Simulation of Ground-Water Flow and

Areas Contributing Ground Water to

Production Wells, Cadillac, Michigan

By C.J. Hoard and D.B. Westjohn

Prepared in cooperation with the city of Cadillac, Michigan

Scientific Investigations Report 2004-5175

U.S. Department of the Interior

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

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

U.S. Geological Survey, Reston, Virginia: 2005

For sale by U.S. Geological Survey, Information Services

Box 25286, Denver Federal Center

Denver, CO 80225

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endorsement by the U.S. Government.

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

reproduce any copyrighted materials contained within this report.

Suggested citation: 

Hoard, C.J., and Westjohn, D.B., 2005, Simulation of Ground-Water Flow and Areas Contributing 

Ground Water to Production Wells, Cadillac, Michigan: U.S. Geological Survey Scientific Investigations Report 2004-5175, 18 p.
Contents

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

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

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

Previous Studies.................................................................................................................................3

Description of Study Area.................................................................................................................3

Simulation of Ground Water Flow..............................................................................................................5

Model Development...........................................................................................................................5

Boundaries ..........................................................................................................................................5

Stresses ...............................................................................................................................................7

Discretization ......................................................................................................................................8

Model Calibration and Sensitivity..................................................................................................10

Delineation of Contributing Areas............................................................................................................10

Optimized Scenario..........................................................................................................................10

Alternate Scenario...........................................................................................................................12

Limitations of Model Simulations...................................................................................................13

Summary ......................................................................................................................................................16

Acknowledgments......................................................................................................................................17

References Cited ........................................................................................................................................17

Figures

1-3. Maps showing:

1. Location of the Clam River watershed, Wexford and Missaukee Counties, 

Michigan. .......................................................................................................................................2

2. Altitude of land surface and spatial distribution of estimated effective recharge 

(modified from Holtschlag, 1996) in the Clam River watershed, Michigan. .......................4

3. Surficial glacial deposits in the Clam River watershed, Michigan. .....................................5

4. Hydrogeologic section from West to East through the Cadillac well field, 

Cadillac, Michigan................................................................................................................................6

5-6. Maps showing:

5. Potentiometric surface map for the intermediate aquifers (>1050 ft above 

NGVD 29), Clam River watershed, Michigan...........................................................................7

6. Potentiometric surface map for the deep aquifer (<1050 ft above NGVD 29), 

Clam River watershed, Michigan...............................................................................................8

7. Conceptual diagram of ground-water flow for the Clam River watershed, 

Cadillac, Michigan................................................................................................................................9

8. Map showing lateral discretization and location of specified head boundaries 

for the ground-water flow model of the Clam River watershed, 

Cadillac Michigan...............................................................................................................................11
iv

9. Graph showing observed and simulated heads (water levels) for the calibrated 

 ground-water flow model of the Clam River watershed, Michigan.................................11

10-13. Maps showing:

10. Distribution of head (water level) residual (difference between observed and 

simulated heads) for the calibrated flow model for the Clam River watershed, 

 Cadillac, Michigan....................................................................................................................12

11. Model-simulated heads, and head residuals for observations in the deep aquifer 

 (layer 4), Clam River watershed, Michigan. .........................................................................13

12. Ten-year contributing area for scenario with optimized parameters, Cadillac 

 municipal-well field, Cadillac, Michigan. .............................................................................15

13. Ten-year contributing area for scenario with alternate parameters, Cadillac 

 municipal-well field, Cadillac, Michigan. .............................................................................16

Tables

1. Results of selected aquifer tests in the aquifer units underlying the Clam River 

 watershed, Michigan ............................................................................................................................9

2. Parameter values for optimized model and alternate model of the Clam River 

 watershed, Michigan. .........................................................................................................................14

Conversion Factors and Abbreviations

> and < symbols indicate greater than or less than, respectively.

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.
Abstract

Ground water is the primary source of water for domestic, municipal, and industrial use within the northwest section 

of Michigan’s Lower Peninsula. Because of the importance 

of this resource, numerous communities including the city of 

Cadillac in Wexford County, Michigan, have begun local wellhead protection programs. In these programs, communities 

protect their ground-water resources by identifying the areas 

that contribute water to production wells, identifying potential 

sources of contamination, and developing methods to cooperatively manage and minimize threats to the water supply.

The U.S. Geological Survey, in cooperation with the 

city of Cadillac, simulated regional ground-water flow and 

estimated areas contributing recharge and zones of transport to 

the production well field. Ground-water flow models for the 

Clam River watershed, in Wexford and Missaukee Counties, 

were developed using the U.S. Geological Survey modular 

three-dimensional finite-difference ground-water flow model 

(MODFLOW 2000). Ground-water flow models were calibrated using the observation, sensitivity, and parameter estimation packages of MODFLOW 2000. Ground-water-head 

solutions from calibrated flow models were used in conjunction with MODPATH, a particle-tracking program, to simulate 

regional ground-water flow and estimate areas contributing 

recharge and zones of transport to the Cadillac productionwell field for a 10-year period. 

Model simulations match the conceptual model in that 

regional ground-water flow in the deep ground-water system 

is from southeast to northwest across the watershed. Areas 

contributing water were determined for the optimized parameter set and an alternate parameter set that included increased 

recharge and hydraulic conductivity values. Although 

substantially different hydrologic parameters (assumed to 

represent end-member ranges of realistic hydrologic parameters) were used in alternate numerical simulations, simulation 

results differ little in predictions of the size of the contributing 

area to the city well field. However, increasing recharge and 

hydraulic conductivity values appreciably affected the shape 

of the contributing area and zone of contribution of reacharge. 

