43°30'53"

Washington

County

0 5 MILES

0 5 KILOMETERS

WISCONSIN

West Bend

Silver Lake

Little Cedar Lake Big Cedar Lake

STUDY AREA

43°13'27"

88°19'50" 88°06'39"

U.S. Department of the Interior

U.S. Geological Survey

Simulation of the Shallow Aquifer in the

Vicinity of Silver Lake, Washington County,

Wisconsin, Using Analytic Elements

Water-Resources Investigations Report 02–4204

Prepared in cooperation with the

Silver Lake Protection and Rehabilitation District
Simulation of the Shallow Aquifer in the 

Vicinity of Silver Lake, Washington County, 

Wisconsin, Using Analytic Elements

By C.P. Dunning, J.C. Thomas, and Y-F. Lin

U.S. GEOLOGICAL SURVEY

Water-Resources Investigations Report 02-4204

Prepared in cooperation with the

Silver Lake Protection and Rehabilitation District

Middleton, Wisconsin

2003
U.S. DEPARTMENT OF THE INTERIOR

GALE A. NORTON, Secretary

U.S. GEOLOGICAL SURVEY

Charles G. Groat, Director

For additional information write to: Copies of this report can be purchased from:

District Chief U.S. Geological Survey 

U.S. Geological Survey Branch of Information Services

8505 Research Way Box 25286

Middleton, WI 53562-3586 Denver, CO 80225-0286

The use of firm, trade, and brand names in this report is for identification purposes only and does

not constitute endorsement by the U.S. Government.
CONTENTS III

CONTENTS

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

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

Purpose and scope....................................................................................................................................................... 3

Hydrogeologic setting ................................................................................................................................................. 3

Acknowledgements..................................................................................................................................................... 7

Methods................................................................................................................................................................................. 7

Development of the analytic-element model ........................................................................................................................ 9

Conceptualization........................................................................................................................................................ 9

Construction ................................................................................................................................................................ 11

Calibration................................................................................................................................................................... 12

Simulation of shallow ground-water flow ............................................................................................................................ 13

Hydrologic budget for Silver Lake ............................................................................................................................. 13

Ground-water recharge areas for Silver Lake ............................................................................................................. 16

Simulation of pumping from the shallow aquifer ....................................................................................................... 16

Solute flux toward Silver Lake ................................................................................................................................... 21

Model limitations ........................................................................................................................................................ 21

Summary ............................................................................................................................................................................... 22

References............................................................................................................................................................................. 22

Appendix:

USGS water chemistry analyses and physical measurements for Silver Lake, Washington County, Wisconsin ........... 25

FIGURES

1–2. Maps showing:

1. Location of Washington County, Wisconsin, and Silver Lake study area....................................................... 2

2. Lakes, creeks, and glacial stratigraphy of the Silver Lake study area, Washington County, Wisconsin......... 4

3. Graph showing measured Silver Lake stage, flow to Silver Lake from southwest springs, and flow from

Silver Lake to Silver Creek, Washington County, Wisconsin, February–December, 1977 ................................ 6

4. Map showing analytic elements and calibration targets in the Silver Lake model area, Washington County,

Wisconsin ............................................................................................................................................................ 8

5. Figure showing conceptual model, in cross-sectional view, of the interaction of lakes, precipitation, 

evaporation, and shallow ground-water-flow in the vicinity of Silver Lake, Washington County, Wisconsin .. 10

6. Map showing comparison of simulated to measured head targets in the calibrated Silver Lake, Washington 

County, Wisconsin, analytic-element model ....................................................................................................... 13

7. Scatter plot comparing simulated heads to measured heads for the calibrated Silver Lake, Washington

County, Wisconsin, analytic-element model ....................................................................................................... 14

8–11. Maps showing:

8. Simulated water table from the calibrated Silver Lake, Washington County, Wisconsin, analytic-element

model ............................................................................................................................................................ 15

9. Hydrologic budget for Silver Lake, Washington County, Wisconsin, based on the calibrated analyticelement model............................................................................................................................................... 17

10. Ground-water recharge areas and times-of-travel to Silver Lake, Washington County, Wisconsin ............... 18

11a. Locations of three simulated wells around Silver Lake, Washington County, Wisconsin .............................. 19

11b. Simulated fully-penetrating well pumping 75 gallons per minute from west side of Silver Lake, 

Washington County, Wisconsin.................................................................................................................... 19

11c. Simulated fully-penetrating well pumping 75 gallons per minute from east side of Silver Lake, 

Washington County, Wisconsin.................................................................................................................... 20

11d. Simulated fully-penetrating well pumping 75 gallons per minute from southeast side of Silver Lake, 

Washington County, Wisconsin.................................................................................................................... 20
IV CONTENTS

TABLES

1. Summary of analytical results for water-quality samples from Silver Lake and other lakes in southeastern 

Wisconsin........................................................................................................................................................ 5

2. Measured and simulated streamflow, Washington County, Wisconsin .............................................................. 9

3. Resistance and width of lakes and streams in the Silver Lake, Washington County, Wisconsin, 

analytic-element model................................................................................................................................... 11

4. Relation of lake stage and discharge used for lake specified line-sink representing Silver Lake, 

Washington County, Wisconsin, in the analytic-element model..................................................................... 12

5. Average solute concentrations in ground water and resulting mass flux toward Silver Lake, 

Washington County, Wisconsin ...................................................................................................................... 21
CONVERSION FACTORS, VERTICAL DATUM, AND ABBREVIATIONS V

CONVERSION FACTORS, VERTICAL DATUM, AND ABBREVIATIONS 

Multiply By To Obtain

Length

inch (in.) 25.4 millimeter (mm)

foot (ft) .3048 meter (m)

mile (mi) 1.609 kilometer (km)

acre (ac) 43,560 square feet (ft2

)

Discharge

cubic feet per day (ft3/d) 8.32 liters per day (L/d)

cubic feet per second (ft3

/s) 2,446,575.5 liters per day (L/d)

Hydraulic Conductivity*

feet per day (ft/d) .3408 meters per day (m/d)

Temperature in degrees Celsius (°C) can be converted to degrees Fahrenheit (°F) by use of the following equation:

°F = 1.8 (°C) + 32.

Sea level: In this report, “sea level” refers to the National Geodetic Vertical Datum of 1929 (NGVD of 1929)a geodetic datum derived 

from a general adjustment of the first-order level nets of both the United States and Canada, formerly called Sea Level Datum of 1929.

* Hydraulic conductivity: The standard unit for hydraulic conductivity is cubic foot per day per square foot of aquifer cross-sectional area 

(ft3/d)/ ft2. In this report, the mathematically reduced form, feet per day (ft/d), is used for convenience.

Transmissivity: Transmissivity is the product of horizontal hydraulic conductivity and saturated thickness.

Water year: Water year is the 12 month period from October 1 through September 30. The water year is designated by the calendar year in 

which it ends.

Abbreviated water-quality units used in this report: Chemical concentration is given in milligrams per liter (mg/L). Milligrams per liter 

is a unit expressing the concentration of chemical constituents in solution as weight (milligrams) of solute per unit volume (liter) of water. 

One thousand micrograms per liter is equivalent to one milligram per liter. 

Specific conductance is given in microsiemens per centimeter at 25 degrees Celsius (μS/cm at 25°C).

Dissolved oxygen (DO) is given in milligrams per liter (mg/L).

Other abbreviations used in this report

Kg/d kilograms per day

in/yr inches per year

Abstract 1

Abstract

Shallow ground-water flow in the vicinity of 

Silver Lake, Washington County, Wisconsin, was 

investigated to develop an understanding of the 

hydrology of the shallow aquifer, define a water 

balance for the lake, delineate ground-water 

recharge areas for the lake, and to estimate solute 

flux toward the lake. A single-layer, steady-state, 

analytic-element model was used to simulate shallow ground-water flow. Regional model parameters include a recharge rate of 4 inches per year, 

hydraulic conductivity of 50 feet per day and a 

model base of 800 feet above sea level. A model 

inhomogeneity was added to represent deviations 

from these regional values for an area roughly 

coincident with the Kettle Moraine Area that trends 

through the study area. Model calibration was 

accomplished by varying the regional parameter 

values and those of the inhomogeneity through 

trial-and-error to determine a best-fit match 

between simulated and measured values for head 

and streamflow targets. There was no change to the 

regional parameter values as a result of calibration, 

however, the calibrated values for the inhomogeneity are: recharge rate of 12 inches per year, hydraulic conductivity of 20 feet per day, and a model 

base of 900 feet. These changes represent a four- to 

five-fold reduction in transmissivity within the 

inhomogeneity as compared to the regional model.

A Silver Lake water budget was defined 

using both published hydrologic data and simulations using the calibrated model. Model simulations show that 1.08 cubic feet per second of 

ground water enters Silver Lake on the upgradient 

(primarily western) side and 0.08 cubic feet per 

second recharges to ground water on the downgradient (primarily eastern) side. Net precipitation 

(precipitation minus evaporation) on the lake is 

0.04 cubic feet per day. Collectively, these waterbudget terms provide a residual value of 1.04 cubic 

feet per second flow to Silver Creek at the north 

end of Silver Lake, which is a very good match to 

the range of measured flow (0.7 to 5.2 cubic feet 

per second). Ground-water recharge areas for 

Silver Lake are largely on the western side of the 

lake. The recharge area for the northern two-thirds 

of Silver Lake is west toward Big Cedar Lake. 

