Simulation of the Regional Ground-Water-Flow System and 

Ground-Water/Surface-Water Interaction in the 

Rock River Basin, Wisconsin

Scientific Investigations Report 2009–5094

Prepared in cooperation with the Rock River Coalition

U.S. Department of the Interior

U.S. Geological Survey
Cover: Photograph of the Rock River. (Photograph taken by Suzanne Wade, Rock River 

Coalition, Jefferson, Wisconsin.)
Simulation of the Regional Ground-Water-Flow 

System and Ground-Water/Surface-Water 

Interaction in the Rock River Basin, Wisconsin

By Paul F. Juckem

Prepared in cooperation with the Rock River Coalition

Scientific Investigations Report 2009–5094

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

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

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Juckem, P.F., 2009, Simulation of the regional ground-water-flow system and ground-water/surface-water interaction 

in the Rock River Basin, Wisconsin: U.S. Geological Survey Scientific Investigations Report 2009-5094, 38 p.
iii

Contents

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

Introduction.....................................................................................................................................................2

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

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

Study Methods ...............................................................................................................................................6

Conceptual Model of the Ground-Water-Flow System .........................................................................10

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

Sources and Sinks of Water .............................................................................................................10

Hydrogeologic Boundaries ...............................................................................................................12

Hydraulic Properties of the Ground-Water-Flow System .....................................................................12

Hydraulic Conductivity.......................................................................................................................12

Recharge..............................................................................................................................................13

Riverbed Resistance...........................................................................................................................13

Ground-Water Withdrawals.......................................................................................................................15

Simulation of the Regional Ground-Water-Flow System.......................................................................15

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

Model Calibration................................................................................................................................20

Sensitivity Analysis ............................................................................................................................22

Evaluation of Simulated Results of the Rock River Basin Model.........................................................25

Simulated Gaining and Losing River Reaches ...............................................................................25

Simulated Ground-Water Basins .....................................................................................................25

Simulation of Relatively Local Ground-Water-Capture Areas for Rivers .................................29

Model Limitations.........................................................................................................................................31

Summary........................................................................................................................................................31

Acknowledgments.......................................................................................................................................32

References....................................................................................................................................................33

Appendixes ...................................................................................................................................................37

Appendix 1. Public-Supply Wells..................................................................................................37

Appendix 2. Irrigation, Industrial, and Commercial Supply Wells...........................................37

Appendix 3. Public, Irrigation, Industrial, and Commercial Supply Wells in Illinois.............37

Appendix 4. Ground-Water Observation Network Water-Level Targets. ..............................37

Appendix 5. Well Construction Report Water-Level Targets. ..................................................37
iv

Figures

Figure 1. Map showing location of the Rock River Basin in Wisconsin ........................ 3

Figure 2. Map showing land cover in the Rock River Basin ....................................... 4

Figure 3. Map showing surficial sediments in the Rock River Basin ........................... 6

Figure 4. Stratigraphic units and corresponding lithologies in the Rock River Basin ......... 7

Figure 5. Generalized west-to-east geologic section for the Rock River Basin ............... 8

Figure 6. Generalized map showing the extent of the uppermost bedrock units in the

Rock River Basin ........................................................................... 9

Figure 7. Generalized conceptual model of ground-water flow in the Rock River Basin ...... 11

Figure 8. Map showing estimated infiltration rates for soils in the Rock River Basin ......... 14

Figure 9. Map showing ground-water withdrawal from public-supply wells in the

GFLOW model of the Rock River Basin ................................................... 16

Figure 10. Map showing ground-water withdrawal from agricultural, industrial, and

commercial wells in the GFLOW model of the Rock River Basin ..................... 17

Figure 11. Map showing features of the GFLOW model of the Rock River Basin ............... 19

Figure 12. Comparison of measured and simulated water levels for the

GFLOW model of the Rock River Basin ................................................... 22

Figure 13. Map showing water-level residuals for the GFLOW model of the Rock River Basin 23

Figure 14. Map showing base-flow residuals for the GFLOW model of the Rock River Basin 24

Figure 15. Map showing simulated water-table altitude and ground-water flow directions

from the GFLOW model in the Rock River Basin ....................................... 26

Figure 16. Map showing simulated gaining and losing river and lake shorelines in the

Rock River Basin ........................................................................... 27

Figure 17. Map showing simulated ground-water and mapped surface-water

contributing areas for select tributaries to the Rock River ........................... 28

Figure 18. Map showing simulated areas of relatively local ground water captured by

rivers in the Rock River Basin ............................................................ 30

Tables

Table 1. Physical and demographic characteristics for select tributary basins in the

Rock River Basin ........................................................................... 5

Table 2. Previously reported horizontal hydraulic conductivities (feet per day) and

calibrated values from the regional model ............................................. 13

Table 3a. Calibration results for ground-water level targets and associated weights used

for calibration with the parameter estimation program PEST ........................ 21

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

for calibration with the parameter estimation program PEST ........................ 21

Table 4. Hydrologic characteristics and simulated results for selected tributary river

basins in the Rock River Basin ............................................................ 29
v

Conversion Factors and Datums

Conversion Factors

Inch/Pound to SI

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) 2.590 square kilometer (km2) 

Flow rate

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

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

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

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

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

million gallons per year (Mgal/yr) 3,745 cubic meter per year (m3/yr)

inch per hour (in/h) 25.4 millimeter per hour (mm/h)

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)

Transmissivity**

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

Horizontal flux

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

*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.

**Transmissivity: The standard unit for transmissivity is cubic foot per day per square foot times 

foot of aquifer thickness [(ft3/d)/ft2]*ft. In this report, the mathematically reduced form, foot 

squared per day (ft2/d), is used for convenience.

Datums

Vertical coordinate information is referenced to the National Geodetic Vertical Datum of 1929 

(NGVD 29).

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

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

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Abstract

A regional, two-dimensional, areal ground-water-flow 

model was developed to simulate the ground-water-flow 

system and ground-water/surface-water interaction in the Rock 

River Basin. The model was developed by the U.S. Geological 

Survey (USGS), in cooperation with the Rock River Coalition. 

The objectives of the regional model were to improve 

understanding of the ground-water-flow system and to develop 

a tool suitable for evaluating the effects of potential regional 

water-management programs. The computer code GFLOW 

was used because of the ease with which the model can 

simulate ground-water/surface-water interactions, provide a 

framework for simulating regional ground-water-flow systems, 

and be refined in a stepwise fashion to incorporate new data 

and simulate ground-water-flow patterns at multiple scales. 

The ground-water-flow model described in this report 

simulates the major hydrogeologic features of the modeled 

area, including bedrock and surficial aquifers, ground-water/

surface-water interactions, and ground-water withdrawals 

from high-capacity wells. The steady-state model treats the 

ground-water-flow system as a single layer with hydraulic 

conductivity and base elevation zones that reflect the 

distribution of lithologic groups above the Precambrian 

bedrock and a regionally significant confining unit, the 

Maquoketa Formation. In the eastern part of the Basin where 

the shale-rich Maquoketa Formation is present, deep groundwater flow in the sandstone aquifer below the Maquoketa 

Formation was not simulated directly, but flow into this 

aquifer was incorporated into the GFLOW model from 

previous work in southeastern Wisconsin. Recharge was 

constrained primarily by stream base-flow estimates and was 

applied uniformly within zones guided by regional infiltration 

estimates for soils. The model includes average ground-water 

withdrawals from 1997 to 2006 for municipal wells and from 

1997 to 2005 for high-capacity irrigation, industrial, and 

commercial wells. In addition, the model routes tributary 

base flow through the river network to the Rock River. The 

parameter-estimation code PEST was linked to the GFLOW 

model to select the combination of parameter values best able 

to match more than 8,000 water-level measurements and baseflow estimates at 9 streamgages.

Results from the calibrated GFLOW model show 

simulated (1) ground-water-flow directions, (2) ground-water/

surface-water interactions, as depicted in a map of gaining and 

losing river and lake sections, (3) ground-water contributing 

areas for selected tributary rivers, and (4) areas of relatively 

local ground water captured by rivers. Ground-water flow 

patterns are controlled primarily by river geometries, with 

most river sections gaining water from the ground-water-flow 

system; losing sections are most common on the downgradient 

shore of lakes and reservoirs or near major pumping centers. 

Ground-water contributing areas to tributary rivers generally 

coincide with surface watersheds; however the locations 

of ground-water divides are controlled by the water table, 

whereas surface-water divides are controlled by surface 

topography. Finally, areas of relatively local ground water 

captured by rivers generally extend upgradient from rivers 

but are modified by the regional flow pattern, such that these 

areas tend to shift toward regional ground-water divides for 

relatively small rivers.

It is important to recognize the limitations of this 

regional-scale model. Heterogeneities in subsurface properties 

and in recharge rates are considered only at a very broad 

scale (miles to tens of miles). No account is taken of vertical 

variations in properties or pumping rates, and no provision is 

made to account for stacked ground-water-flow systems that 

have different flow patterns at different depths. Small-scale 

flow systems (hundreds to thousands of feet) associated with 

minor water bodies are not considered; as a result, the model 

is not currently designed for simulating site-specific problems. 

Despite its limitations, the model serves as a framework for 

understanding the regional pattern of ground-water flow 

and as a starting point for a generation of more targeted and 

detailed ground-water models that would be needed to address 

emerging water-supply and water-quality concerns in the Rock 

River Basin. 

Simulation of the Regional Ground-Water-Flow System 

and Ground-Water/Surface-Water Interaction in the 

Rock River Basin, Wisconsin

By Paul F. Juckem
2 Simulation of the Regional Ground-Water-Flow System and Ground-Water/Surface-Water Interaction, Rock River Basin, Wisconsin

Introduction

The Rock River and its tributaries drain a geologically 

complex landscape containing numerous rivers, lakes, 

and wetlands (fig. 1) in a predominantly agricultural area 

of southeastern Wisconsin (fig. 2). Water quality of the 

Rock River is a concern for Federal, State, county, and 

local resource managers, particularly in regard to high 

concentrations of nutrients (nitrate and phosphate) in ground 

water and surface water. At least one study (Earth Tech, 2000) 

was done to explain phosphorous loading in surface waters in 

the Rock River Basin; however, the hydrologic model used 

for that study did not account for ground-water flow through 

aquifers, and therefore the model was not able to evaluate 

ground-water levels, ground-water-flow patterns or groundwater/surface-water interaction along stream reaches. Several 

countywide ground water investigations have been completed 

in the Rock River Basin, but a comprehensive ground-waterflow study of the basin has been lacking. Prior to the study 

described in this report, little was known about ground-waterflow patterns or ground-water/surface-water interactions in the 

basin. 

