U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2009–5244

In cooperation with the Tri-County Regional Planning Commission 

Model Refinement and Simulation of Groundwater Flow in 

Clinton, Eaton, and Ingham Counties, Michigan

MICHIGAN

LAKE 

ERIE

CLINTON

43°

45°

EATON

INGHAM

LAKE

MICHIGA

N

LAKE

H

UR

ON

Model Refinement and Simulation of 

Groundwater Flow in Clinton, Eaton, and 

Ingham Counties, Michigan

By Carol L. Luukkonen

In cooperation with the Tri-County Regional Planning Commission 

Scientific Investigations Report 2009–5244

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2010

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Luukkonen, C.L., 2009, Model refinement and simulation of groundwater flow in Clinton, Eaton, and Ingham Counties, 

Michigan: U.S. Geological Survey Scientific Investigations Report 2009–5244, 53 p.
iii

Acknowledgments

The author gratefully acknowledges the assistance of Jon Coleman, Executive Director of the Tri-County Regional Planning Commission, and Christine Spitzley, Environmental 

Programs Planner of the Tri-County Regional Planning Commission, for their coordination of 

community involvement, meetings, and distribution of project results. William Maier, Lansing 

Board of Water and Light (LBWL); Douglas MacDonald, Michigan State University; and 

Michael St. Bernard, East Lansing and Meridian Township Water Authority, furnished much 

data on groundwater withdrawals and well characteristics. John Malouin, formerly with the 

LBWL, supplied geochemical data for Lansing-area wells. Randall Roost, William Maier, and 

Thomas Savage, LBWL, supplied data for optimization scenarios. The author also appreciates 

report review comments received from James Brode, associate-senior hydrogeologist, Fishbeck, Thompson, Carr and Huber.

Paul Barlow, USGS hydrologist, assisted with using and interpreting the optimization programs and reviewed the draft report. David Westjohn, formerly with the USGS, provided many 

hydrogeological and historical insights about the study area and was instrumental in initiating 

this project. The author also appreciates the assistance of Lori Fuller, USGS geographer, for her 

interpretation and determination of urban areas from aerial photos, and Michael Eberle, USGS 

editor, for his review of the draft report.

v

Contents

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

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

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

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

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

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

Geologic Setting....................................................................................................................................3

Hydrogeologic Setting .........................................................................................................................5

Groundwater Withdrawals..................................................................................................................6

Water Levels and Streamflow ............................................................................................................6

Groundwater-Flow Models ........................................................................................................................11

Conceptual Model...............................................................................................................................11

Numerical Models ..............................................................................................................................12

Spatial and Temporal Discretization.......................................................................................12

Model Refinement .....................................................................................................................15

Recharge Distribution ......................................................................................................15

Glacial Aquifer Discretization.........................................................................................15

Saginaw Formation Discretization.................................................................................15

Boundary Conditions.................................................................................................................16

Hydraulic Properties .................................................................................................................17

Groundwater Withdrawals.......................................................................................................17

Steady-State Model Calibration..............................................................................................18

Transient Model Development and Calibration ....................................................................19

Sensitivity Analysis....................................................................................................................20

Groundwater-Flow Simulations.................................................................................................................29

Investigation of Reduced Recharge ................................................................................................29

Delineation of Contributing Areas....................................................................................................31

Optimization Scenarios......................................................................................................................32

Model Assumptions and Limitations ........................................................................................................36

Summary and Conclusions.........................................................................................................................39

References Cited..........................................................................................................................................41

Appendix 1. Chemistry of Lansing Area Well Water..............................................................................45

Figures

1–2. Maps showing:

1. Location of the Tri-County regional model area in the Lower Peninsula 

of Michigan...........................................................................................................................2

2. Location of communities and the nine-township area surrounding 

Lansing, Michigan ...............................................................................................................4
vi

3. Diagram showing stratigraphic nomenclature and hydrogeologic units, 

Tri-County region, Michigan .......................................................................................................5

4. Map showing groundwater levels in the Saginaw aquifer in the model area, 

Tri-County region, Michigan .......................................................................................................7

5–6. Graphs showing:

5. Groundwater withdrawals from the Saginaw aquifer and glacial deposits, 

Tri-County region, 1910–2005 .............................................................................................8

6. Comparison of groundwater withdrawals from the North and 

South Lansing areas, Michigan, 1915–2005 ....................................................................8

7–8. Maps showing:

7. USGS streamgaging stations and observation wells, Tri-County region, 

Michigan ...............................................................................................................................9

8. Model boundary and refined grid area, Tri-County region, Michigan ......................13

9–16. Graphs showing:

9. Annual average precipitation in the Tri-County region, Michigan ............................16

10. Relations between simulated water levels in the glacial deposits and 

Saginaw aquifer, and streamflow from the 1996 and 2009 models in the 

Tri-County region, Michigan ............................................................................................20

11. Relation between observed and simulated transient water levels in 

observation wells in the Lansing area, Michigan ........................................................22

12. Relation between observed and simulated transient water levels in 

Tri-County-region observation wells ..............................................................................24

13. Relation between observed and simulated transient streamflows in the 

Tri-County region, Michigan ............................................................................................26

14. Water-budget components and change in components by stress period, 

Tri-County model................................................................................................................28

15. Net storage, by year, during transient simulations with reduced recharge 

and reduced recharge with increased pumping..........................................................31

16. Net storage, by month, during transient simulations with reduced recharge 

and reduced recharge with increased pumping..........................................................32

17–20. Maps showing:

17. Simulated 10-year time-of-travel areas for selected production wells 

in the nine-township area, Tri-County region, Michigan ............................................33

18. Optimized wells in the Lansing area, Michigan............................................................34

19. Optimized wells for areas A and B with a specified maximum pumping rate 

of 0.5 million gallons per day............................................................................................37

20. Optimized wells for areas A and B with a specified maximum pumping rate 

of 1 million gallons per day...............................................................................................38
vii

Appendix Figures

1–1. Graph showing trilinear diagrams of Lansing area, Michigan, groundwater 

samples. A, Total dissolved solids (TDS) concentrations less than 500, 

and B, greater than 1,000 milligrams per liter........................................................................46

1–2. Map showing distribution of hardness, in milligrams per liter CaCO3, from 

samples from 2003–5, Lansing area, Michigan......................................................................48

1–3 – 1–7 Graphs showing:

1–3. Major ion concentrations, in milligrams per liter, for 1930–2006, Lansing area, 

Michigan .............................................................................................................................49

1–4. Major ion concentrations for northern and southern wells for 1930–2005, 

Lansing area, Michigan ....................................................................................................50

1–5. Trilinear diagrams of water samples collected from northern Lansing area, 

Michigan, wells A, before 1970, and B, after 1970 .......................................................51

1–6. Relation of chloride to sulfate concentrations collected from northern Lansing 

area, Michigan, wells A, before 1970, and B, after 1970 .............................................52

1–7. Comparison of major-ion concentrations from water samples collected from 

northern Lansing area, Michigan, wells before and after 1970 .................................53 

Tables

1. USGS streamgaging stations and observation wells in the Tri-County region, 

Michigan ......................................................................................................................................10

2. Transient model details for model representing early 1900s to 2005, Tri-County 

region, Michigan.........................................................................................................................14

3. Parameter estimates for coefficients multiplying matrices that describe the 

spatial variation of hydraulic properties in the Tri-County region, Michigan...................19

4. Water-level observations used in transient model calibration for the Tri-County 

region, Michigan.........................................................................................................................21

5. Transient model details for monthly stress periods for the Tri-County region, 

Michigan ......................................................................................................................................30

6. Summary of optimization formulations and results for the Tri-County region, 

Michigan ......................................................................................................................................34
viii

Conversion Factors and Datums

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) .3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square foot (ft2) 929.0 square centimeter (cm2)

square foot (ft2) .09290 square meter (m2)

square mile (mi2) 2.590 square kilometer (km2) 

Volume

gallon (gal) 3.785 liter (L) 

gallon (gal) 0.003785 cubic meter (m3) 

million gallons (Mgal) 3,785 cubic meter (m3)

cubic foot (ft3) 28.32 cubic decimeter (dm3) 

cubic foot (ft3) .02832 cubic meter (m3) 

Flow and recharge rates

inch per year (in/yr) 0.3048 millimeter per year (mm/yr)

foot per day (ft/d) .3048 meter per day (m/d)

cubic foot per second (ft3/s) .02832 cubic meter per second (m3/s)

gallon per day (gal/d) .003785 cubic meter per day (m3/d)

million gallons per day (Mgal/d) .04381 cubic meter per second (m3/s)

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) 

Leakance

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

*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.

Vertical coordinate information is referenced to the North American Vertical Datum of 1929 

(NVGD 29).

Horizontal coordinate information is referenced to the Michigan State Plane Coordinate System, 

South Zone.

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

Concentrations of chemical constituents in water are given either in milligrams per liter (mg/L) 

or micrograms per liter (μg/L) 
Model Refinement and Simulation of Groundwater Flow in 

Clinton, Eaton, and Ingham Counties, Michigan

By Carol L. Luukkonen

pumping rates. During these two simulation years, monthly 

recharge rates were reduced by about 30 percent, and monthly 

withdrawal rates for Lansing area production wells were 

increased by 15 percent. The reduction in the amount of water 

available to recharge the groundwater system affects the upper 

model layers representing the glacial aquifers more than the 

deeper bedrock layers. However, with a reduction in recharge 

and an increase in withdrawals from the bedrock aquifer, 

water levels in the bedrock layers are affected more than those 

in the glacial layers. Differences in water levels between 

simulations with reduced recharge and reduced recharge with 

increased pumping are greatest in the Lansing area and least 

away from pumping centers, as expected. Additionally, the 

increases in pumping rates had minimal effect on most simulated streamflows. 

Additional simulations included updating the estimated 

10-year wellhead-contributing areas for selected Lansing-area 

wells under 2006–7 pumping conditions. Optimization of 

groundwater withdrawals with a water-resource management 

model was done to determine withdrawal rates while minimizing operational costs and to determine withdrawal locations to 

achieve additional capacity while meeting specified head constraints. In these optimization scenarios, the desired groundwater withdrawals are achieved by simulating managed wells 

(where pumping rates can be optimized) and unmanaged wells 

(where pumping rates are not optimized) and by using various 

combinations of existing and proposed well locations.

Introduction

The Tri-County region, which consists of Clinton, 

Eaton, and Ingham Counties, covers 1,697 mi2 in the southcentral part of the Lower Peninsula of Michigan (fig. 1). A 

groundwater-flow model was developed in 1996 by the U.S. 

Geological Survey (USGS) to investigate groundwater flow 

in the Saginaw aquifer (Holtschlag and others, 1996; Luukkonen and others, 1997a, b), which underlies the majority 

of these three counties. Since compilation of the Tri-County 

regional groundwater-flow model in 1996, the model has been 

used frequently to address water-resources issues such as the 

delineation of contributing areas to local municipal wells as 

part of local Wellhead Protection Programs. As pumping rates 

Abstract

A groundwater-flow model that was constructed in 1996 

of the Saginaw aquifer was refined to better represent the 

regional hydrologic system in the Tri-County region, which 

consists of Clinton, Eaton, and Ingham Counties, Michigan. 

With increasing demand for groundwater, the need to manage withdrawals from the Saginaw aquifer has become more 

important, and the 1996 model could not adequately address 

issues of water quality and quantity. An updated model was 

needed to better address potential effects of drought, locally 

high water demands, reduction of recharge by impervious 

surfaces, and issues affecting water quality, such as contaminant sources, on water resources and the selection of pumping 

rates and locations. The refinement of the groundwater-flow 

model allows simulations to address these issues of water 

quantity and quality and provides communities with a tool that 

will enable them to better plan for expansion and protection of 

their groundwater-supply systems. Model refinement included 

representation of the system under steady-state and transient 

conditions, adjustments to the estimated regional groundwater-recharge rates to account for both temporal and spatial 

differences, adjustments to the representation and hydraulic 

characteristics of the glacial deposits and Saginaw Formation, and updates to groundwater-withdrawal rates to reflect 

changes from the early 1900s to 2005.

Simulations included steady-state conditions (in which 

stresses remained constant and changes in storage were not 

included) and transient conditions (in which stresses changed 

in annual and monthly time scales and changes in storage 

within the system were included). These simulations included 

investigation of the potential effects of reduced recharge due 

to impervious areas or to low-rainfall/drought conditions, 

delineation of contributing areas with recent pumping rates, 

and optimization of pumping subject to various quantity 

and quality constraints. Simulation results indicate potential 

declines in water levels in both the upper glacial aquifer and 

the upper sandstone bedrock aquifer under steady-state and 

transient conditions when recharge was reduced by 20 and 

50 percent in urban areas. Transient simulations were done to 

investigate reduced recharge due to low rainfall and increased 

pumping to meet anticipated future demand with 24 months 

(2 years) of modified recharge or modified recharge and 
600,000

550,000

500,000

450,000

400,000

350,000

1,850,000 1,900,000 1,950,000

EASTING, IN FEET

NORTHING, IN FEET

2,000,000 2,050,000 2,100,000

CLINTON COUNTY

Regional model 

boundary

Lansing

Upper Peninsula

Lower Peninsula

EATON COUNTY

INGHAM COUNTY

88°

47°

45°

43°

86°

Base map from the Michigan Resource 

Information System, Michigan Department 

of Environmental Quality

2 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

Figure 1. Location of the Tri-County regional model area in the Lower Peninsula of Michigan.

and well locations have changed, these contributing areas have 

been periodically updated. The 1996 USGS model has also 

provided insight about new areas for well development and the 

effects of groundwater withdrawals in these areas, and it has 

addressed possible effects of proposed options such as injection wells or contamination-remediation wells. 

Since 1996, demand for water of sufficient quantity and 

quality has continued to increase considerably in the greater 

Lansing area (fig. 2). In fact, use of groundwater exceeded 

1 billion gallons for July 2002, a new all-time high (William 

Maier, Lansing Board of Water and Light (LBWL), oral commun., 2002). The concentration of dissolved solids is increasing in some areas of Lansing’s well field (William Maier, 

LBWL, oral commun., 2003). Additional concerns include 

potential effects of drought, high water demands, impervious 

surfaces, and discovery of additional contaminant sources and 

how each of these may affect water levels, streamflow, and the 

selection of pumping rates and locations. As a result, the need 

to manage withdrawals from the Saginaw aquifer has become 

increasingly important. 

The 1996 model is a regional-scale model that required 

refinement to adequately address these issues of water quality 

and quantity. Additional information is now available from 

detailed site-specific models that have been developed in the 

greater Lansing area and from an electronic database of well 

records (Wellogic) developed by the Michigan Department 

of Environmental Quality (MDEQ). Analysis and incorporation of this information would enable model refinements to 

improve model-prediction capabilities and would provide a 

means to simulate more complex regional and more localized 

water-withdrawal scenarios. 

In 2004, the Lansing area communities working with the 

Tri-County Regional Planning Commission (TCRPC) and 

the USGS began a long-term plan for continued enhancement 

of the USGS regional groundwater-flow model. Participating communities are Alaiedon Township, Bath Township, 

Delhi Township, Delta Township, City of East Lansing, 
Description of Study Area 3

City of Eaton Rapids, City of Lansing, City of Williamston, 

Eaton Rapids Township, Lansing Township, Michigan State 

University, Meridian Township, Oneida Township, Vermontville Township, Village of Dimondale, Watertown Township, Williamstown Township, and Windsor Township (fig. 

2). The communities concluded that refinement of the 1996 

USGS model would improve understanding of the regional 

hydrologic system in the Lansing area and help ensure that 

the model continues to be a valuable tool to assist with planning for expansion and protection of the water supplies of the 

Lansing-area communities.

Purpose and Scope

This report describes the refinement of the simulated 

aquifer and recharge characteristics of the 1996 Tri-County 

regional groundwater-flow model and the simulations done 

with this updated model (hereafter referred to as the “2009 

model”). The 2009 numerical model is able to simulate the 

groundwater-flow system under steady-state and transient conditions. Simulation results show potential effects of reduced 

recharge and increased withdrawals on groundwater levels and 

streamflow. Particle-tracking analysis was used with results 

from flow simulations to delineate contributing areas to production wells. Simulation results also show how the model can 

be used with optimization techniques to evaluate alternative 

groundwater pumping scenarios under selected management 

constraints. The limitations of the model for assessing groundwater levels and flow and for delineating contributing areas 

are described. Characterization of the geochemical changes in 

water quality revealed by historical data for selected Lansingarea wells is included in the appendix.

Previous Studies

Several previous studies have contributed to the knowledge of the groundwater resources in the Tri-County region 

and to the development of the 2009 model. With regard to 

background conditions, Wood (1969) described the hydrogeology and geochemistry of groundwater in the Saginaw 

Formation. Vanlier and others (1973) described water-supply 

development and management alternatives in the Tri-County 

region. The Tri-County Regional Planning Commission 

(1992) completed a regional feasibility study on watersupply development. 

With regard to groundwater-flow modeling, one of the 

earliest local efforts was that of Wheeler (1967), who developed an electric analog model of groundwater flow in the 

Saginaw Formation in the Lansing area, Mich. A report by 

Holtschlag and others (1996) documents how the regional 

groundwater-flow model was developed and used to determine 

contributing areas for most production wells in the Tri-County 

region. Two reports describe refinement of the original 1996 

model using reduced grid spacing and the results of additional groundwater-flow simulations in the north Lansing area 

(Luukkonen and others, 1997a, b).

Description of Study Area

In this report, the area in and surrounding Lansing, which 

is referred to as the “nine-township area,” consists of Alaiedon, Bath, Delhi, Delta, Dewitt, Lansing, Meridian, Watertown, and Windsor Townships (fig. 2). The nine-township area 

is the principal area of groundwater withdrawals in the TriCounty region. Groundwater is withdrawn primarily from the 

Saginaw aquifer, which consists of water-bearing sandstones 

within the Grand River and Saginaw Formations of Pennsylvanian age. Aquifers in the glacial deposits and other bedrock 

units are important groundwater sources in some places. The 

primary geologic, hydrogeologic, and water-use characteristics that affect groundwater flow in the Saginaw aquifer are 

described in the following sections. 

Geologic Setting

In the Tri-County region, Cambrian through Pennsylvanian age sedimentary and Upper Jurassic rocks overlie Precambrian basement. Triassic, Lower and Middle Jurassic, and 

Cretaceous rocks are missing (Mandle and Westjohn, 1989). 

Glacial deposits of Pleistocene age overlie Pennsylvanian and 

Upper Jurassic rocks. 

Pennsylvanian rocks form the uppermost bedrock unit 

in the Tri-County region. The altitude of the surface of the 

Pennsylvanian rocks ranges from about 850 ft in the south 

to about 600 ft in the north. Pennsylvanian rocks are thickest 

in the west-central part of Clinton County and generally thin 

to the south. They are absent in the extreme eastern part of 

Ingham County.

The stratigraphic relation is not clear between the 

Saginaw Formation, Parma Sandstone, and the underlying 

Bayport Limestone (fig. 3). The Parma Sandstone is composed 

of medium- to coarse-grained sandstone and is generally less 

than 100 ft thick (Cohee and others, 1951). Interpretation of 

geophysical logs indicates that the lower part of the Pennsylvanian rock sequence is predominantly shale, whereas the 

upper part is predominantly sandstone. Thus, the Pennsylvanian rocks younger than the Parma Sandstone can be divided 

into a lower confining unit and an upper sandstone aquifer 

(Westjohn and Weaver, 1996). 

Discontinuous lenses of sandstone, shale, coal, and limestone in the Pennsylvanian bedrock units have been formally 

subdivided into two formations. The uppermost massive, 

coarse-grained sandstones form the Grand River Formation; 

all remaining Pennsylvanian rocks are considered part of the 

underlying Saginaw Formation (Mandle and Westjohn, 1989). 