Assuming a porosity of 20 percent, model results 

indicate that the 50-year time-of-travel for recharge 

to Silver Lake does not extend to Big Cedar Lake. 

The recharge area for the southern one-third of Silver Lake is west toward Little Cedar Lake. Model 

results indicate that time of travel for recharge to 

Silver Lake from Little Cedar Lake is about 15 

to 20 years. For travel times greater than 15 or 

20 years, the ground-water recharge area for Little 

Cedar Lake and inflow from Big Cedar Lake also 

should be considered recharge affecting Silver 

Lake. Solute flux toward Silver Lake was calculated based on simulated ground-water flux and 

measured concentrations in the upgradient piezometers and observation wells.

INTRODUCTION

Silver Lake is a ground-water seepage lake located 

in central Washington County, southeastern Wisconsin 

(fig. 1). Because of its strong hydraulic connection to 

shallow ground-water flow, Silver Lake could be 

affected adversely by stresses to the shallow aquifer. 

The shallow aquifer is defined here to comprise the 

unconsolidated glacial sediments, generally 100 to 

300 feet thick, overlying the bedrock. In order to assess 

Simulation of the Shallow Aquifer in the Vicinity of Silver 

Lake, Washington County, Wisconsin, Using Analytic 

Elements

By C.P. Dunning, J.C. Thomas, and Y-F. Lin
2 Simulation of the Shallow Aquifer in the Vicinity of Silver Lake, Washington County, Wisconsin, Using Analytic Elements

Figure 1. Location of Washington County, Wisconsin and Silver Lake study area.

43°30'53"

Washington

County

0 5 MILES

0 5 KILOMETERS

WISCONSIN

West Bend

Silver Lake

Little Cedar Lake Big Cedar Lake

WASHINGTON COUNTY

STUDY AREA

43°13'27"

88°19'50" 88°06'39"
INTRODUCTION 3

the potential effects on Silver Lake of stresses to the 

shallow aquifer, a study was undertaken in 2000 by the 

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

Silver Lake Protection and Rehabilitation District 

(SLPRD). The SLPRD was awarded a Lake Management Planning Grant for the study administered by the 

Wisconsin Department of Natural Resources. The study 

began in 2000 with the following objectives: (1) estimate hydraulic parameter values for the shallow aquifer, (2) determine a hydrologic budget for Silver Lake, 

(3) simulate the ground-water recharge areas for Silver 

Lake, and (4) estimate flux of selected solutes toward 

Silver Lake.

Purpose and Scope

This report discusses the hydrogeology of Silver 

Lake and the shallow aquifer, and presents groundwater simulation results that support the hydrologic 

interpretations. This report also includes information on 

available hydrologic data, new data collected during the 

study, the conceptualization of the hydrogeologic setting of Silver Lake and the shallow aquifer, details on 

model construction and calibration, a hydrologic budget, and delineation of ground-water recharge areas for 

Silver Lake. Ground-water solute flux toward the lake 

also is discussed. An analytical element model was used 

to simulate shallow ground-water flow in the study area.

Hydrogeologic Setting

Silver Lake is located in central Washington 

County, Wisconsin, southwest of the city of West Bend 

(fig. 1). In this part of the county, Silurian dolomite bedrock is overlain by 100 to 300 ft of glacial sediments 

(Mickelson and Syverson, 1997). The altitude of the 

Silurian dolomite bedrock surface varies by hundreds of 

feet over the study area as a result of erosion by prePleistocene rivers and late-Pleistocene glaciers.

As the glaciers retreated between 15,000 and 

13,000 years ago, sand and gravel derived from existing 

deposits or from the underlying dolomite bedrock were 

deposited on stagnant ice by meltwater streams flowing 

south. These deposits compose the shallow aquifer in 

central Washington County. Within the study area these 

glacial deposits are named the Holy Hill Formation 

(Mickleson and Syverson, 1997), of which two distinct 

members are recognized: the Horicon Member and the 

New Berlin Member. An additional member consisting 

of intermixed Horicon and New Berlin Members is 

named Undifferentiated Deposits of the Holy Hill Formation (fig. 2). All three members are described as 

being “poorly to moderately well sorted, poorly to well 

stratified, gravel and sand” (Mickleson and Syverson, 

1997). It is the Undifferentiated Member of the Holy 

Hill Formation that forms the Kettle Moraine Area 

(fig. 2) in southeastern Wisconsin. The term moraine 

identifies a distinct ridge of unsorted, unstratified glacial sediments (Bates and Jackson, 1980) deposited, in 

this case, between the retreating Green Bay and Lake 

Michigan lobes of the Wisconsinan glaciation. The term 

kettle identifies depressions formed in the moraine by 

the melting of ice blocks buried under the glacial sand 

and gravel (Bates and Jackson, 1980). Water has filled 

the lower-lying kettles creating the present-day lakes. 

Silver Lake and most of the other lakes of Washington 

County are aligned along the contacts between the 

Undifferentiated Member of the Holy Hill Formation 

and either the Horicon Member on the west or the New 

Berlin Member on the east (fig. 2). 

Silver Lake is a seepage lake with springs, about 

117.6 ac in area, with a maximum depth of 45 ft (Poff 

and Threinen, 1962). Water flows north from Silver 

Lake into Silver Creek to Paradise Valley Lake (also 

known as Hackbarth Lake) and Lucas Lake (fig. 2). 

From Lucas Lake, Silver Creek flows into the Milwaukee River (not shown). West of Silver Lake lie Little 

Cedar Lake (246 ac) and Big Cedar Lake (932 ac). 

Water flows east from Big Cedar Lake through a stream 

and associated wetland to Little Cedar Lake, and then 

south from Little Cedar Lake into Cedar Creek. Neither 

of these lakes has a direct surface-water connection 

with Silver Lake or its associated downstream lakes. 

No streams flow into Silver Lake; the lake is fed by 

ground-water seepage and small springs discharging 

near the shoreline (Poff and Threinen, 1962). The primary spring complex is found on the southwest shore of 

the lake, and flow was measured during 1976 and 1977 

to be a nearly constant 0.1 ft3

/s (CDM/Limnetics, 1977) 

(fig. 3). Water flows from the north end of Silver Lake 

over a small dam (crest elevation 999.27 ft above sea 

level) into Silver Creek (John Behrens, Silver Lake 

Sewer District, written commun., 2001). All references 

to datum altitude or lake stage are based on the National 

Geodetic Vertical Datum of 1929. Flow from Silver 

Lake measured during February to December 1977 

ranges from 0.7 to 5.2 ft3

/s (CDM/Limnetics, 1977) 

(fig. 3). Monthly staff-gage measurements during 1977 
4 Simulation of the Shallow Aquifer in the Vicinity of Silver Lake, Washington County, Wisconsin, Using Analytic Elements

Figure 2. Lakes, creeks, and glacial stratigraphy of the Silver Lake study area, Washington County, Wisconsin

(stratigraphy after Mickelson and Syverson, 1997).

Horicon Member

of the Holy Hill

Formation

New Berlin Member

of the Holy Hill Formation

Undifferentiated Deposits

of the Holy Hill Formation

in the Kettle Moraine Area

Big Cedar Lake

Little Cedar Lake

Silver Lake

Paradise

Valley Lake

Lucas Lake

Silver Creek Cedar Creek

Kettle Moraine Area

0 1 MILE

0 1 KILOMETER

Altitude 1,031 feet

Altitude

1,013 feet

Altitude

 999 feet

43°25'

43°22'30"

88°15' 88°12'30"
INTRODUCTION 5

show lake stage varies over 0.23 ft (CDM/Limnetics, 

1977) (fig. 3). Daily stage measurements during 2000 

show a low lake stage of 999.30 ft and a high lake stage 

of 999.50 ft (John Behrens, Silver Lake Sewer District, 

written commun., 2001). The shoreline of Silver Lake is 

almost entirely developed with vacation and year-round 

homes. Ground water from the shallow aquifer is the 

primary source of domestic and municipal water supply 

in the area.

Precipitation that infiltrates through the ground to 

the water table is called recharge. Factors that affect the 

average annual recharge to the shallow aquifer in the 

Silver Lake study area include depth of precipitation, 

land cover, topography, and aquifer lithology. Recharge 

is estimated to vary greatly across the Washington 

County area—from a high of 12 in/yr to zero recharge 

in discharge areas such as wetlands (Douglas Cherkaur, 

University of Wisconsin-Milwaukee, written commun., 

2001). 

Lake chemistry in southeastern Wisconsin is 

described in Surface Water Resources of Washington 

County by Poff and Threinen (1962), and Understanding Lake Data by Shaw and others (1986). A study was 

conducted specifically for Silver Lake by CDM/Limnetics and included water chemistry analyses for samples collected from March 1976 to January 1977 

(CDM/Limnetics, 1977). In addition, the USGS sampled and analyzed water from Silver Lake during 1996 

and 1997. Selected data from these four sources are 

summarized in table 1. Data from the USGS sampling 

and analysis are included in the appendix.

Phosphorus, often the limiting nutrient for algae 

and weed growth in lakes, can have various anthropogenic sources including septic systems and fertilizer 

run-off (Shaw and others, 1986). Wisconsin lakes generally have phosphorus concentrations between 0.010 

and 0.040 mg/L (Lillie and Mason, 1983). Average 

phosphorus concentrations equal to or less than 

0.025 mg/L suggest good water quality, whereas phosphorus concentrations in excess of 0.055 mg/L suggest 

poor water quality (Lillie and Mason, 1983). Silver 

Lake phosphorus data (table 1) indicate a range from 

0.005 to 0.102 mg/L (CDM/Limnetics, 1977; USGS, 

1997 and 1998); however, the greatest concentrations 

usually are associated with samples taken immediately 

above the lake-bottom sediments and may not represent 

general lake water quality. 

