model imperfections) that are impossible to truly 

quantify. In this application, the qualitative assignment of 

weights represents expert knowledge about both the model and 

the system, and weights were assigned based on such criteria.

The decision not to recalibrate all parameters in the 

model was motivated by the fact that the previous calibration 

of hydraulic conductivity was made based on many data points 

used by Kelson and others (2002). Hydraulic conductivity is 

an inherent property that, in an aquifer like this one, does not 

change over time. Recharge, on the other hand, can change 

owing to climate variability in addition to inherent material 

properties. Recharge also represents an important factor in 

controlling the water balance of the system. The expansion of 

the model domain, therefore, combined with a more recently 

available dataset, motivated recalibration of recharge. The 

hydraulic conductivity inhomogeneity that was added to 

represent thinning of the aquifer also is outside the domain of 

the Kelson and others (2002) model. The conceptualization 

of thinning of the aquifer was implemented by drawing the 

zonal boundary, but the degree to which the resulting change 

in hydraulic conductivity was implemented needed to be 

informed by the site-specific data, so recalibration was necessary for that parameter.

The modeled lake-stage targets, after partial recalibration, matched the field measurements to within 0.1 ft. The 

streamflow results were not as close, both as expected owing 

to their temporal uncertainty and as enforced through weighting. Figure 2 shows a comparison of measured and modeled 

streamflow results both before and after partial recalibration. 

The largest changes owing to partial recalibration were seen in 

the values with the largest magnitude: namely, North Branch 

of the Oconto River and Swamp Creek. These two targets also 

are expected to have the largest residuals (difference between 

measured and simulated values). The target data for Swamp 

Creek predates the recalibration data for the expanded model 

area. As a result, the residual at Swamp Creek was expected 

to be higher than at other locations. The North Branch of the 

Oconto River has a headwater section in the main hydraulic 

conductivity region of the model but crosses the boundary to 

the southeast hydraulic conductivity inhomogeneity as it progresses downstream. The oversimulation of flow in the North 

Branch of the Oconto River could be mitigated by increasing hydraulic conductivity of either hydraulic conductivity 

inhomogeneity in the model. The fact that the North Branch 

of the Oconto River observation is affected by attributes of 

more than one hydraulic conductivity inhomogeneity results 

in less leverage on either inhomogeneity. The residuals in the 

other observations are already low, so a compromise in the 

North Branch of the Oconto River observation is required and 

a lower residual is not obtainable. 

Simulation of the Shallow 

Groundwater-Flow System to Assess 

Areas Contributing Recharge to 

Existing and Proposed Wells in the 

Forest County Potawatomi Community

Existing and proposed wells at five locations were the 

subject of the analysis in this report. In this section, the simulated areal extent of areas contributing recharge to each of 

the proposed and existing wells are presented and discussed. 

Areas contributing recharge were assessed using the GFLOW 

model adapted to the FCPC area conditions as discussed 

earlier in this report. The areas contributing recharge to the 

wells were delineated by backward particle tracking from 

the well to the area of recharge. Mathematical particles of 

water were placed within the well screen at the bottom of the 

aquifer and traced backwards toward the water table for 5- and 

10-year periods using the updated model. The well screens 

were simulated as fully penetrating the aquifer thickness. By 

use of a porosity of 0.2, which is on the lower end of the range 

and typical of sand (Freeze and Cherry, 1979), estimates of 

the time required for a particle of water in the contributing 

area to reach the well also were calculated. Using the lower 

range porosity value is conservative because lower porosity 

results in higher velocity which, in turn, results in larger areas 

contributing recharge for the specified time scales. Simulated 

areas contributing recharge are shown in figures 3–13 for 5- 

and 10-year travel times.