In Eaton and Ingham Counties, erosion removed most of the 

Grand River Formation; as a result, only a few large remnants are present today (Vanlier and others, 1973). In Clinton 

County, the Grand River Formation, although removed by erosion after deposition over a large part of the county, is as much 

as 125 ft thick in some areas (Vanlier and others, 1973). These 

assignments between formations are somewhat uncertain, 

however, because no lithologic differences or stratigraphic 
600,000

550,000

500,000

450,000

400,000

350,000

1,850,000 1,900,000 1,950,000

EASTING, IN FEET

EXPLANATION

Nine-township area

North Lansing area

South Lansing area

1996 Tri-County regional model boundary

NORTHING, IN FEET

2,000,000 2,050,000 2,100,000

Lansing

Dimondale

Fowler

Grand

Ledge

Westphalia

Sunfield

Vermontville Potterville

Charlotte

Olivet Leslie

Mason

Eaton Rapids

Stockbridge

Webberville

Williamston

East 

Lansing

DeWitt

Ovid

Elsie

Bellevue

St. Johns

Maple Rapids

DELTA

LANSING MERIDIAN

WATERTOWN

ONEIDA

EATON 

RAPIDS

WILLIAMSTOWN

VERMONTVILLE

DEWITT

BATH

WINDSOR

DELHI

ALAIEDON

10 KILOMETERS

0 5 10 MILES

0 5

Base map from the Michigan Resource 

Information System, Michigan Department 

of Environmental Quality

4 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

Figure 2. Location of communities and the nine-township area surrounding Lansing, Michigan.

horizons mark a change from one formation to the next (Westjohn and Weaver, 1996). 

The Jurassic red beds that separate Pennsylvanian rocks 

from overlying glacial deposits in some areas of the Lower 

Peninsula are either entirely absent or only marginally present 

in the Tri-County region (Westjohn and others, 1994). The 

red beds are often poorly consolidated or unconsolidated and 

consist primarily of clay, mudstone, siltstone, sandstone, shale 

and gypsum. The red beds, which are relatively impermeable and are considered a confining unit, impede the vertical 

flow of water between glacial deposits and bedrock aquifers 

(Westjohn and others, 1994). For the purposes of this study, all 

deposits between the top of the Pennsylvanian rocks and the 

land surface were assumed to be glacial deposits.

The glacial features in Michigan are the result of ice 

advances during late Wisconsin time (35,000 to 10,000 years 

before present). The glacial deposits in Ingham County range 

in thickness from less than 10 ft to more than 300 ft. The 

glacial deposits are absent in a small area near Grand Ledge; 

the thickest glacial deposits are in the northwestern part of the 
Stratigraphic Unit Hydrogeologic Unit 

(generalized thickness range)

Glacial deposits quifers in the glacial deposits 

(0-300 feet)

Grand River Formation

Saginaw Formation

Saginaw aquifer 

(150-400 feet)

Saginaw confining unit 

(5-100 feet)

Bayport Limestone

Michigan Formation

Marshall Sandstone

Parma Sandstone

Michigan confining unit 

(50-250 feet)

Marshall aquifer 

(100-150 feet)

Parma-Bayport aquifer 

(50-100 feet)

Peri

o

d

Quaternary Pennsylvanian Mississippian

A

Description of Study Area 5

Figure 3. Stratigraphic nomenclature and hydrogeologic units, Tri-County region, Michigan. 

(Note: Figure denotes relation between units present in the Tri-County region and not the complete 

depositional history from the Mississippian through Quaternary periods. The Parma Sandstone is 

considered by some researchers to form the basal part of the Pennsylvanian Saginaw Formation. Other 

researchers have assigned the lower part of the Parma Sandstone to the late Mississippian. Dashed 

line indicates uncertainty in the placement of the Parma Sandstone into the Pennsylvanian or the 

Mississippian periods. The Parma Sandstone is hydraulically connected to the Bayport Limestone and 

these units together form the Parma-Bayport aquifer.)

study area. Glacial deposits are of three principal types: (1) 

a well-sorted mixture of silt, sand, and gravel, such as valley 

outwash, outwash plains, eskers, kames, and buried outwash, 

deposited by streams of meltwater draining from glaciers; (2) 

a layered sequence of silt, sand, and clay deposited in glacial 

lakes; and (3) an unsorted mixture of clay, silt, sand, gravel, 

and boulders, such as till, deposited directly from the melting 

ice (Vanlier and others, 1973). None of these types of deposits 

is regionally continuous (Mandle and Westjohn, 1989). 

Hydrogeologic Setting

Glacial deposits form the uppermost aquifer in the TriCounty region. Groundwater flow in the glacial deposits is 

generally from south to north, away from topographic divides 

and toward surface-water bodies. Aquifers in the glacial 

deposits are composed primarily of coarse alluvial and outwash materials. Long, narrow ridges of sand and gravel, called 

eskers, are present in Ingham and Eaton Counties and in parts 

of Clinton County, primarily in the southeast. Esker deposits 

yield water to municipal wells in Williamston and, historically, yielded water in Mason. Buried outwash deposited by 

preceding glaciers was covered by layers of till deposited 

during a later glacial advance. The most extensive areas of 

buried outwash deposits are in the northern part of Ingham 

County, the northeastern part of Eaton County, and the southern part of Clinton County. These areas of buried outwash are 

a potential source of water to wells; however, most wells in 

these areas are completed in bedrock aquifers because of the 

better quality of water available at depth. Till is present over 

much of the region and is generally not a source of water to 

wells (Vanlier and others, 1973). Locally, the till may include 

thin beds of sand and gravel that are a source of water or may 

overlie bodies of sand and gravel that may yield moderate to 

large supplies of water (Vanlier and others, 1973). Lake plain 

deposits, consisting of beds of clay, silt, and sand deposited in 

glacial lakes, underlie parts of Clinton County; however, these 

deposits generally are thin and in most places are not sources 

of water to wells (Vanlier and others, 1973). The MDEQ 
6 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

Public-Water-Supply database indicates ranges of transmissivity for the glacial deposits of 615 to 127,000 ft2

/d in Eaton 

County and 540 to 20,050 ft2/d in Clinton County (Michigan 

Department of Environmental Quality, 2009).

The Saginaw aquifer is in the water-bearing sandstones 

in the Grand River and Saginaw Formations. The Saginaw 

aquifer can be thought of as an aquifer system consisting of 

three sandstone units separated by an upper, interbedded-series 

unit and a lower shale unit (David Westjohn, U.S. Geological Survey, oral commun., 2005). Division of the Saginaw 

aquifer into these units is uncertain in some areas because of 

incomplete or missing well-log data or heterogeneities within 

and varying thicknesses of these units in the formation. Most 

groundwater flow in the Saginaw aquifer is from south to 

north, although a small amount is toward local pumping centers (fig. 4). Flow across the eastern part of Ingham County, 

where the sandstone of the Saginaw Formation is very thin or 

absent, is minimal. The Saginaw aquifer is recharged principally by leakage from the glacial deposits primarily in areas 

where aquifers in the glacial deposits are in direct connection 

with the Saginaw aquifer, but also minimally through confining unit(s) consisting of a lower till unit in the glacial deposits and (or) an upper shale unit in the Saginaw Formation. 

Groundwater discharges locally from bedrock to the glacial 

deposits beneath valleys of major streams (Holtschlag and others, 1996). The Grand River and Saginaw Formations act as a 

single hydrologic unit, so the chemical characteristics of water 

in these formations are very similar. Nearly all wells tapping 

these formations yield water that is suited to household needs. 

The water is generally hard or very hard and contains iron, 

although in some localities the Saginaw Formation yields soft 

water (Vanlier and others, 1973). 

Analyses of aquifer-test data indicate a wide range of 

transmissivities within the Saginaw aquifer. Wood (1969) 

reported that pumping tests indicated a relatively constant 

permeability of the sandstone in the Saginaw Formation of 

about 100 gal/d/ft2 (13 ft/d). The permeability of the shale 

is more variable, ranging from 0.01 to 1.0 gal/d/ft2 (0.001 to 

0.13 ft/d) (Wood, 1969). Transmissivities that range from 130 

to 2,700 ft2/d were reported for the Saginaw aquifer within the 

Tri-County region by Vanlier and Wheeler (1968). This range 

in transmissivities reflects variations in the total thickness of 

the sandstone beds and variations in the permeability of the 

sandstone. The MDEQ Public-Water-Supply database (that 

includes data from selected public-supply well locations) indicates ranges of transmissivity for the Saginaw aquifer of 840 

to 3,240 ft2/d in Eaton County and 450 to 3,890 ft2/d in Clinton 

County (Michigan Department of Environmental Quality, 

2009). Measured porosities and vertical hydraulic conductivities range from 4 to 34 percent and 0.0001 to 55 ft/d, respectively (Westjohn and Weaver, 1996). 

Groundwater Withdrawals

Groundwater is the principal source of water supply for 

the Tri-County region. The majority of communities rely on 

groundwater from the Saginaw aquifer; however, groundwater from aquifers in the glacial deposits is important in some 

areas. The communities of Lansing, Webberville, Ovid, and 

Fowler initially withdrew water from the glacial deposits. 

These communities later added wells drilled into the Saginaw aquifer. According to data for 2005, Eaton Rapids, Elsie, 

Fowler, Lansing, Mason, Williamston, and St. Johns use combinations of wells completed in aquifers in the glacial deposits 

and the Saginaw aquifer; the communities of Dewitt, East 

Lansing, Grand Ledge, Leslie, Ovid, Potterville, Webberville, 

and Westphalia withdraw water from the Saginaw aquifer. 

The communities of Charlotte, Maple Rapids, Sunfield, and 

Vermontville depend on groundwater from aquifers in the 

glacial deposits. A small amount of groundwater is withdrawn 

from the Marshall aquifer in southwestern Eaton County by 

the communities of Bellevue and Olivet.

For communities within the study area, data on withdrawals from 1970 to 1990 were primarily based on records 

furnished by municipal suppliers, published in annual data 

reports of the USGS (Huffman and Thompson, 1971, 1973; 

Huffman, 1974a, 1974b, 1975, 1976, 1977, 1979a, 1979b; 

1980; 1981; 1982; 1983; 1984; 1985; 1986; 1988; Huffman 

and Whited, 1988; 1989; 1991; 1993), or included in previous studies of the area. Additional data are available in a 

report by Baltusis and others (1992), who summarized sources 

and annual withdrawals of groundwater for communities in 

the Lower Peninsula of Michigan. In the Tri-County region, 

groundwater withdrawals increased steadily from early 1900 

to the late 1970s (fig. 5). Withdrawals were more constant 

from the late 1970s to 2004 and increased in 2005, with most 

of this increase likely attributed to expansion of municipal 

service areas. Before 1970, withdrawals were concentrated in 

the north Lansing area; after 1970, withdrawals were divided 

among wells located over a larger area, with more wells 

installed primarily in the south (figs. 2 and 6). 

Water Levels and Streamflow

Water-level and streamflow data are both needed to assist 

with model calibration to indicate how well the model represents the actual groundwater-flow system (fig. 7 and table 1). 

Groundwater levels in wells screened across the water table 

indicate the position of the water table; wells tapping deeper 

parts of an aquifer indicate the composite hydraulic head over 

the screened or open interval. Water-level data are available from well logs from the MDEQ Wellogic database and 

from observation wells in the Tri-County region. Within the 

Tri-County region, water-level data are available from almost 

23,300 well logs with well installation dates ranging from 

1912 to 2005. Data from about 11,900 of these wells, along 

with data from 34 observation wells that were measured for 
800

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600,000

550,000

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450,000

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350,000

1,850,000 1,900,000 1,950,000

EASTING, IN FEET

EXPLANATION

NORTHING, IN FEET

2,000,000 2,050,000 2,100,000

900 Groundwater-level contour—Shows altitude of 

potentiometric surface. Contour interval 50 

feet. Datum is NGVD 29. Dashed where 

approximately located.

Model area

Base map from the Michigan Resource 

Information System, Michigan Department 

of Environmental Quality 10 KILOMETERS

0 5 10 MILES

0 5

Description of Study Area 7

Figure 4. Groundwater levels in the Saginaw aquifer in the model area, Tri-County region, Michigan. 

(Data from Holtschlag and others, 1996.)

various intervals during 1930 to 2005, were used during calibration of the transient model. The observation-well data are 

thought to be more accurate; however, many of these observation wells are in the Lansing area and are affected by pumping. 

Therefore, inclusion of data from well logs serves as additional control on simulation results by providing water-level 

information in areas not affected by pumping. Data compiled 

during development of the 1996 model also were used during 

calibration of the 2009 steady-state model to allow comparison between the original and refined models. These 1996 data 

consisted of 2,932 water-level measurements from well logs, 

805 groundwater levels from water-surface altitudes posted for 

lakes and topographic contour crossings of perennial streams, 

and 130 observation-well measurements. Measurements in 

the upper layer were not restricted to a particular time period; 

however, measurements in the lower layer were restricted to 

the period 1984–92 because of local trends in the historical 

groundwater-head data associated with changes in pumping 

conditions (Holtschlag and others, 1996).

Streamflow data are available from continuous-record 

gaging stations for which daily mean streamflows are computed for 1 or more years. Streamflow can be subdivided 

into direct-runoff and base-flow components. Direct runoff is 

associated with the component of precipitation that exceeds 

the infiltration capacity of the soil and flows overland directly 

into streams. Base flow is associated with the component of 
Glacial deposits

Saginaw aquifer

WITHDR

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ALS, I

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 1910 1915 1920 1925 1930 1935 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

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1910 1920 1930 1940 1950 1960 1970 1980 1990 2000

YEAR

North wells

South wells

WITHDRAWALS, IN MILLION GALLONS 

PER DAY

8 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

Figure 6. Comparison of groundwater withdrawals from the North and South Lansing 

areas, Michigan, 1915–2005. (See figure 2 for the locations of these areas.) 

Figure 5. Groundwater withdrawals from the Saginaw aquifer and glacial deposits, Tri-County region, 1910–2005. (Data 

from William Maier, Lansing Board of Water and Light, written commun.; Douglas MacDonald, Michigan State University, 

written commun.; Michael St. Bernard, East Lansing and Meridian Township Water Authority, written commun.; Huffman 

and Thompson, 1971, 1973; Huffman, 1974a, 1974b, 1975, 1976, 1977, 1979a, 1979b, 1980; 1981, 1982, 1983, 1984, 1985, 1986, 

1988; Huffman and Whited, 1988, 1989, 1991, 1993; and Baltusis and others, 1992.)
!

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EXPLANATION

10 KILOMETERS

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Maple River

Red Cedar 

 River

Thornapple 

 River

Grand 

River

Looking Glass 

 River

W18

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C4 Streamgaging-station location and identifier

W7 Observation-well location and identifier

Base map from the Michigan Resource 

Information System, Michigan Department 

of Environmental Quality

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EASTING, IN FEET

Description of Study Area 9

Figure 7. USGS streamgaging stations and observation wells, Tri-County region, Michigan.
10 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

Table 1. USGS streamgaging stations and observation wells in the Tri-County region, Michigan.

[Locations of stations and wells are shown on figures 7 and 13.]

Streamgaging stations

Map 

index

USGS gaging–station 

number Station name Drainage area (mi2) Period of record

C1 04110000 Orchard Creek at state HWY 106 near Munith 49 1944–56

C2 04111379 Red Cedar River near Williamston 163 1975–89, 2001–7

C3 04111500 Deer Creek near Dansville 16.3 1954–2007

C4 04112000 Sloan Creek near Williamston 9.34 1954–2007

C5 04112500 Red Cedar River at East Lansing 355 1903, 1931–2007

C6 04112850 Sycamore Creek near Holt 80.6 1975–80, 1989–90, 1994–97

C7 04113000 Grand River at Lansing 1,230 1901–6, 1934–2007

C8 04113097 Carrier Creek near Lansing 12.1 1975–80

C9 04114000 Grand River at Portland 1385 1952–82, 1988–2007

C10 04114498 Looking Glass River near Eagle 280 1944–96, 2001–7

C11 04111000 Grand River at Eaton Rapids 661 1950–82, 1995–2007

C12 04112904 Mud Lake Drain at Lansing 4.25 1975–76

Observation wells

Map 

index Well number Well name Aquifer Period of observations

W1 424618084340401 Quarantine Farm Saginaw 1944–93, 2005–6

W2 424637084360601 Capital City Airport Saginaw 1960–88

W3 425408084323601 US-27 Glacial 1948–95, 2000, 2005–6

W4 430047084333801 St. Johns Saginaw 1964–84

W5 430454084230901 Village of Elsie Saginaw 1947–72

W6 424058084380301 Steifel Glacial 1965–2001, 2003, 2005–6

W7 424108084363201 Roscommon St. Saginaw 1993–95, 2005–06

W8 424435084365001 Robins Road Saginaw 1954–2005

W9 424524084452501 Grand Ledge Saginaw 1948–74

W10 423058084181801 Dansville State Game Area Glacial 1963, 1973–76, 1988–92, 2005–6

W11 423127084321901 Cedar Well Saginaw 1945–54, 1960–2007

W12 423503084263701 Mason Old #2 Saginaw 1948–74

W13 423532084274001 Kerns Rd Saginaw 1965–91, 2003, 2005–6

W14 423805084311801 Holt Saginaw 1982–2007

W15 423812084302801 Delhi Twp Saginaw 1961–66

W16 423933084213801 Lotte Saginaw 1964–92

W17 424040084351401 Davis Park Saginaw 1991–94, 2005–6

W18 424111084360701 Maybel Saginaw 1945–93, 2005–6

W19 424225084261401 Okemos Saginaw 1976–93, 2005–6

W20 424235084311201 Fenner Arboretum Saginaw 1968–82, 1991–2007

W21 424300084201001 Sherwood Rd Saginaw 1963–80, 2005–6

W22 424303084295001 Spartan village Saginaw 1946–84, 1986–92

W23 424312084321801 Pennsylvania (P-5) Saginaw 1931–95, 2005–6
Groundwater-Flow Models 11

Table 1. USGS streamgaging stations and observation wells in the Tri-County region, Michigan.—Continued

[Locations of stations and wells are shown on figures 7 and 13.]

Observation wells—Continued

Map 

index Well number Well name Aquifer Period of observations

W24 424324084331801 Scott Park Saginaw 1971–75, 1980–88, 1993–95

W25 424324084331802 Townsend Saginaw 1929–71

W26 424349084252501 Meridian Twp. Saginaw 1968–92

W27 424424084340301 Logan Saginaw 1960–2007

W28 424455084274601 Marble School Saginaw 1953–80, 2005

W29 424502084331301 Seymour Saginaw 1961–80, 1986–2007

W30 424521084342101 Muskegon Street Saginaw 1991–94

W31 423120084215301 Kelly Rd Saginaw 2003

W32 423245084231601 Hawley Rd Saginaw 2003

W33 423318084230201 Dexter Trail Saginaw 2003

precipitation that infiltrates the soil and percolates below the 

plant-rooting depth, where it can enter (recharge) the groundwater system. Base-flow characteristics of streams were used 

to help determine the amount of precipitation that recharges 

groundwater in the Tri-County region. In this study, streamflow partitioning (Rutledge, 1993) was used to estimate base 

flow to streams for the transient calibration by use of data 

from 10 continuous-record gaging stations over each period 

of record. Similar to the water-level data, streamflow data 

determined for the 1996 model were used during calibration of 

the 2009 steady-state model. The 1996 data consisted of baseflow estimates at 10 continuous-record gaging stations and 

25 partial-record gaging stations.