Simulation results indicate that the region immediately to the 

south and southeast of the well field is contributing water to 

the production wells. Detailed aquifer characterization would 

be needed to describe and simulate the heterogeneous glacial 

deposits in the watershed.

Introduction

About 46 percent of Michigan’s population relies on 

ground water as a source of drinking water (Alley and others, 1999). In an effort to protect these and other groundwater resources, the U.S. Environmental Protection Agency 

(USEPA) passed amendments to the Safe Drinking Water 

Act in 1986. One of these amendments encourages states 

to implement wellhead protection programs (WHPP) (Legal 

Information Institute, 2004). The State of Michigan Department of Environmental Quality (MDEQ) oversees the State 

WHPP and provides guidelines on how to assess the vulnerability of ground-water resources used for municipal water 

supplies. In addition, the MDEQ reviews and approves plans 

to protect areas contributing recharge to wells from sources of 

ground-water contamination. 

The city of Cadillac, in Wexford County, Michigan 

(fig. 1), is developing a wellhead protection plan for their 

production well field. As part of the WHPP, the contributing area needs to be delineated. The U.S. Geological Survey 

(USGS) entered into a cooperative agreement in 2000 with the 

city of Cadillac to simulate regional ground-water flow and 

estimate areas contributing recharge (areas on land surface that 

contribute water to wells) and zones-of-transport (areas in the 

subsurface that contribute water to wells) to the production 

well field. For this report, the term contributing area refers to 

both the area contributing recharge (surface) and the zoneof-transport (subsurface) contributing water to a well. Model 

simulations will provide a basis for management decisions 

concerning the ground-water resources of the Clam River 

watershed.

By C.J. Hoard and D.B. Westjohn

Simulation of Ground-Water Flow and Areas Contributing 

Ground Water to Production Wells, Cadillac, Michigan
2 Simulation of Ground-Water Flow and Areas Contributing Ground Water to Production Wells, Cadillac, Michigan

85° 20 ’1 "

85 ° 30 ’1"

85 ° 25 ’1"

44 ° 14 ’58"

85 ° 35 ’1"

44 ° 19 ’58"

Base From U.S. Geological Survey Digital Data, 1983

1:250,000. Michigan Georef Coordinate System

Cadillac

Clam River

Figure 1. Location of the Clam River watershed, Wexford and Missaukee Counties, Michigan.

Wexford County Missaukee County

City of 

Cadillac

Clam River

Watershed

Haring

Township

MICHIGAN

0 1 2 3 4 MILES

0 1 2 3 4 KILOMETERS
 3

Purpose and Scope

The purpose of this report is to describe the development and calibration of a regional ground-water flow 

model used in conjunction with a particle-tracking model 

to understand regional ground-water flow and estimate the 

Wellhead Protection Area (WHPA) for the city of Cadillac’s 

production wells. This type of analysis assists waterresource managers in addressing concerns about protection 

and availability of their ground-water resources. In addition, 

this approach to identifying WHPA’s can be applied in other 

areas of the State.

A conceptual model of the Clam River watershed was 

constructed on the basis of hydrogeologic data collected 

during this and previous investigations. A steady-state 

numerical model, developed on the basis of the conceptual 

model, was calibrated and optimized using MODFLOW 

2000. A hypothetical scenario using high aquifer recharge 

rates and hydraulic-conductivity estimates was performed. 

The effect of different model parameters representing various characteristics of the ground-water system had on the 

resulting contributing area is also described.

Previous Studies

Before 1960, the city of Cadillac used Lake Cadillac 

(fig. 1) for their municipal water supply (Michigan State 

University Extension, 2002). Exploratory drilling indicated 

three sand and gravel aquifers termed the “shallow”, “intermediate”, and “deep” aquifers. Clay-confining units separate 

the aquifers. As part of the conversion to ground water for 

municipal use, aquifer tests were performed in the areas that 

became the city’s well field. Jones, Henry and Williams 

Consulting Engineers (1959) performed the initial tests and 

concluded that the deep aquifer (>265 feet below ground 

surface) was the best option for the city. Their evaluation of 

the data indicated that the deep aquifer had a high transmissivity (214 ft/d), was confined, and was likely protected 

from shallow sources of environmental contamination 

(Jones, Henry, and Williams Consulting Engineers, 1959). 

Keck Consulting Services (1987) evaluated the same aquifer 

test and estimated the volume of water leaking through the 

clay confining unit that overlies the deep aquifer. Results 

of the Keck analysis indicate that this clay confining unit is 

leaky and transmits about 4.2 percent of the water withdrawn from the well field, or as much as 103 gal/min (Keck 

Consulting Services, 1987). Aquifer-test information also 

is available for the production wells for Haring Township, 

which is just north of the city of Cadillac (fig. 1) (J.L. Wilcox & Associates, 1986). These data indicate that the deep 

aquifer underlying Haring Township has hydraulic properties similar to those of the deep aquifer underlying Cadillac.

Cadillac placed their well field in the industrial park 

in an effort to minimize distance to the major water users 

(Michigan State University Extension, 2002). Contamination by metals, and volatile organic compounds (VOC’s) 

was discovered in water samples from the shallow aquifer 

near the well field as early as 1978 (E.C. Jordan Co., 1986). 