For each location, except the town of Blackwell, two 

pumping rates were evaluated: an average pumping rate and 

a maximum pumping rate. The average pumping rate corresponds to typical pumping conditions, while the maximum 

rate is an estimate of the highest rate (and thus the largest area 

contributing recharge) that might be anticipated as a sensitivity run. All pumping rates were provided by the FCPC. At 

Blackwell, the wells were not yet installed when the analysis 

was performed, so only the average representative rate was 

provided by the FCPC. Table 3 shows the pumping rates for 

each well and figure 1 shows the locations of the wells.
8 Simulation of the Shallow Groundwater-Flow System in the Forest County Potawatomi Community, Wisconsin

0

0.5x106

1.0x106

1.5x106

2.0x106

Colburn

Creek

Swan

Creek

Otter

Creek

Torpee

Creek

North Branch

Oconto River

Swamp

Creek

0

0.5x106

1.0x106

1.5x106

2.0x10 6

Target name

Streamflow, in cubic feet per day Streamflow, in cubic feet per day

Values before partial recalibration

Values after partial recalibration 

Measured

Modeled

Measured

Modeled

Figure 2. Chart showing measured and modeled results for streamflow targets before (top panel) and after 

(bottom panel) partial recalibration of the GFLOW model by using PEST. 
Simulation of the Shallow Groundwater-Flow System 9

Table 3. Existing and proposed wells with both average and 

maximum flow rates, provided by the Forest County Potawatomi 

Community, Forest County, Wisconsin.

[N/A, not applicable]

Well name

Average 

flow rate 

(gallons 

per minute)

Maximum 

flow rate 

(gallons 

per minute)

Lois Crow Drive 25 30

Devils Lake North 11 17

Devils Lake South 34 40

Bug Lake North 89 150

Bug Lake South 70 80

Carter North 60 105

Carter North Additional 80 100

Carter South 88 88

Blackwell North 60 N/A

Blackwell South 60 N/A

Figures 3 and 4 show the simulated areas contributing recharge for the wells at Bug Lake Road under average 

and maximum pumping rates, respectively. Under average 

conditions, the simulated areas contributing recharge do not 

intersect any surface-water features, although at maximum 

conditions, the simulated area contributing recharge for the 

Bug Lake North well at 10-year travel time intersects Bug 

Lake.

Figures 5 and 6 show the simulated area contributing recharge for the well at Lois Crow Drive under average 

and maximum pumping rates, respectively. Under average 

and maximum conditions, the simulated areas contributing 

recharge do not intersect any surface-water features. However, 

several houses are located within the 5-year area. 

Figures 7 and 8 show the simulated areas contributing 

recharge for the wells at Devils Lake Lane under average 

and maximum pumping rates, respectively. Under average 

and maximum conditions, the simulated areas contributing 

recharge do not intersect any surface-water features. Three 

buildings are within the simulated areas contributing recharge.

Figure 9 shows the simulated areas contributing recharge 

for the North and South wells at the town of Blackwell under 

the average pumping conditions. The simulated 10-year area 

contributing recharge for the Blackwell North well intersects 

Swan Creek.

Figures 10 and 11 show the simulated areas contributing recharge for the wells at the town of Carter under average 

and maximum pumping rates, respectively. Under average 

and maximum conditions, the simulated areas contributing 

recharge intersect the infiltration ponds north of the casino. 

These ponds may be a potential source of water to the Carter 

North and Carter South wells.

Figures 12 and 13 show the simulated areas contributing recharge for the wells at the town of Carter under average 

and maximum pumping rates, respectively, with an additional 

proposed well simulated further north of the Carter North 

well. Under average and maximum conditions, the simulated 

areas contributing recharge from the original Carter North and 

Carter South wells intersect the ponds north of the casino, and 

the simulated area contributing recharge for the additional 

proposed well further north is limited to forested land.

Assumptions and Limitations

Given the relatively high hydraulic conductivity of the 

aquifer, relatively high net annual precipitation, and presence 

of springs and perennial headwater streams, the groundwater 

and surface-water systems are assumed to be in close hydrologic connection in the study area, and elevations of surfacewater features are assumed to be approximate water levels for 

the underlying groundwater system. A single-layer groundwater-flow model was assumed to be appropriate for this application because the groundwater-flow system is relatively thin 

and laterally extensive. Steady-state conditions were assumed 

to be appropriate for this system because hydraulic conductivity is high, and distances between surface-water features are 

relatively small (Kelson and others, 2002). These characteristics help dampen the effects of periodic transient stresses 

applied to the system (Haitjema, 1995). Steady-state assumptions, which ignore groundwater release from storage, can be 

expected to result in an estimate of the higher range of system 

response (such as water-level drawdown owing to pumping) to 

a hydrologic stress.

Limitations of the model result from these assumptions. 

Namely, local three-dimensional flow and transient system 

response expected near wells and surface-water features are 

only approximately represented. In addition, local features 

of the groundwater system (for example, local variations in 

hydraulic conductivity and recharge) are only approximated 

by the parameterization used in the regional model of Kelson 

and others (2002).