Chloride is not found naturally in Wisconsin 

ground water except where carbonate rocks are present. 

Chloride concentrations measured in Silver Lake 

(table 1) range from 9.0 to 19.0 mg/L (CDM/Limnetics, 

1977; U.S. Geological Survey, 1997 and 1998), and are 

consistent with values typically found in southeastern 

Wisconsin (Shaw and others, 1986). 

Alkalinity values in excess of 180 mg/L are considered to represent very hard water and result in the precipitation of marl (CaCO3) (Shaw and others, 1986). 

Silver Lake is considered to be a hard lake (table 1), as 

are Big Cedar Lake, Little Cedar Lake, Lucas Lake and 

Table 1: Summary of analytical results for water-quality samples from Silver Lake and other lakes in 

southeastern Wisconsin

[mg/L, milligrams per liter; μS/cm, microsiemens per centimeter; CaCO3, calcium carbonate; –, not reported values; >, greater than]

Reference Phosphorus

(mg/L)

Chloride

(mg/L)

Total alkalinity as CaCO3

(mg/L)

Specific conductance

(μS/cm)

CDM/Limnetics, 1977 a, b

a

Silver Lake, Washington County.

b

Sampled on an approximately monthly basis from March 29, 1976, through January 19, 1977. Sampled at surface and 

every 10 feet to 40 feet of depth.

0.010–0.057 c

c

Greater values are from samples just above bottom sediments.

9.0–13.9 193–293 250–520

Poff and Threinen, 1962 – 6.1–8.2 d

d

Pike Lake, Washington County (8 miles southwest of Silver Lake).

 194, 202 a,e

e

Two data points.

 355, 365 a,e

Shaw and others, 1986 f

f

Lakes of southeastern Wisconsin, original data are from Lillie and Mason, “Limnological Characteristics of Wisconsin 

Lakes”, 1983.

 0.010–0.040 >10 >180 –

U.S. Geological Survey, 1996; 

U.S. Geological Survey, 1997 a 0.005–0.102 c 19 240 442–598
6 Simulation of the Shallow Ground-Water System in the Vicinity of Silver Lake, Washington County, Wisconsin Using Analytic 

Elements

Figure 3. Measured Silver Lake stage, flow to Silver Lake from southwest springs, and flow from Silver Lake to Silver Creek, Washington County, Wisconsin, February–December 1977.

6543210

February March April May June July August September October November December

1977

999.54999.44999.34999.24

Measured stage of Silver Lake

Measured flow from Silver Lake to Silver Creek

Measured flow to Silver Lake from southwest springs

No

data

No

data

No

data

No

data

No

data

MEASURED FLOW (IN CUBIC FEET PER SECOND)

LAKE STAGE (IN FEET ABOVE MEAN SEA LEVEL)
METHODS 7

Paradise Valley Lake (Poff and Threinen, 1962). Marl 

formation often is considered beneficial because phosphorus precipitates along with CaCO3, thereby reducing the amount of this limiting nutrient available for 

algae blooms (Shaw and others, 1986).

Specific conductance is a measure of the ability of 

water to transmit an electrical current and is associated 

with the concentration of organic and inorganic solutes 

(Water Quality Association, 1999). Because many of 

these organic and inorganic ions are necessary for the 

growth of plants and algae, specific conductance can be 

used as an indirect measure of lake fertility (Poff and 

Threinen,1962). Reported specific conductance values 

in Silver Lake range from 250 to 598 μS/cm (table 1).

Acknowledgments

The authors would like to acknowledge the contributions of the following people and organizations. The 

Board of Commissioners of the Silver Lake Protection 

and Rehabilitation District supported the objectives of 

the study, and two commissioners, Gary Coates and 

John Behrens, assisted with site visits and collection of 

various data used in the study. Jeffrey Thornton of the 

Southeast Wisconsin Regional Planning Commission 

provided assistance in establishing the scope of the 

investigation and setting the work into the larger framework of southeastern Wisconsin. James Rauman and 

Bernard Ellefson of the USGS installed lake stage and 

precipitation instruments on the shoreline of Silver 

Lake. Madeline Gotkowitz of the Wisconsin Geologic 

and Natural History Survey and Michael Merrit of the 

USGS provided technical review of the report. Gail 

Moede of the USGS provided editorial review of the 

report. Jim Krohelski and Randy Hunt of the USGS provided invaluable assistance with many aspects of the 

study including review of conceptual models and the 

analytic-element model.

METHODS

An analytic-element (AE) ground-water-flow 

model was developed for the Silver Lake study area to 

simulate shallow ground-water flow and its interaction 

with surface-water features. The AE model, developed 

with the use of the computer program GFLOW (Haitjema, 1995), is a single-layer, steady-state model, in 

which the aquifer is assumed to be infinite. The AE 

model makes use of the Dupuit-Fochheimer approximation which assumes ground-water flow in the single 

layer is horizontal. This approximation is valid when 

the aquifer is thin relative to its extent, as is the case in 

the Silver Lake study area.

Important hydrologic features are represented in 

the AE model domain as analytic elements or strings of 

analytic elements (line-sinks). Each element provides a 

solution to the ground-water-flow equation, and the 

additive effect of many individual solutions (superposition) is a solution for ground-water flow. Because a 

solution for ground-water flow can be evaluated at any 

point in the model domain, AE models do not make use 

of model cells or a grid. Regional values for aquifer 

parameters and rate of recharge are applied across the 

entire AE model domain. The model domain comprises 

both a far-field and a near-field (fig. 4). The far-field is 

beyond the area of interest, but is included in the model 

to properly define hydrologic boundary conditions for 

the near-field. Far-field elements usually are coarsely 

defined and consist only of water-level information. 

The location and elevation of all surface-water features 

were estimated using USGS topographic data.

The near-field is the area of primary interest and 

contains any important local hydrologic inhomogeneities, that is, areas where recharge and/or aquifer parameter values differ appreciably from regional values. A 

hydrologic inhomogeneity can be represented in the AE 

model as an area defined by model elements within 

which the non-regional parameter values are present. 

Near-field analytic elements are more precisely defined 

than those in the far-field. Specifically, near-field elements have more line-sink vertices (and, therefore, 

solutions) and contain information on the width and 

resistance of the represented feature (Strack, 1989; Haitjema, 1995; Hunt and Krohelski, 1996; Hunt and others, 1998). Silver Lake is represented in the AE model 

as a line-sink lake using the lake package in GFLOW, 

and as such, width and resistance parameters account 

for lake-bottom resistance (Henk Haitjema, Haitjema 

consultants, written commun. to Wisconsin Department 

of Natural Resources, March, 2002). The head along the 

element is constant (the lake stage) and will be determined iteratively during the solution process. Net precipitation on the lake is defined by adding an 

inhomogeneity representing evaporation. The GFLOW 

lake package has been shown to provide results similar 

to the MODFLOW lake package (LAK1) for lakes in 

northern Wisconsin (Hunt and others, written commun., 

2001). 
8 Simulation of the Shallow Aquifer in the Vicinity of Silver Lake, Washington County, Wisconsin, Using Analytic Elements

Figure 4. Analytic elements and calibration targets in the Silver Lake model area, Washington County, Wisconsin, 

(a) far-field, (b) near-field.

43°25'

43°22'30"

88°15' 88°12'30"

0 5 MILES

0 5 KILOMETERS

0 1 MILE

0 1 KILOMETER

43°25'

43°22'30"

88°15'

88°12'30"

Extent of far field

Extent of near field

Boundary of hydrologic inhomogeneity

Analytic elements

Hydraulic head target

Streamflow target

EXPLANATION

Site 1

Site 2

Site 3

Big Cedar

Lake

Cedar Creek

Little Cedar 

Lake

Silver Lake

Silver Lake dam

Paradise Valley Lake

Lucas Lake

Silver

Creek

Milwaukee

River

(a) Far-field

(b) Near-field

Boundary of hydrologic inhomogeneity
DEVELOPMENT OF THE ANALYTIC-ELEMENT MODEL 9

Calibration of the AE model was performed 

through trial-and-error changes to hydrologic parameters to minimize the difference between simulated and 

measured hydraulic heads, and simulated and measured 

streamflows. Whereas it would be ideal for all head and 

streamflow targets for a model to have been measured 

at the same instant in time, and for conditions during 

those measurements to reflect the long-term average 

conditions, this is rarely the case. In this study, the available data had been collected over many years, and represent different seasons as well as different conditions 

(relatively wet or dry years).

Hydraulic-head targets are static (non-pumping) 

water-level elevations measured in wells within the 

near-field of the AE model. Head targets used for calibrating the Silver Lake AE model came from three 

sources: the USGS Ground-Water Site Inventory 

(GWSI) database, the Wisconsin Department of Natural 

Resources Groundwater Retrieval Network (GRN), and 

the CDM/Limnetics report (1977). These data were 

sorted and selected to identify a final set of head targets. 

The GRN database contains construction information for water-supply wells, including measured static 

water level (head). Many wells were found in the nearfield of the Silver Lake model domain. The number of 

wells was reduced to a manageable 35 by using wells 

constructed over 3 consecutive and recent water years, 

1992, 1993, and 1994, a time during which many new 

wells were constructed. Because GRN wells are located 

only by quarter/quarter section, each well was located 

more precisely within the model domain, when possible, by using the street address, and topographic and 

plat maps.