As a result, various hydrogeologic studies were done to 

describe the contaminant plumes and select remediation 

strategies to protect the well field. E.C. Jordan Co. (1986) 

was among the first organizations to study the relations 

among industrial park activities, water quality, and the 

hydrogeology of the area immediately around the well field. 

Investigations by WW Engineering and Science (1989a, 

1989b, 1994), Environmental Science and Engineering 

Inc. (1996, 2000), QST Environmental (1998), and Roy F. 

Weston Inc. of Michigan (2001, 2002) provided additional 

information on aquifer characteristics, types of contaminant 

plumes and their migration paths, and the treatment strategies used to remediate the shallow aquifer. 

Despite the large amount of hydrogeologic information available for the area near Cadillac’s production well 

field, little hydrogeologic information was available for the 

greater Cadillac area. Leverett and Taylor (1915), as well 

as Stewart (1948), described the surficial geologic deposits 

of Wexford County. A geophysical study by Westjohn 

(1989) generated a subsurface geologic model of the area 

near Lake Mitchell (fig. 1). Additional work by Thomson 

(1969) describes the hydrology of the Manistee River system in various counties in northwestern Michigan, including 

Wexford County.

Description of Study Area

The study area is the Clam River watershed, which is 

in southeastern Wexford County and southwestern Missaukee County (fig. 1). Wexford County is in the northwestern 

portion of Michigan’s Lower Peninsula (fig. 1), and the city 

of Cadillac is the county seat. Cadillac is the largest user 

of ground water in the area, largely because of the extensive base of industrial consumers of water resources. The 

Clam River watershed, which is part of the Muskegon River 

drainage system, is an area of about 96 mi2. The total relief 

of the watershed area is approximately 350 ft, with topographic highs in the northwestern and southeastern portions 

of the watershed, and a topographic low near the center of 

the watershed (fig. 2). Surface-water drainage is toward the 

northeast and drains into the Clam River (fig. 1).

The prominent surface-water features in the Clam 

River watershed are Lakes Mitchell and Cadillac, near 

the center of the watershed (fig. 1). Lake Mitchell is the 

larger of the two lakes, with an area of approximately 4.15 

mi2; the lake is about 22 ft deep at its deepest point. Lake 

Cadillac is 1.83 mi2 and is roughly 28 ft deep at its deepest point (Frier, 1978). The lakes are joined by a canal that 

has effectively made the water levels of the two lakes the 

same. The Clam River is the only outlet for Lake Cadillac 

and drains to the northeast (fig. 1). A control structure on 

the Clam River maintains water levels in the lakes in the 

Introduction
4 Simulation of Ground-Water Flow and Areas Contributing Ground Water to Production Wells, Cadillac, Michigan

range from 1,288.9 to 1,290.0 ft above NGVD 29, depending 

on the season (Michigan State University Extension, 2002). 

Various smaller lakes, all less than 0.2 mi2, are also located 

in the watershed and include Woodward, Pleasant, Berry, 

and the Twin Lakes (fig. 1).

On average, the watershed receives 32.5 in of precipitation in a year (Midwest Climate Center, 2003). Of that 

precipitation, an average of 10 in/yr enters the ground-water 

system as effective recharge (Holtschlag, 1996). However, recharge in the area is not spatially uniform (fig. 2) 

(Holtschlag, 1996). The upland areas, which consist of 

coarse-grained glacial deposits, receive more recharge than 

the lowland areas, which consist of finer-grained glacial 

deposits. 

The lithologic units that underlie the Clam River watershed include unconsolidated glacial material and bedrock. 

Cadillac and all other users of ground water in the study 

area rely on ground water withdrawn from sand-and-gravel 

deposits that are part of a thick sequence (from 600 to over 

900 ft) of Pleistocene glacial deposits (Westjohn and others, 

1994). Bedrock that underlies these glacial deposits consists 

principally of sandstone, shale, carbonate, and evaporites 

of Mississippian to Pennsylvanian age. However, there 

has been no need to use bedrock aquifers for water supply 

because the overlying glacial deposits predominantly are 

permeable sand and gravel, and these deposits provide the 

quantity and quality of ground water needed for industrial, 

commercial, and domestic use. 

Maps of surficial deposits in Michigan (fig. 3) (Martin, 1955; Farrand and Bell, 1982) show the Clam River 

watershed coincides with an east-west trending oblateshaped area where glacial deposits consist of outwash sand 

and gravel. Maps by Martin (1955), and Farrand and Bell 

(1982) show a sequence of moraines surrounding the Clam 

River watershed (fig. 3). Many exposures of these mapped 

moraines were examined during the present study and it was 

determined that these exposures are composed of coarse 

sand and gravel.

One interpretation of the origin of these glacial deposits 

is that the area is part of an extensive sequence of stagnation-deglaciation deposits (using the nomenclature of Bates 

and Jackson, 1987) that formed by mass wasting of large, 

isolated ice blocks at the end of the Pleistocene Epoch. The 

Clam River watershed appears to be the former location of 

85° 20’ 1”

85°30’ 1"

85° 25’ 1"

44°14’ 58"

85° 35 ’1"

44° 19 ’ 58"

High : 1,623

Low : 1,279

17.6 − 20.0

15.1 − 17.5

12.6 − 15.0

10.1 − 12.5

7.6 −10.0

5.0 −7.5

EXPLANATION

LAND- SURFACE ALTITUDE

(Feet above NGVD 29)

RECHARGE

(Inches per year)

Figure 2. Altitude of land surface and spatial distribution of estimated effective recharge (modified from Holtschlag, 1996

in the Clam River watershed, Michigan.