Groundwater-Flow Models

The U.S. Geological Survey modular three-dimensional 

finite-difference numerical groundwater-flow model MODFLOW-2000 (Harbaugh and others, 2000) was used to 

simulate groundwater flow in the Tri-County region. MODFLOW-2000 allows the simulation of steady-state or transient 

groundwater flow in three dimensions with leakage between 

model layers. In addition, MODFLOW-2000 contains processes that allow inclusion of observations and comparison 

of measured and calculated values, development of parameter sensitivities, and estimation of parameter values (Hill 

and others, 2000). Simulation of groundwater flow is made 

possible by first developing a conceptual model of the flow 

system and then developing a numerical model that is consistent with the conceptual model. Results of simulations with 

the models described in this report numerically illustrate the 

potential effects of natural and anthropogenic influences on 

water levels and flows and evaluate various pumping scenarios 

under different management constraints. Model refinement 

and the calibration of the steady-state and transient models are 

described below. 

Conceptual Model

The conceptual model describes groundwater flow within 

the Tri-County region and surrounding areas and includes 

delineation of aquifers, confining units, and groundwater-flowsystem boundaries. Groundwater flow in the glacial deposits 

is unconfined and generally from south to north, away from 

topographic divides and towards surface-water bodies. Thus, 

surface-water drainage divides are assumed to be groundwater-flow divides for groundwater in the glacial deposits. 

Most groundwater flow in the Saginaw aquifer is from 

south to north, although a small amount is toward local pumping centers. Flow across the east and west model area, where 

the sandstones of the Saginaw Formation are very thin or 

absent, is minimal. Generally, groundwater flows toward the 

Maple River, which forms the northern hydrologic boundary 

of the model area; locally, some groundwater flows toward the 

southern hydrologic boundary. Flow between aquifers in the 

glacial deposits and the Saginaw Formation is limited where 

confining unit(s) consisting of a lower till unit in the glacial 

deposits and (or) an upper shale unit in the Saginaw Formation 

are present. Groundwater also discharges locally from bedrock 

to the glacial deposits in the valleys of major streams. Local 

and regionally extensive confining materials limit the vertical 

movement of water between sandstone units in some areas 

within the Saginaw Formation. Groundwater is confined in 

the Saginaw aquifer except for a small area near Grand Ledge 

where the Saginaw Formation outcrops along part of the 

Grand River. For the purposes of this model, the bottom of the 

Saginaw aquifer is assumed to be impermeable.
12 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

Numerical Models

The model area consists of Clinton, Eaton, and Ingham 

Counties along with parts of Ionia, Shiawassee, Jackson, and 

Livingston Counties (fig. 8). This large area is simulated to 

minimize boundary effects on model-calculated heads, flow 

rates, and flow directions in the interior part of the model 

by allowing natural physical and hydrologic boundaries to 

be used as much as possible. The placement of boundaries 

distant from the nine-township area also allows for development of predictive simulations within the center of the TriCounty area to investigate water availability and the effects of 

water withdrawals. 

Model development includes the specification of grid 

characteristics, boundary conditions, and input variables, 

such as hydraulic properties of the aquifers and pumping 

rates. Model calibration then proceeds with the comparison 

of model-simulated heads (water levels) and streamflows 

with measured values of heads and streamflows for steadystate or transient conditions. Under the steady-state assumption there is no change in groundwater storage during the 

simulated period; that is, all water entering the model area 

through the boundaries or as recharge is assumed to leave the 

model area through the boundaries, rivers, or wells. Groundwater withdrawals and recharge rates remain constant during 

the steady-state simulation. During a transient simulation, 

water is released from or taken into aquifer storage. Heads 

change with time as a result of this transfer of water. When 

the transfer to and from storage stops, the groundwater-flow 

system reaches steady state and heads stabilize (Anderson and 

Woessner, 1992). Groundwater withdrawals and recharge rates 

can change during the transient simulation. Steady-state and 

transient models are both useful for simulating the groundwater-flow system. Average conditions are used in steady-state 

models to predict long-term average heads and flows. Transient models can be used to help predict responses to both 

short-term and long-term changes in stresses. For this study, 

the groundwater-flow model was calibrated to both steadystate and transient conditions in order to simulate the response 

of the groundwater-flow system under different conditions.

The refined steady-state model was developed to represent conditions in the Tri-County area under average 1991–95 

pumping conditions because water-level and streamflow data 

both were available for calibration and the model had previously been calibrated to these conditions. With the relative 

constancy of withdrawals since the early 1970s (fig. 5) and 

the constancy of average precipitation rates, the assumption 

of steady-state conditions during 1991–95 is believed to be 

appropriate, and measured heads and streamflows used for 

calibration are assumed to represent long-term average conditions. Simulation results from the 2009 model were compared 

to simulation results from the 1996 model to check that the 

model refinements had not changed the representation of the 

groundwater-flow conditions in the area. 

Transient models were developed to investigate the 

groundwater-flow-system response to changes in recharge 

and withdrawal rates from the early 1900s to 2005 and to 

investigate various water-supply management scenarios. Available data on groundwater withdrawals and observations for 

each time period were averaged to be representative of average recharge years. Groundwater withdrawal rates varied over 

the transient simulations on the basis of available recorded 

and estimated data. Historic precipitation data were used to 

assist with determining variations in groundwater recharge 

rates. Available data for water levels and streamflow were 

compared to simulated values for each model stress period. 

The following sections describe details of model development, 

calibration, and results of simulations with the steady-state and 

transient models.

Spatial and Temporal Discretization

The model area covers about 3,500 mi2; about 62 percent 

of this area consists of active model cells. The area is approximately 61 mi long (north-south) and 58 mi wide (east-west). 

Part of the southern model boundary was extended beyond the 

1996 model extent to permit model simulations in the Eaton 

Rapids and Eaton Rapids Township area (fig. 8). The model 

consists of 338 rows and 307 columns of grid cells that vary in 

size. Smaller grid cells in the central part of the model permit 

representation of smaller scale flows and pumping where the 

majority of groundwater withdrawals occur. In the central part 

of the model area, each cell is approximately 660 by 660 ft. 

Cell spacing increases outward from the central part of the 

model area in each direction by a factor of 1.2 to a maximum 

grid spacing of about 1,330 ft. Each grid cell is assigned the 

average aquifer properties for the volume of aquifer represented by the cell; variations in properties within a grid cell 

cannot be represented. Glacial deposits are known to vary considerably in lithology and thickness over short distances (tens 

to hundreds of feet). This variability makes exact representation of the detailed hydrogeology difficult in a regional-scale 

model. Therefore, hydraulic properties of the units within the 

model layers are generalized to represent the regional groundwater-flow system.

Land-surface elevation data for most of the model area 

are available from USGS 30-m datasets with a vertical resolution of 5–10 ft. This information was used to construct model 

layers by subtracting depths of estimated layers (determined 

from well-log data) from the land-surface elevation. The initial 

estimates of water-level elevations also were developed by 

subtracting the depth to water recorded on well logs from the 

land-surface elevations. In areas where the geologic materials composing a layer are absent, the layer was assigned a 

minimal thickness and the hydraulic properties of the overlying layer. Additional delineation of layer surfaces in areas of 

sparse data was accomplished by interpolating from known 

nearby points. The lowermost model layer (layer 10) represents the material underlying the Saginaw aquifer and was 

included because well logs indicate that some wells may be 

completed below the bottom of the Saginaw aquifer. This 

layer was assigned a constant thickness of 50 ft over the whole 

model area.
550,000

600,000

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450,000

400,000

350,000

300,000

1,850,000 1,900,000 1,950,000

EASTING, IN FEET

EXPLANATION

NORTHING, IN FEET

2,000,000 2,050,000 2,100,000

Model area with refined grid cells

County boundary

1996 Tri-County regional model boundary, dashed where 

1996 and 2009 boundaries do not coincide.

2009 Tri-County regional model boundary

2009 model constant-head boundary

Lansing

EATON COUNTY

IONIA COUNTY SHIAWASSEE COUNTY

INGHAM COUNTY

LIVINGSTON 

COUNTY

JACKSON COUNTY

CLINTON COUNTY

10 KILOMETERS

0 5 10 MILES

0 5

Base map from the Michigan Resource 

Information System, Michigan 

Department of Environmental Quality

Groundwater-Flow Models 13

Figure 8. Model boundary and refined grid area, Tri-County region, Michigan.

Transient calibration requires specifying how the simulation period will be divided into stress periods and the number 

of time steps within each stress period. The stress periods and 

time steps specify the length of time used in determining the 

groundwater-flow solution and times when selected stresses, 

such as groundwater withdrawals and recharge rates, can 

change during the simulation. The use of stress periods offers 

the option of changing some of the parameters or stresses 

while the simulation is in progress (Anderson and Woessner, 

1992). The initial stress period for the transient model was 

steady state and was specified to simulate predevelopment 

conditions, with recharge rates equal to those developed for 

the 1996 model and with no groundwater withdrawals. The 

subsequent 16 stress periods were based on available pumping 

data and analysis of observation-well water-level data. Stressperiod length varied from 20 years to 1 year, with earlier stress 

periods generally covering the longer time periods because 

little water-level data are available for the early 1900s and 
14 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

stresses on the system were mild. Shorter stress periods were 

selected for the 1960s and early 1970s because of more concentrated pumping and larger water-level drawdowns during 

this interval. The initial transient stress period covers pre-1920 

conditions, with the remaining 15 stress periods spanning 

the remaining time. The last stress period represented 2005 

conditions (table 2). After calibration, additional stress periods 

were added to the transient model to simulate pumping conditions that vary by month. The additional stress periods cover 

8 years, with each year represented by 12 (monthly) stress 

periods. Pumping conditions vary, with the first 6 years representing average recent pumping conditions (as specified by 

several water-supply systems in the nine-township area) and 

the next 2 years (years 7 and 8) representing varied withdrawal 

and (or) recharge rates. The new transient model (with a total 

of 113 stress periods) was run under the same conditions for 

6 years, until the change in storage during the last year became 

minimal. Changes in water levels and flows could then be 

attributed to the modeled changes in recharge or withdrawal 

rates and not to changes in the amount of water in storage.

Selection of each time step is important because the 

values of time discretization can affect the accuracy of the 

numerical calculations. Ideally, use of small nodal spacing and 

small time steps is desirable so that the numerical representation approximates the groundwater-flow equation as closely 

as possible (Anderson and Woessner, 1992). Time steps can 

be increased as the simulation progresses. The groundwaterflow solution is sensitive to rapidly fluctuating water levels 

caused by introducing a stress; thus, small time steps are often 

used at the beginning of each new stress period to allow the 

early response of the system to be accurately simulated. Even 

with a large time step, the solution becomes more accurate as 

steady state is reached. As a rule of thumb, the solution should 

proceed through five time steps, during which there are no 

appreciable changes in values of sources and sinks or boundary conditions, before the solution is considered accurate 

(Marsily, 1986). The number of time steps within each stress 

period varied from 12 to 40. A multiplier of 1.5 on the length 

of each time step within a stress period was used to allow the 

initial time steps in each stress period to be relatively short and 

later time steps to be relatively long. For comparison of model 

results to observations, the groundwater-flow solution for the 

last time step of each stress period was used. For the transient 

model representing monthly time scales, the number of time 

steps during the initial 17 stress periods was reduced to permit 

faster processing time. The number of time steps within the 

first 16 transient stress periods varied from 12 to 20; the number of time steps in each subsequent stress period varied from 

14 time steps for each month to 34 for the final 3 months.

Table 2. Transient model details for model representing early 1900s to 2005, Tri–County region, Michigan. 

[Mgal/d, million gallons per day]

Stress 

period Stress period type

Time interval 

represented by 

stress period

Stress period 

length 

(days)

Simulated 

pumping

(Mgal/d)

Initial 

recharge 

multiplier

Final 

recharge 

multiplier

1 Steady-state Predevelopment — 0 1 1

2 Transient Pre-1920 3,650 3.6 1 1

3 Transient 1921–38 6,570 10.5 1.04 1

4 Transient 1939–48 3,650 16.4 1.06 1.06

5 Transient 1949–54 2,190 22.3 1.04 1.09

6 Transient 1955–62 2,920 26.7 .98 .94

7 Transient 1963–68 2,190 36.0 .98 .91

8 Transient 1969–72 1,460 40.5 1.08 1.15

9 Transient 1973–82 3,650 43.6 1.07 1.12

10 Transient 1983–90 2,920 41.7 1.15 1.22

11 Transient 1991–95 1,825 42.6 1.16 1.22

12 Transient 1996–99 1,460 41.6 1.03 1.03

13 Transient 2000–2001 730 40.2 1.2 1.2

14 Transient 2002 365 40.0 .83 .83

15 Transient 2003 365 40.5 .94 .87

16 Transient 2004 365 43.4 1.16 1.22

17 Transient 2005 365 46.1 1.08 1.08
Groundwater-Flow Models 15

Model Refinement

In 1997, the 1996 regional model was refined to better 

represent flow within the nine-township area surrounding Lansing (Luukkonen and others, 1997a, b) (fig. 2). The uniform 

cell size in the 1996 model was modified to a variably-spaced 

grid, and simulated pumping rates were updated to reflect 

1995 and 1997 pumping conditions. In 2003, the model was 

further refined to better represent flow within the Mason and 

Vevay Township area (Luukkonen and Simard, 2004). The 

hydraulic characteristics of the glacial deposits and the Saginaw aquifer were modified to better represent local conditions. 

The grid spacing was also modified in the Vevay Township 

area, and groundwater withdrawal rates by the city of Mason’s 

production wells were updated to reflect average rates representative of mid-May 2003 pumping conditions. In the 2003 

model, groundwater-recharge rates were not changed from the 

values used in the 1996 and 1997 regional models. 

For the current study to develop the 2009 model, the 

2003 model was further refined to allow simulation of scenarios that would most benefit water-resources managers and 

improve representation of the groundwater-flow system in the 

Tri-County region. These refinements included: (1) adjustments to the estimated regional groundwater recharge rates to 

account for temporal and spatial differences in local areas, (2) 

adjustments to the representation and hydraulic characteristics 

of the glacial deposits and Saginaw Formation, (3) representation of the system under steady-state and transient conditions, 

and (4) updates to groundwater withdrawal rates to reflect 

changes through time from the early 1900s to 2005.

Recharge Distribution

Precipitation is the ultimate source of groundwater and 

surface-water resources in the Tri-County region. In the earlier 

models, the spatial distribution of recharge was based on an 

analysis relating base-flow characteristics of streams to land 

use and basin characteristics (Holtschlag, 1994). On the basis 

of the 1994 study, the minimum average annual recharge in the 

Tri-County region is 4.4 in/yr, and the maximum is 16.5 in/yr; 

the spatial average groundwater recharge rate is 6.7 in/yr. This 

estimate of recharge was used in the 2009 steady-state model 

to facilitate comparison between the 1996 and refined 2009 

model simulation results. 

Temporal changes in recharge were determined for use 

in the transient models. Over the region, mean precipitation 

ranges from a maximum of about 32 in/yr in the southwest to 

about 30 in/yr elsewhere (Eichenlaub and others, 1990, p. 90). 

Historical precipitation data were collected for nine stations 

with data ranging from 1931 to 2005. The lowest annual average precipitation amounts of less than 24 in/yr were in 1953, 

1958, and 1962–63 (fig. 9). Highest annual average precipitation amounts of greater than 39 in/yr were in 1942, 1975, and 

1985. In this study, groundwater recharge is assumed to be 

some percentage of precipitation and to vary with annual precipitation amounts. Average recharge for the regional model 

area is less than precipitation; however, local recharge rates 

may approach, exceed, or be appreciably less than the average 

precipitation rate. Because of a lack of site-specific information on local or regional groundwater recharge rates, recharge 

for model simulations is assumed to vary temporally on the 

basis of the observed variations in precipitation rates; specifically, on the percentage change from the average precipitation 

rate of 30 in/yr. For monthly intervals, estimated recharge was 

assumed to vary on the basis of calculated average base-flow 

values because this produced the best match between simulated and observed values. This assumption allows for better 

representation of actual groundwater recharge rates than 

would be possible by using the average monthly variation 

in precipitation because evapotranspiration rates are higher 

during the spring and summer, thus reducing the amount of 

precipitation available to recharge the groundwater system. 

However, this approach is based on the assumption that there 

is no lag between the timing of recharge and the timing of 

discharge into streams. Because of the generally better match 

between simulated and observed streamflows using variations 

in base-flow values than was achieved using variations in 

precipitation, this approach is believed to be appropriate for 

the monthly time scales used for the simulation. Over smaller 

time scales, the difference in timing between recharge and 

discharge to streams would likely become more significant.

Glacial Aquifer Discretization

For the 2009 model, the glacial aquifer materials were 

subdivided to better represent flow through the glacial deposits 

in the Tri-County region. Well logs from the Wellogic database 

were analyzed to determine the thickness and extent of glacial 

aquifer units. Owing to the variability of the glacial materials, 

regional units with similar hydraulic properties could not be 

determined. Therefore, three units were determined to represent the glacial materials. The uppermost glacial unit (layer 1) 

ranges in thickness from less than 1 ft to 284 ft and was made 

thickest for deposits adjacent to rivers to minimize problems 

associated with model convergence of calculated water levels. 

The remaining glacial materials were subdivided equally to 

create layers 2 and 3, each of which ranges in thickness from 

less than 1 ft to 83 ft. 

Saginaw Formation Discretization

For the 2009 model, the Saginaw Formation also was 

subdivided into multiple units to (1) better represent flow 

within the aquifer; (2) permit more detailed representation 

of the individual production-well characteristics, such as the 

elevations of the open intervals, and (3) allow for scenarios 

investigating contaminant movement. More than 17,900 well 

logs from the Wellogic database were analyzed to determine 

the thickness and extent of Saginaw aquifer-system units 

(sandstones, the interbedded series, and shale beds). The 

Saginaw Formation materials were divided into an uppermost 

shale unit overlying three aquifer units that are separated by an 

interbedded series consisting of shale and sandstone lenses and 
3

3

3445

9

56

677

7

88

9

99

0

YEAR

PRECIPITATION, IN INCHES

0

5

10

15

20

25

30

35

40

45

19 1

19 5

19 9

19 3

19 7

19 1

1

55

19 9

19 3

19 7

19 119 5

19 9

19 319 7

1

91

19 5

19 9

2 03

16 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

a lowermost shale unit. The uppermost shale confining unit 

(layer 4) ranges in thickness from 0 to 117 ft and is thickest 

in Clinton County and the northern part of Eaton County. The 

shale unit is absent in parts of Lansing and is thinnest over 

most of southern Ingham and Eaton Counties. The uppermost 

sandstone aquifer unit (layer 5) ranges in thickness from 0 

to 130 ft and is thickest in the central Tri-County region and 

northern Clinton County. The interbedded-series confining unit 

(layer 6) ranges in thickness from 0 to 158 ft and is thickest 

in the eastern, western, and northern Tri-County region. The 

intermediate sandstone aquifer unit (layer 7) ranges in thickness from 0 to 154 ft and is thickest in central and northern 

part of the Tri-County region. The lower shale confining unit 

(layer 8) ranges in thickness from 0 to 150 ft and is thickest 

in the central and northern part of the Tri-County region. The 

lowermost sandstone aquifer unit (layer 9) ranges in thickness 

from 0 to 200 ft and is thickest in Ingham and Eaton County. 

Boundary Conditions

Boundary conditions refer to hydraulic conditions at cells 

where flow can enter or exit the model. Boundaries are classified as either external or internal. External boundaries form a 

perimeter around, and define, the active model area. Internal 

boundaries represent river locations using head-dependentflow cells and recharge using specified-flow cells. Boundary 

conditions are specified for each layer of the model.

Boundary conditions for the upper three layers of the 

model that represent the glacial deposits consist of both 

external and internal boundaries. External boundaries for the 

upper layer are constant head and no flow. No-flow boundaries 

are located at surface-water drainage divides and groundwater 

divides; constant-head cells are located along the Grand River 

on the south and the Maple and Grand Rivers on the north. 