The calibration of the model performed by Kelson 

and others (2002) was partially updated to account for the 

expanded areal extent of the present model. The hydraulic 

conductivity values in the original Kelson and others (2002) 

model were retained as they were informed by more data than 

the new measurements in the expanded area. Recharge, however, is expected to change in response to climatic variability, 

so the recharge value was updated. 
10 Simulation of the Shallow Groundwater-Flow System in the Forest County Potawatomi Community, Wisconsin

!!

88°50' 88°49'45" 88°49'30"

45°35'

45°34'45"

45°34'30"

Pumping well

5-year area contributing recharge (average)

10-year area contributing recharge (average)

5-year area contributing recharge of each well, 

calculated by fixed radius method (Watkins, 2004)

EXPLANATION 0

0 600 1,200 FEET

80 160 320 METERS

B u g

L a k e

Bug Lake Road

Base map from digital data sources:

ESRI USA Imagery (2010)

Figure 3. Map showing simulated areas contributing recharge using the GFLOW model for average pumping conditions 

(North well, 89 gallons per minute; South well, 70 gallons per minute) at Bug Lake Road, Forest County Potawatomi 

Community, Forest County, Wisconsin. 
Simulation of the Shallow Groundwater-Flow System 11

!!

88°50' 88°49'45" 88°49'30"

45°35'

45°34'45"

45°34'30"

Pumping well

5-year area contributing recharge (average)

10-year area contributing recharge (average)

5-year area contributing recharge of each well, 

calculated by fixed radius method (Watkins, 2004)

EXPLANATION 0

0 600 1,200 FEET

80 160 320 METERS

Bug Lake Road

B u g

L a k e

Base map from digital data sources:

ESRI USA Imagery (2010)

Figure 4. Map showing simulated areas contributing recharge using the GFLOW model for maximum pumping 

conditions (North well, 150 gallons per minute; South well, 80 gallons per minute) at Bug Lake Road, Forest County 

Potawatomi Community, Forest County, Wisconsin. 
12 Simulation of the Shallow Groundwater-Flow System in the Forest County Potawatomi Community, Wisconsin

!

88°49'30" 88°49'15" 88°49'

0

0 400 800 FEET

50 100 200 METERS

Lois Crow 

Drive

45°33'45"

45°33'30"

Potawatomi Terrace

Pumping well

5-year area contributing recharge (average)

10-year area contributing recharge (average)

5-year area contributing recharge of each well, 

calculated by fixed radius method (Watkins, 2004)

EXPLANATION

Base map from digital data sources:

ESRI USA Imagery (2010)

Figure 5. Map showing simulated areas contributing recharge using the GFLOW model for average pumping conditions 

(25 gallons per minute from each well) at Lois Crow Drive, Forest County Potawatomi Community, Forest County, 

Wisconsin. 
Simulation of the Shallow Groundwater-Flow System 13

!.

Lois Crow 

Drive

Potawatomi Terrace

88°49'30" 88°49'15" 88°49'

0

0 400 800 FEET

50 100 200 METERS

45°33'45"

45°33'30"

Pumping well

5-year area contributing recharge (average)

10-year area contributing recharge (average)

5-year area contributing recharge of each well, 

calculated by fixed radius method (Watkins, 2004)

EXPLANATION

Base map from digital data sources:

ESRI USA Imagery (2010)

Figure 6. Map showing simulated areas contributing recharge using the GFLOW model for maximum pumping 

conditions (30 gallons per minute from each well) at Lois Crow Drive, Forest County Potawatomi Community, Forest 

County, Wisconsin. 
14 Simulation of the Shallow Groundwater-Flow System in the Forest County Potawatomi Community, Wisconsin

!

!

88°50'15" 88°50' 88°49'45"

45°33'30"

45°33'15"

0 50

0 400 800 FEET

100 200 METERS

Potawatomi Terrace

Wa SE Gishek Drive

D

e

vils L

a

k

e L

a

n

e De

vils Lak

e Lan

e

Pumping well

5-year area contributing recharge (average)

10-year area contributing recharge (average)

5-year area contributing recharge of each well, 

calculated by fixed radius method (Watkins, 2004)

EXPLANATION

Base map from digital data sources:

ESRI USA Imagery (2010)

Figure 7. Map showing simulated areas contributing recharge using the GFLOW model for average pumping conditions 

(North well, 11 gallons per minute; South well, 34 gallons per minute) at Devils Lake Lane, Forest County Potawatomi 

Community, Forest County, Wisconsin. 
Simulation of the Shallow Groundwater-Flow System 15

!.