0 1 2 3 4 MILES

0 1 2 3 4 KILOMETERS
 5

a massive ice block. Evidence from geophysical logs, geologic logs, and exposures of glacial sediment indicate that 

as this ice block down wasted during the end of the Pleistocene, outwash fans formed away from the large isolated ice 

mass. These outwash fans formed the ridges that surround 

the watershed. Lakes Cadillac, Mitchell, Woodward, Pleasant, and the extensive wetlands area that forms a large part 

of the watershed, likely mark the location of an extensive 

area where outwash deposits collapsed inward toward melting, buried ice blocks. A representative hydrogeologic section is shown in figure 4, which illustrates the four primary 

aquifers and three primary confining units underlying the 

study area as considered in this study. For this study, the 

intermediate aquifer has been divided into two units (1 and 

2). In general, the altitudes of occurrence of the aquifers are 

given below.

 Simulation of Ground-Water Flow

Simulation of Ground-Water Flow

Model Development

The conceptual model of the Clam River watershed 

incorporates locations and effects of hydrologic boundaries, the general pattern of ground-water flow, sources and 

sinks of water, and the aquifers and confining units (fig. 4) 

in the Clam River watershed. Changes to the conceptual 

model can be made as more information is collected and 

the ground-water system is better understood. The sections 

below describe this conceptual model.

Boundaries

Ground-water system boundaries were chosen to coincide with the surface-water-drainage divide of the watershed. Along northern and southern portions of the study 

area, no-flow boundaries were used whereas specified-head 

(water level) boundaries were used along the northwestern 

85° 20’ 1“

85° 30’ 1"

85°25’ 1"

44° 14’ 58"

85° 35’ 1"

44° 19’ 58"

0 1 2 3 4 MILES

0 1 2 3 4

EXPLANATION

End moraines of coarsetextured till

Glacial outwash sand and 

gravel and postglacial alluvium

Lacustrine sand and gravel

Road

KILOMETERS

Geology by Farrand and Bell, 1982

Figure 3. Surficial glacial deposits in the Clam River watershed, Michigan.

Shallow aquifer 1,300 - 1,278 ft above NGVD 29

Intermediate aquifer 1 1,273 - 1,139 ft above NGVD 29

Intermediate aquifer 2 1,135 - 1,073 ft above NGVD 29

Deep aquifer 1,050 - 700 ft above NGVD 29
6 Simulation of Ground-Water Flow and Areas Contributing Ground Water to Production Wells, Cadillac, Michigan

Cadillac

Well Field

Deep aquifer

Model Layer 4

Deep clay confining unit

Intermediate aquifer 2

model layer 3

Intermediate aquifer 1

model layer 2

Clay

breach

Intermediate Clay

Confining Unit

Shallow aquifer

model layer 1

Shallow clay 

confining unit

Cadillac Well Field

WELL LITHOLOGY

EXPLANATION

Figure 4. Hydrogeologic section from west to east through the Cadillac well field

Cadillac, Michigan.

0 0.2 0.4 0.6 0.8 1 MILE

0 0.2 0.4 0.6 0.8 1 KILOMETER

Vertical scale greatly exaggerated

1,300

1,250

1,200

1,150

1,100

1,050

1,000

 950

1,300

1,250

1,200

1,150

1,100

1,050

1,000

950

DEPTH BELOW LAND SURFACE, IN FEET

Land surface
 7

and southeastern boundaries. The specified head boundaries 

were assigned on the basis of potentiometric-surface maps 

generated from a combination of measured water levels 

and water levels reported on geologic logs. For the shallow 

and intermediate aquifers, ground-water flow is from the 

highlands in the northwest and southeast towards the lowlands in the center of the study area (figs. 2,5,7). However, 

the ground-water flow pattern in the deep aquifer reflects 

a regional trend in ground-water flow from the southeast 

toward the northwest (figs. 6,7). As a result, the specified 

head boundaries for the deep aquifer were assigned to match 

the potentiometric surface of the deep aquifer. 

The top and bottom of the model are both treated as 

no-flow boundaries. Land-surface altitude was used for the 

top no-flow boundary. An altitude of 700 ft was used for 

the bottom no-flow boundary; this was chosen arbitrarily 

because little is known about ground-water flow at that 

depth. 

Stresses 

Sources of water in the watershed include recharge 

from precipitation, surface-water features, and injection 

well discharge. Recharge was applied to the uppermost 

active model layer based on Holtschlag’s (1996) estimates 

(fig. 2,7). The surface-water features were conceptualized 

as perched on low-permeability materials. Altitudes of 

lake surfaces from topographic maps were used to establish 

heads (water levels) for lakes in the study area. Riverhead stresses were assigned as 1 ft lower than land-surface 

altitude based on the 30-meter digital elevation model. Permeability values from Calver (2001) were used to estimate 

bed-material conductance for lakes and rivers. Additional 

recharge was applied to the model to simulate an injection 

well used as part of a remediation system for contaminated 

ground water. Recharge from that well was approximately 

200 gal/min (James Skipper, Michigan Department of Environmental Quality, oral commun., 2003). 