The study described in this report was conducted by the 

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

River Coalition. The primary objectives of the study were to 

improve understanding of the hydrogeology of the Rock River 

Basin, evaluate ground-water/surface-water interaction and 

base-flow contribution to the Rock River and its tributaries, 

and estimate patterns of ground-water flow. These objectives 

were achieved by developing a regional framework model, 

using the numerical computer code GFLOW, to simulate 

the ground-water-flow system of the basin. This framework 

model describes the regional characteristics of the groundwater-flow system without including the hydrogeologic detail 

or data density that would be necessary for answering sitespecific questions. A calibrated framework model can be used 

with confidence to simulate a regional ground-water-flow 

system but with less confidence to simulate local-scale flow. 

A framework model is a tool that can be used to improve 

the overall understanding of the hydrology of a region by 

testing alternative conceptual models of the ground-waterflow system. Additionally, a framework model can be used to 

highlight areas where more hydrogeologic or water-quality 

data are needed. Finally, a framework model serves as a 

foundation from which local or site-specific models can be 

developed through refinement; having such as foundation 

benefits local-scale modeling efforts by reducing model 

construction time, reducing data-collection and interpretation 

efforts, and furnishing a simulated connection to the regional 

flow system.

A regional framework model integrates the most 

important components of the shallow and deep parts of the 

ground-water-flow system. In the Rock River Basin, the 

ground-water and surface-water systems are believed to be 

hydraulically well connected and, as a result, the groundwater-flow model is constructed to include many aspects of 

the surface-water network. The simulation of ground-water 

flow and its interaction with the surface-water network is a 

necessary foundation for understanding and protecting the 

basin’s water resources. By improving the understanding of 

the hydrology of the Rock River Basin, this study provides a 

basis for interpreting previously collected water-quality data 

and managing water resources for the future. Another benefit 

of the study is that the sources and amount of base-flow 

contribution to the Rock River from its tributaries are more 

systematically described.

The hydrogeologic foundation that underlies the model 

of the Rock River Basin draws from previous geologic and 

hydrologic studies. The bedrock geology of the basin is 

described in a regional study by Young (1992) and is mapped 

by Mudrey and others (1982), with a digital representation by 

Cannon and others (1997). Other reports present descriptions 

of the soil and unconsolidated deposits of the area (Schwarz 

and Alexander, 1995; Soller and Packard, 1998) and of 

individual counties (Clayton and Attig, 1997; Mickelson and 

Syverson, 1997; Clayton, 2001). The general hydrology of the 

basin is described in a USGS Hydrologic Investigations Atlas 

(Cotter and others, 1969) and a Geologic Society of America 

field trip guide book (Holt and others, 1970). Additional 

hydrogeologic detail can be found in county geology and 

ground-water-resources reports and water-table maps for 

9 of the 10 counties in the basin: Columbia County (Harr 

and others, 1978), Dane County (Cline, 1965; Bradbury and 

others, 1995; Bradbury and others, 1999), Dodge County 

(Devaul and others, 1983), Fond du Lac County (Newport, 

1962; Batten, 2004), Jefferson County (Borman and Trotta, 

1976), Rock County (LeRoux, 1963), Walworth County 

(Borman, 1976; Evans, 2004a), Washington County (Young 

and Batten, 1980; Evans, 2004c), and Waukesha County 

(Gonthier, 1975; Evans, 2004b). A few county- and regionalscale ground-water-flow models cover parts of the basin, 

including Dane County (Krohelski and others, 2000), Rock 

County (Gaffield and others, 2002), and the seven counties of 

the Southeastern Wisconsin Regional Planning Commission 

(Feinstein and others, 2005b).
Introduction 3

Horicon Marsh

Yahara River

Badfish

Creek

Tu r t l e

C r e e k

Koshkonong

Creek C r a w f i s

h

R i v e r

Johnson Creek

Bark

River

East Br

Rock R

R o

c

k

R i v e r

1

2

3

4 5

6

7

8

10

9

Rock River Basin

88°30'

89°

43°30'

43°

EXPLANATION

Lakes

Main trunk of the 

Rock River

Other streams

County boundary

Rock River Basin boundary

Tributary site described

in table 1

City

2

0 10 20 MILES

0 10 20 KILOMETERS

ROCK

DANE

COLUMBIA

DODGE WASHINGTON

JEFFERSON

WAUKESHA

WALWORTH

FOND DU

LAC

GREEN

Fulton

Beloit

Janesville

Milford

Jefferson

Horicon

Fort

Atkinson

Mayville

Waterloo

Watertown

Madison

Sun

Prairie

Fond du Lac Brandon

89°30'

Base map compiled and modified from digital data sources: 

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

Figure 1. Location of the Rock River Basin in Wisconsin.
4 Simulation of the Regional Ground-Water-Flow System and Ground-Water/Surface-Water Interaction, Rock River Basin, Wisconsin

EXPLANATION

Open water (4) 

Land cover (percent of total)

Urban (10)

Agriculture (68)

Forest (9)

County boundary

Rock River Basin 

boundary

Wetland (9)

88°30'

89°

43°30'

43°

0 10 20 MILES

0 10 20 KILOMETERS

89°30'

Base map compiled and modified from digital data sources: 

U.S. Geological Survey, 1:250,000. Land cover data from 

Wisconsin Department of Natural Resources, 1998.

Figure 2. Land cover in the Rock River Basin.
Introduction 5

Purpose and Scope

The purpose of this report is to describe the hydrogeology 

of the Rock River Basin and to describe the development 

and applications of a computer model that simulates regional 

ground-water flow in the basin. Geologic and hydrologic 

data used during this study consisted of interpretive maps, 

previously published reports, and historical streamflow and 

water-level measurements. The report includes a summary 

of selected hydrogeologic data, conceptualization of the 

hydrogeologic setting of the basin, and details on the 

construction and calibration of a one-layer, steady-state, 

analytic element model that simulates ground-water flow and 

its interaction with surface-water features at a coarse, regional 

scale. On the basis of model simulations, maps are presented 

that illustrate (1) ground-water-flow directions, (2) gaining 

and losing river reaches, (3) areas contributing ground-water 

recharge to selected tributaries, and (4) areas of relatively local 

ground water captured by rivers.

Physical Setting

The Rock River Basin covers approximately 3,700 mi2

and includes major hydrologic features such as the Yahara, 

Crawfish, and Bark Rivers, as well as the Horicon Marsh. 

The Rock River (fig. 1) originates north of the Horicon Marsh 

near the town of Brandon in Fond du Lac County and flows 

south approximately 140 mi through Wisconsin to the Illinois 

border at Beloit, Wis. The river continues to flow south and 

west through Illinois before entering the Mississippi River 

near Moline, Ill. The basin north of Beloit, Wis., receives 

about 34 in. of precipitation annually, with temperatures that 

typically range from lows around 10oF in the winter to highs 

around 85oF in the summer (Natural Resources Conservation 

Service, 2002). Land cover in the basin is dominated by 

agriculture, but it also includes local areas of predominantly 

urban, wetland, forest, and open-water (fig. 2; Wisconsin 

Department of Natural Resources, 1998). Table 1 summarizes 

land cover and demographic information for the basin and 

selected tributary watersheds. 

The Rock River Basin is part of the Eastern Ridges 

and Lowlands physiographic region of Wis. (Martin, 1965), 

and is covered by a mixture of glacial sediments that overlie 

layers of east-sloping sedimentary bedrock. Impermeable, 

Precambrian crystalline bedrock (for example, granite or 

quartzite) underlies the entire basin at depth. The surface of 

this crystalline bedrock is spatially variable and becomes 

deeper to the south toward the Illinois Basin and to the east 

toward the Michigan Basin. Above the crystalline rock are 

many layers of sedimentary bedrock (sandstone, shale and 

dolomite) of Cambrian age (Jordan, St. Lawrence, Lone 

Rock, Wonewoc, Eau Claire, and Mount Simon Formations), 

Ordovician age (Maquoketa, Galena, Platteville, Glenwood, 

St. Peter, Shakopee, and Oneota Formations), Silurian age, and 

Devonian age. Sediment carried by glacial ice and meltwater 

was deposited over the bedrock across most of the basin 

(fig. 3) during the Wisconsin Glaciation (10,000–25,000 years 

ago). Stratigraphic names used in this report are based on the 

nomenclature of Ostrom (1967) and Mickelson and others 

(1984), as presented in figure 4. A generalized geologic cross 

section for the Rock River Basin is shown in figure 5, with the 

uppermost bedrock formations shown in map view in figure 6. 

Table 1. Physical and demographic characteristics for select tributary basins in the Rock River Basin (Wisconsin Department of 

Natural Resources, 1998).

[Abbreviation: mi2, square mile]

Site 

number in 

figure 1

Tributary name

Surfacewater-basin 

area (mi2

)

Population

(2000)

Land cover, in percent

Forest Urban Agriculture Wetland and 

open-water

1 Rock River upstream from Beloit (excludes 

Turtle Creek)

3,464 742,000 8 10 68 13

2 Turtle Creek at the Rock River 288 43,000 8 10 80 2

3 Yahara River near Fulton 518 292,000 6 20 63 11

4 Koshkonong Creek near Koshkonong Lake 161 31,000 9 9 71 11

5 Bark River at the Rock River 344 61,000 16 9 57 18

6 Crawfish River at Milford 762 63,000 5 6 76 12

7 Rock River at Robert Street at Fort Atkinson 2,237 280,000 8 8 69 15

8 Rock River near Horicon 456 31,000 5 6 71 17

9 West Branch Rock River at State Highway 49 

near Waupun

113 13,000 3 7 82 9

10 East Branch Rock River near Mayville 183 18,000 8 8 75 9
6 Simulation of the Regional Ground-Water-Flow System and Ground-Water/Surface-Water Interaction, Rock River Basin, Wisconsin

EXPLANATION

Surficial sediments 

(percent of total)

Coarse-grained stratified (27)

Fine-grained stratified (2)

Organic (1)

Till (69)

Water (1)

County boundary

Rock River Basin

88°30'

89°

43°30'

43°

0 10 20 MILES

0 10 20 KILOMETERS

89°30'

Base map compiled and modified from digital data sources: 

U.S. Geological Survey, 1:250,000. Surficial sediments data 

modified from Soller and Packard, 1998.

Figure 3. Surficial sediments in the Rock River Basin.

Study Methods

An analytic element ground-water-flow model, using 

the computer program GFLOW (Haitjema, 1995), was 

developed to simulate the regional ground-water-flow 

system and its interaction with surface-water features. This 

modeling program simulates ground-water flow on the basis 

of the Dupuit-Forchimer assumptions, which simplify a 

three-dimensional flow system into a two-dimensional, areal 

flow system. These assumptions are well suited for the large 

Rock River Basin where the ratio of horizontal to vertical 

dimensions is very large; that is, the total aquifer thickness 

does not exceed 2,000 ft, where as the Rock River Basin 

extends over 90 mi (475,000 ft). A complete description of 

analytic element modeling is beyond the scope of this report, 

but a brief description follows. 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. 
Study Methods 7

Stratigraphic nomenclature Lithology Aquifers

and

regional confining unit

Sand and gravel aquifer

Carbonate aquifer

Regional confining unit

Sandstone aquifer

Precambrian crystalline

basement rocks

Metamorphic,

igneous

System/age Formation

Quaternary

Devonian

Silurian

Ordovician

Cambrian

Precambrian

Maquoketa

Galena

Platteville

Glenwood

St. Peter

Shakopee and Oneota

Jordan

St. Lawrence

Lone Rock

Wonewoc

Eau Claire

Mt. Simon

Sandstone

and dolomite,

with

interbedded

shale and

siltstone

(leaky

confining

units)

Dolomite

Dolomite

Sand and gravel,

glacial till

Shale

Abbreviations

Q

D

S

Os

Oa

O

p

Om

C;

Ct

Cw

Cec

Cm

p

C

Figure 4. Stratigraphic units and corresponding lithologies in the Rock River Basin. (Modified from Feinstein 

and others, 2005b.)