The GWSI database contained 308 wells for Washington County. Forty-five of these wells, located by latitude and longitude, fell within the near-field study area 

and are included as head targets. Dates for these head 

data range from 1930 to 1993. Eight wells close to Silver Lake were selected from the CDM/Limnetics report 

and included as head targets. These head data are all 

from 1976 and 1977. From the three sources, 88 nearfield head targets were identified to be used for model 

calibration.

The only historical measurements of streamflow 

found for the study area were for Silver Creek immediately downstream of Silver Lake dam (CDM/Limnetics, 

1977) (site 1, fig. 4, table 2). As part of this study, additional measurements were made at that location. Flow 

measurements also were made at two new locations: on 

the creek between Big Cedar and Little Cedar Lakes, 

and about 0.6 mi downstream of Little Cedar Lake (sites 

2 and 3, fig. 4, table 2). Streamflow was measured using 

a Pygmy current meter and standard USGS methods 

(Rantz and others, 1982). Base-flow conditions 

(approximately steady-state) were inferred from historical measurements of Silver Creek below Silver Lake 

(fig. 3) (CDM/Limnetics, 1977), and flow measured at 

the other two locations was believed to be base flow 

based on comparison to historical records of the nearby 

Milwaukee River gage in Cedarburg.

DEVELOPMENT OF THE ANALYTICELEMENT MODEL

To simulate ground-water flow in the Silver Lake 

study area, hydrologic features and aquifer properties 

must be identified in a conceptual model. Development 

of the AE model is based on the conceptual model that 

represents those important hydrologic features. Once 

the AE model is calibrated to hydraulic-head and 

streamflow targets, it can be used to simulate shallow 

ground-water flow in the study area. 

Conceptualization

A conceptual model of the study area was developed to establish a framework for AE model development (fig. 5). The shallow aquifer is composed of 

laterally extensive, unconsolidated glacial deposits of 

the Holy Hill Formation. These deposits primarily are 

stratified sand and gravel, and range in thickness across 

Table 2. Measured and simulated streamflow, Washington 

County, Wisconsin

[values in cubic feet per second]

Location Site 

numbera

a

Sites shown on figure 4b.

Observed Simulated

Below Silver Lake 1 0.7. to 5.2 b

b

Measurements taken on July 27, 2000, September 14, 

2000 and November 21, 2000.

1.24 c

c

Calculated as residual in water balance.

Between Big Cedar

and Little Cedar Lakes 

2 11.4 d

d

Measurement taken on November 21, 2000.

9.5

Cedar Creek at 

Pleasant Valley Rd 

3 13.2 d 13.0
10 Simulation of the Shallow Aquifer in the Vicinity of Silver Lake, Washington County, Wisconsin using Analytic Elements

the study area from 100 to 300 ft (Mickelson and Syverson, 1997). Although the underlying Silurian dolomite 

bedrock can be a productive aquifer, its hydraulic conductivity (about 0.6 ft/day) is much less than the overlying unconsolidated sand and gravel (Mickleson and 

Syverson, 1997; Poff and Threinen, 1962). Therefore, 

the highly transmissive glacial sediments are considered to be an aquifer bounded on the bottom by low 

transmissivity bedrock. The irregularity of the bedrock 

surface and the hilly terrain of the Kettle Moraine result 

in a shallow aquifer with a variable saturated thickness 

across the study area. The hilly terrain also results in 

variable depth to ground water across the study area 

(fig. 5).

The depth of Silver Lake and the thickness and 

character of the shallow aquifer determine whether Silver Lake captures all the upgradient water flowing 

toward it, or if some will flow underneath the lake. The 

maximum and mean depths of Silver Lake are about 

45 ft and 20 ft, respectively (Poff and Threinen, 1962). 

The shallow aquifer generally is about 100 ft thick 

around Silver Lake, though it varies substantially, from 

about 50 to about 200 ft (Mickleson and Syverson, 

1997). Flow-through seepage (that is, lakes that receive 

ground-water discharge on one side, and recharge the 

aquifer on the opposite side) becomes more prevalent as 

the length of the lake parallel to mean ground-water 

flow direction increases relative to the aquifer thickness 

(Nield and others, 1994). Lower aquifer anisotropy 

(ratio of horizontal to vertical hydraulic conductivity) 

and lower lake-bed resistance also favor flow-through 

seepage. The shallow aquifer under Silver Lake is relatively thin (about 100 ft) compared to the east-west distance across the Lake (about 1,400 ft). Whereas there 

are no specific data on aquifer anisotropy or lake-bed 

resistance, the presence of springs on the western shore 

indicates that the lake is a discharge area. These conditions suggest that it is likely most of the upgradient 

water flowing toward Silver Lake will be captured and 

little will flow underneath.

The shallow aquifer is recharged by precipitation 

(minus interception and evapotranspiration) that falls 

across the study area. Ground water moves from topographically high areas to topographically low areas 

(higher potential to lower potential). Therefore, ground 

water generally moves toward surface-water features in 

topographic lows. Because of the strong hydraulic connection between the lakes and ground water, the conceptual model suggests water flows through the shallow 

aquifer from Big Cedar Lake (stage is about 1,031 ft) to 

Little Cedar Lake (stage is about 1,013 ft) to Silver Lake 

(stage is about 999 ft) (figs. 2 and 5). It is likely that 

Figure 5. Conceptual model, in cross-sectional view, of the interaction of lakes, precipitation, evaporation, and shallow

ground-water flow in the vicinity of Silver Lake, Washington County, Wisconsin.

Little Cedar

Lake

Milwaukee

River

Silver

Lake

Big Cedar

Lake

West East

Shallow aquifer

EXPLANATION

General direction of ground-water flow

Evaporation and transpiration

Sand and gravel

Silurian dolomite

Low hydraulic conductivity

Sand and gravel

Bedrock

999 ft

1,013 ft 1,031 ft

Saturated thickness

Depth to water

Precipitation

High hydraulic conductivity

Not to scale
DEVELOPMENT OF THE ANALYTIC-ELEMENT MODEL 11

Silver Lake receives ground water on its western, 

upgradient side, and contributes to ground water on its 

eastern, downgradient side. In addition, because Silver 

Lake is the headwater for Silver Creek, some of the 

ground water that flows into Silver Lake on the west 

flows north out of the lake to Silver Creek. Lake stage 

and flow to Silver Creek is controlled by a fixed elevation dam; therefore, lake storage (volume) changes only 

slightly during the year.

In addition to ground-water flow into and out of the 

lake, other lake-budget components that were considered for Silver Lake are precipitation falling on the lake 

and evaporation from the lake surface (fig. 5). In this 

part of southeastern Wisconsin, annual precipitation on 

a free-water surface exceeds evaporation from that surface by about 3 in/yr (Novitzki, 1982). Overland flow of 

precipitation to Silver Lake was not considered to be an 

important component of the hydrologic budget because 

of the permeable nature of the sand and gravel deposits 

—infiltration will likely always exceed precipitation.

Construction

Based on the conceptual model and preliminary 

parameter optimization using the optimization code 

UCODE (Poeter and Hill, 1998), regional values were 

chosen for recharge (4 in/yr), average horizontal 

hydraulic conductivity (50 ft/day), and base elevation of 

the aquifer across the model (800 ft). An area within the 

model domain in which hydrologic parameter values 

are different appreciably from the regional values is a 

hydrologic inhomogeneity. A single hydrologic inhomogeneity was added to the model (fig. 4a). The shape 

of this inhomogeneity and its values represent an area 

with appreciably different model base elevation, and 

possibly hydraulic conductivity and recharge for the 

Kettle Moraine Area that trends through central Washington County (fig. 2).

The near-field of the AE model contains analytic 

elements (line sinks) that represent hydrologic features 

of primary interest, including Silver Lake, Silver Creek, 

Big Cedar and Little Cedar Lakes, Cedar Creek, Paradise Valley Lake, Lucas Lake, and portions of the Milwaukee River, as well as some surrounding wetlands 

and streams (fig. 4b). In the near-field, model elements 

have attributes of width and resistance. The model elements were assigned widths that best represent the feature. For example, streams were assigned widths of 3 to 

10 ft, the Milwaukee River was assigned widths of 25 to 

100 ft, and lakes were assigned widths of 25 to 500 ft 

(table 3). Resistance is a measure of how difficult it is 

for water to move between surface-water features and 

the shallow aquifer. All near-field streams and rivers 

were assigned a value of 0.5 ft/ft/day for resistance, and 

lakes were assigned a value of 1.0 ft/ft/day (table 3).

Silver Lake was unique among the lakes in the 

model in that it was represented by a lake-specified element, and as such provided a steady-state simulation of 

Silver Lake stage by iterating to a balance of net precipitation on the lake, ground-water inflow and outflow, 

and surface-water outflow (Hunt and others, in press). 

