Prepared in cooperation with the Sokaogon Chippewa Community and Indian Health Service 

Simulation of the Shallow Groundwater-Flow System near 

Mole Lake, Forest County, Wisconsin 

Scientific Investigations Report 2011–5080 

U.S. Department of the Interior

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

Wisconsin 

By Michael N. Fienen, Paul F. Juckem, and Randall J. Hunt 

Prepared in cooperation with the Sokaogon Chippewa Community and 

Indian Health Service 

Scientific Investigations Report 2011–5080

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

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

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Suggested citation:

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.
iii

Acknowledgments

The authors thank Matt Zoch of the Indian Health Services for originating and supporting this 

study and Roman Ferdinand and Dori McGeshick of the Sokaogon Chippewa Community for field 

support. Reviews by David Saad and Christopher Hoard of the U.S. Geological Survey are also 

appreciated and their comments improved this manuscript. 
iv

Contents

Acknowledgments........................................................................................................................................iii

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

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

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

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

Data Sources.........................................................................................................................................3

Methods...........................................................................................................................................................3

Development of a Conceptual Model................................................................................................6

Description of the Regional GFLOW Model .....................................................................................6

Refinement of the Regional Model near Mole Lake ..............................................................7

Application of the Model to Simulate Areas Contributing Recharge to Existing and 

Proposed Wells near Mole Lake....................................................................................................7

Assumptions and Limitations.......................................................................................................................8

Summary and Conclusions...........................................................................................................................8

References Cited............................................................................................................................................9

Figures

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

and overview of major model elements (modified from Kelson and others, 2002)............2

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

assuming the base scenario of three wells pumping 32 gallons per minute......................4

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

simulating the high pumping scenario of three wells pumping 70 gallons per minute.....5
v

Conversion Factors and Abbreviations, Datums, and 

Abbreviated Water-Quality Units

Multiply By To obtain

Length

inch (in) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2

) 259.0 hectare (ha)

Volume

gallon (gal) 3.785 liter (L) 

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)

gallon per day (gal/d) 0.003785 cubic meter per day (m3

/d)

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 Datums of 1983 and 1997 

(NAD 83, 97).

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.

Simulation of the Shallow Groundwater-Flow System near 

Mole Lake, Forest County, Wisconsin

By Michael N. Fienen, Paul F. Juckem, and Randall J. Hunt

Abstract

The shallow groundwater system near Mole Lake, Forest County, Wis. was simulated using a previously calibrated 

regional model. The previous model was updated using 

newly collected water-level measurements and refinements to 

surface-water features. The updated model was then used to 

calculate the area contributing recharge for one existing and 

two proposed pumping locations on lands of the Sokaogon 

Chippewa Community. 

Delineated 1-, 5-, and 10-year areas contributing recharge 

for existing and proposed wells extend from the areas of 

pumping to the northeast of the pumping locations. Steadystate pumping was simulated for two scenarios: a base pumping scenario using pumping rates that reflect what the Tribe 

expects to pump and a high pumping scenario, in which the 

rate was set to the maximum expected from wells installed 

in this area. In the base pumping scenario, pumping rates of 

32 gallons per minute (gal/min; 46,000 gallons per day (gal/d)) 

from the existing well and 30 gal/min (43,000 gal/d) at each 

of the two proposed wells were simulated. The high pumping 

scenario simulated a rate of 70 gal/min (101,000 gal/d) from 

each of the three pumping wells to estimate of the largest areas 

contributing recharge that might be expected given what is 

currently known about the shallow groundwater system. The 

areas contributing recharge for both the base and high pumping scenarios did not intersect any modeled surface-water 

bodies; however, the high pumping scenario had a larger areal 

extent than the base pumping scenario and intersected a septic 

separator. 

Introduction

A new groundwater-pumping regime has been proposed 

by the Sokaogon Chippewa Community (SCC) that includes 

ongoing pumping from an existing well with additional 

pumping from two proposed wells on the Mole Lake Indian 

Reservation near the village of Mole Lake, Forest County, 

Wis. (fig. 1). A study was performed by the U.S. Geological Survey (USGS), in cooperation with the SCC and Indian 

Health Services, to delineate the area contributing recharge to 

each of the three 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 encountered by water entering wells and have 

utility for assessing a well’s vulnerability to contamination. 