An infinite aquifer is assumed in analytic element 

modeling. The problem domain (model area) does not require 

a grid or involve interpolation between cells (as are required 

for finite difference or finite element methods). To construct an 

analytic element model, the modeler enters features important 

for controlling ground-water flow (for example, wells and 

surface-water features) 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. The effects of these 

individual solutions are added together to form a solution 

for any location in the simulated ground-water-flow system. 

Because the solution is not confined to a grid, heads and flows 

can be computed anywhere in the model domain without 

interpolating between grid cells. 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 

that do not vary with time). A primary value of large-scale 

analytic element modeling is to identify the main features 

controlling ground-water flow. These features can then be used 

to better define local conditions, test hypotheses, and answer 

site-specific questions as specific local data are incorporated 

into the model. The analytic element method and comparisons 

of analytic element to finite-difference numerical model 

techniques have been discussed by others (Haitjema, 1995; 

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

The GFLOW model was calibrated by means of 

parameter-estimation techniques. Numerous publications 

detail the advantages of parameter estimation (for example, 

Poeter and Hill, 1997; Kelson and others, 2002). Briefly, 

the primary benefit of a properly prepared and executed 

parameter-estimation calibration over typical trial-and-error 

calibration is the ability to automatically calculate parameter 

values (for example, hydraulic conductivity and recharge) 

that are a quantified best fit between simulated model output 

and observed data (for example, ground-water levels and 

streamflows). In addition, parameter sensitivity can be 

quantified and assessed. In this study, the GFLOW model was 

coupled with the parameter estimation code PEST (Doherty, 

2008).
8 Simulation of the Regional Ground-Water-Flow System and Ground-Water/Surface-Water Interaction, Rock River Basin, Wisconsin Yahara Lakes Crystalline bedrock Maquoketa Formation Rock River Sand and gravel 1,000 800 600 400 200

0

-200-400

1,0008006004002000-200-400

Datum is NGVD 29 Modified from Kammerer and others, 1998

FEET FEET

Primarily

carbonates Primarily sandstones and shales

E

W

Rock River Basin

Figure 5. Generalized west-to-east geologic section for the Rock River Basin. Abbreviations for the geologic units are explained in figure 4.
Study Methods 9

EXPLANATION

Bedrock

Silurian (undifferentiated)

Ordovician

Maquoketa Formation

Galena, Platteville and 

St. Peter Formations

Shakopee and Oneota Formation

Cambrian (undifferentiated)

Precambrian

County boundary

Rock River Basin boundary

88°30'

89°

43°30'

43°

0 10 20 MILES

0 10 20 KILOMETERS

89°30'

Base map compiled and modified from digital data sources: 

U.S. Geological Survey, 1:250,000. Bedrock data modified 

from King and Beikman, 1974.

Figure 6. Generalized map showing the extent of the uppermost bedrock units in the Rock River Basin.
10 Simulation of the Regional Ground-Water-Flow System and Ground-Water/Surface-Water Interaction, Rock River Basin, Wisconsin

Conceptual Model of the GroundWater-Flow System

Before simulating a ground-water system, a 

conceptualization of the system is essential because it forms 

the basis for model development. The conceptualization 

is a necessary simplification of the natural system because 

inclusion of all of the complexities of the natural system into 

a computer model is not feasible given the existing knowledge 

of the subsurface and current computer capabilities. Steps in 

the development of the conceptual model are (1) definition 

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

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

hydrologic boundaries encompassing the area of interest. 

The first two of these steps were accomplished by review and 

interpretation of available geologic and hydrogeologic data. 

The third step was accomplished through the model design. 

The conceptual model of the ground-water-flow system 

is shown in figure 7. The vertical scale of the conceptual 

model diagram has been greatly exaggerated to illustrate the 

geologic units; regional flow through the aquifers is primarily 

horizontal.

Aquifers and Confining Units

Three generalized regional aquifers and one regional 

confining unit are present in the Rock River Basin, based 

on the hydrogeologic units simulated for seven counties in 

southeastern Wisconsin (fig. 4; Feinstein and others, 2005b). 

Glacial sediments of varying thickness and permeability 

cover most of the basin and form a relatively thin sand and 

gravel aquifer above bedrock aquifers. In the eastern part 

of the basin, dolomite bedrock of Devonian and Silurian 

age forms a shallow carbonate bedrock aquifer above the 

Maquoketa Formation, which is a regional confining unit 

(figs. 5 and 7). (Dolomite is a carbonate rock similar to 

limestone.) The Maquoketa Formation is an approximately 

200-ft-thick layer of shale that separates the carbonate 

aquifer from an underlying, predominantly sandstone, 

bedrock aquifer. The underlying aquifer is composed of 

layers of dolomite, sandstone, and shale consisting of the 

Galena, Platteville, Glenwood, St. Peter, Shakopee, Oneota, 

Jordan, St. Lawrence, Lone Rock, Wonewoc, Eau Claire, and 

Mount Simon Formations. The combined thickness of these 

bedrock formations is substantial, generally on the order of 

600 ft to 1,200 ft except in the far eastern part of the basin, 

where the thickness begins to increase by thousands of feet. 

Impermeable Precambrian crystalline basement rock forms the 

lower boundary of the ground-water-flow system.

The Maquoketa Formation is absent in most of the 

western part of the basin (figs. 5 and 6). In map view, 

the western edge of the Maquoketa “subcrop” is a linear 

representation of where the base of the Maquoketa Formation 

directly underlies the glacial sediments; that is, the Maquoketa 

Formation is present to the east of the subcrop beneath 

Devonian and Silurian age rocks, but has been removed by 

erosion west of the subcrop. In the conceptual model for the 

Rock River Basin, the sand and gravel aquifer is combined 

with the carbonate aquifer east of the Maquoketa subcrop 

(fig. 7). West of the Maquoketa subcrop, the carbonate aquifer 

is absent, and the sand and gravel aquifer is combined with the 

sandstone aquifer. In the conceptual model and the one-layer 

GFLOW model, flow within the sandstone aquifer east and 

below the Maquoketa subcrop has been ignored. Specifically, 

horizontal and vertical flow into the deep sandstone aquifer 

east of the Maquoketa subcrop has been incorporated into the 

conceptual and GFLOW models as a specified rate of groundwater flow, but ground-water flow within the sandstone aquifer 

itself has not been simulated directly below the Maquoketa 

Formation (see the “Model Construction and Assumptions” 

section). This simplification was used because of the natural 

hydrogeologic setting (shallow and deep aquifers separated by 

a major regional confining unit); limitations of the one-layer, 

two-dimensional ground-water-flow model; and the purpose 

of the Rock River Basin model, which includes simulation of 

shallow ground-water flow and ground-water/surface-water 

interaction. Ground water in the deep sandstone aquifer below 

the Maquoketa Formation has limited interaction with local 

surface-water bodies, and flow directions do not correspond 

with those above the Maquoketa Formation (Feinstein and 

others, 2005b). This deep aquifer has been simulated by others 

(Feinstein and others, 2005b) east of the subcrop.

Sources and Sinks of Water

The primary source of water to the ground-water-flow 

system is recharge to the water table. Recharge takes place 

nearly everywhere in the Rock River Basin except in groundwater discharge areas associated with surface-water bodies. 

Recharge rates tend to be spatially varied because of factors 

such as soil infiltration rates, ground slope and relative 

topographic position, and vegetative cover. However, these 

local differences tend to average out over large areas, such as 

the area drained by the Rock River and its tributaries.

Ground-water sinks are areas or features where water 

discharges from the ground-water-flow system, including 

surface-water features such as rivers, lakes, and wetlands. 

Pumping wells are another type of sink, capturing ground 

water that would otherwise discharge to surface-water bodies. 

In areas of large ground-water withdrawals, especially in 

surficial aquifers, rivers that otherwise would capture ground 

water may instead locally recharge the ground-water system. 

Only a small amount of the total recharge to the water table 

within the Rock River Basin is captured by wells. Locally, 

however, areas with large annual withdrawals (for example, 

the city of Madison) can capture a substantial portion of the 

local recharge. 
Conceptual Model of the Ground-Water-Flow System 

11

Yahara Lakes Rock River 1,000

800600400200

0

-200-400

1,0008006004002000-200-400

Datum is NGVD 29

FEET FEET

Ground-water recharge

Local and regional

ground-water-flow

patterns

Combined sand and gravel

and sandstone aquifer

Combined sand and gravel 

and carbonate aquifer

Flow into the sandstone aquifer

below the Maquoketa Formation

Impermeable base

E W

Rock River Basin

(not directly simulated

in GFLOW model)

Conceptual

pumping

well

Figure 7. Generalized conceptual model of ground-water flow in the Rock River Basin. The Maquoketa Formation is implicity simulated as part of the combined sand 

and gravel and carbonate aquifer.
12 Simulation of the Regional Ground-Water-Flow System and Ground-Water/Surface-Water Interaction, Rock River Basin, Wisconsin

A secondary ground-water sink within the Rock River 

Basin is the subsurface movement of ground water across 

its boundaries into neighboring basins. This interbasin 

flow is generally not a substantial component of the water 

budget for the shallow part of the flow system (including 

the unconsolidated deposits and the upper bedrock) because 

the topographic boundary of a basin is generally a close 

approximation of the divide that separates shallow ground 

water flowing within the basin from shallow ground water 

flowing outside the basin. However, deeper flow in the 

sandstone aquifer can cross surface-water boundaries in 

response to gradients controlled by large sinks such as major 

pumping centers. For example, regional ground-waterflow simulations of southeastern Wisconsin (Feinstein and 

others, 2005b) show that the deep ground-water divide in the 

sandstone aquifer is several miles west of the shallow groundwater divide and that there is a net loss of ground water from 

the Rock River Basin through the deep sandstone aquifer 

below the Maquoketa Formation. The one-layer framework 

model has incorporated results from the SEWRPC model 

(Feinstein and others, 2005b) to account for this deep groundwater flow out of the basin (see the “Model Construction and 

Assumptions” section). 

Water flows from areas of recharge (sources) to areas 

of discharge (sinks) through the ground-water-flow system. 