!.

88°50'15" 88°50' 88°49'45"

45°33'30"

45°33'15"

0 50

0 400 800 FEET

100 200 METERS

Pumping well

5-year area contributing recharge (average)

10-year area contributing recharge (average)

5-year area contributing recharge of each well, 

calculated by fixed radius method (Watkins, 2004)

EXPLANATION

Potawatomi Terrace

Wa SE Gishek Drive

D

e

vils L

a

k

e L

a

n

e De

vils Lak

e Lan

e

Base map from digital data sources:

ESRI USA Imagery (2010)

Figure 8. Map showing simulated areas contributing recharge using the GFLOW model for maximum pumping conditions 

(North well, 17 gallons per minute; South well, 40 gallons per minute) at Devils Lake Lane, Forest County Potawatomi 

Community, Forest County, Wisconsin. 
16 Simulation of the Shallow Groundwater-Flow System in the Forest County Potawatomi Community, Wisconsin

!

!

88°37'45" 88°37'30" 88°37'15" 88°37'

45°29'45"

45°29'30"

45°29'15"

0

0 750 1,500 FEET

100 200 400 METERS

Swamp

Creek

Pumping well

5-year area contributing recharge (average)

10-year area contributing recharge (average)

EXPLANATION

Highway H

Highway H

Base map from digital data sources:

ESRI USA Imagery (2010)

Figure 9. Map showing simulated areas contributing recharge using the GFLOW model for average pumping conditions 

(60 gallons per minute from each well) at the town of Blackwell, Forest County Potawatomi Community, Forest County, 

Wisconsin. 
Simulation of the Shallow Groundwater-Flow System 17

0

0 750 1,500 FEET

100 200 400 METERS

CASINO

88°38' 88°37'45" 88°37'30" 88°37'15" 88°37'

45°24'30"

45°24'15"

45°24'

45°23'45"

PONDS !

!

Industrial Park Road

Highway 32

Pumping well

5-year area contributing recharge (average)

10-year area contributing recharge (average)

5-year area contributing recharge of each well, 

calculated by fixed radius method (Watkins, 2004)

EXPLANATION

Base map from digital data sources:

ESRI USA Imagery (2010)

Figure 10. Map showing simulated areas contributing recharge using the GFLOW model for average pumping 

conditions (North well, 60 gallons per minute; South well, 88 gallons per minute) at the town of Carter, Forest County 

Potawatomi Community, Forest County, Wisconsin. 
18 Simulation of the Shallow Groundwater-Flow System in the Forest County Potawatomi Community, Wisconsin

!

!

0

0 750 1,500 FEET

100 200 400 METERS

CASINO

88°38' 88°37'45" 88°37'30" 88°37'15" 88°37'

45°24'30"

45°24'15"

45°24'

45°23'45"

PONDS

Industrial Park Road

Highway 32

Pumping well

5-year area contributing recharge (average)

10-year area contributing recharge (average)

5-year area contributing recharge of each well, 

calculated by fixed radius method (Watkins, 2004)

EXPLANATION

Base map from digital data sources:

ESRI USA Imagery (2010)

Figure 11. Map showing simulated areas contributing recharge using the GFLOW model for maximum pumping 

conditions (North well, 105 gallons per minute; South well, 88 gallons per minute) at the town of Carter, Forest County 

Potawatomi Community, Forest County, Wisconsin. 
Simulation of the Shallow Groundwater-Flow System 19

!

!

!

0

0 750 1,500 FEET

100 200 400 METERS

CASINO

88°38' 88°37'45" 88°37'30" 88°37'15" 88°37'

45°24'30"

45°24'15"

45°24'

PONDS Industrial Park Road

Highway 32

Pumping well

5-year area contributing recharge (average)

10-year area contributing recharge (average)

EXPLANATION

Base map from digital data sources:

ESRI USA Imagery (2010)

Figure 12. Map showing simulated areas contributing recharge using the GFLOW model for average pumping conditions 

with an additional proposed well (additional North well, 80 gallons per minute; North well, 60 gallons per minute; South 

well, 88 gallons per minute) at the town of Carter, Forest County Potawatomi Community, Forest County, Wisconsin. 
20 Simulation of the Shallow Groundwater-Flow System in the Forest County Potawatomi Community, Wisconsin

!