The upper boundary of the upper layer is the water table, 

which is represented as specified flow and receives flow at a 

rate equal to recharge to the system. Internal boundaries for 

the upper three layers are head-dependent-flow cells representing rivers and lakes. Head values for the rivers and lakes were 

based on contour data shown on USGS 7.5-minute topographic quadrangle maps; linear interpolation was used, where 

necessary, to estimate values at cells between contours. Flow 

into or out of river cells is governed by stream stage, simulated head in the river cell, and conductance of the streambed 

material (McDonald and Harbaugh, 1988). River cells are 

located in glacial layers 1, 2, and 3 and in the layer 4 shale 

where the Saginaw Formation crops out near Grand Ledge in 

Eaton County. In addition to the internal river boundary cells, 

external boundary conditions for layer 4 simulating the upper 

bedrock shale unit are represented by no-flow cells. 

Figure 9. Annual average precipitation in the Tri-County region, Michigan. (No data available 

for 1948–49. Average precipitation for reported data at stations from Lansing Capital City 

Airport, 1948–2006; St. Johns, 1938–2006; Charlotte, 1931–2006; Dimondale 1 WSW, 1978–2004; 

Eaton Rapids, 1941–2006; Grand Ledge 1 NW, 1941–2002; East Lansing Experiment Farm, 

1949–1960; East Lansing 4S, 1957–2006; and Williamston 3NE, 1921–2006.)
Groundwater-Flow Models 17

Boundary conditions for the lower six layers representing the remaining bedrock units are constant head and no flow. 

No-flow boundaries are along the boundaries of the outermost 

active cells in the upper layers, except where constant-head 

cells are along Grand River on the south. For the most part, 

the no-flow cells are located where little sandstone is present 

in the Saginaw Formation. In the north, the no-flow cells cause 

water to discharge to the Grand and Maple Rivers, consistent 

with the conceptual model. The lower boundary of the lowermost layer is the bottom of the model and is assumed to be a 

no-flow boundary. 

Hydraulic Properties

Hydraulic properties used in model simulations include 

layer hydraulic conductivities and leakances and streambed 

conductances. Aquifer hydraulic properties affect groundwater 

flow through model layers; estimates for both horizontal and 

vertical hydraulic conductivities are described in subsequent 

sections. Leakances affect groundwater flow between layers. In MODFLOW, leakances, calculated from the vertical 

hydraulic conductivities and the layer thicknesses of the 

overlying and underlying layers, were calculated during model 

simulations and are not described further in this section. 

Streambed conductance affects vertical flow of groundwater 

from an aquifer to a river (stream) or from a river (stream) to 

an aquifer. 

The hydraulic properties of the glacial and bedrock aquifers and confining units were based on the estimated values 

determined for the 1996 model. These estimates were, in turn, 

based on values from previous studies, analysis of aquifer-test 

and recovery data compiled prior to this study, and representative values reported by Freeze and Cherry (1979). 

Initial estimates of hydraulic conductivity ranged from 

22.3 to 87.5 ft/d for the glacial aquifer units (model layers 1, 2, 

and 3). Horizontal hydraulic conductivity estimates are highest 

in the central and eastern parts of the model area and lowest 

in the northern and southern parts of the model area. Vertical 

hydraulic conductivity estimates were initially determined 

to be 0.1 times the horizontal hydraulic conductivity of the 

glacial layers. 

In order to better represent the connection between the 

glacial and bedrock aquifer materials, initial estimates of the 

hydraulic conductivity for the shale confining unit (model 

layer 4) were based on the materials making up the lowermost 

glacial unit and the uppermost bedrock unit. Well locations 

with glacial aquifer materials directly overlying a bedrock 

sandstone unit were assigned higher hydraulic conductivities 

than locations with till overlying shale. Initial estimates ranged 

from 0.0004 to 0.435 ft/d. Layer 4 horizontal hydraulic conductivity estimates are highest in the southern model area and 

lowest in the central and northeastern model area. 

The initial estimate for the horizontal hydraulic conductivity of the sandstone bedrock aquifer units (model layers 5, 

7, and 9) was specified as a constant value of about 11 ft/d. 

The sandstone transmissivity estimates vary according to the 

sandstone thickness and are highest in the central and northern 

model area and lowest in the southern model area. Vertical 

hydraulic conductivity estimates were initially determined 

to be 0.1 times the horizontal hydraulic conductivity of the 

sandstone layers. 

Initial estimates for the horizontal hydraulic conductivity of the interbedded-series confining unit (model layer 6) 

and the lowermost shale confining unit (model layer 8) were 

0.1 ft/d and 0.01 ft/d, respectively. Vertical hydraulic conductivity estimates were initially determined to be 0.1 times the 

horizontal hydraulic conductivity of each bedrock unit. The 

horizontal hydraulic conductivity for the bottom bedrock unit 

was estimated to be a constant value of 8 ft/d, and the vertical hydraulic conductivity was estimated to be 0.1 times the 

horizontal value, or 0.8 ft/d.

Streambed conductance is calculated as the product of 

the hydraulic conductivity of the streambed materials, stream 

length, and stream width, divided by the streambed thickness. 

Stream lengths for cells representing rivers were equal to the 

length of the stream segment in each cell. Stream widths varied according to the size of the stream and were assigned values ranging from 10 ft for most streams to 300 ft for the Grand 

River. Streambed thicknesses were assumed to equal 1 ft. 

Streambed hydraulic conductivities initially were assigned an 

estimated value of 2.3 ft/d (which had been previously determined during calibration of the 1996 model). 

Groundwater Withdrawals

Groundwater withdrawals were simulated in those cells 

containing a pumping well from each layer corresponding to 

an open interval in the well and were based on estimated or 

reported values. Simulated groundwater withdrawals for the 

steady-state model corresponded to the average of 1991–95 

pumping conditions so that model results calculated by the 

refined 2009 ten-layer model could be compared to simulated model results calculated by the 1996 two-layer model. 

Groundwater withdrawals totaled 42.6 Mgal/d in the steadystate model. Groundwater withdrawals from the glacial aquifer 

were simulated by use of the WEL package (McDonald and 

Harbaugh, 1988) as being withdrawn from model layer 3. 

Groundwater withdrawals from the bedrock aquifer were 

simulated by use of the MNW package (Halford and Hanson, 

2002), with the open interval determined from well logs as 

the interval between the bottom of the casing and the bottom 

of the well; withdrawals from wells could then be simulated 

throughout the entire thickness of the modeled bedrock unit 

ranging from model layers 4 thru 10. The MNW package 

allows simulation of wells that are completed in multiple 

aquifer units and distributes withdrawals among model layers 

on the basis of water-level differences and the hydraulic characteristics of the units intercepted by the simulated well. For 

the transient simulations, pumping rates were varied according 

to estimated or measured rates and ranged from 3.6 Mgal/d 

prior to 1920 (stress period 2) to 46.1 Mgal/d in 2005 (stress 

period 17). For the transient simulations representing monthly 
18 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

conditions, pumping rates were varied to represent monthly 

averages in 2005. Monthly withdrawals were highest from 

June to September and ranged from 36.3 Mgal/d in December 

to 51.3 Mgal/d in September. 

Steady-State Model Calibration

Model calibration is the process of reducing the difference between observed and simulated water levels and streamflows by adjusting model parameters. MODFLOW-2000 

(Hill and others, 2000) contains observation, sensitivity, and 

parameter-estimation processes as part of the groundwatermodeling computer program. The observation process allows 

comparison of observed and model-calculated values. The 

sensitivity process determines the sensitivity of predicted 

hydraulic heads and flows to specified model parameters or, in 

combination with the observation process, determines sensitivities for the simulated values associated with observations 

(Hill and others, 2000). The parameter estimation process is 

described later in this section.

Model fit is evaluated by comparing the magnitude and 

distribution of the residuals between simulated and observed 

water levels and flows. Simulated water levels and flows can 

be plotted against observed values, and the deviation from 

a straight line gives one indication of model fit. Plotting 

the residuals, which are the observed minus the simulated 

values, shows the distribution and indicates possible biases 

in the model. A generally random distribution of positive and 

negative water-level residuals can indicate that the model 

is not overpredicting or underpredicting water levels over 

parts of the model area. For this study, model calibration was 

achieved by manual trial-and-error adjustment of parameters 

and by use of the automated parameter-estimation program in 

MODFLOW-2000. 

For the steady-state model simulation, available miscellaneous and continuous water-level and flow observations 

compiled for the 1996 model were used for calibration. These 

observations were weighted for the parameter-estimation process to account for differences in measurement accuracy and 

differences in units of measurement. This weighting strategy 

allows those measurements with a higher degree of confidence 

to have more effect on parameter estimates and ensures that 

both water-level and flow data, which are measured in different units, affect parameter estimates. Water-level observations 

collected during this or previous USGS studies generally were 

assigned a higher degree of confidence because datums commonly are established by field surveys and measurements are 

obtained by use of well-documented protocols. Water-level 

observations from other sources were assigned a lower degree 

of confidence because of the uncertainty associated with estimating a datum from a topographic map, measuring depth to 

water in a recently developed or currently used domestic well, 

and fluctuations in levels of surface-water bodies. Streamflow 

data included daily mean discharge data from streamgaging 

stations and miscellaneous streamflow-measurement data from 

sites where continuous data are not collected.

Parameterization is the process of identifying those 

aspects of the simulated groundwater-flow system that are 

to be represented by estimated parameters (Hill and others, 

2000). Possible choices for parameters in a groundwater-flow 

model include groundwater recharge rates and the hydraulic 

characteristics of the aquifers, confining units, and streambed 

materials. Typically, it is impossible to estimate all parameters 

of interest because of limitations in the datasets available for 

calibration. Therefore, in this study, automated parameter 

estimation was combined with manual adjustments of some 

parameters to investigate their effects on model fit. Parameters 

were selected to scale the initial estimates of horizontal and 

vertical hydraulic conductivity for each model layer, the initial 

estimate of riverbed conductance, and the initial estimate 

of recharge. Examination of parameter sensitivities by use 

of processes within the model indicated that the parameters 

representing recharge, horizontal hydraulic conductivities in 

layers in 1, 5, 7, and 9, and vertical hydraulic conductivities 

in layers 4 and 8 had the highest sensitivities and were most 

likely candidates for parameter estimation (that is, predicted 

heads and/or flows would be the most sensitive to changes in 

these parameters). 

All initial model-parameter estimates were based on final 

parameter estimates from the calibrated 1996 model except 

the estimated vertical hydraulic conductivities of the glacial 

and Saginaw aquifers and the estimated hydraulic properties 

for the bedrock shale layers. The 1996 model represented 

the glacial and Saginaw units as individual layers; the 2009 

model represents the glacial unit as three layers and the 

Saginaw as seven. The initial estimate for the glacial vertical 

hydraulic conductivity was based on the 1996 model estimate 

of vertical leakance between the glacial and Saginaw layers 

because this value itself was based primarily on the glacial 

materials. During calibration, this initial estimate was found 

to be too low and the model would not converge; therefore, 

it was multiplied by 10 for each glacial layer (table 3). The 

estimate of glacial horizontal hydraulic conductivity ranged 

from 12.7 to 107.2 ft/d, and the vertical hydraulic conductivity estimate ranged from 0.0001 to 0.027 ft/d. The estimated 

horizontal hydraulic conductivity for the shale (layer 4) ranged 

from 0.01 to 4.5 ft/d, and the vertical hydraulic conductivity 

estimate ranged from 0.000009 to 0.0032 ft/d. The estimated 

horizontal hydraulic conductivity of the sandstone (layers 5, 7, 

and 9) equaled 11 ft/d, and the vertical hydraulic conductivity 

estimate equaled 1.1 ft/d. Horizontal hydraulic conductivity 

estimates for the interbedded series (layer 6) and the lower 

shale (layer 8) equaled 0.1 ft/d and 0.01 ft/d, respectively. The 

estimated riverbed conductance was doubled to equal 4.6 ft/d. 

Simulation results for the refined 2009 ten-layer model were 

compared to simulated values from the 1996 two-layer model. 

The agreement between observed and simulated groundwater levels and streamflow was similar for the two models 

(fig. 10). The sum of squared weighted residuals (SSWR) for 

heads decreased from 16,170 in the 1996 model to 10,452 

in the 2009 model; the SSWR for streamflow measurements 

increased slightly from 350 in the 1996 model to 415 in the 

2009 model.
Groundwater-Flow Models 19

Transient Model Development and Calibration

Development of a transient model builds on the existing knowledge and input data for the steady-state model and 

allows investigation of changes in stresses, such as pumping 

or recharge, while accounting for changes in storage. For the 

transient model simulations, additional information must be 

specified, including the storage characteristics of the aquifers, 

and the initial conditions. Storativity describes the capacity of 

an aquifer to transfer water to and from storage (Anderson and 

Woessner, 1992). For a confined aquifer, the storage coefficient is equal to the volume of water released per unit area 

of aquifer per unit decline in head. For an unconfined aquifer, 

the equivalent term is specific yield, which is defined as the 

volume of water released per unit surface area of aquifer per 

unit decline in the water table. The initial conditions define the 

head distribution at the beginning of the simulation and serve 

as a boundary condition in time. 

Typically, storage coefficients range from 1.0×10-3 to 

1.0×10-5 for confined aquifers (Freeze and Cherry, 1979). The 

specific yields of unconfined aquifers are generally higher than 

the storativities of confined aquifers and range from about 

0.01 to 0.45 (Anderson and Woessner, 1992). Releases from 

storage in unconfined aquifers represent an actual dewatering 

of soil pores, whereas releases from storage in confined aquifers represent only the secondary effects of water expansion 

and aquifer compaction caused by changes in fluid pressure 

(Freeze and Cherry, 1979). In the model, the specific yield of 

the upper glacial layers was estimated to be 0.1, whereas the 

initial estimate of storage coefficient for the bedrock layers 

was 1.0×10-5. The sensitivity of model results to these values 

was investigated during model calibration.

As with the steady-state model, transient model calibration also was achieved by manual trial-and-error adjustment of 

parameters and by use of the automated parameter-estimation 

program in MODFLOW-2000. Available miscellaneous and 

continuous water-level and flow observations from USGS 

observation locations and the Wellogic database were used for 

calibration (table 4). As in the steady-state model, parameter 

sensitivities indicated that horizontal hydraulic conductivities 

for layers 1, 5, 7, and 9 and the vertical hydraulic conductivity 

for layer 4 had the highest sensitivities and were most likely 

to be able to be estimated by parameter estimation. These 

values were adjusted during model calibration, along with the 

riverbed conductance and vertical hydraulic conductivity of 

the interbedded series. During the initial calibration runs, all 

layers were represented as confined. During final calibration 

runs, the glacial units (layers 1, 2, and 3) were represented as 

unconfined with rewetting of dry cells active. The final estimates for the multiplication coefficients that scale the initial 

estimates of horizontal and vertical hydraulic conductivity for 

each model layer and the initial estimate of riverbed conductance are listed in table 3. 

Simulated water levels and streamflows for each stress 

period of the transient simulation were compared to observed 

water levels and flows (figs. 11–13). In most cases, the simulated water levels were higher than observed water levels, 

especially during the stress periods in the middle of the transient simulation in which pumping was concentrated in a small 

part of the model area. However, many observations were 

near pumping wells. The simulated water level represents the 

average water level in the cell in each layer; that is, the average of the lowered water levels at the well location and the 

higher water levels away from the well and beyond the cone 

of depression formed as a result of groundwater withdrawals. 

This model-simulated value is not the actual water level that 

would be observed in a well pumping in an area with the layer 

and hydraulic characteristics that are used in the model and, 

thus, cannot be compared directly with the actual observed 

drawdown at the pumping well. Drawdown at the location of 

Table 3. Parameter estimates for coefficients multiplying matrices that describe the spatial variation of hydraulic properties in the 

Tri-County region, Michigan.

Layer 

number Description Horizontal hydraulic conductivity Vertical hydraulic conductivity

Initial Final Initial Final

1 Glacial materials 1.0 1.2 10.0 5.0

2 Glacial materials 1.0 1.2 10.0 5.0

3 Glacial materials 1.0 1.2 10.0 5.0

4 Upper shale unit 1.0 1.0 1.0 .5

5 Upper sandstone aquifer 1.0 .75 1.0 1.0

6 Interbedded series unit 1.0 1.0 1.0 .1

7 Intermediate sandstone aquifer 1.0 .75 1.0 1.0

8 Lower shale unit 1.0 1.0 1.0 1.0

9 Lower sandstone unit 1.0 .75 1.0 1.0

10 Saginaw confining unit/Parma 1.0 1.0 1.0 1.0
600

650

700

750

800

850

900

950

1000

1050

600

650

700

750

800

850

900

950

1000

1050

SIMULATED WATER LEVEL SIMULATED WATER LEVEL

OBSERVED WATER LEVEL, IN FEET ABOVE NGVD29

OBSERVED WATER LEVEL, IN FEET ABOVE NGVD29

-20

0

20

40

60

80

100

120

Streamflow

OBSERVED STREAMFLOW, IN CUBIC FEET PER SECOND

2009 model 1996 model

2009 model 1996 model

2009 model 1996 model

SIMULATED STREAMFLOW, 

IN CUBIC FEET PER SECOND

Saginaw

Glacial

600 700 800 900 1000

600 700 800 900 1000

0 20 40 60 80 100 120

20 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

the well in the cell would be greater than the simulated value. 

The simulation results from the transient stress periods do 

match the trend in water levels seen for the observation wells 

in the area. Simulated streamflows also generally match the 

trends determined from base-flow measurements for gaging 

stations in the model area; however, the simulated streamflows 

are generally lower than the observed values. Streamflow 

varies from year to year and within any given year. Base-flow 

measurements were based on available data; however, not all 

streams were gaged during the entire period of the transient 

simulation. Therefore, some base-flow estimates were based 

on data from only a few years of the transient stress period 

and may not have been representative of the actual base flow 

that occurred during the entire time interval represented by the 

stress period. In addition, the transient model does not include 

any water that is added to the stream from any external point 

source, such as from a water-treatment plant, so simulated 

values are expected to be lower than actual observed values.

Simulation results can be analyzed to show the waterbudget components and the changes in these components over 

time (fig. 14). The major components of the Tri-County model 

budget are recharge into the groundwater system and discharge out of the groundwater system to streams and surfacewater features (fig. 14a). Recharge from streams and other 

surface-water features and discharge out of the groundwater 

system through the model boundaries (along the Maple and 

Grand Rivers, which are represented as constant head cells in 

the model) are the next most important fluxes in the modeled area. Compared to the major components, withdrawal of 

water by wells is a relatively small component of the overall groundwater-system budget. With development and the 

addition of wells, a new discharge is superimposed upon a 

previously stable system that is at equilibrium, and it must be 

balanced by an increase in the recharge of an aquifer, or by a 

decrease in the old natural discharge, or by a loss of storage 

in the aquifer, or by a combination of changes in recharge, 

discharge, or storage. The relative contributions of changes in 

storage, changes in recharge, and changes in discharge evolve 

with time, potentially over a period of years, decades, or even 

centuries. The long-term source of water to discharging wells 

typically is a change in the amount of water entering or leaving the system. The role of pumping and changes in storage 

over time is more evident in the changes in the water-budget 

components over time (fig. 14 b, c); model results indicate 

that changes in storage occur mostly in response to changes in 

recharge. Recharge into the groundwater system and discharge 

to streams and surface-water features are the water-budget 

components with the largest changes.

Sensitivity Analysis

The calibrated model is influenced by uncertainty in the 

model parameters, which are average values based on limited data available from well drillers’ logs or previous studies. A sensitivity analysis can help determine the effect of 

uncertainty in the estimated aquifer parameters, stresses, and 

Figure 10. Relations between simulated water levels in the 

glacial deposits and Saginaw aquifer, and streamflow from the 

1996 and 2009 models in the Tri-County region, Michigan.
Groundwater-Flow Models 21

boundary conditions on model results. During a sensitivity 

analysis, calibrated values for model parameters are systematically changed within reasonable ranges to determine the 

magnitude of the changes in water levels and streamflows 

from the calibrated solution (Anderson and Woessner, 1992). 