Of the recharge that enters the regional ground-water-flow 

system, part flows through local systems with short flow paths 

(usually less than about 2 mi). Local systems are common in 

the sand and gravel aquifer. Some of the water flows through 

a regional system with longer flow paths (on the order of 

tens of miles). The regional system generally consists of the 

sandstone and carbonate aquifers. Flow is largely horizontal 

in the local and regional systems except in regional discharge 

areas, where deep ground water flows upward to surface-water 

sinks. The presence of major vertical fractures can enhance 

local vertical flow.

Hydrogeologic Boundaries

The ground-water-flow model consists of two domains: 

the near field and the far field. The near field is the area of 

interest, which for this study is the entire Rock River Basin. 

The near-field rivers and lakes are represented by linesink1

networks (Haitjema, 1995) that route base flow (the portion 

of total flow derived from ground water) downstream. The 

degree of ground-water/surface-water interaction in the near 

field depends on the riverbed sediment resistance (thickness 

divided by hydraulic conductivity) and the elevation difference 

between the river stage and the water table. The far field is 

the area surrounding the near field that contains hydrologic 

features that control the ground-water flow toward or away 

from the near field. These are rivers and lakes that border the 

Rock River Basin, and they are simulated with coarse linesink 

networks and little or no resistance between the surface-water 

features and the ground-water system. The function of the 

far field is to resolve the ground-water divides near the edge 

of the basin that determine, for the most part, what water is 

available for discharge to rivers and wells within the near 

field. The headwaters of the river systems surrounding the 

Rock River Basin were simulated as near-field linesinks in 

order to allow the river to “go dry” and be removed from the 

solution if the water table falls below the stream elevation - 

an important consideration near ground-water divides where 

ephemeral streams (streams with no base flow, only runoff 

from precipitation) tend to be prevalent.

Hydraulic Properties of the GroundWater-Flow System

Initial estimates of hydraulic conductivity, recharge, and 

riverbed resistance for the regional ground-water-flow model 

were based on available geologic and hydrologic data. The 

following is a brief description of these estimates. 

Hydraulic Conductivity

Hydraulic conductivities of the geologic units in the 

area have been estimated by others (table 2) through the 

use of specific-capacity tests, aquifer pumping tests, and 

hydrogeologic modeling. Horizontal hydraulic conductivities 

of the sand and gravel aquifer are reported to range from 0.2 

to 100 ft/d. Measured horizontal hydraulic conductivities 

in the carbonate and sandstone aquifers range from 0.07 to 

31 ft/d (Young, 1992). Vertical hydraulic conductivity in the 

sandstone and carbonate aquifers is generally ten to hundreds 

of times lower than the corresponding horizontal hydraulic 

conductivity estimates; vertical hydraulic conductivity 

of confining units, such as the Maquoketa Formation, 

is thousands of times lower than horizontal hydraulic 

conductivity of the aquifers (Feinstein and others, 2005b). In 

effect, the Maquoketa Formation forms a nearly impermeable 

boundary to vertical flow in the eastern part of the Rock River 

Basin. Although these ranges are useful for characterizing the 

system, the model requires specific values for the hydraulic 

conductivity across large regions, or zones, in the flow 

system. Thus, values associated with zones of locally uniform 

hydraulic conductivity were treated as calibration parameters. 

Values used in the modeling described here were initialized by 

using reasonable values, with the final values determined by 

use of PEST (Doherty, 2008) and constrained to a reasonable 

range based on available measurements and estimates 

(table 2).

1

A linesink is a mathematical representation of a hydrologic sink, such as a 

stream (Haitjema, 1995).
Hydraulic Properties of the Ground-Water-Flow System 13

Recharge

Rates of recharge are varied because of differing 

precipitation rates and amounts, soil infiltration rates, slope of 

the land, relative topographic position, vegetative cover, and 

other factors. This spatial variability is difficult to estimate, 

but it often has minimal significance at regional scales. 

Thus, average recharge rates were applied uniformly across 

individual zones in the regional model and were loosely 

associated with patterns of soil infiltration properties (fig. 8; 

Schwarz and Alexander, 1995). For example, a zone of 

potentially high recharge was delineated around a contiguous 

area with relatively high soil infiltration rates in the eastcentral part of the basin. Average ground-water recharge 

rates were expected to be within the range reported for the 

Rock River Basin by Gebert and others (2007) and Cherkauer 

(2001, 2004). Recharge rates were treated as calibration 

parameters, with the values constrained to reasonable ranges 

and determined by use of the parameter estimation code PEST 

to match observed water levels and base flows. 

Riverbed Resistance

Estimates of riverbed resistance are needed to simulate 

the interaction between surface water and ground water. 

Riverbed resistance is equal to the thickness of a riverbed 

or lakebed divided by its vertical hydraulic conductivity, 

and in this study was estimated as ranging from 0.5 day for 

rivers to 2 days for lakes2. These values correspond to a 1-ft 

sediment thickness and vertical hydraulic conductivities 

of 2 ft/d and 0.5 ft/d, respectively. This range of riverbed 

resistance is between values (0.3 to 2 days) simulated for 

rivers and lakes in Waukesha County (Hunt and others, 2000), 

Washington County (Dunning and others, 2003), and Rock 

County (Gaffield and others, 2002). Because of the relative 

insensitivity of the regional flow system to riverbed resistance 

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

adjusted during calibration. 

Table 2. Previously reported horizontal hydraulic conductivities (feet per day) and calibrated values 

from the regional model. 

[The sand and gravel aquifer is combined with the carbonate aquifer where it is above the Maquoketa Formation; it has 

been combined with the sandstone aquifer where the Maquoketa Formation and overlying carbonate aquifer are absent]

Hydrogeologic unit

Horizontal hydraulic conductivity, in feet per day

Feinstein and 

others (2005b)

Krohelski and 

others (2000)

Gaffield and 

others (2002)

Young 

(1992)

This 

report

Sand and gravel aquifer 0.2–100 0.5–7

6.5

4.7 Carbonate 

aquifer

Devonian 30 – 0.07–2

where 

absent

Silurian 1–4 – –

Maquoketa 0.0003–0.3 – –

Sandstone 

aquifer

Galena 0.04–0.3

5

–

6.6

Platteville

Glenwood

1.2–6 0.9–6.8

St. Peter 

Shakopee

Oneota

Jordan 

St. Lawrence 0.24–2.4 0.34–5

Lone Rock

Wonewoc 2.4–8.4 2.9–31

Eau Claire 0.6–3.6

10

0.7–3.9

Mount Simon 1.2–6 1.3–11

2

The unit “day” is a mathematical reduction resulting from thickness, in 

feet, being divided by hydraulic conductivity, in feet per day.
14 Simulation of the Regional Ground-Water-Flow System and Ground-Water/Surface-Water Interaction, Rock River Basin, Wisconsin

EXPLANATION

High-recharge zone boundary

less than 3

3 to 6 

greater than 6

County boundary

Rock River Basin boundary

Infiltration rate, inches per hour

43°

Base map compiled and modified from digital data sources: 

U.S. Geological Survey, 1:250,000. Infiltration data modified 

from Schwarz and Alexander, 1995.

89°30' 89° 88°30'

43°30'

0 10 20 MILES

0 10 20 KILOMETERS

Figure 8. Estimated infiltration rates for soils in the Rock River Basin. Also shown is a zone of high 

recharge rate simulated in the GFLOW model.
Simulation of the Regional Ground-Water-Flow System 15

Ground-Water Withdrawals

Ground-water withdrawals from all aquifers west 

of the Maquoketa subcrop and from aquifers above the 

Maquoketa Formation (where present) were incorporated 

into the GFLOW model, as per the conceptual model design 

(Appendixes 1, 2 and 3). Wells that withdraw ground water 

from aquifers below the Maquoketa Formation were excluded 

from the model. Pumping rates for individual public-supply 

wells in and around the Rock River Basin were computed as 

the annual average rate reported by each utility from 1997 

to 2006 (fig. 9). Annual withdrawal rates were not available 

for industrial, commercial, and agricultural high-capacity 

wells during this period. Instead, estimated withdrawals from 

industrial, commercial, and irrigation wells in and around the 

Rock River Basin (fig. 10) for the period from 1997 to 2005 

were based on either reported rates prior to 1990 or the type 

of water use (for example, crop irrigation, manufacturing) 

indicated on the well permit application. Pumping from 

small, individual private wells in the Rock River Basin is 

not included in the model because the discharge from these 

wells is widely distributed and relatively small (especially 

when including return flow from septic systems), so it has a 

negligible effect on the overall regional water table.

Total high-capacity-well withdrawal in the Rock River 

Basin (excluding withdrawal from below the Maquoketa 

Formation) is about 40,700 Mgal/yr. Municipal water supplies 

in the basin withdrew an average of about 30,800 Mgal/yr 

of ground water from 1997 to 2006, or roughly 75 percent 

of the total ground water withdrawn from all high-capacity 

wells. The largest municipal withdrawals in the model were 

in the five communities of Madison (11,850 Mgal/yr, of 

which about 15 percent is pumped from outside of the Rock 

River Basin) and Sun Prairie (870 Mgal/yr) in Dane County; 

Janesville (4,800 Mgal/yr) and Beloit (2,410 Mgal/yr) in 

Rock County; and Watertown (1,070 Mgal/yr) in Jefferson 

County. Ground-water withdrawal rates for irrigation (3,540 

Mgal/yr) and industrial and commercial uses (6,350 Mgal/yr) 

in the basin totaled about 9,890 Mgal/yr from 1997 to 2005. 

Industrial withdrawals are substantial in Madison, Waterloo, 

Jefferson, and Beloit (fig. 10). Irrigation is used for agriculture 

throughout the basin and is particularly focused in an area 

north of Beloit and east of the Rock River (fig. 10). The 

ground-water-flow model of the Rock River Basin included 

withdrawal wells from outside of the basin (figs. 9 and 10), 

because ground-water withdrawal can influence the location of 

ground-water divides (Feinstein and others, 2005b). Total well 

withdrawal in the GFLOW model from outside of the surfacewater basin was about 16,020 Mgal/yr. 

Simulation of the Regional GroundWater-Flow System

An analytic element ground-water-flow model of the 

Rock River Basin was developed by use of the computer 

program GFLOW (Haitjema, 1995). The model simulates the 

ground-water-flow system and its interaction with surfacewater features. The model consists of one layer and simulates 

steady-state conditions (no change in water levels over time). 

Simulated rivers, zones of hydraulic conductivity, and zones of 

uniform areal recharge are shown in figure 11.

Model Construction and Assumptions

Initial model development included estimating the 

elevation of the base of the ground-water system, a recharge 

rate, and a horizontal hydraulic conductivity. The base of 

the model (200 ft below sea level, or NAVD 88,) roughly 

corresponds with the average crystalline bedrock elevation 

in the Rock River Basin. East of the Maquoketa subcrop, 

the base of the model (400 ft above NAVD 88) roughly 

corresponds with the average elevation of the base of the 

Maquoketa Formation. The sand and gravel aquifer was 

combined with (1) the underlying carbonate aquifer east of the 

Maquoketa subcrop, or (2) the sandstone aquifer west of the 

subcrop, which resulted in a single bulk hydraulic conductivity 

for each of these two zones. In two-dimensional areal models, 

where transmissivity (horizontal hydraulic conductivity 

multiplied by aquifer thickness) of a single layer represents 

the flow system, the base elevation is correlated with hydraulic 

conductivity. Therefore, parameter calibration focused on 

horizontal hydraulic conductivity in each zone rather than the 

aquifer base elevations. 