 Simulation of Ground-Water Flow 

85°20’1

85°30’1"

85°25’1"

44°14’58"

85°35’1"

44°19’58"

1,200 −1,225

1,226 −1,250

1,251 −1,275

1,276 −1,300

1,301 −1,325

1,326 −1,350

1,351 −1,377

0 1 2 3 4 MILES

0 1 2 3 4 KILOMETERS

No Data

EXPLANATION

WATER-LEVEL ALTITUDE

(Feet above NGVD 29)

Figure 5. Potentiometric surface map for the intermediate aquifers (greater than 1050 ft above NGVD 29),

Clam River watershed, Michigan.
8 Simulation of Ground-Water Flow and Areas Contributing Ground Water to Production Wells, Cadillac, Michigan

Another major stress in the ground-water system was 

discharge from wells. Thirty-seven wells near the city of 

Cadillac were discharging water from the system at an 

approximate rate of 5116 gal/min during the model simulation (James Skipper, Michigan Department of Environmental Quality, oral commun., 2003; Larry Campbell, city of 

Cadillac, written commun., 2003; WW Engineering and Science, 1994). Twenty-nine of the wells were used as part of 

the remediation system in the industrial park near the Cadillac well field (fig. 4). Seven production wells were used by 

Haring Township and the city of Cadillac. The remaining 

well was used to supply cooling water for an energy cogeneration plant about 1 mi west of the well field. 

Discretization

Based on hydrogeologic descriptions recorded on 

well logs, geophysical logs of oil and gas wells, analysis 

of surface-geophysical surveys, and other information, the 

ground-water system underlying the Clam River watershed 

was divided into four model layers (fig. 4). The clay confining units were not modeled as separate layers but instead 

simulated the restriction of flow between aquifers. The 

layers corresponded to the aquifers described previously. 

Given the highly variable nature of the glacial deposits in 

this area, the continuity and extent of the various layers is 

difficult to delineate. In locations with a high density of 

water wells, the hydrogeology is better understood than 

in areas where well information is sparse. The layers are 

consistent with data from the well-field area. Hydraulic 

properties of these units estimated from aquifer tests are 

shown in table 1. A porosity of 30 percent (Freeze and 

Cherry, 1979) was used for all aquifers underlying the 

study area. 

The numerical ground-water flow model was developed using the USGS modular three-dimensional finitedifference code MODFLOW 2000 (Harbaugh and others, 

2000). All simulations reflect steady-state conditions, 

which indicate no net gain or loss of water in the system 

with time (storage effects are not simulated). As described 

above, the three clay confining units were not simulated as 

layers, but were simulated by including the confining-unit 

hydraulic conductivity and thickness in the calculation of 

vertical conductance between model layers (Harbaugh and 

85°20’1"

85°30’1"

85°25’

1"

44°14’58"

85°35’1"

44°19’58"

1,050 −1,086

1,087 −1,121

1,122 −1,157

1,158 −1,193

1,194 −1,229

1,230 −1,264

1,265 −1,300

0 1 2 3 4 MILES

0 1 2 3 4 KILOMETERS

EXPLANATION

WATER-LEVEL ALTITUDE

(Feet above NGVD 29)

No Data

Figure 6. Potentiometric surface map for the deep aquifer (less than 1050 ft above NGVD 29),

Clam River watershed, Michigan.
 Simulation of Ground-Water Flow 9

Recharge

Deep flow pattern

Northwest

Southeast

Well Discharge

Figure 7. Conceptual diagram of ground-water flow for the Clam River watershed, Cadillac, Michigan.

Shallow flow pattern

Recharge

Table 1. Results of selected aquifer tests in the aquifer units underlying the Clam River watershed, Michigan

[ ft/d, feet per day]

Location Date of

test

Screened Interval

(feet below ground

surface)

Hydrologic Unit and Model 

Layer

Horizontal

Hydraulic

Conductivity 

Cadillac Industrial Park 1996 20-35 Shallow aquifer, layer 1 129.6

Cadillac Industrial Park 1989 44-138 Intermediate aquifer, layer 2 74.0

South of Lake Cadillac 1980 84-104 Intermediate aquifer, layer 2 43.9

Cadillac Industrial Park 1989 152-213 Intermediate aquifer, layer 3 163.0

Haring Township Well 

Field 1986 228-268 Deep aquifer, layer 4 109.5

Cadillac Municipal Well 

Field 1987 237-246

Clay-confining unit between

intermediate and deep

aquifers

 1

.031

Cadillac Municipal Well 

Field 1959 275-430 Deep aquifer, layer 4 214.7

 Denotes vertical hydraulic conductivity through the clay-confining unit 1
10 Simulation of Ground-Water Flow and Areas Contributing Ground Water to Production Wells, Cadillac, Michigan

others, 2000, p. 29-31). The presence of clay units indicated 

on well logs within glacial sediments in the Clam River 

watershed were compiled and arranged according to thickness and altitude. Top and bottom altitudes of the clay units 

were interpolated across the model grid using an inversedistance weighted algorithm to form the three separate clay 

confining units. For cases where the interpolated clay units 

were interpreted to be absent, a breach in the clay unit was 

simulated by increasing its simulated vertical hydraulic 

conductivity (fig. 4). 

Areal recharge estimates for the model were incorporated using a multiplier array. A multiplier array (Harbaugh 

and others, 2000) was established throughout the grid based 

on recharge values estimated by Holtschlag (1996). A 

parameter representing recharge in the watershed then was 

linked to this multiplier array so that all recharge values in 

the multiplier array were multiplied by the new adjusted 

parameter value. 