Parameters specified for this lake element include the 

bottom elevation of Silver Lake (defined as 975 ft), 

resistance (defined as 1 ft/ft/day), and net precipitation 

on the lake (total precipitation minus evaporation 

defined as 3 in/yr). In addition, measured spring flow of 

0.1 ft3

/s from the southwest end of the lake was added 

as overland flow to the lake distributed uniformly along 

the lake element. Also defined in the model is the relation between lake stage and lake area, and lake stage 

and outflow over the Silver Lake Dam. Lake area was 

considered to be a constant 5,122,656 ft2

 (117.6 ac) over 

the relatively small range of stage change. The relation 

between lake stage and outflow was derived from 

monthly lake stage and daily flow measurements taken 

Table 3. Resistance and width of lakes and 

streams in the Silver Lake, Washington County, 

Wisconsin, analytic-element model

Surface-water 

feature

Resistancea

(in days)

a

Resistance is thickness of lake or stream bottom 

sediments (feet) divided by their hydraulic conductivity 

(feet per day)

Width

(in feet)

Big Cedar Lake 1.0 500

Little Cedar Lake 1.0 100

Silver Lake 1.0 100

Paradise Lake 1.0 25

Lucas Lake 1.0 25

Silver Creek .5 3

Silver Creek to 

Milwaukee River

 .5 5

Stream from Big Cedar 

to Little Cedar Lake

 .5 10

Cedar Creek .5 10

Milwaukee River .5 25 or 100
12 Simulation of the Shallow Aquifer in the Vicinity of Silver Lake, Washington County, Wisconsin using Analytic Elements

during 1977 (fig. 3) (CDM/Limnetics, 1977) adjusted 

for recent survey information at the dam (John Behrens, 

Silver Lake Sewer District, written commun., 2001). 

Based on this relation, outflow to Silver Creek ranges 

from 0.8 to 3.3 ft3

/s for a range of stages 999.34 to 

999.57 ft (table 4). Therefore, with lake bottom elevation and resistance specified, net precipitation on the 

lake specified, and the lake area/stage and lake outflow/stage relations specified, the calibrated model simulates a steady-state lake stage that is in balance with 

discharge from the aquifer to the lake and recharge from 

the lake to the aquifer. 

Calibration

Calibration of the AE model was performed 

through trial-and-error changes to hydrologic parameters to minimize the difference between simulated and 

measured heads and streamflows. Regional values for 

recharge and hydraulic conductivity were varied, as 

were values for recharge, hydraulic conductivity, and 

base elevation within the inhomogeneity. Recharge values were varied between 2 in/yr and 18 in/yr, hydraulic 

conductivity values were varied over two orders of 

magnitude from 1 ft/day to 100 ft/day. The shape of the 

inhomogeneity also was varied though kept generally 

coincident with the Kettle Moraine Area shown in 

figure 2. 

Following calibration of the Silver Lake AE model, 

the match of simulated heads to measured heads generally was good. In figure 6, triangles represent these 

results at target locations. An upward-pointing triangle 

indicates that the model simulated a head greater than 

measured at a given target location, and a downwardpointing triangle indicates that the model simulated a 

head lower than measured. Targets simulated high and 

those simulated low are found distributed across the 

model. The lack of clustering of high- or low-modeled 

targets indicates the model is relatively accurate across 

the entire domain. Additional evidence that the model 

simulation reasonably represents shallow ground-water 

flow is the scatter plot comparing simulated heads to 

measured heads (fig. 7) showing a good correlation with 

scatter on both sides of the line of perfect agreement. 

Calibration statistics for these 88 head targets also are 

presented in figure 7. The maximum difference between 

simulated and measured heads was 35.8 ft greater and 

50.9 ft less than measured. The average difference (AD) 

between simulated and measured heads was -0.2 ft, and 

the mean difference was -1.5 ft. The mean absolute difference (MAD) is the mean of the absolute values of the 

differences in simulated and measured heads, and is 

10.8 ft for the calibrated model. The root mean squared 

(RMS) difference is the square root of the average of the 

squared differences in simulated and measured heads, 

and is 14.7 ft. The value of calibration criteria that is 

acceptable is subjective, but can be evaluated on the 

basis of the change in heads over the model domain. For 

instance, if the ratio of the RMS difference to the head 

difference across the model domain is small, the errors 

represent a small part of the overall model response 

(Anderson and Woessner, 1992). For the Silver Lake 

model, measured heads range over almost 200 ft, as 

compared to the RMS difference of 14.7, resulting in a 

relatively small ratio. The calibrated model also accurately simulated measured streamflow at the three locations (fig. 4 and table 2); however, it is a small 

streamflow data set. If additional measurements at these 

sites or measurements at additional sites provide more 

precise steady-state flow data, recalibration of the 

model may be warranted.

The calibrated values for global recharge and 

hydraulic conductivity did not change from their initial 

values (4 in/yr recharge and 50 ft/day hydraulic conductivity). Calibrated values for the inhomogeneity were 

12 in/yr for recharge and 20 ft/day for hydraulic conductivity. In addition, the model base was raised from 

800 to 900 ft in the inhomogeneity. This change in 

hydraulic conductivity and model base elevation represents a 4- to 5-fold reduction in transmissivity in the 

area represented by the inhomogeneity. All simulations 

discussed in the following section of the report use only 

these calibrated values.

Table 4. Relation of lake stage

and discharge used for lake 

specified line-sink representing 

Silver Lake, Washington County, 

Wisconsin, in analytic-element

model

[ft3/s, cubic feet per second]

Lake stage

(ft above sea level)

Discharge

(ft3/s)

999.57 3.3

999.54 2.8

999.44 1.8

999.34 .8
SIMULATION OF SHALLOW GROUND-WATER FLOW 13

During model calibration it was found that calibration to head targets was most sensitive to hydraulic conductivity and recharge values defined for the 

inhomogeneity, and less sensitive to global values. Conversely, calibration to streamflow sites 2 and 3 was sensitive primarily to global hydraulic conductivity and 

recharge (outside of the inhomogeneity). This sensitivity appears to be because streamflow at both sites 

depends appreciably on the flow coming from Big 

Cedar Lake, which lies outside the inhomogeneity.

SIMULATION OF SHALLOW GROUNDWATER FLOW

The calibrated AE model provides a simulated 

water table for the Silver Lake study area (fig. 8). The 

general ground-water flow direction is shown to be 

from west to east with lakes and streams affecting the 

regional pattern. The simulation also shows ground 

water discharging to Silver, Big Cedar, and Little Cedar 

Lakes over most of their upgradient (western) shorelines. The downgradient (eastern) sides of these lakes 

are shown to be recharging to ground water. Backward 

particle tracking from the bottom of the aquifer on the 

eastern, downgradient side of Silver Lake suggests that 

the lake captures almost all of the upgradient ground 

water through the entire aquifer thickness. A notable 

exception is the shallower and narrower north end of the 

lake where a greater proportion of particles are found to 

flow under the lake from west to east. Whereas the calibrated model can be used for general interpretive evaluation of the Silver Lake area, it also can be used to test 

potential changes affecting the watershed. For instance, 

the effect of a pumping well placed upgradient or downgradient of the lake could be simulated. Specific 

changes to ground-water recharge areas (such as adding 

impervious areas like parking lots) could be simulated. 

The model provides a tool for assessing the effect of a 

wide range of activities or land-management choices.

Hydrologic Budget for Silver Lake

Simulated ground-water flow provided by the AE 

model can be combined with reported precipitation and 

evaporation values for Silver Lake to estimate the 

steady-state surface-water flow from the lake to Silver 

Figure 6. Comparison of simulated to measured head targets in the calibrated Silver Lake, Washington County, 

Wisconsin, analytic-element model.

Big Cedar

Lake

Little

Cedar

Lake

Silver

Lake

43°22'30"

43°24'

88°15' 88°12'30"

0 1 MILE

0 1 KILOMETER

Simulated head is 11.7 feet

lower than measured

Simulated head is 28.8 feet

lower than measured

Simulated head is 30.9 feet

greater than measured

Simulated head is 12.4 feet

greater than measured

Greater than measured

Lower than measured

Simulated head—

Size is proportional to difference

greater than or lower than measured

EXPLANATION
14 Simulation of the Shallow Aquifer in the Vicinity of Silver Lake, Washington County, Wisconsin, Using Analytic Elements

Figure 7. Scatter plot comparing simulated heads to measured heads for the calibrated Silver Lake, 

Washington County, Wisconsin, analytic-element model.

860 900 940 980 1,020 1,060

Line of perfect agreement

860

900

940

980

1,020

1,060

MEASURED HEADS, IN FEET ABOVE SEA LEVEL

SIMULATED HEADS, IN FEET ABOVE SEA LEVEL

Number of measurements

Maximum difference 35.8 feet

Minimum difference -50.9 feet

Average difference (AD) -0.2 feet

Median difference -1.5 feet

Mean absolute difference (MAD) 10.8 feet

Root mean squared difference (RMS) 14.7 feet

88
SIMULATION OF SHALLOW GROUND-WATER FLOW 15

Creek. Comparison of this estimated flow to measured 

values provides an additional calibration point to 

increase confidence in the AE simulation and its usefulness. A hydrologic budget for Silver Lake can be 

defined by the following equation and represented in 

figure 9.

∆S = P – E + GWin – GWout + SWin – SWout , (1)

where

∆S is change in lake storage,

P is precipitation falling directly on the lake,

E is water evaporated from the lake surface,

GWin is ground water discharging to the lake,

GWout is lake water recharging ground water,

SWin is surface-water flow to the lake, and

SWout is flow out of the lake to Silver Creek.

The following assumptions and simplifications 

have been made:

• GWin includes 0.10 ft3/s measured spring flow 

into Silver Lake, 

• there is no surface-water flow (SWin) into Silver 

Lake, 

• overland flow to Silver Lake is negligible, and

• lake storage does not change over time 

(∆S = 0), that is, ground-water flow is at 

steady state (lake stage, and, therefore, volume, is controlled by a dam).