As depicted in the conceptual model (fig. 7) and as 

mentioned previously, flow within the sandstone aquifer east 

of and below the Maquoketa subcrop has been ignored in 

the one-layer GFLOW model. However, vertical flow out 

of the carbonate aquifer and into the deep sandstone aquifer 

below the Maquoketa Formation has been incorporated into 

the GFLOW model as a uniform areal leakage rate based on 

results from a multilayer model of southeastern Wisconsin 

(Feinstein and others, 2005b). This vertical leakage out of the 

Rock River Basin model (about 0.1 in/yr; Daniel Feinstein, 

U.S. Geological Survey, written commun., 2008) was 

simulated as a reduction in recharge to the carbonate aquifer 

above the Maquoketa Formation (fig. 11). This implementation 

(reducing recharge at the water table rather than removing 

water at the base of the aquifer, because of model limitations) 

maintains the appropriate overall water budget, but it may 

induce minor biases in the simulated vertical flow path of 

ground water in the carbonate aquifer (see sections 3.2.6 

and 3.5 of Haitjema, 1995). Such potential biases (slightly 

shallower flow paths) are expected to be minor considering the 

small leakage rate through the Maquoketa Formation (about 

1 percent of recharge). 
16 Simulation of the Regional Ground-Water-Flow System and Ground-Water/Surface-Water Interaction, Rock River Basin, Wisconsin

88°30'

89°

43°30'

43°

EXPLANATION

County boundary

Rock River Basin boundary

0 10 20 MILES

0 10 20 KILOMETERS

Extent of the Maquoketa 

Formation

0.0−40.0

40.1−200.0

200.1−800.0

800.1−1,500.0

Annual average withdrawal rate (1997–2006), 

in millions of gallons per year

Base map compiled and modified from digital data sources: 

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

Figure 9. Ground-water withdrawal from public-supply wells in the GFLOW model of the Rock River Basin. Only wells that 

withdraw water from aquifers above the Maquoketa Formation are included in the GFLOW model where the Maquoketa 

Formation is present.
Simulation of the Regional Ground-Water-Flow System 17

EXPLANATION

County boundary

Rock River Basin boundary

0 10 20 MILES

0 10 20 KILOMETERS

Extent of the Maquoketa Formation

0.0−40.0

40.1−200.0

200.1−800.0

800.1−1,500.0

Estimated withdrawal rate (1997–2005), 

in millions of gallons per year

88°30'

89°

43°30'

43°

Base map compiled and modified from digital data sources: 

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

Beloit

Jefferson

Waterloo

Madison

Figure 10. Ground-water withdrawal from agricultural, industrial, and commercial wells in the GFLOW model of the Rock 

River Basin. Only wells that withdraw water from aquifers above the Maquoketa Formation were included in the GFLOW model 

where the Maquoketa Formation is present. Estimated withdrawal rate based on historical rates or application (crop irrigation, 

manufacturing, etc.).
18 Simulation of the Regional Ground-Water-Flow System and Ground-Water/Surface-Water Interaction, Rock River Basin, Wisconsin

Horizontal flow into the deep sandstone aquifer below 

the Maquoketa Formation has been incorporated into the 

GFLOW model by means of discharge-specified linesinks 

along the trace of the Maquoketa subcrop as delineated in 

the multilayer model of southeastern Wisconsin (Feinstein 

and others, 2005b). Horizontal flux (in units of square feet 

per day) across the Maquoketa subcrop was multiplied by 

the layer thickness (feet) and totaled for all layers below the 

Maquoketa Formation on a cell-by-cell basis in the multilayer 

model (layers 9-18 described by Feinstein and others, 2005b). 

This volumetric discharge (cubic feet per day) was summed 

for a series of horizontally adjacent cells and was then divided 

by the length (feet) of a corresponding discharge-specified 

linesink in the GFLOW model to compute an equivalent 

flux across the Maquoketa subcrop for the GFLOW model. 

Because discharge-specified linesinks in GFLOW extend 

the full thickness of the model and can not be assigned to a 

specific aquifer (for example, to remove water solely from 

the sandstone aquifer west of the Maquoketa subcrop), the 

discharge-specified linesinks probably capture some water 

from the carbonate aquifer in the GFLOW model. The 

effect on simulated ground-water-flow patterns caused by 

this discrepancy between the multilayered SEWRPC model 

(Feinstein and others, 2005b) and the GFLOW model is 

expected to be slight because the total ground water withdrawn 

by the discharge-specified linesinks represents only about onethird of the total flow through the aquifers near the subcrop; 

and of this, about 75 percent is withdrawn from the sandstone 

aquifer because of the approximate 3-to-1 transmissivity ratio 

between the sandstone and carbonate aquifers. Moreover, 

the influence of the discharge-specified linesinks is expected 

to be relatively local. Nonetheless, simulated flow paths 

in the carbonate aquifer may show a small local deviation 

(horizontally refracted) due to the discharge-specified linesinks 

near the Maquoketa subcrop. Future refinements to the model 

that focus on ground-water flow in only near-surface aquifers 

may benefit from the removal of local discharge-specified 

linesinks (in addition to other potential aquifer refinements) 

for proper simulation of flow paths in the shallow aquifers.

The river network for the Rock River Basin (fig. 1) is 

represented in the GFLOW model as a series of linesinks 

(fig. 11). Multiple linesinks are joined into linesink strings 

representing individual reaches for each river. The river 

gradient (change in water-surface elevation over distance) 

assigned to a linesink is based on data from 7.5-minute 

topographic quadrangle maps. GFLOW solves for the 

exchange between ground water and surface water at the 

center of each linesink. 

In the near field of the model–that is, within and 

immediately adjacent to the Rock River Basin–each linesink is 

assigned a width based on stream order and field observations; 

widths ranged from about 10 to 500 ft. Each near-field linesink 

is also assigned a resistance term that, once multiplied by the 

river width and the difference between the fixed river level 

and calculated water-table elevation adjacent to the river, 

accounts for the ground-water flow across the riverbed. As 

defined previously, the resistance is equal to the thickness 

of the riverbed divided by its hydraulic conductivity. In the 

regional model, a single value of resistance equal to 0.5 

day was applied to all rivers. Initial parameter sensitivities 

demonstrated that the model results were not sensitive to 

changes in riverbed resistance when varied over reasonable 

ranges; therefore, the values for all rivers were fixed for all 

model runs. 

Large lakes were simulated as linesinks with resistance 

along their shorelines and assigned widths based on the 

approximate distance from shoreline to shoreline (Haitjema, 

2005) and a uniform resistance of 2 days; small lakes were 

ignored. Within the perimeter of each simulated lake, the 

recharge rate applied to the lake represents precipitation minus 

evaporation rather than ground-water recharge. Recharge to 

lakes in the model, as well as the Horicon Marsh, was set 

equal to 2.0 in/yr on the basis of estimates of precipitation 

minus evaporation in Wisconsin (Novitzki, 1982). The 

Horicon Marsh was further simulated as an area of high 

hydraulic conductivity (1,000 ft/d), through which internal 

ditches were simulated by use of linesinks. 

Near-field linesinks are linked so that streamflow is 

routed from near the headwaters at higher elevations through 

tributaries to the main trunk of rivers at lower elevations. 

During the routing through the river network, the amount of 

water captured from and lost to the ground-water-flow system 

by the river is tabulated. This accounting allows the amount 

of water simulated in the river at any point to be compared to 

flows recorded at streamgages. In general, streamflow consists 

of (1) overland flow derived mostly from storms and (2) base 

flow derived from ground-water discharge. Only the baseflow component of streamflow is simulated with the GFLOW 

model. 

Linesinks also represent water bodies in the model far 

field outside the Rock River Basin (fig. 11). However, these 

far-field elements are assigned no resistance or width. The 

assigned stage for each far-field linesink is equivalent to 

the water-table elevation along the linesink. The far-field 

linesinks, therefore, act as fixed water-level conditions that 

serve as major sinks for ground water that discharges outside 

the basin. In this manner, the far-field water bodies help to 

define the ground-water divide around the outer perimeter of 

the basin.

Other inputs to the GFLOW model include recharge 

zones and pumping wells. Recharge zones were evaluated 

on the basis of soil infiltration rates (fig. 8; Schwarz and 

Alexander, 1995), with the simulated recharge value 

estimated through model calibration. Recharge was simulated 

uniformly across the basin, except where stream base flows 

and hydrogeologic conditions indicated that recharge over a 

large area differed from that of the rest of the basin (fig. 8; 

Schwarz and Alexander, 1995). Wells are assumed to be fully 

penetrating (screened from the water table to the model base) 

and to have constant pumping rates, as described previously 

(see the “Ground-Water Withdrawals” section). 
Simulation of the Regional Ground-Water-Flow System 19

88°30'

89°

43°30'

43°

EXPLANATION

Near-field linesink

Far-field linesink

Simulated area receiving recharge (6.3 inches per year)

High-recharge zone (10.1 inches per year)

Lake simulated with precipitation minus evaporation equal to 2 inches per year

Horicon Marsh, simulated with high hydraulic conductivity (1,000 feet per day) and precipitation 

minus evaporation equal to 2 inches per year

Specified-discharge linesink representing horizontal ground-water flow into (gold) the GFLOW model (ground-water flow out of the 

sandstone aquifer below the Maquoketa Formation) or out (purple) of the GFLOW model (into the sandstone aquifer below the Maquoketa 

Formation). Thickness of line indicates the specified flux, ranging from 0 to 14 square feet per day along each line segment.

Extent of the Maquoketa Formation; simulated with a raised base elevation (400 feet), hydraulic conductivity of 4.7 feet per day, 

and recharge reduced by leakage through the Maquoketa Formation (0.1 inch per year)

County boundary

Rock River Basin boundary

0 10 20 MILES

0 10 20 KILOMETERS

Figure 11. Features of the GFLOW model of the Rock River Basin. The area (white) west of the Maquoketa Formation was 

simulated as a sandstone aquifer with base elevation of -200 feet and hydraulic conductivity of 6.6 feet per day.
20 Simulation of the Regional Ground-Water-Flow System and Ground-Water/Surface-Water Interaction, Rock River Basin, Wisconsin

Model Calibration

Ground-water model calibration is a process whereby 

simulated values of ground-water levels and base flows 

are compared to observed values. The GFLOW model was 

calibrated with the aid of the parameter estimation program 

PEST (Doherty, 2008). The PEST program automatically 

adjusts parameter values within a reasonable range, and 

compares simulated ground-water levels and stream base 

flows to measured water levels and base flows after each 

run of the GFLOW model. Model calibration is considered 

complete when simulated and observed water levels and flows 

match reasonably well and values for parameters (in this 

model, hydraulic conductivity and recharge) are considered 

reasonable. The primary benefit of a properly constructed 

parameter-estimation routine is the capacity to automatically 

calculate parameter values that are a quantified best fit 

between simulated and observed data (for example, groundwater levels and stream base flow). 