The village of Mole Lake and the proposed wells reside 

in an area encompassed by a previously published model of 

the regional shallow groundwater system (Kelson and others, 

2002) (fig. 1). To improve understanding of shallow groundwater flow in the local Mole Lake area, additional field data 

collection, model refinement, and model simulations were 

completed by the USGS, in cooperation with the SCC. The 

locally refined model was then used to evaluate areas contributing recharge to wells under an expected pumping regime 

(base pumping scenario) and a maximum expected pumping 

scenario (high pumping scenario). 

Previously published values of horizontal hydraulic 

conductivity used in the updated model included 32.8 ft/d 

for the regional glacial and sandstone aquifers and 10.8 and 

19.4 ft/d for two local inhomogeneity inclusions located to 

the east of the site area (fig. 1). These values are listed under 

“Q80 without Lake Lucerne” in table 1 of Kelson and others (2002). Groundwater recharge in the calibrated regional 

model was 7.2 in/yr. The recharge and hydraulic conductivity 

values chosen for the updated model reflected low recharge 

and low streamflow conditions. 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 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. 
2 Simulation of the Shallow Groundwater-Flow System near Mole Lake, Forest County, Wisconsin

89°10'0"W 89°0'0"W 88°50'0"W 88°40'0"W 88°30'0"W

0 2.5 5 1.25 MILES

0 3 6 1.5 KILOMETERS

45°40'0"N

45°30'0"N

45°20'0"N

Metonga

Lake

Location of existing

and proposed wells

55

Lake Lucerne

Rice Lake

Rolling Stone

Lake

32

32

55

US8 US8

Mole Lake

Swamp Creek

Sokaogon Chippewa Community Lands

EXPLANATION

Hydraulic conductivity inhomogeneity

Nearfield analytic elements representing lakes

Outline of recharge boundary

Farfield analytic elements

Nearfield line elements representing nonrouted streams

Nearfield line elements representing routed streams

Town of Crandon

Approximate location of ore body

Forest County

Oconto County

Langlade County

Oneida

County

Base map compiled and modified from digital data sources:

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

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

elements (modified from Kelson and others, 2002). 
Methods 3

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 community of 

Mole Lake, Wis. and the surrounding areas. Simulations were 

performed using the model to delineate the areas contributing 

recharge to three pumping wells corresponding to two pumping scenarios selected by the SCC. 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 the model refinement and new data collection focused on 

the shallow groundwater-flow system near Rice Lake, Swamp 

Creek, and the community of Mole Lake.

Physical Setting

The study area (fig. 1) is located in southwestern Forest County, Wis. Seepage and drainage lakes are common in 

the area and influence the groundwater-flow system. The two 

proposed and one existing wells are located near Rice Lake 

(figs. 2 and 3), and Swamp Creek flows near the site on the 

east and south into Rice Lake (figs. 1–3). The regional area 

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.

Data Sources

With the few exceptions noted below, this study is based 

on the previously published model of Kelson and others 

(2002). Surface-water elevations for Rice Lake, Swamp Creek, 

and Mole Lake were specified in the current model using 

data collected on April 30, 2010, and are more representative 

of current conditions. The water elevation in Rice Lake was 

1,532 ft in the original model but was updated to 1,533.01 ft 

in the new measurements, and the elevation in Mole Lake 

was updated from 1,552 to 1,548.33 ft. The updated elevation in Swamp Creek was 1,533.53 ft. All surface-water level 

measurements are reported as feet and are referenced to the 

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

small change in water level in Rice Lake further indicates 

that the calibrated parameters from the original model are 

applicable. Although the change in Mole Lake is greater, the 

influence of this lake is buffered by the location of Swamp 

Creek. The locations of existing and proposed groundwater 

wells, and a nearby septic separator, were determined during 

this field investigation. The septic separator is an installation at 

which solid and liquid wastes are separated in sewage prior to 

ultimate discharge. This differs from a leach field in that waste 

does not typically infiltrate here, although if a leak to the water 

table were to occur, intersection with the area contributing 

recharge would be important to consider in management.