Because ∆S and SWin are assumed to equal zero, 

equation 1 can be rewritten as

SWout = (P – E) + (GWin – GWout) (2)

In the form given in equation 2, the flow from Silver Lake into Silver Creek (SWout) is calculated as a 

residual in the hydrologic budget. Annual precipitation 

on the lake is about 3 in/yr greater than evaporation 

(Novitzki, 1982), that is, the term P minus E is 3 in/yr. 

Considering the area of Silver Lake (117.6 ac), 3 in/yr 

is equal to 0.04 ft3/s. Based on calibrated model results, 

Figure 8. Simulated water table from the calibrated Silver Lake, Washington County, Wisconsin, analytic-element model.

Big Cedar

Lake

Little

Cedar

Lake

Silver

Lake

43°22'30"

43°24'

88°15' 88°12'30"

0 1 MILE

0 1 KILOMETER

1035

1030

1025

1020

1015

1005 10001010

995

990

985

980

1035

1030

1025

1020

1015

1005

1000

1010

995

990

985

980

EXPLANATION

Simulated water-table contour—

Contour interval is 5 feet.

Datum is sea level.

1030
16 Simulation of the Shallow Aquifer in the Vicinity of Silver Lake, Washington County, Wisconsin using Analytic Elements

GWin minus GWout is 1.00 ft3/s. Therefore, streamflow 

out of Silver Lake (SWout) is equal to the sum of the 

terms (P-E) and (GWin – GWout) resulting in

SWout = (0.04 ft3/s) + (1.00 ft3/s) = 1.04 ft3/s

Streamflow from Silver Lake of 1.04 ft3/s compares well to new and historical measurements of 

streamflow from Silver Lake ranging from 0.7 to 

5.2 ft3/s (table 3). The higher end of this flow range 

likely represents flow over the dam during short-term 

elevated lake stages resulting from storm events. 

Because the AE model simulates steady-state conditions, that is, long-term average (baseflow) conditions, 

it more properly reflects the lower end of the range of 

measured streamflow. The water budget for Silver Lake 

is summarized in figure 9.

Ground-Water Recharge Areas for Silver 

Lake

Activities in ground-water-recharge areas can have 

a direct effect on Silver Lake water quantity and quality. 

Delineation of recharge areas for ground water flowing 

to Silver Lake is important for the protection of the lake, 

and for making land-management decisions. Groundwater recharge areas for Silver Lake were simulated by 

using backward-particle tracking in the AE model. 

Mathematical water particles were placed at the bottom 

of the aquifer along the upgradient side of Silver Lake 

and tracked backward in time for 10, 20 and 50 years 

(fig. 10). Aquifer porosity of 20 percent was assumed 

based on the unconsolidated and variably sorted nature 

of the sand-and-gravel deposits composing the shallow 

aquifer (Freeze and Cherry, 1979). The distance and 

area covered by the particles in those time intervals 

define the ground-water recharge areas. The northern 

two-thirds of Silver Lake receives its recharge from the 

area between Silver Lake and Big Cedar Lake, however, 

the 50-year time-of-travel does not extend all the way to 

Big Cedar Lake (fig. 10). The southern one-third of Silver Lake receives its recharge from the area between 

Silver Lake and Little Cedar Lake. The 10-year time-oftravel for this part of Silver Lake does not extend all the 

way to Little Cedar Lake, but the 20-year time of travel 

does reach the eastern shore of Little Cedar Lake. 

Therefore, for times of travel greater than 15 or 

20 years, the recharge area of Little Cedar Lake also 

should be considered a recharge area for Silver Lake. 

Because Little Cedar Lake receives surface-water flow 

from Big Cedar Lake, it also should be considered a 

potential recharge area for the southern portion of Silver 

Lake for times-of-travel greater than 15 or 20 years. 

Forward particle tracking confirmed the areas of contribution delineated by the backward tracking. Once 

ground water enters Silver Lake, whether it comes from 

the northern two-thirds or southern one-third of the 

western shoreline, the water likely becomes wellmixed.

The porosity value given the shallow aquifer is a 

controlling factor in the simulated time-of-travel for the 

mathematical water particles tracked backward from 

Silver Lake to define the ground-water recharge areas. 

Porosity greater than 20 percent would decrease the distance traveled by particles over a given time, and porosity less than 20 percent would increase the distance 

traveled. However, over the range of reasonable porosity values (15 to 25 percent), the difference in distance 

traveled is small (plus or minus 20 percent of the distance traveled at 20 percent porosity). 

Simulation of Pumping from the Shallow 

Aquifer

The effect of a pumping well on the shallow aquifer 

and Silver Lake can be evaluated anywhere in the model 

near-field. As examples, wells were added to the calibrated model at three locations, one west of Silver Lake 

(upgradient), one directly east of Silver Lake (downgradient), and one further to the southeast of Silver Lake 

(fig. 11a). The latter location is near a newly built shopping center in an area where future development is 

likely. Each simulated well is represented as fully penetrating and pumps at a rate of 0.17 ft3

/s (75 gallons per 

minute—about average for municipal wells in the 

nearby city of West Bend). The effect of each well is 

simulated independently of the others.

Simulated pumping at each location is shown to 

lower the water table locally (figs. 11b, c, and d). Backward particle tracking was used to define the upgradient 

area contributing recharge to each well. The contributing areas extend to the west; Silver Lake is included in 

the contributing areas for the two downgradient wells. 

Because simulated flows from the shallow aquifer to 

Silver Lake and from Silver Lake to the shallow aquifer 

are small, 1.08 and 0.08 ft3

/s respectively (fig. 9), the 

model simulates that the wells affect the lake water balance. The effect can be seen in slightly lowered lake 

stage and reduced outflow to Silver Creek. The simu-
Simulation of Pumping from the Shallow Aquifer 17

Figure 9. Hydrologic budget for Silver Lake, Washington County, Wisconsin, based on the

calibrated analytic-element model.

P

E

Silver

Lake

GWin Ground-water flow into Silver Lake

GWout Ground-water flow out of Silver Lake

SWin Surface-water flow into Silver Lake

SWout Surface-water flow out of Silver Lake into Silver Creek

P Precipitation falling on the surface of Silver Lake

E Evaporation from the surface of Silver Lake 

EXPLANATION

Precipitation

Evaporation

Direction of ground-water flow

Direction of surface-water flow

Equation definitions

SWout = 1.04 cubic feet per second

P - E = 0.04 cubic feet per second

GWout = 0.08 cubic feet per second

SWin = 0.0 cubic feet per second

GWin = 1.08 cubic feet per second

∆S = 0.0 cubic feet per second

0 .25 MILE

0 .25 KILOMETER
18 Simulation of the Shallow Aquifer in the Vicinity of Silver Lake, Washington County, Wisconsin, Using Analytic Elements

Figure 10. Ground-water recharge areas and times-of-travel to Silver Lake, Washington County, Wisconsin.

EXPLANATION

Contributing area with

time-of-travel to Silver Lake

of 50 years or less

0–10 years

11–20 years

21–50 years

50-year

10-year

20-year

43°25'

43°22'30"

88°15' 88°12'30"

0 1 MILE

0 1 KILOMETER

Big Cedar Lake

Little Cedar Lake

Silver Lake

Paradise

Valley Lake

Lucas Lake

Cedar Creek

Silver Creek
Simulation of Pumping from the Shallow Aquifer 19

Figure 11b. Simulated fully-penetrating well pumping 75 gallons per minute from west side of Silver 

Lake, Washington County, Wisconsin.

Little

Cedar

Lake

Silver

Lake

1028

1026

1024

1022

1020

1018

1016

1014

1012

1010

1008

1006

1004

1002

1000

998

996

994

992

990

988

986

984

982

980

978

976

974

972

970

968

1028

1026

1024

1022

1020

1018

1016

1014

1012

1010

1008

1006

1004

1002

1000

998

996

994

992

990

988

986

984

982

980

978

976

974

972

970

968

1024

1022

1020

43°23'51"

43°22'35"

88°14'11" 88°12'03"

0 .5 MILE

0 .5 KILOMETER

EXPLANATION

Simulated water-table contour—

Contour interval is 2 feet.

Datum is sea level.

Flowpath to well

1010

Figure 11a. Locations of three simulated wells around Silver Lake, Washington County, Wisconsin.

Little

Cedar

Lake

Silver

Lake

1028

1026

1024

1022

1020

1018

1016

1014

1012

1010

1008

1006

1004

1002

1000

998

996

994

992

990

988

986

984

982

980

978

976

974

972

970

968

966

964

1028

1026

1024

1022

1020

1018

1016

1014

1012

1010

1008

1006

1004

1002

1000

998

996

994

992

990

988

986

984

982

980

978

976

974

972

970

968

966

964

1024

1022

1020

0 .5 MILE

0 .5 KILOMETER

43°23'51"

43°22'35"

88°14'11" 88°12'03"

EXPLANATION

Simulated water-table contour—

Contour interval is 2 feet.

Datum is sea level.

Simulated well

1010
20 Simulation of the Shallow Aquifer in the Vicinity of Silver Lake, Washington County, Wisconsin, Using Analytic Elements

Figure 11c. Simulated fully-penetrating well pumping 75 gallons per minute from east of Silver Lake, 

Washington County, Wisconsin.