!

!

0

0 750 1,500 FEET

100 200 400 METERS

CASINO

88°38' 88°37'45" 88°37'30" 88°37'15" 88°37'

45°24'30"

45°24'15"

45°24'

PONDS Industrial Park Road

Highway 32

Pumping well

5-year area contributing recharge (average)

10-year area contributing recharge (average)

EXPLANATION

Base map from digital data sources:

ESRI USA Imagery (2010)

Figure 13. Map showing simulated areas contributing recharge using the GFLOW model for maximum pumping with an 

additional proposed well (additional North well, 100 gallons per minute; North well, 105 gallons per minute; South well, 

88 gallons per minute) at the town of Carter, Forest County Potawatomi Community, Forest County, Wisconsin. 
References Cited 21

Summary and Conclusions

The U.S. Geological Survey (USGS), in cooperation with 

the Forest County Potawatomi Community (FCPC) in Forest 

County, Wisconsin, simulated areas contributing recharge for 

seven existing and three proposed wells at five locations in the 

shallow groundwater-flow system. The existing wells were 

the subject of a 2004 source-water evaluation in which areas 

contributing recharge were calculated using the fixed-radius 

method. The motivation for this project was to improve the 

level of detail of areas contributing recharge for the existing 

wells and to provide similar analysis for the proposed wells. 

The calculations of areas contributing recharge for the existing 

and proposed wells provide an estimate of the source of water 

to the wells.

The simulations of the shallow groundwater system in 

the area of interest used the framework of an existing model 

developed in 2002 by Kelson and coworkers. In that work, 

a two-dimensional, steady-state, Analytic Element Method 

(AEM) groundwater-flow model of the regional, shallow 

groundwater-flow system was developed and calibrated using 

the computer code, GFLOW, in conjunction with the UCODE 

parameter estimation program. For this study, the existing 

regional model was updated by including new measurements 

of water elevations for Lake Lucerne, Lake Wabikon, Devils 

Lake, and Lake Metonga (October 2010) and by expanding the 

areal extent of the model. A partial recalibration, focused on 

the newly added region of the model, was performed using the 

general parameter estimation software package, PEST.

The updated model was used to calculate 5- and 10-year 

areas contributing recharge for the 10 wells at average and 

maximum pumping rates. Simulated areas contributing 

recharge for the FCPC wells intersected surface-water features 

at Bug Lake and the town of Blackwell, Wisconsin. Simulated 

areas contributing recharge intersected ponds at the town of 

Carter, Wisconsin, and buildings at Devils Lake and Lois 

Crow Drive. In all other cases, areas contributing recharge 

intersected neither surface-water nor cultural features.

References Cited 

Bhatt, Kailash, 1993, Uncertainty in wellhead protection area 

delineation due to uncertainty in aquifer parameter values: 

Journal of Hydrology, v. 149, no. 4, p. 1–8.

Doherty, John, 2010, PEST—Model—Independent parameter estimation, user manual (5th ed.): Brisbane, Australia, 

Watermark Numerical Computing, 336 p.

Fienen, M.N., Juckem, P.F., and Hunt, R.J., 2011, Simulation 

of the shallow groundwater-flow system near Mole Lake, 

Forest County, Wisconsin: U.S. Geological Survey Scientific Investigations Report 2011–5080, 9 p.

Freeze, R.A., and Cherry, J.A., 1979, Groundwater: Englewood Cliffs, N.J., Prentice-Hall, 604 p.

Haitjema, H.M., 1995, Analytic element modeling of groundwater flow: San Diego, Calif., Academic Press, 394 p.

Hunt, R.J., 2006, Ground water modeling applications using 

the analytic element method: Ground Water, v. 44, no. 1, 

p. 5–15.

Hunt, R.J., Anderson, M.P., and Kelson, V.A., 1998, Improving a complex finite-difference ground water flow model 

through the use of an analytic element screening model: 

Ground Water, v. 36, no. 6, p. 1011–1017.

Hunt, R.J., Haitjema, H.M., Krohelski, J.T., and Feinstein, 

D.T., 2003, Simulating ground water-lake interactions—

Approaches and insights: Ground Water, v. 41, no. 2, 

p. 227–237.