Methods

The two-dimensional model used for this study is an 

analytic element groundwater-flow model (GFLOW, Haitjema, 

1995) that was previously 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 analytic elements is beyond 

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

An infinite aquifer is assumed in analytic element modeling. The problem domain (model area) does not require a grid 

or involve interpolation between cells. 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. Because the solution is not confined to a grid, heads and 

flows can be computed anywhere in the model domain without 

nodal averaging. 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 analytic element method and 

comparisons of analytic element to finite-difference numerical 

model techniques have been discussed by others (Haitjema, 

1995; Hunt and Krohelski, 1996; Hunt and others 1998; Hunt 

and others, 2003; and Hunt, 2006).

The regional GFLOW model of Kelson and others (2002) 

was calibrated with the parameter estimation code UCODE 

(Poeter and Hill, 1998). Details about the calibration and data 

are provided in Kelson and others (2002). 
4 Simulation of the Shallow Groundwater-Flow System near Mole Lake, Forest County, Wisconsin

1545

1540

1535

Location of septic separator

Prop1 4B

Prop2

Rice

Lake

Swamp Creek

55

55

88°57'45"W 88°57'30"W

45°29'50"N

EXPLANATION

45°29'40"N

0 460 920 230 FEET

0 100 200 50 METERS

Base map compiled and modified from digital

data sources: U.S. Department of Agriculture (2006)

Piezometric head contours (numbers indicate feet MSLD)

Sokaogon Chippewa Community Lands

Proposed or existing pumping well 

1-year area contributing recharge

5-year area contributing recharge

10-year area contributing recharge

Bounding streamlines delineating zones of contributing recharge

Figure 2. Map showing simulated areas contributing recharge using the GFLOW model assuming the base scenario of three wells 

pumping 32 gallons per minute. 
Introduction 5

1545

1540

1535

Location of septic separator

Prop1 4B

Prop2

Rice

Lake

Swamp Creek

55

55

88°57'45"W 88°57'30"W

Base map compiled and modified from digital

data sources: U.S. Department of Agriculture (2006)

45°29'50"N

0 460 920 230 FEET

0 100 200 50 METERS

EXPLANATION

45°29'40"N

Piezometric head contours (numbers indicate feet MSLD)

Sokaogon Chippewa Community Lands

Proposed or existing pumping well 

1-year area contributing recharge

5-year area contributing recharge

10-year area contributing recharge

Bounding streamlines delineating zones of contributing recharge

Figure 3. Map showing simulated areas contributing recharge using the GFLOW model simulating the high pumping scenario of three 

wells pumping 70 gallons per minute. 
6 Simulation of the Shallow Groundwater-Flow System near Mole Lake, Forest County, Wisconsin

Development of a Conceptual Model

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. 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. 

The regional groundwater system in the Mole Lake area 

is a relatively thin (ranging from about 15 to 150 ft in thickness) glacial aquifer overlying comparatively impermeable 

Precambrian igneous and metamorphic rocks (Soller and 

Packard, 1998). Groundwater moves from higher to lower 

hydraulic potential (areas of higher groundwater levels to 

areas of lower groundwater levels). As a result, groundwater 

generally discharges to surface-water features or pumping 

wells and recharges in areas distributed areally throughout the 

study area. Accurate locations of surface-water features and 

pumping wells are, therefore, critical to simulating the local 

groundwater-flow system in the vicinity of Mole Lake.

Description of the Regional GFLOW Model 

The regional GFLOW model used in this work is 

described in Kelson and others (2002). The mining site was 

proposed to target the ore body in the area generally indicated 

by the hydraulic conductivity inhomogeneities as identified in 

figure 1. The 900-mi2 regional model, outlined in figure 1 by 

the recharge-area boundary, encompasses both Mole Lake and 

Rice Lake and the area of the existing and proposed wells.