Little

Cedar

Lake

Silver

Lake

1028

1026

1024

1022

1020

1024

1022

1020

1018

1016

1014

1012

1010

1008

1006

1004

1002

1000

998

996

994

992

990

988

986

984

982

980

978

976

974

972

970

968

966

964

1028

1026

1024

1022

1020

1024

1022

1020

1018

1016

1014

1012

1010

1008

1006

1004

1002

1000

998

996

994

992

990

988

986

984

982

980

978

976

974

972

970

968

966

964

43°23'51"

43°22'35"

88°14'11" 88°12'03"

0 .5 MILE

0 .5 KILOMETER

EXPLANATION

Simulated water-table contour—

Contour interval is 2 feet.

Datum is sea level.

Flowpath to well

1010

Figure 11d. Simulated fully-penetrating well pumping 75 gallons per minute from southeast side of 

Silver Lake, Washington County, Wisconsin.

Little

Cedar

Lake

Silver

Lake

1026

1024

1022

1020

1018

1016

1014

1012

1010

1008

1006

1004

1002

1000

998

996

994

992

990

988

986

984

982

980

978

976

974

972

970

968

1024

1022

1020

1028

1026

1024

1022

1020

1018

1016

1014

1012

1010

1008

1006

1004

1002

1000

998

996

994

992

990

988

986

984

982

980

978

976

974

972

970

968

1024

1022

1020

43°23'51"

43°22'35"

88°14'11" 88°12'03"

0 .5 MILE

0 .5 KILOMETER

EXPLANATION

Simulated water-table contour—

Contour interval is 2 feet.

Datum is sea level.

Flowpath to well

1010
Simulation of Pumping from the Shallow Aquifer 21

lated stage of Silver Lake is lowered very little—

0.005 to 0.013 ft—by the pumping wells (figs. 11b, c, 

and d). Based on the historical relation between Silver 

Lake stage (as controlled by the dam) and Silver Creek 

outflow (table 4), GFLOW provides Silver Creek outflow for these same simulations of pumping wells. The 

simulated outflow from Silver Lake to Silver Creek is 

reduced by 0.05 to 0.14 ft3

/s (figs. 11b, c, and d).

Solute Flux Toward Silver Lake

Ground water flowing toward Silver Lake carries 

with it dissolved chemical constituents (solutes). However, ground water sampled from piezometers or monitoring wells on shore can have markedly different 

chemistries from water discharging across the sediment-water interface. This difference is true particularly 

for nutrients, such as nitrogen and phosphorus, and 

redox sensitive species (Krabbenhoft and Webster, 

1995), largely because some biotic and abiotic chemical 

processes are concentrated near the sediment-water 

interface. Because of the chemical dynamics present at 

the sediment-water interface, it is important to sample 

pore water in the littoral regions of lakes in order to estimate chemical constituent loading from ground-water 

discharge (Krabbenhoft and Webster, 1995). Specifically, this sampling should be done within about 3 ft of 

the sediment-water interface. A reasonable estimate of 

the flux of chemical constituents through the interface 

into Silver Lake cannot be done with analytical data 

from the available piezometers and observation wells; 

this would require a more thorough understanding of 

the character of the interface, its chemistry, and its 

effect on non-conservative constituents.

Concentrations measured in piezometers and 

observation wells during the course of the CDM/Limnetics study (CDM/Limnetics, 1977), however, can be 

used to estimate the flux of chemical constituents 

toward the interface. With the use of the 1976/1977 data 

for wells upgradient of Silver Lake, average concentrations for ground water approaching the aquifer/lake 

interface have been calculated for total nitrogen, chloride, and phosphorus (table 5). The mass flux of these 

solutes to this interface can be calculated by using the 

ground-water flux (GWin) provided by the AE model—

1.08 ft3/s. Table 5 shows the daily solute mass flux for 

constituents calculated by multiplying average concentrations by the ground-water flux. This provides an 

upper estimate of potential flux to the lake because reactions that typically occur at the sediment-water interface 

tend to reduce constituent concentrations.

Model Limitations

As with any ground-water model, the Silver Lake 

AE model is a simplification of actual ground-water 

flow, with proportional limitations on model precision 

and application. For instance, the contrast in transmissivity represented by the inhomogeneity is based on 

regional geology and model calibration. Whereas 

changes in transmissivity largely are related to variations in saturated thickness and hydraulic conductivity, 

the scale at which these factors can vary is much smaller 

than the scale of the inhomogeneity. Therefore, 

although general conclusions can be reached about 

ground-water flow across the inhomogeneity and in the 

vicinity of Silver Lake, evaluation of site-specific questions may require additional information or refinement 

Table 5. Average solute concentrations in ground water and resulting mass flux toward Silver Lake, Washington County, 

Wisconsin

[mg/L, milligrams per liter; ft3/s, cubic feet per second; L/d, liters per day; Kg/d, kilograms per day]

Constituent

Average concentration in 

upgradient observation 

wells

(mg/L)

Daily ground water flux 

toward Silver Lake

(ft3/s)

Daily ground water 

flux toward Silver Lake

(L/d)

Daily solute mass flux 

toward Silver Lake

(Kg/d)

Total Nitrogen 3.65 1.08 2,642,302 9.64

Chloride 12.4 1.08 2,642,302 32.76

Phosphorous .023 1.08 2,642,302 .06
22 Simulation of the Shallow Aquifer in the Vicinity of Silver Lake, Washington County, Wisconsin using Analytic Elements

of the model. In addition, the AE model employs the 

Dupuit-Fochheimer approximation that assumes 

ground-water flow is horizontal, so the model will not 

accurately represent the water table in areas where 

strong vertical gradients and/or flow are present. This 

limitation is not perceived to be a problem in the vicinity of Silver Lake. As a steady-state representation, seasonal fluctuations in Silver Lake and the shallow 

aquifer are not simulated.

SUMMARY

Silver Lake, in central Washington County, southeastern Wisconsin, could be affected adversely by 

hydrologic stresses to the shallow aquifer. In order to 

assess the potential effects of these stresses the U.S. 

Geological Survey, in cooperation with the Silver Lake 

Protection and Rehabilitation District, began a study in 

2000.

Silver Lake is a kettle lake located in the Kettle 

Moraine Area. Silver Lake is about 117.6 ac in area, and 

is fed by small springs discharging near the shoreline 

and ground-water seepage. No streams flow into Silver 

Lake. Water flows from the north end of Silver Lake 

over a small dam into Silver Creek. Hydraulic parameter values for the shallow aquifer were estimated 

through characterization of the study area and calibration of the AE model. Based on results of the calibrated 

model, hydraulic conductivity of the shallow aquifer 

ranges from 20 to 50 ft/d—lower in the Kettle Moraine 

Area and higher in the surrounding areas. Also based on 

the calibrated model, recharge rates vary from 4 to 

12 in/yr—higher in the Kettle Moraine Area and lower 

in surrounding areas.

The hydrologic budget components for Silver Lake 

have been determined and their values estimated. 

Streamflow from Silver Lake was computed as a residual in the hydrologic budget and compared to measured 

flows. Precipitation on the lake minus evaporation from 

the lake is reported in the literature to be about 0.04 ft3/s 

(3 in/yr). Model results show ground-water flow into 

Silver Lake is 1.08 ft3

/s, and flow from Silver Lake to 

the shallow aquifer is 0.08 ft3

/s. The residual of 

1.04 ft3/s is the streamflow from Silver Lake to Silver 

Creek and closely matches the low end of the range of 

measured flows.

Ground-water-recharge areas for Silver Lake have 

been simulated by using backward tracking of particles 

in the AE model. Assuming a porosity of 20 percent, 

areas were defined for travel times of 10, 20, and 

50 years. Model simulations show that nearly all the 

ground water flowing to Silver Lake comes from 

recharge areas to the west. The recharge area for the 

northern two-thirds of Silver Lake lies west toward Big 

Cedar Lake, though the 50-year time-of-travel does not 

extend all the way to Big Cedar Lake. The recharge area 

for the southern one-third of Silver Lake lies west 

toward Little Cedar Lake. The simulated time of travel 

from Little Cedar Lake to Silver Lake is between 15 and 

20 years.

Three wells pumped independently from the shallow aquifer at locations west, east, and southeast of Silver Lake were simulated. The simulated pump rate (75 

gpm [0.17 ft3

/s]) is about twice the modeled flow from 

Silver Lake to the shallow aquifer (0.08 ft3

/s) and about 

one-sixth the simulated flow from the shallow aquifer to 

Silver Lake (1.08 ft3/s ). The simulated wells have an 

effect on the water balance of the lake. Depending on 

the placement of the well, the simulated stage of Silver 

Lake is lowered 0.005 to 0.013 ft, and the simulated outflow from Silver Lake to Silver Creek is reduced by 

0.05 to 0.14 ft3/s.

The solute flux toward Silver Lake was estimated 

by using average concentrations measured in observation wells and the simulated ground-water flux. However, in order to estimate solute mass loading to Silver 

Lake from ground-water discharge, it would be necessary to characterize the nature of the sediment-water 

interface, as well as the chemistry of the pore water in 

the lake littoral region (within about 3 ft of the interface). Concentrations of solutes like nitrogen and phosphorus would likely be lowered by biotic and abiotic 

processes near the sediment-water interface.

REFERENCES

Anderson, M.P., and Woessner, W.W., 1992, Applied 

Groundwater Modeling: San Diego, Calif., Academic 

Press, 381 p.

Bates, R.L., and Jackson, J.A., 1980, Glossary of Geology, 

Second Edition: Falls Church, Virginia, American Geological Institute, 749 p.