Model sensitivity as described by the SSWR (sum of squared 

weighted residuals) or simulated water levels and flows was 

investigated by increasing and decreasing the multiplication 

coefficient for each hydraulic property. In some cases, the 

change had little effect on model results; in other cases, the 

change had a substantial effect, or the model failed to converge. The transient model was most sensitive to changes in 

horizontal and vertical hydraulic conductivities in the glacial 

units (layers 1, 2, and 3), vertical hydraulic conductivity in the 

shale unit (layer 4), horizontal hydraulic conductivities in the 

sandstone (layers 5, 7, and 9), and vertical hydraulic conductivity in the interbedded series (layer 6). With higher glacial 

horizontal hydraulic conductivity, the SSWR was generally 

higher for both water-level and streamflow observations; the 

water-table surface was generally lower during early stress 

periods, with more drawdown during later stress periods. With 

higher glacial vertical hydraulic conductivity, the water-table 

surface was generally lower during early stress periods with 

less drawdown observed during later stress periods. Lower 

glacial vertical hydraulic conductivities resulted in very little 

change in the SSWR. Lower vertical hydraulic conductivities 

in the upper shale unit resulted in lower water levels; however, 

some changes in this parameter resulted in model runs that did 

not converge. Lower horizontal hydraulic conductivities in the 

sandstone resulted in lower SSWR and a closer match between 

observed and simulated drawdowns, whereas higher horizontal hydraulic conductivities in the sandstone resulted in little 

change in the SSWR for water levels and streamflows. Higher 

vertical hydraulic conductivities in the interbedded-series values resulted in a lower initial water-level surface during early 

stress periods and less drawdown during later stress periods.

Transient model sensitivity to changes in the riverbed 

conductance, recharge, and storage parameters also was 

investigated during the sensitivity analysis. Both increases 

and decreases to the riverbed conductance parameter resulted 

in only slight changes in the SSWR. Changes in recharge had 

very little effect on simulated water levels, whereas increased 

recharge resulted in higher simulated streamflows. Recharge 

estimates for most stress periods were modified slightly within 

reasonable ranges to improve streamflow estimates. Storage 

estimates also were modified within reasonable ranges to 

improve the agreement between observed and model simulated values. Model fit was improved with increased glaciallayer specific yield, increased storage in shale layer 4, and 

increased storage in the sandstone layers. Increasing specific 

Table 4. Water-level observations used in transient model calibration for the Tri-County region, Michigan.

[Wellogic is an electronic database of water well records that is maintained by the Michigan Department of Environmental Quality. “—” denotes no 

observation wells available]

Stress 

period

Time interval

represented by 

stress period

USGS observation wells Wellogic database wells

Observations in the 

Saginaw aquifer

Observations in the 

glacial aquifer

Wells in the 

Saginaw aquifer

Wells in the 

glacial aquifer

1 Predevelopment — — — —

2 Pre-1920 — — 1 —

3 1921–38 2 — — —

4 1939–48 8 1 18 2

5 1949–54 11 1 18 1

6 1955–62 15 1 50 —

7 1963–68 20 3 929 50

8 1969–72 20 3 1056 128

9 1973–82 20 3 1338 437

10 1983–90 19 3 1084 389

11 1991–95 18 3 1022 101

12 1996–99 6 1 1007 81

13 2000–2001 6 2 1094 357

14 2002 6 — 982 243

15 2003 10 1 830 199

16 2004 6 — 302 27

17 2005 15 3 98 16
425,000

475,000

500,000

450,000

400,000

1,900,000 1,925,000 1,950,000

EASTING, IN FEET

NORTHING, IN FEET

1,975,000 2,000,000

Lansing

East 

Lansing

Cedar Well

750

775

800

825

850

0 20 40 60 80 100

TIME, IN YEARS

Davis Well

825

850

875

TIME, IN YEARS

WA

TER LEVEL, IN FEET

 ABOVE SEA LEVEL

observed simulated

0 20 40 60 80 100

Fenner Well

750

775

800

825

850

0 20 40 60 80 100

TIME, IN YEARS

WA

TER LEVEL, IN FEET

 ABOVE SEA LEVEL

Lansing P5 Well

750

775

800

825

850

0 20 40 60 80 100

TIME, IN YEARS

WATER LEVEL, IN FEET

 ABOVE SEA LEVEL

Logan Well

675

700

725

750

775

800

825

850

0 20 40 60 80 100

TIME, IN YEARS

WA

TER LEVEL, IN FEET

 ABOVE SEA LEVEL

Maybel Well

825

850

875

0 20 40 60 80 100

TIME, IN YEARS

WA

TER LEVEL, IN FEET

 ABOVE SEA LEVEL

Robins Well

750

775

800

825

850

0 20 40 60 80 100

TIME, IN YEARS

WA

TER LEVEL, IN FEET

 ABOVE SEA LEVEL

Seymour Well

600

650

700

750

800

850

0 20 40 60 80 100

TIME, IN YEARS

WA

TER LEVEL, IN FEET

 ABOVE SEA LEVEL

Spartan Well

750

775

800

825

850

0 20 40 60 80 100

TIME, IN YEARS

WA

TER LEVEL, IN FEET

 ABOVE SEA LEVEL

WA

TER LEVEL, IN FEET

 ABOVE SEA LEVEL

Stiefel Well

825

850

0 20 40 60 80 100

TIME, IN YEARS

WATER LEVEL, IN FEET

 ABOVE SEA LEVEL

Townsend and Scott Park Wells

750

775

800

825

850

0 20 40 60 80 100

TIME, IN YEARS

WA

TER LEVEL, IN FEET

 ABOVE SEA LEVEL

22 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan Groundwater-Flow Models 23

Figure 11.  Relation between observed and simulated transient water levels in observation wells in the Lansing area, Michigan.
400,000

500,000

550,000

450,000

1,850,000 1,900,000 1,950,000

EASTING, IN FEET

NORTHING, IN FEET

2,000,000

DeWitt

St. Johns

Williamston

Lansing

Mason

Grand

Ledge

East 

Lansing

observed simulated

Quarantine Well

725

750

775

800

825

850

TIME, IN YEARS

WATER LEVEL, IN FEET

 ABOVE SEA LEVEL

0 20 40 60 80 100

CC Airport Well

TIME, IN YEARS

WATER LEVEL, IN FEET

 ABOVE SEA LEVEL

775

800

825

850

0 20 40 60 80 100

Holt Well

TIME, IN YEARS

WATER LEVEL, IN FEET

 ABOVE SEA LEVEL

850

875

900

0 20 40 60 80 100

Kerns Well

850

875

900

TIME, IN YEARS

WATER LEVEL, IN FEET

 ABOVE SEA LEVEL

0 20 40 60 80 100

Mason Old Well

850

875

900

TIME, IN YEARS

WATER LEVEL, IN FEET

 ABOVE SEA LEVEL

0 20 40 60 80 100

Lotte Well

875

900

925

TIME, IN YEARS

WATER LEVEL, IN FEET

 ABOVE SEA LEVEL

0 20 40 60 80 100

Dansville Well

TIME, IN YEARS

WATER LEVEL, IN FEET

 ABOVE SEA LEVEL

925

950

975

1000

0 20 40 60 80 100

Okemos Well

825

850

TIME, IN YEARS

WATER LEVEL, IN FEET

 ABOVE SEA LEVEL

0 20 40 60 80 100

Sherwood Well

825

850

875

TIME, IN YEARS

WATER LEVEL, IN FEET

 ABOVE SEA LEVEL

0 20 40 60 80 100

Meridian Well

775

800

825

850

TIME, IN YEARS

WATER LEVEL, IN FEET

 ABOVE SEA LEVEL

WATER LEVEL, IN FEET

 ABOVE SEA LEVEL

0 20 40 60 80 100

US 27 Well

775

800

TIME, IN YEARS

WATER LEVEL, IN FEET

 ABOVE SEA LEVEL

0 20 40 60 80 100

St Johns Well

650

675

700

725

750

775

TIME, IN YEARS

WATER LEVEL, IN FEET

 ABOVE SEA LEVEL

0 20 40 60 80 100

650

675

700

725

TIME, IN YEARS

WATER LEVEL, IN FEET

 ABOVE SEA LEVEL

0 20 40 60 80 100

Elsie Well

Marble Well

775

800

825

850

875

TIME, IN YEARS

0 20 40 60 80 100

24 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan Groundwater-Flow Models 25

Figure 12.  Relation between observed and simulated transient water levels in Tri-County-region observation wells..
400,000

500,000

C9

C8

C7

C10

C11

C12

C3

C4

C6

C5

C2

C1

550,000

600,000

450,000

350,000

1,850,000 1,900,000 1,950,000

EASTING, IN FEET

NORTHING, IN FEET

2,000,000 2,050,000 2,100,000

Lansing

East 

Lansing

observed simulated

Grand River at Lansing

10

0

20

30

40

50

60

70

80

TIME, IN YEARS

FLOW, IN CUBIC FEET 

PER SECOND

0 20 40 60 80 100

Red Cedar at East Lansing

0

20

40

60

80

100

120

0 20 40 60 80 100

TIME, IN YEARS

FLOW, IN CUBIC FEET 

PER SECOND

Red Cedar at Williamston

0

20

40

60

80

100

0 20 40 60 80 100

TIME, IN YEARS

FLOW, IN CUBIC FEET 

PER SECOND

Deer Creek

2

0

4

6

8

10

12

TIME, IN YEARS

FLOW, IN CUBIC FEET 

PER SECOND

0 20 40 60 80 100

Sycamore Creek

0

10

20

30

40

50

0 20 40 60 80 100

TIME, IN YEARS

FLOW, IN CUBIC FEET 

PER SECOND

Grand River at Portland

0

50

100

150

200

250

300

TIME, IN YEARS

0 20 40 60 80 100

FLOW, IN CUBIC FEET 

PER SECOND

Looking Glass River

0

50

100

150

200

250

TIME, IN YEARS

0 20 40 60 80 100

FLOW, IN CUBIC FEET 

PER SECOND

Sloan Creek

0 20 40 60 80 100

TIME, IN YEARS

FLOW, IN CUBIC FEET 

PER SECOND

0

1

2

3

4

5

Orchard Creek

TIME, IN YEARS

0

5

10

15

20

25

30

35

FLOW, IN CUBIC FEET 

PER SECOND

0 20 40 60 80 100

26 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan Groundwater-Flow Models 27

Figure 13.  Relation between observed and simulated transient streamflows in the Tri-County region, Michigan.
Water Budget by Stress Period

FLOW, IN MILLION GALLONS PER DAY

Change in Water Budget Components by Stress Period

-1,000

-800

-600

-400

-200

0

200

400

600

800

1,000

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

STRESS PERIOD

Wells out

Boundaries out

Storage sink

River out

Recharge in

In thru boundaries

River in

Storage source

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

STRESS PERIOD

CHANGE IN WATER BUDGET COMPONENT,

IN MILLION GALLONS PER DAY -600

-400

-200

0

200

400

600

Boundaries out

In thru boundaries

Storage source

Recharge in

Wells out

Storage sink

River out

River in

Change in Water Budget Components by Stress Period

STRESS PERIOD

CHANGE IN WATER BUDGET COMPONENT,

IN MILLION GALLONS PER DAY -75

-50

-25

0

25

50

75

100

125

1

(predevelopment)

4 (1939-48) 7 (1963-68) 10 (1983-90) 13 (2000-2001) 16 (2004)

Storage source

Wells out

Storage sink

A

B

C

28 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

Figure 14. Water-budget components and change in components by stress period, 

Tri-County model. (Note change of scale between graphs B and C.)
Groundwater-Flow Simulations 29

yield in the layers representing the glacial aquifer continued 

to improve model agreement between observed and simulated water levels, but the agreement between observed and 

simulated streamflows worsened. Changes to storage in the 

interbedded series and lower shale units resulted in very little 

change to the calculated SSWR. 

Groundwater-Flow Simulations

As stated previously, the Tri-County groundwater-flow 

model has been used to address numerous water-resource 

issues. For this study, scenarios were selected to build upon 

previous simulations and to advance understanding of the 

regional groundwater-flow system. These scenarios include 

(1) the potential effects of reduced recharge due to urban areas 

or low rainfall/drought conditions on water levels, (2) delineation of contributing areas under 2006–7 pumping conditions, 

and (3) optimization of pumping subject to various quality and 

quantity constraints.

Investigation of Reduced Recharge

Several steady-state and transient scenarios investigated 

changes in water levels predicted by the model with reduced 

recharge due to urban areas and low-rainfall/drought conditions. Simulations investigating reduced recharge in urban 

areas were done with both the steady-state and transient 

models. Simulations investigating reduced recharge due to 

low rainfall were done with the transient model representing 

monthly conditions.

To investigate spatial differences in recharge that may 

arise from impervious surfaces, aerial photos for the TriCounty region from 1984, 1994, and 2003 were analyzed to 

determine areas that are primarily urban and that are assumed 

for the purposes of this study to be largely impermeable. 

Because some of these urban areas are likely connected to 

storm sewers, where runoff water collects and is released into 

a nearby stream, this water may be unavailable to recharge 

the surrounding groundwater-flow system. However, rainfall 

on some of these areas, such as roads or rooftops, likely runs 

off to adjacent medians or yards where it does recharge the 

local groundwater-flow system. In addition, some recharge 

can occur beneath paved urban areas because of leaking pipes. 

Investigation of the nature of each urban impervious area and 

the status of each municipal system was beyond the scope of 

this study. Therefore, for model simulations, these urban areas 

were assumed to represent areas of reduced recharge. 

Recharge rates in areas determined to be urban by 

aerial-photo interpretation were reduced by 20 percent and 

50 percent for those model stress periods corresponding to the 

aerial photo dates. As mentioned above, the actual change in 

recharge caused by urban areas is unknown, so these reductions of 20 and 50 percent permit investigation of effects due 

to low or moderate reductions in recharge. Some urban areas 

were smaller than or only encompassed a small part of a cell; 

in these areas, recharge was not reduced. Urban areas for 

1984, 1994, and 2003 occupied 1,902, 2,237, and 2,665 model 

cells, respectively. Under steady-state conditions, only urban 

areas based on the 2003 air photo were simulated with reduced 

recharge. Recharge rates also were reduced by 50 percent for 

an area approximately 2,000 ft surrounding Lake Lansing in 

Meridian Township. The potential effects of rapid growth in 

this area on water levels are of interest to the township. This 

simulation accounts for reduced recharge entering the model 

through the upper model surface, but it does not account 

for, nor reduce any, recharge that may enter the groundwater 

system as leakage from Lake Lansing. To fully account for 

the potential effects of reduced recharge due to development 

around the lake, flow from Lake Lansing may need to be 

included.

Steady-state simulation results indicate the following 

potential declines in hydraulic head:

• Slightly more than 2 ft in the upper glacial unit 

(layer 1) and less than 2 ft in the upper bedrock 

sandstone unit (layer 5) with a 20-percent reduction in 

recharge in urban areas.

• Slightly more than 6 ft in the upper glacial unit (layer 

1) and slightly more than 4 ft in the upper bedrock 

sandstone unit (layer 5) with a 50-percent reduction in 

recharge in urban areas. 

• Less than 0.6 ft in the upper glacial unit (layer 1) and 

less than 0.2 ft in the upper bedrock sandstone unit 

(layer 5) with a 50-percent reduction in recharge for 

the area surrounding Lake Lansing. 

Transient simulation results indicate the following potential declines in hydraulic head: 

• Slightly more than 1 ft in both the upper glacial 

unit (layer 1) and the upper bedrock sandstone unit 

(layer 5) with a 20-percent reduction in recharge in 

urban areas. 

• Slightly more than 3 ft in the upper glacial unit 

(layer 1) and less than 3 ft in the upper bedrock 

sandstone unit (layer 5) with a 50-percent reduction in 

recharge in urban areas. 

• Less than 0.3 ft in the upper glacial unit (layer 1) and 

less than 0.2 ft in the upper bedrock sandstone unit 

(layer 5) with a 50-percent reduction in recharge for 

the area surrounding Lake Lansing. 

Additional transient simulations investigated the impact 

on water levels of reduced recharge due to low-rainfall/

drought conditions and reduced recharge with increased 

groundwater withdrawals. During summer months, recharge 

to the groundwater system can be reduced by evaporation 

and uptake of precipitation by plants; in addition, groundwater withdrawals are often greater to meet demands such as 

lawn watering. Both the lowered recharge rates and increased 
30 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

groundwater withdrawals can affect water levels. Simulations with the transient model were done with 72 months (6 

years) in which recharge and pumping reflected average recent 

conditions (as specified by the water-supply system) followed 

by 24 months (2 years) with modified recharge or modified 

recharge and pumping rates. Thus, at the beginning of the 

year with modified recharge and pumping rates, changes in 

storage were small (less than 2 percent) and water movement 

into storage approximately equaled water movement out of 

storage. To represent reduced recharge due to low rainfall, the 

recharge rate for each month was reduced by about 30 percent. 

The amount of reduction was varied for some summer months 

because of model convergence problems in the months with 

low recharge rates. Over the time interval for the transient 

model, the year of lowest precipitation was 1963 with 22.6 in., 

which is about 70 percent of the average rate of 32 in. To represent possible future groundwater-withdrawal rates, monthly 

rates for Lansing-area production wells were increased by 

15 percent to match the average observed increase in pumping 

from 2004 to 2005 (table 5).

Transient simulations with reduced recharge indicate 

decreases in simulated water levels ranging from 0 to 6 ft at 

observation-well locations and simulated streamflows ranging from 0.5 to 34.7 ft3

/s at streamflow-observation locations. 

Decreases in simulated water levels due to reduced recharge 

ranged from 0 to 6 ft for wells completed in the glacial 

deposits and from 0 to 3 ft for wells completed in the Saginaw aquifer. Transient simulations with reduced recharge and 

increased pumping indicate a lowering of simulated water 

levels ranging from 0 to 6 ft at observation-well locations 

and decreases in simulated streamflows ranging from 0.5 to 

34.7 ft3/s at streamflow-observation locations. Lowering of 

simulated water levels due to reduced recharge and increased 

pumping ranged from 0 to 6 ft for wells completed in the 

glacial deposits and from 0 to 6 ft for wells completed in the 

Saginaw aquifer. The reduction in the amount of water available to recharge the groundwater system affects the upper 

model layers representing the glacial aquifers more than the 

deeper bedrock layers. However, with a reduction in recharge 

and an increase in withdrawals from the bedrock aquifer, water 

levels in the bedrock layers are affected more than those in the 

glacial layers. Differences in water levels between simulations 

with reduced recharge only and those with reduced recharge 

and increased pumping are greatest in the Lansing area and 

smallest away from pumping centers, as expected. Additionally, the increases in pumping rates had minimal effect on 

most simulated streamflows, with the largest differences in 

the Lansing area. For both transient simulations, model input 

variables at the end of year 6 were specified such that water 

movement into storage would approximately equal water 

movement out of storage. With the increase in pumping rates, 

less water is available to discharge to the streams or enter 

storage, and more water is removed from streams and storage. 

With reduced recharge after 2 years (during year 8), water 

movement into storage was about half of water movement 

out of storage; in year 8 with reduced recharge and increased 

pumping, water movement into storage was also nearly half 

that of water movement out of storage (fig. 15). During year 

6, water was removed from storage mostly during the summer 

and fall, from July to November, and water entered storage 

from December to June, although primarily from March to 

May. After 2 years of reduced recharge and reduced recharge 

with increased pumping, water entered storage from December to May, and water moved out of storage from June to 

Table 5. Transient model details for monthly stress periods for the Tri-County region, Michigan.