Although a steady-state model was used (in which 

ground-water levels do not change with time), measured 

water levels used for calibration spanned many years, and 

the location of many data points is somewhat uncertain 

(Appendixes 4 and 5). Simulated ground-water levels 

represent the average long-term water level, whereas measured 

water levels generally do not because water levels in wells 

can be influenced by (1) the depth and length of the well 

screen, (2) locally confined or perched conditions, and (3) 

seasonal variability in water levels. Water-level targets were 

arranged into two categories: (1) median values from 20 

long-term observation wells in and around the Rock River 

Basin, and (2) water levels from 16,282 recently drilled wells 

(water years 1997–2006, or October 1996 to September 

2006) with open intervals above the base of the Maquoketa 

Formation (where present). Well-construction information 

for these 16,282 wells was obtained from Well Construction 

Reports (WCRs; Wisconsin Department of Natural Resources, 

2007), which contain limited information on the location and 

elevation of the well site. On the basis of WCR information, 

the well locations were estimated to the nearest quarterquarter section. Target water levels were computed as the 

average water level for all wells in the same quarter-quarter 

section, which resulted in 8,220 WCR-derived water-level 

targets for calibration. An approximate evaluation of data 

quality is included in the calibration via the PEST weight 

assigned to each target (table 3). Higher weights were assigned 

to the 20 wells with long records and accurately measured 

reference-point elevations; lower weights were assigned 

to the 8,220 WCR-derived targets. The weighted residuals 

between measured and simulated values were used by PEST to 

determine the best fit. 

In addition to water-level targets, base-flow 

measurements used for calibration were obtained from nine 

streamgages in the Rock River Basin that were used by Gebert 

and others (2007) to estimate recharge (table 3b). Gebert and 

others (2007) estimated base flow at these stations by means of 

the Base-Flow Index method (Wahl and Wahl, 1995; Institute 

of Hydrology, 1980a; 1980b) for daily streamflows from water 

year 1970 to water year 1999. Proration of weights assigned 

to the targets in PEST (table 3b) was based on the amount of 

flow so that the influence of both small and large streams on 

the parameter-estimation process was roughly similar to the 

influence of water level targets. 

Only a subset of all possible parameters was estimated 

by PEST. Parameters were excluded if they were insufficiently 

sensitive for automated calibration (for example, riverbed 

resistance). In these cases, the parameter was fixed at a 

reasonable value. Hydraulic conductivities used in the 

calibrated model are listed in table 2 and shown on figure 11. 

Hydraulic conductivity representing the sand and gravel 

aquifer combined with the sandstone aquifer (west of the 

Maquoketa subcrop) was estimated to be about 6.6 ft/d. 

Hydraulic conductivity of the sand and gravel aquifer 

combined with the carbonate aquifer above the Maquoketa 

Formation was estimated to be about 4.7 ft/d. Recharge to 

most of the Rock River Basin was estimated at 6.3 in/yr. A 

higher recharge rate (10.1 in/yr) was calibrated for an area in 

the east-central part of the Basin where soil infiltration rates 

are relatively high (fig. 8; Schwarz and Alexander, 1995). 

The extent of this zone and the calibrated recharge rate match 

well with recharge rates in this area that were estimated with 

a watershed model (Cherkauer, 2001; 2004) and incorporated 

into a multilayer model of southeastern Wisconsin (Feinstein 

and others, 2005b).

Because of the uncertainties associated with some 

target data (location, elevation, seasonal variability, well 

construction, local conditions, etc.), along with simplifications 

inherent in constructing a regional model, perfect agreement 

between the simulated and measured values was not expected. 

Considering the wide range of measured water levels and 

simplifications necessary for the GFLOW model, the resulting 

match of simulated water levels and base flows to measured 

values was closer than expected (fig. 12). Summary statistics 

for the ground-water-level calibration (table 3a) are similar 

to those derived from other regional models in Wisconsin 

(for example: Krohelski and others, 2000, Feinstein and 

others, 2005a, Feinstein and others, 2005b). The mean error 

(a measure of the model bias) for the 20 long-term groundwater observation wells is -1.0 ft (a negative value indicates 

that measured values were less than simulated values); mean 

error for the 8,220 WCR wells is -8.6 ft. The root mean square 

difference (RMSD) and mean absolute difference (MAD), 

respectively, between measured and simulated water levels 
Simulation of the Regional Ground-Water-Flow System 21

are 23.1 and 15.2 ft for the 20 long-term wells and 31.5 and 

23.2 ft for the WCR wells. These RMSD and MAD values 

represent less than 7 percent of the total range of observed 

water levels across the model area. In addition to comparing 

measured and modeled water levels by means of summary 

statistics, spatial comparisons between the measured and 

simulated water levels were made (fig. 13). The agreement 

between simulated water levels and measured water levels in 

observation wells is generally close and shows little spatial 

bias. The match to WCR water levels shows some local 

banding but generally strikes a balance between oversimulated 

(simulated greater than measured value) and undersimulated 

(simulated less than measured value) water levels. Moreover, 

large differences (for example, greater than 60 ft) between 

simulated and observed water levels for WCR targets were not 

unexpected because these targets were not filtered to remove 

those potentially influenced by (1) very deep or very short 

well screens, (2) local confined or perched conditions, or (3) 

seasonally high or low water levels at the time of construction. 

Measured base flows were compared to simulated base 

flows at nine locations (fig. 14). Simulated base flows were 

within 10 percent of estimated base flows at four of the nine 

streamgages and within 40 percent of estimated base flows 

at seven of the nine streamgages (table 3b); this base-flow 

calibration is similar to other regional model calibrations in 

Wisconsin (for example: Krohelski and others, 2000, Feinstein 

and others, 2005a, Feinstein and others, 2005b).

Table 3b. Calibration results for stream base-flow targets and associated weights used for calibration with the parameter estimation 

program PEST.

[ft3/s, cubic foot per second; in/yr, inch per year]

USGS 

station 

identifier

Station name

Target 

base flow 

(ft3

/s)

Simulated 

base flow 

(ft3/s)

Difference 

(ft3

/s and 

percent)

Weight

Estimated 

recharge from 

Gebert and 

others, 2007 

(in/yr)

05426000 Crawfish River at Milford 320 333 -13 (-4%) 2.0e-4 5.8

05431486 Turtle Creek at Carvers Rock Road near Clinton 97 77 20 (21%) 4.0e-4 6.6

05426250 Bark River near Rome 66 65 1 (2%) 4.0e-4 7.4

05427507 Koshkonong Creek near Rockdale 62 58 4 (6%) 4.0e-4 5.6

05424000 East Branch Rock River near Mayville 50 75 -25 (-51%) 4.0e-4 3.8

05423500 South Branch Rock River at Waupun 25 15 10 (39%) 8.0e-4 5.3

05423000 West Branch Rock River near Waupun 17 13 4 (25%) 8.0e-4 5.7

05427718 Yahara River at Windsor 15 14 1 (4%) 8.0e-4 2.7

05427900 Sixmile Creek near Waunakee 8.2 3.9 4.3 (53%) 8.0e-4 2.7

Table 3a. Calibration results for ground-water level targets and associated weights used for calibration with the parameter estimation 

program PEST.

[ME, Mean error; MAD, Mean absolute difference; RMSD, Root mean square difference]

Well 

type

Number of 

targets

ME

(feet)

MAD

(feet)

RMSD

(feet) Weight

Median of time-series values at longterm observation wells20 –1.0 15.2 23.1 10

Well-construction-report data 8,220 –8.6 23.2 31.5 0.8
22 Simulation of the Regional Ground-Water-Flow System and Ground-Water/Surface-Water Interaction, Rock River Basin, Wisconsin

650

750

850

950

1,050

1,150

1,250

650 750 850 950 1050 1,150 1,250

MEASURED WATER LEVEL, IN FEET ABOVE ABOVE NGVD 29

SIMULATED WATER LEVEL, IN FEET ABOVE NGVD 29

Well-construction-report targets

Long-term observation well targets

1:1 line

Figure 12. Comparison of measured and simulated water levels for the GFLOW 

model of the Rock River Basin.

Sensitivity Analysis 

Some uncertainty about the accuracy of models is 

inevitable because the model parameter values are never 

exactly known. However, the importance of each input 

parameter and its effect on simulation results can be evaluated 

through sensitivity tests in which the value of a parameter, 

such as hydraulic conductivity, is adjusted above or below the 

calibrated value and the magnitude of changes in simulated 

ground-water levels and base flows are quantified. In this 

study, PEST was used to calculate the sensitivity of all 

water-level and streamflow observations to changes in each 

parameter value during the calibration process. For the final 

calibrated parameter values, sensitivities computed by PEST 

indicate that water levels and streamflows were most sensitive 

to the recharge rate applied to the basin and the hydraulic 

conductivity of the combined sand and gravel and sandstone 

aquifers west of the Maquoketa subcrop. Less sensitive 

parameters included hydraulic conductivity of the combined 

sand and gravel and shallow carbonate aquifers above the 

Maquoketa Formation, as well as the recharge rate applied to 

the area with high soil-infiltration rates. Insensitive parameters 

included sediment resistance for rivers and lakes and the base 

elevation of the model. Initial sensitivity analyses showed 

similar results and were used to guide selection of parameters 

for estimation.
Simulation of the Regional Ground-Water-Flow System 23

89°

EXPLANATION

Water levels for long-term 

observation wells simulated

Greater than 60 feet too high

20–60 feet too high

20 feet too low to 20 feet too high

20–60 feet too low

Greater than 60 feet too low

Water levels from Wisconsin

well-construction-report sites simulated

Greater than 60 feet too high

20–60 feet too high

20 feet too low to 20 feet too high

20–60 feet too low

Greater than 60 feet too low

Near-field linesink

Far-field linesink

Recharge area

High-recharge zone

Extent of the Maquoketa Formation

Horicon Marsh

Rock River Basin boundary

88°30'

43°30'

43°

0 10 20 MILES

0 10 20 KILOMETERS

Figure 13. Water-level residuals for the GFLOW model of the Rock River Basin.
24 Simulation of the Regional Ground-Water-Flow System and Ground-Water/Surface-Water Interaction, Rock River Basin, Wisconsin

!>

!>

!>

!>

!>

!>

!>

!>

!>

89°

88°30'

43°30'

43°

0 10 20 MILES

0 10 20 KILOMETERS

EXPLANATION

Near-field linesink

Far-field linesink

Recharge area

High-recharge zone

Simulated lake

Horicon Marsh

Extent of the Maquoketa Formation

County boundary

Rock River Basin boundary

Base-flow simulated for gaging stations

!> Greater than 40 percent too high

!> 10−44 percent too high

!> 10 percent too low to 10 percent too high

!> 10−40 percent too low

!> Greater than 40 percent too low

Figure 14. Base-flow residuals for the GFLOW model of the Rock River Basin.
Evaluation of Simulated Results of the Rock River Basin Model 25

Evaluation of Simulated Results of the 

Rock River Basin Model

Results from the regional GFLOW model include 

simulated water levels, flow directions, and ground-water 

interaction with surface-water features. Contours of simulated 

water levels are similar to water-table maps produced 

previously for several Rock River Basin counties. However, 

simulated water levels from the regional model are more 

constrained because the model must also account for all water 

that enters and exits the model, which is not a consideration 

for manually constructed water-table maps. Simulated 

particles of water can also be traced along flow paths in the 

model to illustrate flow directions. Figure 15 shows contours 

of the simulated water table and the path of several simulated 

particles of water flowing downgradient, starting at the water 

table and flowing to discharge locations such as wells and 

rivers. Much of the water that recharges at the water table 

discharges to nearby rivers. 