 The study area was discretized into a finite-difference 

grid consisting of 546 rows, 584 columns, and 4 layers (fig. 

8). Cell spacing of the model grid ranged from approximately 3 ft to 1,000 ft. The cell spacing was refined in 

areas simulating large ground-water withdrawals to avoid 

numerical instability caused by the steep head (water-level) 

gradients resulting from withdrawals.

Model Calibration and Sensitivity

Model simulations were calibrated to water-level 

measurements in consultant reports, well logs, and to measurements made by the USGS, with assistance of the city 

of Cadillac Public Works Department. In all, 315 observation points were used within the observation package in 

MODFLOW 2000 (Hill and others, 2000). Simulations 

during and after model calibration indicate that the model is 

sensitive to changes in the horizontal hydraulic conductivity 

of the deep and intermediate aquifers, the vertical hydraulic 

conductivity of the deep confining unit, and recharge. The 

model was not as sensitive to changes in the hydraulic conductivity of the shallow aquifer, or to vertical hydraulic conductivities of the confining units separating the shallow and 

intermediate (model layers 1 and 2) and the two intermediate (model layers 2 and 3) aquifers, and the simulated breach 

in the clay confining units. Parameters with low sensitivity 

were not estimated during the process; instead, they were set 

to reasonable values based on literature sources. Sensitive 

parameters were adjusted, but parameters with low sensitivity were not adjusted. Recharge was set to 1.5 times the 

values estimated by Holtschlag (1996) (fig. 2), even though 

this parameter was considered sensitive. This condition 

resulted because the recharge rates were set unreasonably 

high during the parameter-estimation process. This process 

iteratively changed parameter values to minimize residuals 

between observed and simulated water levels at the observation points. Final model-calibrated parameter values are 

listed in table 2. A comparison of observed and simulated 

heads is provided in figure 9.

The spatial distribution of head residuals (difference between the observed and simulated heads) for the 

calibrated model is given in figure 10. The mean absolute 

error for the calibrated model was 9.2 ft. Simulated heads 

agree well with the observed heads near the municipal-well 

field (north of Lake Cadillac) with a mean absolute error 

of 4.8 ft. However, head residuals are larger at observation 

wells outside of the well field, indicated by a mean absolute 

error of 15.2 ft. This large error likely is a result of poor 

characterization and the lack of hydrogeologic information in the watershed away from the well field. Despite the 

large head residual for observations distant from Cadillac’s 

well field, the model can still be used as a predictive tool. 

The WHPA will be designated by the State of Michigan 

for the area surrounding the Cadillac production well field. 

Because error associated with head predictions in that area 

is low, the uncertainty in the WHPA delineation probably 

will be low as well. Model-simulated heads for layer 4, 

the deep aquifer, are shown in figure 11. The gradient 

matches the conceptual model of flow from the southeast to 

the northwest in the deep ground-water system. Simulated 

flows were reasonable between aquifers, into and out of 

model boundaries, and for rivers and lakes. The calibrated 

water budget is given below.

All values in cubic feet per day

 IN OUT

Constant head boundaries 24,989,855.3 36,577,247.3

Wells 38,500.0 984,823.6

General Head boundaries 3,925,557.2 232,879.0

(rivers and lakes)

Recharge 8,841,101.0 0.0

Total 37,795,013.5 37,794,949.9

Delineation of Contributing Areas

Optimized Scenario

Following the development of a calibrated groundwater flow model, the particle-tracking program MODPATH (Pollock, 1994) was used to estimate the contributing area and zone of transport area to production wells. 

Essentially, particles are placed on the faces of each model 

cell that is simulating a production well. The particles 

follow an advective-flow field backward from the well, 

thereby indicating the zone-of-transport area (subsurface), 

and if tracked long enough, the contributing area (surface) 

to the well.

A total of 200 particles (40 at each well) were simulated in the optimized model to be released in the well field 
Delineation of Contributing Areas 11

1,050

1,100

1,150

1,200

1,250

1,300

1,350

1,400

1,050 1,100 1,150 1,200 1,250 1,300 1,350 1,400

OBSERVED HEADS, IN FEET ABOVE NGVD 29

Figure 9. Observed and simulated heads (water levels) for the calibrated ground-water 

flow model of the Clam River watershed, Michigan. 

SIMULATED HEADS, IN FEET ABOVE NGVD 29 

EXPLANATION

Specified Head Boundary

Model Grid Cell

Figure 8. Lateral discretization and location of specified head boundaries for the ground-water 

flow model of the Clam River watershed, Cadillac, Michigan.

85°20’1

85°30’1"

85°25’1"

44°14’58"

85°35’1"

44°19’58"

0 1 2 3 4 MILES

0 1 2 3 4 KILOMETERS
12 Simulation of Ground-Water Flow and Areas Contributing Ground Water to Production Wells, Cadillac, Michigan

and tracked backwards from the Cadillac production wells. 

Particle movement was recorded at the end of a 10-year 

time period. The results of the backwards particle tracking 

are illustrated in figure 12. The resulting contributing area, 

shown in pink, is a map view of the composite simulated 

zone-of-transport and area contributing recharge. The 10-

year contributing area extends to the southwest and encompasses an area of 0.34 mi2

.