Initial model development included estimating the elevation of the base of the groundwater system, horizontal hydraulic conductivity, and recharge rate. The base of the model 

(1,100 ft above NAVD 88) roughly corresponds with the top 

of the crystalline bedrock near the area of Mole Lake. In twodimensional areal models, where the transmissivity of a single 

layer represents the flow system, the base elevation is correlated with hydraulic conductivity. Therefore, model calibration 

focused on horizontal hydraulic conductivity rather than the 

aquifer base elevation. As a result, aquifer base elevation was 

held constant and not varied during model calibration. In addition to horizontal hydraulic conductivity, which was assigned 

three values corresponding to different areas of inhomogeneities identified in figure 1, groundwater recharge was also 

considered a calibration parameter; therefore, these parameters 

were varied during model calibration. These parameters were 

estimated using calibration targets that included head values 

in wells and stream discharge at 10 locations at “low-flow” 

periods, which are referred to as the Q80 flow and are defined 

as periods when measured flows are above 80 percent of the 

time, 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. Therefore, estimating recharge corresponding to Q80 flow 

conditions results in a 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.

Published values of horizontal hydraulic conductivity 

values used in the model included 32.8 ft/d for the regional 

glacial and sandstone aquifer, and 10.8 and 19.4 ft/d for two 

local inhomogeneity inclusions located to the east of Mole 

Lake (fig. 1). Groundwater recharge in the calibrated regional 

model was 7.2 in/yr (Kelson and others, 2002). These values 

were all estimated assuming Q80 flow conditions.

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 concentration of field data 

collection. The geometry of the closest near-field elements to 

the three wells was refined relative to the Kelson and others 

(2002) model. These refinements include the channel geometry of Swamp Creek and the shoreline of Rice Lake, and 

they were based on USGS topographic 7-minute quadrangle 

data. 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 Mole Lake that 

are simulated with coarse linesink networks and little or no 

resistance between the surface-water features and the groundwater system. Because an infinite aquifer extent is assumed 

in the analytic element method, the purpose of simulating the 

far-field features is to have the model explicitly simulate the 

general groundwater flow in the region and to buffer the nearfield area of interest from boundary effects. The near-field area 

is focused around the eastern shore of Rice Lake and north of 

Swamp Creek where the well field is proposed.

Streambed resistance in the near field was set equal 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 it ranged from 10 to 100 ft. 
Application of the Model to Simulate Areas Contributing Recharge to Existing and Proposed Wells near Mole Lake 7

Lakes 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 days for all near-field lakes. 

The width assigned to linesinks representing lakes was half 

the length of the shortest axis of the lake represented by the 

linesink. The only pumping simulated in the model was from 

the existing well (4B) and proposed wells Prop1 and Prop2, 

identified in figures 2 and 3. 

Refinement of the Regional Model near 

Mole Lake

The regional groundwater-flow model was locally refined 

in an effort to more accurately simulate local-scale groundwater flow near the proposed and existing wells in the Mole Lake 

area. The Swamp Creek channel geometry and the Mole Lake 

and Rice Lake shorelines were refined by adding detail to the 

linesinks based on USGS topographic 7-minute quadrangle 

maps. This refinement includes more detail of their lateral 

shape and updated water levels in Rice Lake and Mole Lake. 

These updated water levels were measured on April 30, 2010, 

as discussed above, using a real-time kinematic (RTK) globalpositioning 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 referenced to the Universal Transverse 

Mercator coordinate system and the North American Datums 

of 1983 and 1997 (horizontal) and NAVD 88 (vertical) datums 

The water level in Rice Lake increased by 1 ft relative to the 

original model, while the water level in Mole Lake decreased 

by 4 ft.

Application of the Model to Simulate 

Areas Contributing Recharge to 

Existing and Proposed Wells near 

Mole Lake

The areal extent of areas contributing recharge to the 

existing community well (4B) and to two proposed wells 

(Prop1 and Prop2) were assessed by use of the locally refined 

model simulations of the Mole Lake area (figs. 2 and 3). 

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 at the bottom of the aquifer and traced backwards to 

the water table using the updated model. By use of a porosity 

of 0.2, which is on the lower end of the range 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 (figs. 2 and 3). Using the lower range porosity 

value is conservative because it results in larger areas contributing recharge.