[Mgal/d, million gallons per day]

Time interval represented 

by stress period

Stress period length 

(days)

Simulated pumping

2005 (Mgal/d) Future (Mgal/d)

January 31 41.4 45.8

February 28 38.4 42.0

March 31 41.9 47.1

April 30 40.9 45.7

May 31 43.1 48.6

June 30 49.7 55.9

July 31 48.6 55.6

August 31 51.0 57.7

September 30 51.3 56.6

October 31 42.2 46.8

November 30 40.1 44.6

December 31 36.3 40.5
0

50

100

150

200

250

300

Out of storage Into storage

 Year 7 Year 8 Year 7 Year 8

AMOUNT OF WATER, IN MILLION GALLONS

REDUCED RECHARGE REDUCED RECHARGE AND

INCREASED PUMPING

Groundwater-Flow Simulations 31

Figure 15. Net storage, by year, during transient simulations with reduced recharge and reduced recharge 

with increased pumping.

November (fig. 16). The differences observed between year 

6 and year 8 in each simulation would possibly be different if 

the model had not been run for 6 years so that water movement into storage would approximately equal water movement 

out of storage.

Delineation of Contributing Areas

The particle-tracking program MODPATH (Pollock, 

1989) can be combined with MODFLOW-calculated flow in 

each cell to determine the areas of the water table, projected 

up to the land surface, where water that is discharged by a 

well enters the groundwater-flow system. Particle tracking 

simulates the advective movement of groundwater, so the 

effects of diffusion, dispersion, and chemical reactions are not 

considered. Therefore, particle tracking is not intended as a 

substitute for simulating the transport of dissolved chemicals 

in the groundwater-flow system. An estimated porosity of 

15 percent was previously used for particle-tracking simulations (Holtschlag and others, 1996) and, in the absence of 

any additional information, was used for all layers in the 

2009 model.

Groundwater-flow paths, and, thus, particle-tracking 

results, depend in part on the stresses to the groundwater-flow 

system. Different pumping rates or pumping locations will 

change the groundwater-flow patterns in the modeled area 

and result in different zones of contribution and areas contributing recharge to the pumping wells. The area contributing recharge to a pumping well is defined as the surface area 

of the three-dimensional boundary of the groundwater-flow 

system that delineates the location of the water entering the 

groundwater-flow system that eventually flows to the well and 

discharges (Reilly and Pollock, 1993). The zone of contribution to a pumping well is defined as the three-dimensional 

volumetric part of the aquifer through which groundwater 

flows to a pumping well from the area contributing recharge 

(Morrissey, 1989). A wellhead-contributing area for each 

pumping well is defined here as the combination of areal 

extent of the areas contributing recharge and of the zones of 

contribution projected up to the land surface. By tracking particles for a specified amount of time, such as 10 years, time-oftravel areas can be determined. Under steady-state conditions, 

the water discharging from a pumped well is a blend of water 

of different ages or traveltimes. In each specified time-oftravel simulation, it is assumed that model pumping rates and 

pumping locations remain constant indefinitely and that the 

water withdrawn by each simulated well may represent water 

that has entered as recharge or that already was in the zone of 

contribution when the well began pumping. 

A total of 38,700 hypothetical particles were placed on 

the sides of the cells containing selected Lansing-area production wells. These particles were tracked backward using the 

steady-state model along flow paths through the groundwaterflow field until they reached a top cell face in the upper model 

layer or until a specified amount of time elapsed. The position of the particle at the end of the simulation represents 

the location at the water table where the particle enters the 

groundwater-flow system or the location where water would 

flow to the well in the specified amount of time. Groundwater 
Year 8 reduced recharge and increased pumping

Year 6

Year 8 reduced recharge

-80

-60

-40

-20

0

20

40

60

80

100

120

AMOUNT OF WATER, IN MILLION GALLONS

 JAN FEB MAR APR MAY JUNE JULY AUG SEP OCT NOV DEC

32 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

withdrawals of 45.3 Mgal/d representing 2006–7 conditions were specified for this simulation. Because 2007 was a 

somewhat dry year, contributing areas were delineated at a 

time with slightly higher pumping rates than would have been 

achieved using 2005 or 2006 pumping rates. Areas contributing recharge as well as zones of contribution were determined 

for 10, 20, and 40 years using the 2009 model. The areal 

extent of the 10-year time-of-travel wellhead-contributing 

areas encompasses about 29 mi2 (fig. 17). The areal extent of 

the 20-year time-of-travel areas encompasses about 41 mi2, 

and the areal extent of the 40-year time-of-travel areas encompasses about 59 mi2

.

Optimization Scenarios

Simulation results and contributing areas described above 

are based on flow directions resulting from the withdrawal 

rates specified in the model input files. Different withdrawal 

locations and pumping rates must be specified for each 

simulation to illustrate different flow patterns. Optimization 

of groundwater withdrawals with a water-resource management model allows determination of withdrawal locations and 

pumping rates that best meet a specified management objective and series of constraints; such constraints could include 

water-treatment costs and (or) water-quality or water-quantity 

requirements. For example, well locations and pumping 

rates could be selected to maximize pumpage or to minimize 

operational or treatment costs. The groundwater-management 

program GWM (Ahlfeld and others, 2005) can be combined 

with MODFLOW-calculated water levels by using a responsematrix approach to solve several types of groundwater-management formulations. Each management formulation consists 

of a set of decision variables, an objective function, and a 

set of constraints. The objective function can be specified to 

minimize or maximize the sum of some or all the specified 

decision variables, subject to a set of specified constraints. 

These decision variables can be flow-rate decision variables, 

which specify withdrawal rates at wells, or binary variables, 

which define the status of the flow-rate decision variables. 

Constraints can specify upper and lower bounds on the flowrate decision variables; summation of the decision variables; 

or hydraulic-head drawdowns, differences, or gradients. In this 

study, the optimization formulations were solved by using linear programming (LP), in which the objective function and all 

constraints are linear functions of the decision variables. The 

water level at each constraint location is equal to the sum of 

the water level at the constraint location for a base withdrawal 

condition plus the sum of the water-level changes that result 

from changes in withdrawal rates at each site. The response 

coefficients, which describe this change in the groundwater 

levels resulting from stresses at each withdrawal location, 

are assumed to be constant for linear systems (that is, they 

do not vary with changes in the distribution of withdrawal 

rates throughout the groundwater-flow system) (Ahlfield and 

others, 2005).

Figure 16. Net storage, by month, during transient simulations with reduced recharge and reduced recharge 

with increased pumping.
Figure 17

490,000

470,000

450,000

430,000

410,000

390,000

1,890,000 1,910,000 1,930,000

EASTING, IN FEET

NORTHING, IN FEET

1,950,000 1,970,000 1,990,000

Lansing

EATON COUNTY

INGHAM COUNTY

CLINTON COUNTY

Base map from the Michigan Resource 

Information System, Michigan Department 

of Environmental Quality 10 KILOMETERS

0 5 10 MILES

0 5

Groundwater-Flow Simulations 33

Figure 17. Simulated 10-year time-of-travel areas for selected production wells in the nine-township area, 

Tri-County region, Michigan.

For this study, optimization was used with existing production wells to determine the additional capacity available 

from selected wells with low operational costs; it was also 

used with proposed new locations to determine withdrawal 

locations to achieve desired additional withdrawal capacity 

while meeting specified head constraints. In each optimization 

scenario, some wells are managed (where pumping rates can 

be optimized) and some wells are unmanaged (where pumping 

rates are specified and are not optimized during the simulation). Of the existing production wells in the Lansing area, 

78 were selected for optimization on the basis of operational 

costs and pumping history; that is, wells with relatively lower 

costs and higher current pumping rates were selected to be 

managed, and more infrequently used wells with higher costs 

were left unmanaged. Operational costs were based primarily 

on water-treatment expenses because the cost to soften water 

is much greater than the cost of electricity to operate the well 

(William Maier, LBWL, oral commun., 2007). In a first set 

of optimization scenarios (scenarios L1, L2, LS1, LS2; table 

6), relative (that is, not actual) operational costs were used to 

determine pumping rates at the managed existing well locations. In a second set of optimization scenarios (scenarios 

A1, A2, B1, and B2; table 6), existing production wells were 

unmanaged (such that pumping rates remained fixed at 2007 

rates) and proposed new wells were specified as managed. 

Two potential locations for additional wellfield capacity were 

selected for the second set of optimization scenarios. Area 

A south of Lansing in Delhi Township was specified to have 

30 wells, and area B north of Lansing in Dewitt Township 

was specified to have 35 wells. Each well was open vertically 
34 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

to layers 5 through 10, and each occupied an individual cell 

with four to six cells between each well. Both areas had two 

optimization simulations, one for each maximum pumping rate 

of 0.5 and 1 Mgal/d, to determine whether a total combined 

pumpage of 12 Mgal/d could be achieved. Head constraints 

were specified in both sets of scenarios to limit dewatering of 

the glacial deposits and to prevent water levels in the upper 

bedrock aquifer unit from falling below the top of the unit. 

For each optimization scenario, withdrawals from unmanaged 

wells were simulated with the WEL package. Wells previously 

simulated with the MNW package were converted to the WEL 

package, with withdrawals distributed among layers on the 

basis of rates determined by the MNW package. This conversion was necessary because the multiple-layer representation 

in the MNW package accounts for water-level differences 

between multiple producing zones. These water-level differences between aquifers can induce cross-flow between aquifers even when there is no discharge from a well or even under 

pumping conditions (Halford and Hanson, 2002). Therefore, 

specifying withdrawals only with the WEL package means 

that all withdrawals are specified as a discharge of water from 

each cell. Water levels in the lowest glacial unit (layer 3) and 

the upper sandstone unit (layer 5) were compared from simulations with wells represented by the MNW and WEL packages. The majority of differences were less than 1 ft in layer 

3 and less than 0.5 ft in layer 5; therefore, discharge (well 

withdrawal) rates were adequately represented with the WEL 

package in the optimization scenarios. Simulations were done 

with the steady-state model in order to represent the potential 

long-term impacts of the optimized pumping results.

In the first optimization scenario (L1), existing (2007) 

pumpage from the managed wells totaled 25.65 Mgal/d, and 

pumpage from the unmanaged wells totaled 19.65 Mgal/d. 

Managed wells withdrew water from the bedrock units, 

whereas unmanaged wells were in both the glacial and bedrock units. Because the simulation was specified to maximize 

total pumpage, coefficients in the objective function for each 

managed well were assigned values that reflected the relative 

inverse operational cost of each well; that is, wells with relatively low operational costs were given higher weights (coefficient values) and those with relatively high operational costs 

were given lower weights. The wells were divided into four 

groups and assigned relative weights equal to 1.1, 1.2, 1.3, or 

1.4. Therefore, wells with higher costs (and a coefficient of 

1.1) would contribute less to the objective function, and wells 

with lower costs (and a coefficient of 1.4) would contribute 

more. Maximum total pumpage from all managed wells was 

based on water-treatment capacities and specified to be 50 

Mgal/d. A total of 103 head constraints were used to limit 

water-level declines, with 57 in the lower glacial unit (layer 

3) and 46 in the upper bedrock unit (layer 5). These head 

constraints were specified to be the minimum of 5 ft above the 

bottom of layer 3 or 4 ft above the water level in layer 5 under 

steady-state 2007 pumping conditions. In some cases, the 2007 

pumping rates indicated that water levels would be below the 

bottom of layer 3, so these head constraints were specified 

so that the optimized pumping would prevent any additional 

water-level decline beyond that with existing pumping rates. 

It is important to remember that the steady-state model 

represents the long-term effects of the specified groundwater 

withdrawals with every well pumping continuously; so the 

fact that part of the glacial deposits are dry as a result of the 

groundwater withdrawals does not necessarily represent the 

actual conditions in the area with wells pumping intermittently 

at varying rates during the year. Transient simulations would 

be needed to better represent potential impacts of varying 

pumping rates. 

The optimal total withdrawal rate for this management 

formulation (L1) is 31.76 Mgal/d, with 67 managed wells 

pumping (fig. 18). The optimization results indicate that an 

additional 6.11 Mgal/d could be withdrawn above the 2007 

pumping levels, given the specified formulation and constraints (table 6). Six wells that pumped water in 2007 did not 

withdraw water under the optimized conditions, whereas four 

wells that did not pump water in 2007 did withdraw water 

under the optimized conditions. Changing these constraints, 

Table 6. Summary of optimization formulations and results for the Tri-County region, 

Michigan.

Scenario Number of 

managed wells

Number of 

head constraints

Upper bound on 

pumping rates

(in million 

gallons per day)

Additional 

capacity

L1 78 103 Varies 6.11

L2 78 103 1 14.13

LS1 78 103 Varies 5.72

LS2 78 103 Varies 5.66

A1 30 1 0.5 7.98

A2 30 1 1 9.54

B1 35 37 .5 12

B2 35 37 1 12
450,000

460,000

440,000

480,000

490,000

470,000

430,000

402,000

410,000

400,000

1,910,000 1,920,000 1,930,000

EASTING, IN FEET

NORTHING, IN FEET

1,940,000 1,950,000 1,960,000 1,970,000 1,980,000

EXPLANATION

Well selected for withdrawals

Well not selected for withdrawals

Base map from the Michigan Resource 

Information System, Michigan Department 

of Environmental Quality 5 KILOMETERS

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Groundwater-Flow Simulations 35

such as including different wells or changing the maximum 

pumping rate for each well location, would possibly yield 

different optimized pumping rates. Also, it is important to note 

that these steady-state scenarios are based on the assumption 

of constant pumping throughout the year; therefore additional 

pumping capacity might be possible with wells pumping at 

intermittent rates during the year. In the post-optimization 

analysis with the model running the optimized pumping 

rates, 12 of the head constraints were not met (3 of the cells 

were dry), indicating that water levels in those cells were 

below the specified value (with the largest difference being 

3.2 ft). The fact that some constraints were not met with the 

model simulating the optimized pumping rates is mostly a 

reflection of (1) the ability of the model-calculated response 

coefficients to accurately reflect the response of the simulated groundwater system to changes in stress—which, in 

turn, depends on the accuracy of the MODFLOW-calculated 

heads—and (2) the assumption that heads respond linearly to 

changes in the stress rates imposed at the flow-rate decision 

variables. However, the maximum difference of 3.2 ft in the 

value of the head constraint is considered acceptable for the 

goals of this study given the uncertainties in the understanding of the hydrogeologic system and in the true values of the 

model input parameters.

To investigate whether additional capacity might be 

available if pumping rates at managed wells were allowed to 

Figure 18. Optimized wells in the Lansing area, Michigan.
36 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

increase above the maximum rates specified for L1, an additional scenario was done in which the maximum rate for each 

well was set to 1.0 Mgal/d. Head constraints were the same as 

those described above for L1. The optimal total withdrawal 

rate for management formulation (L2) is 39.77 Mgal/d, with 

46 managed wells pumping. The optimization results indicate 

that an additional 14.13 Mgal/d could be withdrawn above the 

2007 pumping levels (table 6), given the specified formulation and constraints. In the post-optimization analysis with the 

model running the optimized pumping rates, 29 of the head 

constraints were not met (10 of the cells were dry), indicating 

that water levels in those cells were below the specified value. 

Even though the specified maximum pumping rates were not 

feasible for each managed well, this scenario indicates that 

additional capacity might be available in some parts of the 

Lansing area, especially considering that this simulation was 

done with the steady-state model representing long-term continuous pumping and, realistically, each well pumps intermittently during the year (usually at less than the maximum rate).

Several scenarios were done to test the sensitivity of 

the optimization results to the relative weights specified for 

the operational costs of each managed well. Two additional 

scenarios were done with different weights for the managed 

wells in the Lansing area; relative weights of 1.0, 1.5, 2.0, and 

2.5 were used for management formulation LS1, and relative 

weights of 0.2, 0.4, 0.6, and 0.8 were used for management 

formulation LS2. Head constraints for each management 

scenario were the same as those described above for L1. The 

optimal total withdrawal rate for management formulation 

(LS1) is 31.37 Mgal/d, with 69 managed wells pumping. The 

optimization results indicate that an additional 5.72 Mgal/d 

could be withdrawn above the 2007 pumping levels (table 6), 

given the specified formulation and constraints. In the postoptimization analysis with the model running the optimized 

rates, 11 of the head constraints were not met (3 of the cells 

were dry), indicating that water levels in those cells were 

below the specified value. The optimal total withdrawal rate 

for management formulation (LS2) is 31.31 Mgal/d, with 

69 managed wells pumping. The optimization results indicate 

that an additional 5.66 Mgal/d could be withdrawn above the 

2007 pumping levels (table 6), given the specified formulation and constraints. In the post-optimization analysis with the 

model running the optimized rates, 11 of the head constraints 

were not met (3 of the cells were dry), indicating that water 

levels in those cells were below the specified value. Thus, 

varying the weights used for the managed wells during the 

solution of the optimization formulations resulted in about the 

same additional capacity above the 2007 pumping rates under 

steady-state conditions.

In the next set of optimization scenarios with the proposed new wells in areas A and B, pumpage from the unmanaged wells totaled 45.3 Mgal/d under 2007 conditions. Managed wells withdrew water from the bedrock units, whereas 

unmanaged wells were in both the glacial and bedrock units. 

The scenarios were done to determine whether some combination of the wells in each area could be pumped to achieve a 

maximum total pumping rate of 12 Mgal/d, with a maximum 

pumping rate for each well of 0.5 Mgal/d in scenarios A1 and 

B1 and of 1.0 Mgal/d in scenarios A2 and B2. Each proposed 

well location was treated the same, with coefficients in the 

objective function for each managed well set to 1. In area A, 

one head-constraint location in layer 3 was sufficient to limit 

water-level declines, whereas in area B, 37 head-constraint 

locations in layer 5 were necessary. With a maximum pumping rate of 0.5 Mgal/d for each well, the optimization model 

indicates that 7.98 Mgal/d could be achieved using 16 wells 

in area A and 12 Mgal/d could be achieved using 24 wells 

in area B (fig. 19; table 6). With a maximum pumping rate 

of 1.0 Mgal/d for each well, optimization indicates that 

9.54 Mgal/d could be achieved using 10 wells in area A and 

12 Mgal/d could be achieved using 13 wells in area B (fig. 20; 

table 6). Withdrawals from area B did not produce the same 

rate of decline in layer 3 as did the withdrawals from wells in 

area A. Areas A and B differ in the specified vertical hydraulic characteristics of layer 4, which is the shale unit between 

the lower glacial unit and the upper bedrock unit. The vertical leakance is higher in area A, indicating more connection 

between the glacial and bedrocks units in area A than in area 

B. However, more site-specific information would be needed 

to determine whether this difference really exists, because the 

hydraulic properties were determined for these areas by using 

wells some distance away (very few local wells are in the 

area). In the post-optimization analysis with the model running the optimized pumping rates for area A with a maximum 

rate of 0.5 Mgal/d per well, one head constraint was not met, 

indicating that water levels in that cell were 0.7 ft below the 

specified value; similarly, with a maximum pumping rate of 

1.0 Mgal/d, one head constraint was not met, indicating that 

water levels in that cell were 0.7 ft below the specified value. 

In the post-optimization analysis with the model running the 

optimized pumping rates for area B with a maximum rate of 

0.5 Mgal/d per well, all constraints were met; with a maximum pumping rate of 1.0 Mgal/d, one head constraint was not 

met, indicating that water levels in that cell were 1.5 ft below 

the specified value. In both cases, these small differences do 

not indicate that the constraint locations would be dry. And, 

as with the previous scenarios, these steady-state simulations 

are based on the assumption that wells pump continuously 

throughout the year.