Alternate Scenario

A separate simulation was performed using a different 

set of values (other than the optimized values) for model 

parameters to test how sensitive the contributing area was to 

these changes. For this alternate scenario, the recharge rate 

was increased to 18 in/yr for the entire watershed. In addition, the hydraulic conductivity values all were increased to 

near the upper limit of the values observed from the aquifer 

tests. The complete list of parameter values used for 

simulation of this alternate scenario is listed in table 2. The 

pumping stresses also were changed to include a hypothetical production well. Well-discharge rates for the optimized 

scenario with five Cadillac production wells then were 

distributed evenly across the six production wells simulated 

in the alternate scenario. Forty particles were added around 

the hypothetical well for a total of 240 particles tracked 

during the simulation.

By changing values of model parameters, a more 

conservative estimate of the contributing area was provided 

in the alternate scenario. Despite the large increase in 

some model parameter values, the alternate contributing 

area is only slightly larger than the contributing area in the 

85°20’ 1"

85° 30’1"

85° 25’ 1"

44°14’ 58"

85° 35’ 1"

44°19’ 58"

0 1 2 3 4 MILES

0 1 2 3 4 KILOMETERS

Lake

Road

−

−

−

−

− 

− −

− −

− −

− −

−

65 50

49 35

34 20

19 5

4 10

11 − 25

26 − 40

41 − 55

EXPLANATION

(Observed minus simulated 

heads, in feet)

HEAD RESIDUAL

Figure 10. Distribution of head (water level) residual (difference between observed and simulated 

heads) for the calibrated flow model for the Clam River watershed, Cadillac, Michigan.
 13

optimized simulation. The result of increasing the model 

parameter values was to enlarge the contributing area from 

0.34 mi2 to 0.48 mi2. The alternate contributing area (fig. 

13) is narrower and extends further towards the south and 

southeast than the optimized contributing (fig. 12). The 

effect of simulating an additional production well also is 

apparent through the extension of the contributing area 

towards the northwest. In close proximity to the well field, 

the alternate contributing area does not extend as far south 

as the optimized contributing area. The narrowing of the 

alternate contributing area is likely because of the combination of the increased hydraulic conductivity of the aquifers 

and the decreased discharge rate per well in the alternate 

scenario simulation. 

Limitations of Model Simulations

Uncertainty with simulated head predictions is a 

concern in all ground-water flow model simulations. The 

accuracy of the head solution is dependent on the data 

available concerning properties of hydrogeologic units, and 

location and effect of boundary conditions. In this model, 

each model layer was simulated as an isotropic unit, meaning that hydraulic properties were uniform in all directions. Although this isotropy probably is not the case for 

the aquifers represented with the model layers, data were 

not available at the scale needed to incorporate anisotropy 

for the simulated layers. A detailed aquifer characterization effort throughout the watershed would be necessary to 

characterize the heterogeneity associated with the glacial 

deposits in this area. The lack of detailed hydrogeologic 

Delineation of Contributing Areas

0 1 2 3 4 MILES

1,097 −1,124

1,125 −1,150

1,151 −1,177

1,178 −1,203

1,204 −1,230

1,231 −1,256

1,257 −1,283

R oads

65 50

49 35

34 20

19

−

−

−

−

−

−

−

−5

−

−

−

−

−4 − 10

11 − 25

26 − 40

41 − 55

0 1 2 3 4 KILOMETERS

85°30’14"

85°25’14"

85° 20’14"

44°14’41"

85°35’14"

44°19’41"

EXPLANATION

SIMULATED HEADS--Water level

(Feet above NGVD 29)

LAYER 4 HEAD RESIDUALS

(Observed minus simulated 

heads, in feet)

Figure 11. Model-simulated heads, and head residuals for observations in the deep aquifer (layer 4), 

Clam River watershed, Michigan.
14 Simulation of Ground-Water Flow and Areas Contributing Ground Water to Production Wells, Cadillac, Michigan

Table 2. Parameter values for optimized model and alternate model of Clam River watershed, Michigan

[in/yr, inches per year; ft/d, feet per day]

Hydrologic unit and model layer Parameter

Value in

optimized model

Value in

alternate 

model

Units

Shallow aquifer; layer 1 Recharge 1

1.50 18 in/yr

Shallow aquifer; layer 1 Horizontal hydraulic 

conductivity 51 120 ft/d

Confining unit between the shallow 

and intermediate 1 aquifers; layers 1 

and 2

Vertical hydraulic

conductivity .03 .03 ft/d

Breach in confining unit between the 

shallow and intermediate 1 aquifers, 

layers 1 and 2

Vertical hydraulic

conductivity 25 36 ft/d

Intermediate aquifer 1; layer 2 Horizontal hydraulic 

conductivity 116 120 ft/d

Confining unit between the 

intermediate 1 and intermediate 2 

aquifers; layers 2 and 3

Vertical hydraulic

conductivity .04 .04 ft/d

Intermediate aquifer 2; layer 3 Horizontal hydraulic 

conductivity 44 120 ft/d

Confining unit between the 

intermediate 2 and deep aquifers; 

layers 3 and 4

Vertical hydraulic

conductivity .01 .01 ft/d

Deep aquifer; layer 4 Horizontal hydraulic 

conductivity 201 278 ft/d

1

 Parameter value is a multiplier of values taken from Holtschlag, (1996); the average areal recharge rate for 

the present calibrated model is 15 in/yr.
 15

information in areas distant from the well field is indicated 

in the large head residuals in the observation wells in these 

areas (fig. 12). 