The GFLOW model for the Rock River Basin integrates 

information over a large area, and direct application of 

the model is designed to address regional scale issues. 

Nonetheless, the model also forms a basis for possible 

future studies of specific parts of the basin, for which local 

refinement or extraction to a three-dimensional model would 

be necessary. 

Following are three aspects of the ground-water-flow 

system to which the regional model has been directly applied 

in this report: 

1. Identification of river reaches that are either gaining 

water from the ground-water-flow system or losing 

streamflow to the ground-water-flow system.

2. Determination of ground-water basins for major 

rivers.

3. Identification of relatively local ground-watercapture areas for rivers. 

Simulated Gaining and Losing River Reaches

In humid climates such as that of Wisconsin, ground 

water typically discharges to surface-water features that are 

in direct connection with the ground-water system. However, 

surface-water discharge to ground water can occur, and it 

most commonly occurs where surface waters are naturally 

or artificially restricted or elevated, such as along the 

downgradient shoreline of a lake or a reservoir where the 

surface-water level has been elevated by a channel restriction 

or a dam. Surface water can also enter an aquifer where 

ground-water-withdrawal wells are near rivers and lakes or 

along river meanders where local hydraulic gradients can be 

complex. 

Results of simulations illustrate regional patterns of 

ground-water/surface-water interaction along the shoreline of 

large lakes and reservoirs in the Rock River Basin (fig. 16). 

The upgradient (upstream) shorelines of the simulated lakes 

and reservoirs, like most river segments, are gaining (colored 

blue in fig. 16). However, some downgradient shorelines 

are losing (highlighted red in fig. 16), indicating that surface 

water is discharging into the ground-water-flow system along 

those segments. Additional losing segments are evident near 

ground-water pumping centers (for example, the Yahara Lakes 

near Madison). Although only large lakes and reservoirs that 

are well connected to the ground-water system were simulated 

in this model, similar ground-water/surface-water interaction 

patterns may occur near smaller lakes and reservoirs. Perched 

water bodies (those above the water table and not well 

connected to the ground-water system) may also lose water 

to the ground-water-flow system, with the amount largely 

dependent upon the permeability of the lakebed sediments. 

Likewise, the simulated results illustrate where headwater 

river segments are simulated as ephemeral (gray in fig. 16), 

indicating that these reaches do not receive ground water from 

the regional flow system. The GFLOW model automatically 

removed these ephemeral reaches from the ground-waterflow simulation during solution of the model. Where a 

more detailed understanding of ground-water/surface-water 

interaction is important, additional local refinement to the 

GFLOW model, or the extraction of a three-dimensional 

MODFLOW model (Harbaugh, 2005), may be necessary. 

Such local simulations would likely be improved by additional 

local data collection to compliment the new modeling 

objectives. 

Simulated Ground-Water Basins

Areas that contribute ground water to major river 

segments can be evaluated by use of ground-water-level 

contours and simulated traces of water particles. Figure 17

shows simulated ground-water basins in relation to surfacewater basins for major tributaries to the Rock River; 

additional information for each tributary basin is listed in 

table 4. Whereas ground-water and surface-water basins 

are commonly similar in size and shape, ground-water and 

surface-water divides can differ locally. This is particularly 

evident near some headwater areas, such as the northwestern 

edge of the Yahara and Crawfish River Basins where the 

surface-water basins extend beyond the ground-water 

basins. The location of ground-water divides is controlled 

by the configuration of the water table, whereas the location 

of surface-water divides is controlled by the land-surface 

topography. Moreover, river geometries, geologic factors, 

recharge, and in some cases pumping, all can influence the 

water table and therefore the location of ground-water divides. 

Further simulation of ground-water basins and contributing 

areas at local scales with refined river systems would result 

in a more accurate evaluation of how much surface-water and 

ground-water divides differ. Likewise, additional water level 

measurements would help to better identify the location and 

temporal movement of local ground-water divides.
26 Simulation of the Regional Ground-Water-Flow System and Ground-Water/Surface-Water Interaction, Rock River Basin, Wisconsin

EXPLANATION

Ground-water flow path

Simulated water-table altitude, 

50-foot contour interval

Lake

Horicon Marsh

Near-field linesink

Far-field linesink

Extent of the Maquoketa Formation

County boundary

Rock River Basin boundary

89°30' 89° 88°30'

43°30'

43°

0 10 20 MILES

0 10 20 KILOMETERS

900

850

800

900 800

850

950

900

900

1000

1050

950

1000

1000

900

900

850

950

1000

1050

950

950

900

850

850

850

850

1000

1000

900

900

900

850

950

800

Figure 15. Simulated water-table altitude and ground-water flow directions from the GFLOW model in the 

Rock River Basin.
Evaluation of Simulated Results of the Rock River Basin Model 27

42°30'

EXPLANATION

Dry segment

Losing segment

Gaining segment

Far-field linesink

Recharge area

High-recharge zone

Simulated lake

Horicon Marsh

Extent of the Maquoketa Formation

County boundary

Rock River Basin boundary

89°30' 89° 88°30' 89°

43°30'

43°

0 10 20 MILES

0 10 20 KILOMETERS

Figure 16. Simulated gaining (blue) and losing (red) river and lake shorelines in the Rock River Basin. 

Linesinks with zero simulated baseflow (dry) are also shown.
EXPLANATION

Tributary surface-water 

basin boundary

Near-field linesink

East Branch Rock River near Mayville Far-field linesink

West Branch Rock River at State Highway 49 near Waupun

Rock River near Horicon

Rock River at Robert Street at Fort Atkinson

Crawfish River at Milford

Bark River at the Rock River

Koshkonong Creek near Koshkonong Lake

Yahara River near Fulton

Turtle Creek at the Rock River

Rock River upstream from Beloit (excludes Turtle Creek)

Ground-water basins for the:

89° 89°30' 88°30'

43°30'

43°

0 10 20 MILES

0 10 20 KILOMETERS

Figure 17. Simulated ground-water and mapped surface-water contributing areas for 

select tributaries to the Rock River.

28 Simulation of the Regional Ground-Water-Flow System and Ground-Water/Surface-Water Interaction, Rock River Basin, Wisconsin
Simulation of Relatively Local Ground-WaterCapture Areas for Rivers 

In addition to delineating ground-water basins for select 

tributaries, the GFLOW model can be used to map areas of 

relatively local ground water that is captured along stream 

reaches. Such a map is useful for understanding the primary 

direction from which a stream reach gains water. For example, 

many head-water streams that are aligned perpendicular to 

regional ground-water-flow patterns gain the majority of their 

base flow along one shoreline, with the other shoreline gaining 

a smaller amount of ground water or potentially losing water 

to the ground-water-flow system. Such information may be 

useful for interpreting local sources of water for a stream and 

associated differences in the water chemistry among individual 

streams.

Traces of water particles were simulated with the 

GFLOW model to evaluate flow directions and delineate areas 

of relatively local ground water captured by streams. Particles 

were released in a series of densely spaced grids across the 

entire basin and tracked forward from the water table to a 

discharge point (river or well). The length of each path line 

was recorded and compared with the median flow path length 

(about 1.6 mi). For this report, relatively local ground-watercapture areas for rivers are defined as the areas in which all 

simulated particle paths flowing from recharge at the water 

table to discharge at a stream were less than 1.6 miles. 

Relatively local ground-water-capture areas for rivers in 

the Rock River Basin generally extend a moderate distance 

upgradient from rivers and are modified by the regional 

flow pattern (fig. 18). For example, the area is centered on 

many rivers but is shifted toward regional ground-water 

divides for relatively small rivers such as Johnson Creek in 

Jefferson County and Badfish Creek in Dane County. The 

areas of relatively local ground-water capture are generalized 

and consider only major tributary rivers; some headwater 

tributaries were not simulated in the GFLOW model. 

Likewise, the area contributing to the Horicon Marsh likely 

extends farther around the marsh than was simulated because 

the marsh was simulated with a high-conductivity zone instead 

of a line sink. Conductivity zones do not stop the path of 

simulated particles because they are not ground-water sinks; 

line sinks can stop the path of simulated particles because 

ground water can discharge to these surface-water features, 

and thereby be removed from the aquifer. The analysis also 

excluded areas from which simulated particles ultimately 

discharged to withdrawal wells. Thus, white areas in figure 18

indicate areas in which simulated particles of water either 

discharged to a withdrawal well or discharged to a river but 

traveled more than 1.6 miles through the ground-water-flow 

system. Local or site-specific flow directions and particle path 

lengths would likely be improved through local refinement of 

the model. Likewise, measurements of local streambed and 

lakebed resistance would help to improve local simulations of 

particle paths.

Table 4. Hydrologic characteristics and simulated results for selected tributary river basins in the Rock River Basin.

[mi2, square mile; ft3/s, cubic foot per second]

Site 

number in 

figure 1

Station name

Surface-waterbasin area 

(mi2

)

Ground-waterbasin area 

(mi2)

Simulated 

base flow 

(ft3/s) 

Area above 

Maquoketa 

subcrop 

(percent of 

surface-waterbasin area)

1 Rock River upstream from Beloit (excludes Turtle Creek) 3,460 3,390 1,450 15

2 Turtle Creek at the Rock River 290 280 98 14

3 Yahara River near Fulton 520 520 164 0

4 Koshkonong Creek near Koshkonong Lake 160 160 67 0

5 Bark River at the Rock River 340 370 199 26

6 Crawfish River at Milford 760 750 333 0

7 Rock River at Robert Street at Fort Atkinson 2,240 2,220 1,020 24

8 Rock River near Horicon 460 420 173 48

9 West Branch Rock River at State Highway 49 near Waupun 110 90 16 0

10 East Branch Rock River near Mayville 180 170 75 99

Evaluation of Simulated Results of the Rock River Basin Model 29
30 Simulation of the Regional Ground-Water-Flow System and Ground-Water/Surface-Water Interaction, Rock River Basin, Wisconsin

EXPLANATION

Areas of relatively local 

ground-water capture by rivers

Near-field linesink

Far-field linesink

County boundary

Rock River Basin boundary

89°30' 89° 88°30'

43°30'

43°

0 10 20 MILES

0 10 20 KILOMETERS

Johnson Cr

Badfish Cr

Dry segment

Figure 18. Simulated areas of relatively local (length of travel less than 1.6 miles) ground water captured by 

rivers in the Rock River Basin. 
Summary 31

Model Limitations

As is the case with all ground-water-flow models, the 

GFLOW model of the Rock River Basin is a simplification 

of the physical system and has corresponding limitations in 

model precision and how the model can be used. For example, 

few first-order (headwater) streams were simulated, and 

larger streams were simulated with a coarse representation. 