Model Assumptions and Limitations

The groundwater-flow model was developed to simulate the regional groundwater-flow system in the Tri-County 

region. Hydraulic properties represented in each layer were 

assumed to be horizontally isotropic; that is, within a cell, 

hydraulic properties are the same in the north-south direction 

as in the east-west direction. Hydraulic properties do vary 

from location to location; however, each grid cell represents 

the average hydraulic properties in the volume of aquifer 
450,000

460,000

Area B

Area A

440,000

480,000

490,000

470,000

430,000

402,000

410,000

400,000

1,910,000 1,920,000 1,930,000

EASTING, IN FEET

NORTHING, IN FEET

1,940,000 1,950,000 1,960,000 1,970,000 1,980,000

EXPLANATION

Well selected for withdrawals

Well not selected for withdrawals

Figure 19

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Information System, Michigan Department 

of Environmental Quality 5 KILOMETERS

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Model Assumptions and Limitations 37

Figure 19. Optimized wells for areas A and B with a specified maximum pumping 

rate of 0.5 million gallons per day.

represented by the cell. Vertical variations in aquifer properties 

within layers and any variations in head or flow within each 

layer are not simulated in the model. Local flows over distances smaller than the dimensions of the grid cell also cannot 

be accurately simulated. Additional geologic and hydrologic 

data, as well as finer discretization of the model, would be 

needed to simulate flow systems in smaller areas. The accuracy of layer surfaces and hydraulic conductivity estimates 

are limited by the available data at well and boring locations. 

Additional control and accuracy could be achieved by inclusion of more data points. 

It is assumed in steady-state model simulations that 

all stresses to the system, including well withdrawals and 

recharge rates, remain constant throughout the simulation. No 

net gain or loss of flow is simulated in the system; that is, in 

the model budget, water entering the model approximately 

equals water leaving the model, and no changes in groundwater storage result. It is assumed in the transient simulations that 

the storage characteristics of each aquifer can be represented 

by average values of either the storage coefficient or specific 

yield that are uniform within each layer. The actual storage 

properties of the aquifers likely differ from location to location. It is assumed in transient simulations that generalized 
450,000

460,000

440,000

480,000

490,000

470,000

430,000

402,000

410,000

400,000

390,000

1,910,000 1,920,000 1,930,000

EASTING, IN FEET

NORTHING, IN FEET

1,940,000 1,950,000 1,960,000 1,970,000 1,980,000

EXPLANATION

Well selected for withdrawals

Well not selected for withdrawals

Figure 20

Area B

Area A

Base map from the Michigan Resource 

Information System, Michigan Department 

of Environmental Quality 5 KILOMETERS

0 5 MILES

0

38 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

Figure 20. Optimized wells for areas A and B with a specified maximum pumping rate 

of 1 million gallons per day.

values of annual and monthly recharge rates vary on the basis 

of available precipitation and estimated base-flow data. Actual 

annual and monthly recharge rates were not measured and may 

vary both regionally and locally from those used in transient 

simulations. Estimates of reduced recharge due to impervious 

areas were generalized because of a lack of site-specific information; furthermore, areas represented as urban in the model 

simulation were based on interpretation of aerial photos and 

were limited by the model cell size (for example, actual urban 

areas, and thus impervious areas, may be larger or smaller 

than those observed). Therefore, effects due to urbanization 

would require more detailed study to determine which urban 

areas actually reduce recharge, and to what extent. Further 

investigation also would be needed to better determine the 

potential effects of any reductions in recharge on water levels 

in this area. Any reductions in recharge that may be caused by 

tiled agricultural fields were not considered in these simulations. Estimates of reduced recharge to represent low rainfall/

drought conditions were based on observed variations in 

annual precipitation data and not on actual drought-condition 

data. Therefore, for this study “drought” was taken to mean a 

time of water shortage, and model results may differ from conditions observed during an actual period defined as a drought. 
Summary and Conclusions 39

Small withdrawals from domestic wells were not 

included because of the difficulty in obtaining reliable data 

and the limitations in representing small-scale flow systems 

(systems considerably smaller than simulated as part of this 

study). However, domestic groundwater withdrawals probably 

are small at the scale of the model. 

Streams and lakes are represented in the model as river 

cells. This type of boundary condition allows for the determination of the amount of flow to and from the river cell; 

however, the amount of water flowing into the cell from an 

upstream cell is not accounted for. Therefore, a river cell could 

lose more water than actually is flowing in the stream. Thus, 

for detailed analysis of flow within particular streams, an 

accounting of actual flow within the stream needs to be part 

of the simulation, but such an accounting was not done for 

this study.

The base of the model is assumed to be impermeable. 

External boundary conditions, which are based on natural 

hydrologic conditions and are distant from the Tri-County 

region well fields, are assumed to have minimal effect on 

water levels and flow in the interior of the model. The model 

may not accurately represent the groundwater-flow system for 

any predictive simulations involving groundwater withdrawals 

near the model boundaries.

The location and size of the areas contributing recharge 

to wells are affected by the hydrogeologic characteristics and 

boundary conditions of the groundwater-flow system, as well 

as the location, depth, and discharge rate of each simulated 

well. Thus, the simulated areal extent of the areas contributing recharge and zones of contribution are dependent on the 

estimated values for the hydraulic characteristics, such as 

transmissivity and riverbed conductance, and on the pumping 

rates of the individual wells. With annual or seasonal variations in pumping rates or pumping locations, the size of areas 

contributing recharge could change. In addition, areas contributing recharge could change in size or location with changes 

in recharge rates or in the way the groundwater-flow system is 

represented. 

The accuracy of particle-tracking simulations is limited 

by the accuracy of the numerical model on which the simulations are based, the estimates of the effective porosity of the 

flow system, and the accuracy of the cell flow velocities in 

approximating the local groundwater-flow velocities. Actual 

effective porosity may differ from location to location and 

from layer to layer. The particle-tracking program considers 

groundwater flow by advection only. If the effects of dispersion were included, the areas contributing recharge could be 

larger. Because flow through fractures is not explicitly simulated in the model, groundwater flow and traveltimes in fractured bedrock, if present, may not be represented accurately. 

The accuracy of optimization scenarios depends on the 

precision of the response coefficients, which is limited by the 

accuracy of the water levels calculated by MODFLOW for 

the numerical model of the hydrologic system. The accuracy 

also is limited by the approximation of the groundwater-flow 

equations (Ahlfield and others, 2005). The accuracy of the 

numerical model depends on the representation of the flowsystem characteristics, including the geologic framework, 

hydraulic properties, and boundary conditions. The error in 

the MODFLOW solution for the groundwater-flow equations is proportional to the size of the grid cells and the length 

of the transient time steps; this error can be decreased with 

smaller grid cells and shorter time steps. During optimization, the response coefficients are used by GWM to predict the 

pumping rates given the specified head constraints; however, 

some head constraints were not met with the model running 

the optimized pumping rates. This may be explained by the 

inaccuracies or approximations noted above or by potential nonlinearities in the system that resulted in a nonlinear 

response of heads to changes in withdrawal rates. Solution 

of the management formulations with linear programming 

(LP) may be inappropriate if the management problem has a 

significant nonlinear response. The presence of water-table 

conditions and head-dependent boundary conditions can create 

nonlinear relations between groundwater heads and flow rates 

to or from the simulated boundary; therefore, use of sequential linear programming (SLP) may be more appropriate for 

these simulations and may improve the accuracy and precision 

of the response coefficients. However, the maximum difference of 3.2 ft in the value of the head constraint is considered 

acceptable for the goals of this study given the uncertainties 

in the understanding of the hydrogeologic system and in the 

true values of the model input parameters. Representation of 

withdrawals from wells with the WEL package for optimization scenarios was based on the apportionment of water from 

or between well cells that was determined by using the MNW 

package during transient model simulations. So, this representation with the WEL package is based on the assumption that 

this apportionment would not change in response to the pumping configurations resulting from the optimization scenarios.

Summary and Conclusions

A previously constructed groundwater-flow model of the 

Saginaw aquifer was refined in order to better represent the 

regional hydrologic system in the Tri-County region, which 

consists of Clinton, Eaton, and Ingham Counties, Michigan. 

The Saginaw aquifer, which is in the Grand River and Saginaw Formations of Pennsylvanian age, is the primary source 

of groundwater for Tri-County residents. With increasing 

demand, the need to manage withdrawals from the Saginaw 

aquifer has become more important, and the existing 1996 

model could not adequately address these issues of water 

quality and quantity. New information was needed to better 

address potential effects on water resources due to drought, 

locally high water demands, changes in pumping due to environmental conditions, inhibition of recharge by impervious 

surfaces, and issues affecting water quality, such as contaminant sources. In 2004, the Lansing-area communities working 

with the Tri-County Regional Planning Commission and the 
40 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

U.S. Geological Survey began a long-term plan for continued refinement of the regional groundwater-flow model. The 

refined groundwater-flow model allows simulations to address 

these issues of water quantity and provides communities with 

a tool that will enable them to better plan for expansion and 

subsequent protection of their groundwater-supply systems.

The 1996 Tri-County regional groundwater-flow model, 

developed for Clinton, Eaton, and Ingham Counties, has been 

used in the past by local water managers to answer questions about protection and availability of their groundwater 

resources and to delineate contributing areas for local Wellhead Protection Programs. Refinements in 1997 and 2003 

enabled the model to better represent flow within the ninetownship area surrounding Lansing and within the Mason and 

Vevay Township area. Refinements for the 2009 version of the 

model included representation of the system under steady-state 

and transient conditions, adjustments to the estimated regional 

groundwater recharge rates to account for both temporal and 

spatial differences, and adjustments to the representation and 

hydraulic characteristics of the glacial deposits and Saginaw 

Formation. The 1996 model consisted of two layers; the upper 

layer represented aquifers in the glacial deposits and the lower 

layer represented the Saginaw aquifer. The refined 2009 model 

consists of 10 layers; the upper 3 layers represent aquifers in 

the glacial deposits and the remaining 7 layers represent the 

multiple bedrock system units (sandstones, interbedded series, 

and shale units). This division of the groundwater-flow system 

into additional layers permits better representation of flow, 

interconnection between the glacial and bedrock aquifers, and 

individual production wells to be better characterized. The 

1996 model simulated groundwater flow under steady-state 

conditions. Average recharge rates representing the spatial 

variation over the model area were calculated for the 1996 

model. The refined 2009 model was calibrated to both steadystate and transient conditions; therefore, recharge rates and 

groundwater withdrawals could both change during the simulation. For the 2009 model, part of the southern boundary was 

extended beyond that modeled in the 1996 model to permit 

simulations in the Eaton Rapids and Eaton Rapids Township 

area. The transient model consists of an initial steady-state 

stress period representing predevelopment conditions and 16 

subsequent stress periods representing time intervals from the 

early 1900s up to 2005. A separate transient model was developed to simulate monthly changes in recharge and groundwater withdrawals based on recent data. This model was run 

under the same conditions for 6 years in order for the change 

in storage to become minimal so that effects after several years 

of withdrawals could be determined. The temporal variation in 

recharge rates for the transient model was based on an analysis 

of historical precipitation data. Estimated recharge rates for 

the transient model stress periods were varied on the basis of 

the percentage change from the average precipitation rate for 

each time interval. For the monthly stress periods, estimated 

recharge rates were varied on the basis of the calculated average base-flow values for 2003–5. Under steady-state conditions, groundwater withdrawals totaled 42.6 Mgal/d. Under 

transient conditions, groundwater withdrawal rates were varied 

according to estimated or measured pumping rates and ranged 

from 3.6 Mgal/d in stress period 2 up to an annual withdrawal 

rate of 46.1 Mgal/d in stress period 17. Monthly withdrawals 

were highest from June to September and ranged from 36.3 

Mgal/d in December to 51.3 Mgal/d in September. Simulations with the refined 2009 model included investigation of the 

potential effects of reduced recharge due to impervious areas 

or low rainfall/drought conditions, delineation of contributing 

areas with recent pumping rates, and optimization of pumping 

subject to various quantity and quality constraints. 

Simulations investigating reduced recharge due to 

impervious areas were done under steady-state and transient 

conditions. Urban areas were determined from 1984, 1994, 

and 2003 aerial photos of the Tri-County region. Recharge was 

assumed to be reduced by 20 and 50 percent because of the 

impervious surfaces in these urban areas. In addition, recharge 

was reduced by 50 percent for an area around Lake Lansing 

to simulate the potential effects of rapid growth on water 

levels in this area. Steady-state simulation results indicate 

potential declines of as much as 2.2 ft in the upper glacial unit 

(layer 1) and 1.7 ft in the upper bedrock sandstone unit (layer 

5) with a 20-percent reduction in recharge in urban areas. 

Steady-state simulation results indicate potential declines of as 

much as 6.2 ft in the upper glacial unit (layer 1) and 4.1 ft in 

the upper bedrock sandstone unit (layer 5) with a 50-percent 

reduction in recharge in urban areas. Steady-state simulation 

results indicate potential declines of less than 0.6 ft in the 

upper glacial unit (layer 1) and less than 0.2 ft in the upper 

bedrock sandstone unit (layer 5) with a 50-percent reduction 

in recharge for the area surrounding Lake Lansing. Transient 

simulation results indicate potential declines of as much as 

1.2 ft in the upper glacial unit (layer 1) and 1.1 ft in the upper 

bedrock sandstone unit (layer 5) with a 20-percent reduction in recharge in urban areas. Transient simulation results 

indicate potential declines of as much as 3.1 ft in the upper 

glacial unit (layer 1) and 2.7 ft in the upper bedrock sandstone 

unit (layer 5) with a 50-percent reduction in recharge in urban 

areas. With a 50-percent reduction in recharge for the area surrounding Lake Lansing, transient simulation results indicate 

potential declines of less than 0.3 ft in the upper glacial unit 

(layer 1) and less than 0.2 ft in the upper bedrock sandstone 

unit (layer 5) .

Simulations investigating reduced recharge due to low 

rainfall and increased pumping to meet anticipated future 

demand were done with the transient model representing 

monthly conditions. Simulations with the transient model were 

done with 72 months (6 years) in which recharge and pumping reflected average recent conditions (as specified by the 

water-supply system) followed by 24 months (2 years) with 

modified recharge or modified recharge and pumping rates. 

Thus, at the beginning of the year with modified recharge and 

pumping rates, changes in storage were small (less than 2 percent) and water movement into storage approximately equaled 

water movement out of storage. During the final two simulation years, monthly recharge rates were reduced by about 30 
References Cited 41

percent, and monthly withdrawal rates for Lansing-area production wells were increased by 15 percent. Transient simulations with reduced recharge indicate decreases in simulated 

water levels ranging from 0 to 6 ft at observation locations and 

simulated flows ranging from 0.5 to 34.7 ft3/s at observation 

locations. Decreases in simulated water levels due to reduced 

recharge ranged from 0 to 6 ft for wells completed in the 

glacial deposits and from 0 to 3 ft for wells completed in the 

Saginaw aquifer. Transient simulations with reduced recharge 

and increased pumping indicate decreases in simulated water 

levels ranging from 0 to 6 ft at observation locations and 

simulated flows ranging from 0.5 to 34.7 ft3/s at observation 

locations. Decreases in simulated water levels due to reduced 

recharge and increased pumping ranged from 0 to 6 ft for 

wells completed in the glacial deposits and from 0 to 6 ft for 

wells completed in the Saginaw aquifer. Differences in water 

levels and streamflows between simulations with reduced 

recharge and reduced recharge with increased pumping are 

greatest in the Lansing area and smallest away from pumping centers. During year 6, water was removed from storage 

mostly during the summer and fall, from July to November, 

and water entered storage the remaining months, although primarily from March to May. After 2 years of reduced recharge 

and reduced recharge with increased pumping, water entered 

storage from December to May, and water moved out of storage from June to November. 

Wellhead-contributing areas (defined for this study as 

the combination of the areal extent of the areas contributing 

recharge and of the zones of contribution projected up to the 

land surface) were delineated for selected Tri-County-region 

production wells by using particle-tracking analysis. Groundwater withdrawals for 2006–7 totaled 45.3 Mgal/d. Results 

of flow simulations indicate that 10-year time-of-travel areas 

cover approximately 29 mi2. The areal extent of the 20-year 

time-of-travel areas encompasses about 41 mi2, and the areal 

extent of the 40-year time-of-travel areas encompasses about 

59 mi2. An estimate of effective porosity of 15 percent for the 

Saginaw and glacial aquifers was used in the computations.

Optimization of groundwater withdrawals with a waterresources management model allows incorporation of constraints on the groundwater-flow solution in order to optimize 

cost savings, water quality, and (or) water quantity. For this 

study, optimization was used with existing production wells to 

determine additional capacity while approximately accounting for operational costs; it was also used with proposed 

new locations to determine withdrawal locations to achieve 

the desired additional capacity while meeting specified head 

constraints. Of the existing production wells in the Lansing 

area, 78 were selected for optimization based on operational 

costs and pumping history and were used during the first set 

of optimization scenarios to determine pumping rates at the 

managed existing well locations. After optimization, pumpage totaled 31.76 Mgal/d with 67 managed wells pumping. 

Six wells that were previously pumping did not withdraw 

water under the optimized conditions, whereas four wells 

that were not pumping in 2007 did withdraw water under the 

optimized conditions. The optimization results indicate that 

an additional 6.11 Mgal/d could be withdrawn above the 2007 

pumping levels, given the specified constraints. With modified maximum pumping rates of 1 Mgal/d for each managed 

well, an additional 14.13 Mgal/d could be withdrawn above 

the 2007 pumping levels, with 46 wells pumping. Changing 

these constraints, such as including different wells or changing the maximum pumping rate for each well location, would 

possibly yield different optimized pumping rates. Varying the 

coefficients for the managed Lansing-area wells used during 

the solution of the optimization formulation resulted in about 

the same additional capacity of between 5 and 6 Mgal/d above 

the 2007 pumping rates under steady-state conditions. In the 

second set of optimization scenarios, the existing production 

wells were unmanaged (so pumping rates remain fixed at 

2007 rates) and proposed new wells were specified as managed. Two potential locations for additional wellfield capacity 

were selected for the optimization scenarios. Area A south of 

Lansing in Delhi Township was specified to have 30 wells, 

and area B north of Lansing in Dewitt Township was specified to have 35 wells. Two optimization simulations were run 

for each area, one for each maximum pumping rate of 0.5 and 

1 Mgal/d, to determine whether a total combined pumpage 

of 12 Mgal/d could be achieved in either area. With a maximum pumping rate of 0.5 Mgal/d for each well, optimization 

indicates that 7.98 Mgal/d could be achieved using 16 wells 

in area A and 12 Mgal/d could be achieved using 24 wells 

in area B. With a maximum pumping rate of 1.0 Mgal/d for 

each well, optimization indicates that 9.54 Mgal/d could be 

achieved using 10 wells in area A and 12 Mgal/d could be 

achieved using 13 wells in area B. It is important to remember 

that the steady-state model used for each of these management scenarios represents the long-term effects of the specified 

groundwater withdrawals with every well pumping continuously; transient simulations would be needed to better represent potential impacts of varying intermittent pumping rates.

References Cited

Ahlfield, D.P., Barlow, P. M., and Mulligan, A.E., 2005, 

GWM—A groundwater management process for the U.S. 

Geological Survey modular groundwater model (MODFLOW-2000): U.S. Geological Survey Open-File Report 

2005–1072, 124 p.

Anderson, M.P., and Woessner, W.W., 1992, Applied groundwater modeling—Simulation of flow and advective transport: San Diego, Calif., Academic Press, 381 p.

Baltusis, M.A., Quigley, M.F., and Mandle, R.J., 1992, 

Municipal ground-water development and withdrawals 

in the central lower peninsula of Michigan, 1870–1987: 

U.S. Geological Survey Open-File Report 91–215, 89 p.
42 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

Cohee, G.V., Macha, Carol, and Holk, Margery, 1951, Thickness and lithology of Upper Devonian and Carboniferous 

rocks in Michigan: U.S. Geological Survey Oil and Gas 

Investigation Chart OC–41.