Errors in head solutions translate to errors in the 

particle-tracking solutions because the numerical methods 

affect one another in model simulation. Reducing uncertainty in the ground-water flow solution also would improve 

the accuracy of the particle-tracking solution. In addition, 

the value used for porosity was not obtained by field measurements, so the estimated value of 30 percent may not be 

an accurate representation. If the effective porosity were 

smaller, then the contributing area would be larger because 

advective flow velocity increases with a decrease in porosity.

 Delineation of Contributing Areas

0 0.25 0.5 1 MILE

85°25’30" 85°24’45" 85°24’

44°15’

44°15’45"

0 0.25 0.5 1 KILOMETER

Base From U.S. Geological Survey Digital Data 

1:24,000 Michigan Georef Coordinate System

EXPLANATION

10-Year Contributing Area

Simulated Production Wells

Figure 12. Ten-year contributing area for scenario with optimized parameters, Cadillac

municipal-well field, Cadillac, Michigan.
16 Simulation of Ground-Water Flow and Areas Contributing Ground Water to Production Wells, Cadillac, Michigan

Summary

About 46 percent of Michigan’s population relies on 

ground water as a source of drinking water. The city of 

Cadillac, in Wexford County, Michigan, is developing a 

wellhead protection plan for their production well field. To 

understand the regional ground-water resources and determine the surface and subsurface areas contributing flow to 

the production well field, the USGS, in cooperation with the 

city of Cadillac began a study in 2000. The study area (96 

mi2) encompasses the Clam River watershed in southeastern Wexford County and part of southwestern Missaukee 

County. The city of Cadillac is the largest user of ground 

water in the watershed. Total relief in the study area is 

approximately 350 ft. Surface-water drainage is toward 

the northeast through the Clam River. On average, the 

watershed receives 32.5 in/yr of precipitation, of which 

approximately 10 in/yr becomes ground water recharge. 

Unconsolidated glacial material and bedrock underlie the 

Clam River watershed. The watershed appears to be the 

former location of a massive ice block of glacial origin. 

Three aquifers termed the “shallow”, “intermediate 1 and 

2”, and “deep” aquifers are separated by clay confining 

units within the glacial deposits.

0 0.25 0.5 1 MILES

85°25’ 30" 85 °24 ’45" 85 °24 ’0"

44 °15 ’

44 °15 ’45"

0 0.25 0.5 1 KILOMETERS

EXPLANATION

10-Year Contributing Area

Simulated Production Wells

Figure 13. Ten-year contributing area for scenario with alternate parameters, Cadillac

municipal-well field, Cadillac, Michigan.

Base From U.S. Geological Survey Digital Data 

1:24,000. Michigan Georef Coordinate System
 17

Ground-water flow simulations developed for the Clam 

River watershed using MODFLOW 2000 were used in 

conjunction with MODPATH to simulate regional groundwater flow and estimate areas that contribute ground water 

to the Cadillac production well field. Model simulations 

were calibrated to 315 water-level observation points. Head 

residuals between observed and simulated heads increased 

at observation points distant from the production well 

field. Simulations indicate that the model is most sensitive 

to recharge, the horizontal hydraulic conductivity of the 

deep and intermediate aquifers, and the vertical hydraulic 

conductivity of the deep confining unit. Model simulations match the conceptual model in that simulated regional 

ground-water flow in the deep ground-water system is 

from the southeast to northwest. The water budget for the 

calibrated model indicates reasonable flows between the 

aquifers and boundaries. Based on the results of groundwater-flow and particle-tracking simulations, the 10-year 

contributing area for the production wells extends southeast 

of the well field, covering an area of 0.34 mi2. Comparison 

of the optimized model parameters to an alternate case with 

increased recharge and hydraulic conductivity values does 

not indicate a major change in contributing area size (from 

0.34 mi2 to 0.48 mi2). However, increasing recharge and 

hydraulic conductivity appreciably affects the shape of the 

contributing area. 

Data were not available at the scale needed to incorporate anisotropy of aquifers and confining units in the 

simulations. A detailed aquifer characterization effort for 

the watershed would be needed to describe and simulate the 

heterogeneity encountered in the study area. Error in head 

solutions in model simulations affects the particle-tracking 

solutions. Reducing uncertainty would improve the accuracy of the particle-tracking solution and, thus, improve the 

accuracy of the delineation of the contributing area.

Acknowledgments

The authors thank Larry Campbell, Director of Utilities 

for the city of Cadillac, for his assistance with data collection and insight on the history of the municipal-well field. 

Brant Fisher, Wayne Kukuk, Richard Mandle and James 

Skipper (MDEQ) provided information about requirements 

for contributing-area delineations, as well as a history of the 

activities associated with the Cadillac production well field. 

Eric Chatterson (Roy F. Weston Inc.) provided information 

regarding water levels and monitoring-well locations for the 

Cadillac well field. We thank all businesses and homeowners that allowed us to measure water levels in their wells.

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Prepared by the Michigan District Publications Unit—Sharon Baltusis 

For more information concerning the research in this report, contact:

Jim Nicholas, District Chief

U.S. Geological Survey

6520 Mercantile Way, Suite 5

Lansing, MI 48911-5991

or visit our Web site at:

http://mi.water.usgs.gov
Hoard, C.J. and Westjohn, D.B.—Simulation of Ground-Water Flow and Areas Contributing Ground Water to Production Wells, 

Cadillac, Michigan—Scientific Investigations Report 2004-5175

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