Hunt, R.J., and Krohelski, J.T., 1996, The application of an 

analytic element model to investigate groundwater-lake 

interactions at Pretty Lake, Wisconsin: Journal of Lake and 

Reservoir Management, v. 12, no. 4, p. 487–495.

Kelson, V.A., Hunt, R.J., and Haitjema, H.M., 2002, Improving a regional model using reduced complexity and parameter estimation: Ground Water, v. 40, no. 2, p. 132–143, 

accessed November 12, 2010, at http://onlinelibrary.wiley.

com/doi/10.1111/j.1745-6584.2002.tb02498.x/abstract.

Poeter, E.P., and Hill, M.C., 1998, Documentation of UCODE, 

a computer code for universal inverse modeling: U.S. Geological Survey Water-Resources Investigation Report 

98–4080, 116 p.

Reilly, T.E., and Pollock, D.W., 1993, Factors affecting 

areas contributing recharge to wells in shallow aquifers: 

U.S. Geological Survey Water-Supply Paper 2412, 21 p.

Soller, D.R., and Packard, P.H., 1998, Digital representation of 

a map showing the thickness and character of Quaternary 

sediments in the glaciated United States east of the Rocky 

Mountains: U.S. Geological Survey Data Series 38, 

CD–ROM.

Trotta, L.C., and Cotter, R.D., 1973, Depth to bedrock in Wisconsin: Wisconsin Geological and Natural History Survey 

State-wide map, scale 1:1,000,000. 

U.S. Department of Agriculture, 2006, National Agriculture 

Imagery Program (NAIP) information sheet, accessed October 31, 2008, at http://www.fsa.usda.gov/Internet/FSA_File/

naip_final_2006_updatep.pdf.

Watkins, G., 2004, Source water assessment, Forest County 

Potawatomi Community, Crandon, Wisconsin: Forest 

County Potawatomi Community Technical Report, 7 p. 
22 Simulation of the Shallow Groundwater-Flow System in the Forest County Potawatomi Community, Wisconsin

Wisconsin Department of Natural Resources, 1995, Wisconsin 

Lakes: PUB-FM-800 95REV, 182 p.

Wolf, P.R., and Ghilani, C.D., 2002, Elementary surveying—An introduction to geomatics (10th ed.): Upper Saddle 

River, N.J., Prentice Hall, 900 p. 
Appendix 1.

The model domain from Fienen and others (2011) is reproduced here, for reference, to indicate 

the old model domain, which was the basis for this expanded model. 
24 Simulation of the Shallow Groundwater-Flow System in the Forest County Potawatomi Community, Wisconsin

89°10' 89° 88°50' 88°40' 88°30'

45°40'

45°30'

Location of existing 

and proposed wells

55

32

32

55

US8 US8

Swamp Creek

Sokaogon-Chippewa Community Lands

EXPLANATION

Hydraulic conductivity inhomogeneity

Nearfield analytic elements representing lakes

Outline of recharge boundary

Far-field analytic elements

Near-field line elements representing nonrouted streams

Near-field line elements representing routed streams

Town of Crandon

Approximate location of ore body

Location of study

WISCONSIN

FOREST COUNTY

OCONTO COUNTY LANGLADE COUNTY

ONEIDA COUNTY

Base map compiled and modified from digital data sources: 

U.S. Geological Survey, 1:250,000

45° 20'

0 5 10 MILES

0 5 10 KILOMETERS

County boundary

Road

Rice Lake

Lake Lucerne

Lake

Metonga

Mole Lake

Rolling Stone

Lake

Figure 1–1. Map showing location of study area near Mole Lake, Forest County, Wisconsin, and overview of 

major model elements (reproduced from Fienen and others, 2011; modified from Kelson and others, 2002). 
Publishing support provided by the U.S. Geological Survey 

Science Publishing Network, Columbus Publishing Service 

Center

For more information concerning the research in this report, 

contact the 

Director, Wisconsin Water Science Center

U.S. Geological Survey

8505 Research Way

Middleton, Wisconsin 53562

http://wi.water.usgs.gov/
Fienen and others—Simulation of the Shallow Groundwater-Flow System in the Forest County Potawatomi Community, Wisconsin—Scientific Investigations Report 2012–5289