Eichenlaub, V.L., Harman, J.R., Nurnberger, F.V., and Stolle, 

H.J., 1990, The climatic atlas of Michigan: Notre Dame, 

Ind., University of Notre Dame Press, 165 p.

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

Halford, K.J., and Hanson, R.T., 2002, User guide for the 

drawdown-limited, multi-node well (MNW) package for 

the U.S. Geological Survey’s modular three-dimensional 

finite-difference ground-water flow model, versions MODFLOW-96 and MODFLOW-2000: U.S. Geological Survey 

Open-File Report 02–293, 33 p.

Harbaugh, A.W., Banta, E. R., Hill, M.C., and McDonald, 

M.G., 2000, MODFLOW-2000, the U.S. Geological Survey 

modular ground-water model—User guide to modularization concepts and the ground-water flow process: 

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Hill, M.C., Banta, E.R., Harbaugh, A.W., and Anderman, 

E.R., 2000, MODFLOW-2000, the U.S. Geological Survey 

modular ground-water model—User guide to the observation, sensitivity, and parameter-estimation processes and 

three post-processing programs: U.S. Geological Survey 

Open-File Report 00–184, 209 p.

Holtschlag, D.J., 1994, A generalized estimate of groundwater recharge rates in the lower peninsula of Michigan: 

U.S. Geological Survey Water-Supply Paper 2437, 81 p.

Holtschlag, D.J., Luukkonen, C.L., and Nicholas, J.R., 1996, 

Simulation of ground-water flow in the Saginaw aquifer, 

Clinton, Eaton, and Ingham Counties, Michigan: U.S. Geological Survey Water Supply Paper 2480, 49 p.

Huffman, G.C., 1974a, Summary of ground-water hydrological data in Michigan in 1972: U.S. Geological Survey 

Report (unnumbered), 90 p.

Huffman, G.C., 1974b, Ground-water data for Michigan—1973: U.S. Geological Survey Report (unnumbered), 

86 p.

Huffman, G.C., 1975, Ground-water data for Michigan—1974: U.S. Geological Survey Report (unnumbered), 

89 p.

Huffman, G.C., 1976, Ground-water data for Michigan—1975: U.S. Geological Survey Open-File Report 

77–139, 56 p.

Huffman, G.C., 1977, Ground-water data for Michigan—1976: U.S. Geological Survey Open-File Report 

77–782, 56 p.

Huffman, G.C., 1979a, Ground-water data for Michigan—1977: U.S. Geological Survey Open-File Report 

79–332, 75 p.

Huffman, G.C., 1979b, Ground-water data for Michigan—1978: U.S. Geological Survey Open-File Report 

80–002, 61 p.

Huffman, G.C., 1980, Ground-water data for Michigan—1979: U.S. Geological Survey Open-File Report 

80–1212, 56 p.

Huffman, G.C., 1981, Ground-water data for Michigan—1980: U.S. Geological Survey Open-File Report 

81–811, 57 p.

Huffman, G.C., 1982, Ground-water data for Michigan—1981: U.S. Geological Survey Open-File Report 

82–754, 55 p.

Huffman, G.C., 1983, Ground-water data for Michigan—1982: U.S. Geological Survey Open-File Report 

83–753, 54 p.

Huffman, G.C., 1984, Ground-water data for Michigan—1983: U.S. Geological Survey Open-File Report 

84–623, 47 p.

Huffman, G.C., 1985, Ground-water data for Michigan—1984: U.S. Geological Survey Open-File Report 

85-420, 50 p.

Huffman, G.C., 1986, Ground-water data for Michigan—1985: U.S. Geological Survey Open-File Report 

86–417W, 50 p.

Huffman, G.C., 1988, Ground-water data for Michigan—1986: U.S. Geological Survey Open-File Report 

88–87, 52 p.

Huffman, G.C., and Thompson, T., 1971, Summary of groundwater hydrological data in Michigan in 1970: U.S. Geological Survey Open-File Report 72–173, 94 p.

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Huffman, G.C., and Whited, C.R., 1988, Ground-water data 

for Michigan—1987: U.S. Geological Survey Open-File 

Report 88–704, 56 p.

Huffman, G.C., and Whited, C.R., 1989, Ground-water data 

for Michigan—1988: U.S. Geological Survey Open-File 

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Huffman, G.C., and Whited, C.R., 1991, Ground-water data 

for Michigan—1989: U.S. Geological Survey Open-File 

Report 91–55, 51 p.
References Cited 43

Huffman, G.C., and Whited, C.R., 1993, Ground-water data 

for Michigan—1990: U.S. Geological Survey Open-File 

Report 92–114, 51 p.

Luukkonen, C.L., Grannemann, N.G., and Holtschlag, D.J., 

1997a, Ground-water flow in the Saginaw aquifer in the 

vicinity of the north Lansing well field, Lansing, Michigan—Part 1, Simulations with a regional model: U.S. Geological Survey Open-File Report 97–569, 13 p.

Luukkonen, C.L., Grannemann, N.G., and Holtschlag, D.J., 

1997b, Ground-water flow in the Saginaw aquifer in the 

vicinity of the north Lansing well field, Lansing, Michigan—Part 2, Simulations with a regional model using a 

reduced cell size: U.S. Geological Survey Open-File Report 

97–570, 25 p.

Luukkonen, C.L., and Simard, Andreanne, 2004, Simulation 

of ground-water flow in the Vevay Township area, Ingham 

County, Michigan: U.S. Geological Survey Open-File 

Report 2004–1270, 34 p.

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framework and groundwater flow in the Michigan basin 

in Swain, L.A., and Johnson, A.I., eds., Regional aquifer 

systems of the United States, Aquifers of the Midwestern 

area: 24th Annual Conference of American Water Resources 

Assoc., Milwaukee, Wis., 1988, AWRA Monograph Series 

13, p. 83–109.

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Orlando, Fla., Academic Press, 440 p.

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three-dimensional finite-difference ground-water-flow 

model: U.S. Geological Survey Techniques of WaterResources Investigations, book 6, chap. A1, 576 p.

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aquifer: U.S. Geological Survey Water-Supply Paper 2338, 

41 p.

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identification of sodium and chloride in natural waters—

Preliminary results, in Proceedings of the 12th Annual 

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Krapac, I.G., Landsberger, S., and O’Kelly, D.J., 2006, 

Characterization and identification of Na-Cl sources in 

ground water: Ground Water, v. 44, no. 2, p. 176–187.

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compute and display pathlines using results from the U.S. 

Geological Survey modular three-dimensional finite-difference ground-water flow model: U.S. Geological Survey 

Open-File Report 89–381, 188 p.

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areas contributing recharge to wells in shallow aquifers: 

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Boca Raton, Fla., C.K. Smoley, 258 p.

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recession of ground-water discharge and for estimating 

mean ground-water recharge and discharge from streamflow 

records: U.S. Geological Survey Water-Resources Investigations Report 93–4121, 45 p.

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regional water feasibility study: Burns and McDonnell; 

Snell Environmental Group; and Dickinson, Wright, 

Moon, Van Busen, and Freeman Report 90–338–4–005 

[variously paged]. 

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area, Michigan: U.S. Geological Survey Open-file Report 

(unnumbered).

Vanlier, K.E., Wood, W.W., and Brunett, J.O., 1973, Watersupply development and management alternatives for Clinton, Eaton, and Ingham Counties, Michigan: U.S. Geological Survey Water-Supply Paper 1969, 111 p. 

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framework of Pennsylvanian and Late Mississippian rocks 

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44 p. 

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Michigan area: East Lansing, Michigan State University, 

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East Lansing, Michigan State University, Ph.D. dissertation, 

104 p.

Prepared by the USGS Columbus Publishing Service Center.

Appemdix 1. Chemistry of Lansing-Area Well Water 45

Appendix 1. Chemistry of Lansing-Area Well Water.

During this study, water-chemistry data from selected 

Lansing-area wells were analyzed to determine any longterm changes in water quality, because water quality can 

affect water-treatment costs. Analysis of water-chemistry data 

and how these data have changed over time is important for 

guiding water-withdrawal decisions and ensuring a sufficient 

quantity of good-quality water. Water-chemistry data may differ between areas because of differences in well-construction 

details—such as well depth, location, and the type of geologic 

materials intercepted by the well—and differences in the types 

of materials both above and below the open interval of the 

well. Differences in water-chemistry data also may be due to 

the current and historical pumping rates of local wells, because 

pumping affects the rate of groundwater movement and the 

directions of flow paths. Pumping may induce the movement 

of poorer quality water near pumping centers or of contaminants from other, more distant areas or underlying aquifers. 

As groundwater moves slowly through geologic materials, the composition of the water changes, usually with 

the addition of dissolved constituents (Freeze and Cherry, 

1979). Thus, water in deeper formations that has had a longer 

residence time in the aquifer may have more dissolved constituents, or dissolved solids, than water that has just entered 

the aquifer system in recharge areas. Removal of water from 

storage can change the quality of the remaining water because 

good-quality water generally is withdrawn first. 

Groundwater flows through geologic materials where 

different rock/water interactions or mixing may affect waterquality characteristics. In addition, water with differing 

constituents may mix as the water moves through the aquifer, 

making comparison of water quality among wells or changes 

through time difficult. Comparison of water-chemistry data 

among wells can include inspection and mathematical calculations, as well as preparation of graphs and maps to determine 

the relation among wells and differences spatially and over 

time. However, comparison of historical data may be problematic because of possible differences in water-quality analysis 

methods and analytes, errors in sample analysis or transcription, or unknown well-pumping history at the time samples 

were collected. The groundwater samples in the Lansing area 

have historically been analyzed by means of the same laboratory methods (Bill Maier, Lansing Board of Water and Light, 

oral commun., 2007). Data were compiled from more than 

4,000 samples collected from 1935 to 2005.

The composition of most natural waters can be characterized in terms of three cationic species (calcium, magnesium, 

and sodium) and three anionic species (bicarbonate, sulfate, 

and chloride). Calculation of the ratio of one ion to another or 

to the total sample concentration is often useful for the determination of similarities or differences among water samples 

(Hem, 1985). 

Trilinear plotting systems are a graphical means of portraying water-chemistry data and were used as early as 1913 

(Hem, 1985). The type of trilinear diagram used during this 

study was independently developed by Hill (1940) and Piper 

(1944). Use of a trilinear diagram aids in the determination of 

whether a water may be classified according to the predominant cation or anion, expressed in milliequivalents per liter 

(meq/L), and can demonstrate whether relations exist among 

individual samples collected at one point in time or over some 

time interval (Hem, 1985). A milliequivalent per liter is the 

unit of concentration equal to the concentration in milligrams 

per liter divided by the equivalent weight (atomic weight 

divided by valence). Each cation value, expressed as a percentage of the total concentration (meq/L) of all cations under consideration, is plotted in the lower left triangle of the diagram. 

Similarly, each anion value, expressed as a percentage of the 

total concentration (meq/L) of all anions under consideration, 

is plotted in the lower right triangle of the diagram. These 

points can then be extended into the central, diamond-shaped 

field by projecting them along lines parallel to the upper edges 

of the central field. The intersection of these projections from 

each lower triangle represents the composition of the water 

with respect to the combination of ions shown. 

Water samples may be grouped by hydrologic or geologic 

categories for comparison and analysis (Hem, 1985). Trilinear 

diagrams of water samples having total dissolved solids (TDS) 

concentrations less than 500 mg/L and TDS concentrations 

greater than 1,000 mg/L are shown in figure 1–1. Samples 

with lower TDS generally plot along the leftmost corner of the 

middle diamond, whereas samples with higher TDS generally 

plot over a larger area of the middle diamond. Water samples 

with lower TDS are classified as the calcium-bicarbonate type 

(Kehew, 2001) because the dominant major ions in the sample 

are calcium and bicarbonate (fig. 1–1A). In water samples with 

higher TDS, calcium also is generally the dominant cation; 

however, magnesium and sodium are high in some samples 

(fig. 1–1B). Water from these samples generally does not have 

a dominant anion because bicarbonate, chloride, and sulfate all 

are present in appreciable amounts in some samples. 
46 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

Figure 1–1. Trilinear diagrams of Lansing area, Michigan, groundwater 

samples. A, Total dissolved solids (TDS) concentrations less than 500, and 

B, greater than 1,000 milligrams per liter.

Percent

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Appemdix 1. Chemistry of Lansing-Area Well Water 47

Within the Tri-County region, the hardness and alkalinity of groundwater are important considerations in optimization scenarios because these water-quality properties affect 

water treatment. Waters with high alkalinity and low hardness 

require less treatment and thus are less costly for the municipal 

water provider to treat. Hardness is generally defined in terms 

of calcium and magnesium and is expressed in terms of an 

equivalent concentration of calcium carbonate. The alkalinity 

of a solution may be defined as the capacity for the solutes it 

contains to react with and neutralize acid. In almost all natural 

waters, alkalinity is produced by dissolved carbon dioxide, 

bicarbonate, and carbonate (Hem, 1985). From samples collected in 2003–5, hardness, as CaCO3

, ranges from 280 to 

1,200 mg/L and is highest in the east-central Lansing area and 

lowest in south Lansing (fig. 1–2). Alkalinity ranges from 260 

to 480 mg/L and also is highest in the east-central Lansing 

area and lowest in south Lansing.

Box plots are another graphical means to allow comparison of data from different time periods or different areas. 

Figure 1–3 shows major ion concentrations of samples for 

time intervals from 1930–38 up to 1996–2005. The samples 

collected in the 1930s and 1940s are assumed to represent 

background conditions because these wells were often pumped 

for an extended time before sample collection (and thus concentrations are believed to be representative of water quality 

from the aquifer), and samples were collected at a time of 

low total withdrawals in the area. Concentrations of calcium, 

magnesium, and sulfate were slightly lower during the middle 

time periods and higher in the early and later periods; the early 

and later concentrations were close to the median background 

concentrations. Bicarbonate concentration was lower during 

the later period, but sodium and chloride concentrations generally were higher during that period. Figure 1–4 shows majorion concentrations for samples from north and south Lansing 

areas. The median values are similar between areas for 

calcium, magnesium, and sodium; median values are slightly 

lower for sulfate and slightly higher for chloride in samples 

from south Lansing. Median values are lower for bicarbonate in samples from south Lansing compared to samples from 

north Lansing. For all major ions, the ranges and maximum 

concentrations are less for water samples from the south area.

The data were further subdivided to consider only the 

northern wells because of the change in pumping distribution 

since the 1970s. These northern wells were generally pumped 

more before 1970 than they were after 1970, when pumping 

was spread out over a larger area (fig. 4). Trilinear diagrams 

of water samples collected before 1970 and after 1970 from 

78 northern wells and from 11 wells collected before 1970 

are shown in figure 1–5. Four wells (PW A, PW B, PW C, 

and PW D) are shown in each graph as an indication of how 

sample concentrations have changed over time. Samples from 

PW A and PW B indicate higher calcium and a broader range 

of bicarbonate concentrations after 1970. Samples from PW C 

and PW D also indicate changes in bicarbonate and chloride 

concentrations between the two time periods. Water collected 

from wells before 1970 is generally characterized by higher 

concentrations of sodium, bicarbonate, sulfate, and chloride 

than water collected from these wells after 1970. Samples 

collected before 1970 are generally characterized by either 

high chloride and low sulfate concentrations or low chloride 

and high sulfate concentrations; after 1970, samples indicate 

generally higher sulfate and lower chloride concentrations 

(fig. 1–6). However, the shift in pumping does not completely 

explain these differences. Not all water samples in the preand post-1970 groups show the same trends in concentrations (fig. 1–7). The median and range in concentrations were 

generally higher for calcium, magnesium, chloride, and sulfate 

in the post-1970 group. The median bicarbonate concentration 

was about the same; however, the range was larger after 1970. 

The range of concentrations for both chloride and sodium are 

less for the post-1970 samples. Other factors were considered in an attempt to explain the observed trends in the data: 

well-construction details such as well depth, well location, 

total rock thickness, drift thickness, sandstone thickness, shale 

thickness, and degree of connection between the bedrock 

and glacial units, known pumping history, and time interval. 

Considered individually, these factors do not explain the data 

trends. Further analysis including multiple factors is needed 

to better explain the observed data trends and water-quality 

changes. 
48 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

Figure 1–2. Distribution of hardness, in milligrams per liter CaCO3, from samples from 2003–5, 

Lansing area, Michigan. NORTHING, IN FEET

Base map from the Michigan Resource EASTING, IN FEET

Information System, Michigan Department 

of Environmental Quality
Appemdix 1. Chemistry of Lansing-Area Well Water 49

Figure 1–3. Major ion concentrations, in milligrams per liter, for 1930–2006, Lansing area, Michigan. (Note the difference in scales on 

the y-axis.)

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Magnesium Bicarbonate

Calcium Chloride

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178 900 410 501 561 372 293 86 565

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178 900 444 590 573 380 299 0 570
50 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

Figure 1–4. Major ion concentrations for northern and southern wells for 1930–2005, Lansing area, Michigan.

30 Number of 

 values

EXPLANATION 

 Schematic boxplot

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75th percentile

Median

25th percentile

Lower adjacent

Lower outside

Lower detached

Upper detached

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3449 466 3360 350 3278 468 3451 461 3474 473 3373 471

1000

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0

 N S

Calcium

 N S

Magnesium

 N S

Sodium

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Bicarbonate

 N S

Chloride

 N S

Sulfate
Appemdix 1. Chemistry of Lansing-Area Well Water 51

Figure 1–5. Trilinear diagrams of water samples collected from northern Lansing area, Michigan, wells 

A, before 1970, and B, after 1970.

Percent

Calcium

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Percent

Percent

PW

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PW D

B

A

Explanation

Percent

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Percent

Percent
52 Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan

Figure 1–6. Relation of chloride to sulfate concentrations collected from northern Lansing area, Michigan, wells 

A, before 1970, and B, after 1970.

0

100

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CHLORIDE CONCENTRATIONS, IN MILLIGRAMS PER LITER

0

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CHLORIDE CONCENTRATIONS, IN MILLIGRAMS PER LITER

0 100 200 300 400 500 600

0 100 200 300 400 500 600

SULFATE CONCENTRATIONS, IN MILLIGRAMS

PER LITER

SULFATE CONCENTRATIONS, IN MILLIGRAMS

PER LITER

B

A
Appemdix 1. Chemistry of Lansing-Area Well Water 53

Figure 1–7. Comparison of major-ion concentrations from water samples collected from northern Lansing area, Michigan, wells 

before and after 1970.

References Cited

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

Hem, J.D., 1985, The study and interpretation of the chemical 

characteristics of natural water (3d ed.): U.S. Geological 

Survey Water-Supply Paper 2254, 264 p.

Hill, R.A. 1940, Geochemical patterns in Coachella Valley, 

California: American Geophysical Union Transactions, 

v. 21, p. 46–49.

Kehew, A.E., 2001, Applied chemical hydrogeology: Upper 

Saddle River, N.J., Prentice Hall, 368 p.

Piper, A.M. 1944, A graphic procedure in the geochemical 

interpretation of water analyses: American Geophysical 

Union Transactions, v. 25, p. 914–923.

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2565 562 2565 562 2565 562 2565 562 2565 562 2565 562

30 Number of 

 values

EXPLANATION 

 Schematic boxplot

x

x

o

o

Upper adjacent

75th percentile

Median

25th percentile

Lower adjacent

Lower outside

Lower detached

Upper detached

Upper outside

1000

800

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0

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Post

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Pre

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Post

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Pre

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Post

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Pre

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Post

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Pre

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Post

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1970

Post

1970

Calcium Magnesium Sodium Bicarbonate Chloride Sulfate


—Model Refinement and Simulation of Groundwater Flow in Clinton, Eaton, and Ingham Counties, Michigan—SIR 2009–5244

Printed on recycled paper