Likewise, local complexities, such as wetlands, springs, 

perched water tables and karst aquifers, were not explicitly 

simulated in the regional model. This approach is well 

suited for a regional model, which is designed to evaluate 

effects of regional stressors (for example, estimated largescale changes in recharge or pumping) on regional features 

such as large streams. However, use of the model to answer 

local-scale questions (for example, questions that focus on 

individual supply wells or a group of supply wells) would 

benefit from local refinement, including refinement and/or 

addition of linesinks and possibly local recalibration of the 

model to additional data for the area. Similarly, depending on 

the specific aquifer(s) targeted for a local refinement, local 

discharge-specified linesinks that represent flow below the 

Maquoketa Formation in the sandstone aquifer may need to be 

reevaluated and potentially removed. In addition, the regional 

model may not perform equally in all locations because 

local geologic complexities were not incorporated into the 

model. For example, the regional model has limited ability 

to delineate ground-water basins for headwater streams and 

supply wells, which are sensitive to local geologic conditions 

that were not simulated in the regional model. 

The model-calibration process focused on long-term 

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

properties of the bulk ground-water-flow system in the Rock 

River Basin. Short-term, transient phenomena (for example, 

seasonal water level fluctuations or periodic changes to 

pumping rates) were not simulated. Steady state models, such 

as the model described in this report, can be used to evaluate 

how the system responds to sustained, long-term changes. 

However, a transient simulation would improve understanding 

of how the system responds to temporary changes. 

Moreover, the flow system contains several layered 

aquifers and confining units that were combined in this model. 

Ground-water flow directions within individual aquifers 

likely vary from that of the system as a whole and would 

need to be simulated with a three-dimensional model, such 

as MODFLOW (Harbaugh, 2005), if three-dimensional flow 

were important. For example, the GFLOW model should not 

be used to determine how deeper parts of the flow system 

respond to pumping from a cluster of wells below confining 

units where flow directions in the deep aquifer do not 

necessarily follow flow directions in the shallow aquifers. 

Instead, the GFLOW model provides a regional framework 

from which a local, three-dimensional model could be 

developed that would be integrated with the regional flow 

system. Simple hand calculations (Haitjema, 2006) can be 

used to evaluate whether a specific question warrants the 

additional resources of a three-dimensional simulation.

In addition, simulated particle paths that were used to 

map relatively local ground-water-capture areas (fig. 18) 

were generated at a regional scale. Local or site-specific flow 

directions and particle path lengths would likely be improved 

through local refinement. In particular, measurements of local 

streambed or lakebed resistance would improve simulations of 

both horizontal and approximate vertical flow paths near these 

surface-water features. Moreover, potential future applications 

of the model for which flow velocities are important (such 

as mapping a time-dependent contributing area to a well, 

such as a “10-year zone of capture”) would benefit from field 

measurements and analyses of porosity, ground-water age, and 

traveltimes. Water-level and base-flow targets alone do not 

provide sufficient information for calibrating ground-water 

velocities and travel times. 

Summary

A regional, one-layer, analytic element ground-waterflow model was developed to simulate the ground-water-flow 

system in the Rock River Basin of southeastern Wisconsin. 

The model was developed by the U.S. Geological Survey 

(USGS), in cooperation with the Rock River Coalition, to 

contribute to the fundamental understanding of the region’s 

hydrogeology. The objectives of the regional model were 

to improve understanding of the ground-water-flow system, 

including ground-water/surface-water interaction, and to 

develop a tool suitable for evaluating the effects of potential 

water-management programs. Simulations made with the 

regional model reproduce ground-water levels and stream 

base flows representative of recent conditions (1997-2006) 

and illustrate ground-water-flow patterns with maps of (1) 

the simulated water table and ground-water-flow directions, 

(2) simulated gaining and losing river and lake sections, 

(3) simulated ground-water contributing areas to tributary 

rivers, and (4) simulated areas of relatively local ground 

water captured by rivers. In addition, the regional model was 

designed as a framework in which more detail could be added 

and from which three-dimensional inset models could be 

developed.

Three generalized regional aquifers and one regional 

confining unit are present in the Rock River Basin. The 

aquifers consist of (1) a sand and gravel aquifer that covers 

the entire basin, (2) a carbonate aquifer that is present below 

approximately the eastern one-quarter of the basin, and (3) 

a sandstone aquifer below the entire basin. The Maquoketa 

Formation, a regional confining unit, separates the carbonate 

aquifer above from the sandstone aquifer below. The 
32 Simulation of the Regional Ground-Water-Flow System and Ground-Water/Surface-Water Interaction, Rock River Basin, Wisconsin

Maquoketa Formation and the carbonate aquifer above it 

have been eroded and are absent in approximately the western 

three-quarters of the basin. Simplifications were incorporated 

into the model to simulate the ground-water-flow system with 

a single layer of differing geologic properties. The sand and 

gravel aquifer is combined with the carbonate aquifer where it 

overlies the Maquoketa Formation; the sand and gravel aquifer 

is combined with the sandstone aquifer where the Maquoketa 

Formation and overlying carbonate aquifer are absent. 

Precambrian crystalline rock forms the base of the groundwater-flow system. 

The analytic element ground-water-flow model code, 

GFLOW, was used to develop the regional ground-water-flow 

model. Model input was obtained from previously published 

geologic and hydrologic data. Pumping rates from municipal 

and private high-capacity wells also were simulated. Model 

calibration included a comparison between modeled and 

field-measured water levels and base flows in simulated rivers. 

After calibration, most measured water levels compared 

favorably to model-calculated water levels; the mean absolute 

difference and root mean squared difference between 

measured and simulated water levels were less than 7 percent 

of the total range in measured water levels. Simulated base 

flows generally matched measured base flows; simulated base 

flows were within 10 percent of the estimated base flow at four 

of nine stream-gage targets. As currently calibrated, the model 

can be used as a regional water-management tool. Because of 

the regional focus, however, the model may need to be refined 

for local-scale simulations. 

Simulated water levels and particle tracking in the 

regional model illustrate ground-water-flow paths from 

recharge areas toward ground-water discharge areas, such as 

rivers and wells. Under current conditions, the Rock River, 

its tributaries, and most large lakes are primarily groundwater discharge locations (gaining reaches), but they include 

reaches and shorelines that lose surface-water to the groundwater-flow system. Losing river reaches and lake shorelines 

tend to be primarily along the downgradient side of lakes or 

reservoirs, near ground-water pumping centers, or along river 

meanders where local hydraulic gradients can be complex. 

Ground-water basins for selected tributary basins generally 

coincide with surface-water basins, but they can differ in 

headwater areas, such as along the north-western edge of the 

Yahara and Crawfish River Basins.

Simulated areas of relatively local ground water captured 

by rivers were estimated by simulating particles of water 

from the water table to discharge features, such as rivers and 

supply wells. For this report, relatively local ground water 

was defined as water that traveled less than 1.6 miles from 

recharge at the water table to discharge at a stream. These 

areas generally extend a moderate distance around the rivers 

and are modified by the regional flow pattern, whereby the 

areas are commonly shifted toward the upgradient groundwater-flow direction for relatively small rivers. For example, 

many head-water streams that flow perpendicular to regional 

ground-water-flow patterns gain the majority of their base flow 

only along one shoreline. Such information may be useful for 

interpreting local sources of water for a stream and associated 

differences in the water chemistry among individual streams. 

For most efficient use, the regional model would require 

periodic updates and improvements as additional field data 

and estimates of future hydrologic stresses become available. 

Local refinements of the model could locally improve 

simulation of flow to rivers, lakes, and wells, especially 

when combined with additional data collection to improve 

characterization of local aquifer properties and recharge rates. 

The model also serves as a framework from which threedimensional MODFLOW (Harbaugh, 2005) models could be 

developed. A combination of regional and local simulations 

would provide a suite of comprehensive tools that could be 

used by water-resources managers to address emerging watersupply and water-quality concerns in the Rock River Basin. 

Acknowledgments

Thanks are extended to many individuals for their 

contributions to the work described in this report. David 

Johnson (WDNR) and James Krohelski (USGS) initiated 

discussions that prompted this study. Suzanne Wade, Rock 

River Coalition and University of Wisconsin-Extension, 

garnered support from numerous communities in the Rock 

River Basin that provided the majority of the funding for 

this work. Suzanne was assisted by members of the Rock 

River Coalition’s Groundwater Issues Team, which included 

Stephen Ales (WDNR), Paula Allen (DATCP/EPA), Tim 

Banwell (Rock County), Dennis Bries (Wisconsin Farm 

Bureau), Jim Congdon (WDNR), Joe Dorava (Rock River 

Coalition and Vierbicher Associates), Ruth Johnson (WDNR), 

Paul Moderacki (Village of Johnson Creek), Ed Morse (WI 

Rural Water Association), Steve Nass (Jefferson County), 

David Neuendorf (UW-Extension), Orson Tingey (University 

of Wisconsin), Rick Wietersen (Rock County), and Steve 

Wilke (City of Lake Mills). Joe Dorava also coordinated the 

GFLOW model project for the Rock River Coalition and did 

a review of the report. Cheryl Buchwald, USGS Wisconsin 

Water Science Center, compiled water-use information for 

high-capacity wells in the model area. Daniel Feinstein, 

Charles Dunning, and Randy Hunt, USGS Wisconsin Water 

Science Center, gave valuable feedback on model design 

and construction throughout the project and furnished results 

from the SEWRPC model (Feinstein and others, 2005b) that 

were incorporated into the GFLOW model. James Krohelski, 

Rodney Sheets, and Ralph Haefner (USGS) did technical 

reviews of the report. Michael Eberle, USGS Columbus 

Publishing Service Center, did an editorial review of the 

report.
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References 37

Appendixes

Appendix data can be accessed by downloading files at http://pubs.usgs.gov/sir/2009/5094.

Appendix 1. Public-Supply Wells.

Appendix 2. Irrigation, Industrial, and Commercial Supply Wells.

Appendix 3. Public, Irrigation, Industrial, and Commercial Supply Wells in Illinois.

Appendix 4. Ground-Water Observation Network Water-Level Targets.

Appendix 5. Well Construction Report Water-Level Targets.
38 Simulation of the Regional Ground-Water-Flow System and Ground-Water/Surface-Water Interaction, Rock River Basin, Wisconsin

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Juckem— Regional Ground-Water-Flow System and Ground-Water/Surface-Water Interaction, Rock River Basin, Wisconsin—Scientific Investigations Report 2009–5094