The simulated 1-, 5-, and 10-year areas contributing 

recharge for the base pumping scenario (fig. 2) (pumping 

rate of 32 gal/min) extend to the north and east of the well 

locations. This is consistent with regional groundwater flow 

emanating from the northeast in this location (Kelson and 

others, 2002). The areas contributing recharge do not overlap 

the location of the septic separator nor do they intersect any 

surface-water features. In the high pumping scenario 

(70 gal/min; fig. 3), similar geometry and orientation of the 

areas contributing recharge are observed. The areas contributing recharge are larger, as expected due to the much higher 

pumping rates simulated, but they still do not intersect surfacewater features. The edges of the areas contributing recharge 

are simulated as very near or encompassing the septic separator on their southern edge at these high simulated pumping 

rates. It should be noted that the simulated areas contributing 

recharge are for scenarios in which all three wells are pumping at a constant rate. Areas contributing recharge presented, 

therefore, represent an average condition over time.
8 Simulation of the Shallow Groundwater-Flow System near Mole Lake, Forest County, Wisconsin

Assumptions and Limitations

Given the relatively high hydraulic conductivity of the 

aquifer, relatively high groundwater-recharge rate, 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 

surface-water features are assumed to be approximate heads 

in the underlying groundwater system. A two-dimensional 

groundwater-flow model was assumed to be appropriate for 

this application because the groundwater-flow system is relatively thin and areally 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 due 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 not repeated because the refinements to 

the model were local, focused on the immediate area near the 

water supply wells. Furthermore, the most important change in 

water level, in Rice Lake, was only 1 ft. The model code has 

been updated since Kelson and others (2002) performed the 

initial calibration. When changes to the code, updated water 

levels (decreased stages in Mole Lake, Rice Lake, and Swamp 

Creek), and refined model elements near the three wells 

are considered, the difference in base flow measured where 

Swamp Creek crosses Highway 55 (the target referred to as 

“Ground water discharge from Swamp Creek @ 55” in table 1 

of Kelson and others (2002)) was 4 percent. Kelson and others 

(2002) reported the target value as 1,709,000 ft3

/d), although 

the updated model reported the target value as 1,780,000 ft3/d. 

This close correspondence indicates the suitability of using 

the updated model without recalibration. Consider, further, 

that the 4-percent discrepancy is simulated base flow that is 

less in the updated model than in the original model; this is a 

conservative finding, in that any error in the shape of the areas 

contributing recharge is larger rather than smaller.

Summary and Conclusions

The Sokaogon Chippewa Community (SCC) in Forest 

County, Wis. has proposed the installation of two new wells 

near Mole Lake, Wis., that will change the groundwaterpumping regime in the shallow groundwater-flow system. The 

calculations of areas contributing recharge for the existing and 

new wells provide an estimate of the source of the water to the 

wells.

The simulations of the shallow groundwater system in the 

area of interest used the framework of a previously published 

model by Kelson and others (2002). In that work, a twodimensional, steady-state, analytic element groundwater-flow 

model of the regional shallow groundwater-flow system was 

developed and calibrated using the computer code GFLOW in 

conjunction with UCODE. The regional model was updated by 

including more detail to the Rice Lake shoreline and Swamp 

Creek channel by using topographic maps and adding updated 

water elevations (measured April 2010) to Rice Lake, Swamp 

Creek, and Mole Lake.

The updated model was used to calculate 1-, 5-, and 

10-year areas contributing recharge for the expected groundwater-pumping rates of approximately 30 gallons per minute 

(gal/min) and at higher pumping rates of 70 gal/min in all 

three wells. Simulated areas contributing recharge for the SCC 

wells under both conditions encompassed an area primarily 

to the north and east of the well locations. The areal extent 

of the high pumping scenario was greater than that simulated 

using the proposed pumping rate base scenario and included a 

potential source of contamination, the septic separator. Neither 

scenario intersected surface-water features in the area of 

contribution.
References Cited 9

References Cited

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. 5–14.

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. 1,011–1,017.

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 Digital Data Series 38, 

CD–ROM.

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.

Wolf, P.R., and Ghilani, C.D., 2002, Elementary surveying—

An introduction to geomatics (10th ed.): Englewood Cliffs, 

N.J., Prentice-Hall, 900 p. 

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 near Mole Lake, Forest County, Wisconsin—Scientific Investigations Report 2011–5080