CDM/Limnetics, 1977, An environmental study of Silver 

Lake and the hydrological and water quality characteristics of its associated watershed for the Inland Lake Protection and Rehabilitation District of Silver Lake, 

Washington County, Wisconsin: Report submitted to 

Silver Lake Protection and Rehabilitation District.
REFERENCES 23

Freeze, R. A., and Cherry, J. A., 1979, Groundwater: New 

Jersey, Prentice-Hall, Inc., 604 p.

Haitjema, H.M., 1995, Analytic Element Modeling of 

Groundwater Flow: San Diego, Calif., Academic Press, 

394 p.

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

model through the use of an analytic element screening 

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

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

D.T., in press, Simulating lake-ground water interactions with models: MODFLOW and analytic element 

approaches: Ground Water.

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

analytic element model to investigate groundwater-lake 

interactions at Pretty Lake, Wisconsin: Journal of Lake 

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

Krabbenhoft, D.P., and Webster, K.E., 1995, Transient 

hydrogeological controls on the chemistry of a seepage 

lake: Water Resources Research, vol. 31, no. 9, 

p. 2295–2305.

Lillie, R.A., and Mason, J. W., 1983, Limnological Characteristics of Wisconsin Lakes: Wisconsin Department of 

Natural Resources Technical Bulletin No. 138, 116 p.

Mickelson, D.M., and Syverson, K.M., 1997, Quaternary 

geology of Ozaukee and Washington Counties, Wisconsin: Wisconsin Geological and Natural History Survey 

Bulletin 91, 56 p.

Neild, S.P., Townley, L.R., and Barr, A.D., 1994, A framework for quantitative analysis of surface water-groundwater interaction - Flow geometry in vertical section: 

Water Resources Research, 30(8), p. 2461–2475. 

Novitzki, R.P., 1982, Hydrology of Wisconsin Wetlands: 

Wisconsin Geological and Natural History Survey 

Information Circular Number 40, 22 p. 

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

UCODE, A computer code for universal inverse modeling: U.S. Geological Survey Water-Resources Investigations Report 98–4080, 116 p.

Poff, R.J., and Threinen, C. W., 1962, Surface Water 

Resources of Washington County: Lake and Stream 

Classification Project, Wisconsin Conservation Department, 65 p.

Rantz, S. E., and others, 1982, Measurement and Computation of Streamflow: U.S. Geological Survey Water-Supply Paper 2175, 631 p.

Shaw, B., Mechenich, C., and Klessig, L., 1986, Understanding Lake Data: G3582, UW-Extension Cooperative. 

Strack, O.D.L., 1989, Groundwater Mechanics: Englewood 

Cliffs, N.J., Prentice–Hall, 732 p.

U.S. Geological Survey, 1997, Water quality and lake-stage 

data for Wisconsin lakes, water year 1996: U.S. Geological Survey Open-File Report 97–123, 134 p.

U.S. Geological Survey, 1998, Water quality and lake-stage 

data for Wisconsin lakes, water year 1997: U.S. Geological Survey Open-File Report 98–78, 129 p.

Water Quality Association, September 24, 1999, Glossary of 

Terms: accessed January 16, 2002, at URL 

http://www.wqa.org/glossary.cfm?gl=2002.

APPENDIX 25

APPENDIX
26 Simulation of the Shallow Aquifer in the Vicinity of Silver Lake, Washington County, Wisconsin, Using Analytic Elements

APPENDIX 

U.S. Geological Survey water-chemistry analyses and physical measurements for Silver Lake, Washington 

County, Wisconsin (U.S. Geological Survey, 1997; U.S. Geological Survey, 1998).
APPENDIX 27

432322088125000 SILVER LAKE NEAR WEST BEND, WI

LOCATION.--Lat 43°23'22", long 88°12'50", in NE 1/4 SW 1/4 sec.27, T.11 N., R.19 E., Washington County, Hydrologic Unit 04040003, 

1.4 mi southwest of West Bend.

PERIOD OF RECORD.--February 1996 to August 1997 (discontinued).

REMARKS.--Lake sampled at northern end of southern basin of lake at the deep hole. Lake ice-covered during February measurements. 

Water-quality analyses by Wisconsin State Laboratory of Hygiene.

WATER-QUALITY DATA, FEBRUARY 13 TO AUGUST 26, 1997

(Milligrams per liter unless otherwise indicated)

 Feb. 13 Apr. 22 June 11 July 24 Aug. 26

 ---------------- ------------- --------------- --------------- ---------------

Lake stage (ft) --- 11.08 11.09 11.15 11.17

Secchi-depth (meters) --- 5.4 2.7 3.1 4.7

Chlorophyll a, phytoplankton (μg/L) --- 2.7 1.7 1.8 2.4

Depth of sample (m) 0.5 13 0.5 13 0.5 13 0.5 13 0.5 14

Water temperature (°C) 2.5 4.0 8.0 6.0 22.0 7.0 26.0 7.5 20.5 8.0

Specific conductance (μS/cm) 511 582 527 526 508 537 472 547 480 598

pH (units) 8.2 7.6 8.2 8.2 8.2 7.5 8.1 7.5 8.2 7.3

Dissolved oxygen 11.4 0.9 12.4 11.2 10.6 0.1 8.7 0.0 9.6 0.0

Phosphorus, total (as P) <0.007 0.060 0.017 <0.008 0.024 0.102 0.014 0.094 0.005 0.083

Phosphorus, ortho, dissolved (as P) --- --- 0.002 0.002 --- --- --- --- --- ---

Nitrogen, NO2 + NO3, diss. (as N) --- --- 0.19 0.19 --- --- --- --- --- ---

Nitrogen, ammonia, dissolved (as N) --- --- 0.22 0.25 --- --- --- --- --- ---

Nitrogen, amm. + org., total (as N) --- --- 0.60 0.70 --- --- --- --- --- ---

Nitrogen, total (as N) --- --- 0.80 0.89 --- --- --- --- --- ---

Color (Pt-Co. scale) --- --- 5 10 --- --- --- --- --- ---

Turbidity (NTU) --- --- 0.50 <0.50 --- --- --- --- --- ---

Hardness, as CaCO3 --- --- 260 250 --- --- --- --- --- ---

Calcium, dissolved (Ca) --- --- 46 44 --- --- --- --- --- ---

Magnesium, dissolved (Mg) --- --- 36 35 --- --- --- --- --- ---

Sodium, dissolved (Na) --- --- 8.9 8.8 --- --- --- --- --- ---

Potassium, dissolved (K) --- --- 1 1 --- --- --- --- --- ---

Alkalinity, as CaCO3 --- --- 240 240 --- --- --- --- --- ---

Sulfate, dissolved (SO4) --- --- 22 21 --- --- --- --- --- ---

Chloride, dissolved (Cl) --- --- 19 19 --- --- --- --- --- ---

Silica, dissolved (SiO2) --- --- 13 13 --- --- --- --- --- ---

Solids, dissolved, at 180°C --- --- 298 294 --- --- --- --- --- ---

Iron, dissolved (Fe) μg/L --- --- <10 <10 --- --- --- --- --- ---

Manganese, dissolved (Mn) μg/L --- --- <0.4 <0.4 --- --- --- --- --- ---

0 30 10 20

0

15

3

6

9

DEPTH, IN METERS 12

0 20 10

450 650 450 550

0

15

3

6

9

DEPTH, IN METERS 12

6 10 7 8 9

0 30 10 20

0

15

3

6

9

12

0 20 10

450 650 450 550

0

15

3

6

9

12

6 10 7 8 9

0 30 10 20

WATER TEMPERATURE (W.T.), IN DEGREES CELSIUS

0

15

3

6

9

12

0 20 10

DISSOLVED OXYGEN (D.O.), IN MILLIGRAMS PER LITER

450 650 450 550

SPECIFIC CONDUCTANCE (S.C.), IN MICROSIEMENS PER CENTIMETER AT 25 DEGREES CELSIUS

0

15

3

6

9

12

6 10 7 8 9

PH, IN STANDARD UNITS

0 30 10 20

0

15

3

6

9

12

0 20 10

450 650 450 550

0

15

3

6

9

12

6 10 7 8 9

0 30 10 20

0

15

3

6

9

12

0 20 10

450 650 450 550

0

15

3

6

9

12

6 10 7 8 9

W.T.

D.O.

S.C.

pH

2-13-97 4-22-97 6-11-97 7-24-97 8-26-97
28 Simulation of the Shallow Aquifer in the Vicinity of Silver Lake, Washington County, Wisconsin, Using Analytic Elements

0

4

1

2

3

CHLOROPHYLL a CONCENTRATION,

IN MICROGRAMS PER LITER

J F M A M J J A S O N D J F M A M J J A S O N D

1996 1997

0

8

2

4

6

SECCHI DEPTH, IN METERS

J F M A M J J A S O N D J F M A M J J A S O N D

1996 1997

CALENDAR YEAR

Figure 3. Surface total phosphorus and chlorophyll a concentrations, and Secchi depths

 for Silver Lake near West Bend, Wisconsin.

0

0.025

0.005

0.010

0.015

0.020

TOTAL PHOSPHORUS CONCENTRATION, 

IN MILLIGRAMS PER LITER

J F M A M J J A S O N D J F M A M J J A S O N D

1996 1997

(Circles indicate laboratory detection limit for selected analyses. Actual concentrations for these particular analyses are less than the plotted circles.)
APPENDIX 29