U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2009–5077

In cooperation with the Barron County Soil and Water Conservation Department

Water Quality and Hydrology of Silver Lake, 

Barron County, Wisconsin, With Special Emphasis on 

Responses of a Terminal Lake to Changes in Phosphorus 

Loading and Water Level

Water Quality and Hydrology of Silver Lake, 

Barron County, Wisconsin, With Special 

Emphasis on Responses of a Terminal Lake 

to Changes in Phosphorus Loading and 

Water Level

By Dale M. Robertson, William J. Rose, and Faith A. Fitzpatrick

In cooperation with the Barron County Soil and Water Conservation Department

Scientific Investigations Report 2009–5077

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

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

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Robertson, D.M., Rose, W.J., and Fitzpatrick, F.A., 2009, Water quality and hydrology of Silver Lake, Barron County, 

Wisconsin, with special emphasis on responses of a terminal lake to changes in phosphorus loading and water level: 

U.S. Geological Survey, Scientific Investigations Report 2009–5077, 38 p.

Cover photos:

Changes in the water levels at two locations on Silver Lake from 2004 (top photos) to 2007 (bottom photos) as viewed 

from the county park on the south shore of the lake.
iii

Contents

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

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

Silver Lake and Its Watershed............................................................................................................2

Effects of Changes in Nutrient Loading, Water Level, and Climate on Water Quality ..............4

 Purpose and Scope .............................................................................................................................6

Study Methods and Sampling Sites............................................................................................................6

Lake-Stage and Water-Quality Monitoring.......................................................................................6

Lake Classification................................................................................................................................8

Stream Monitoring................................................................................................................................8

Meteorology and Atmospheric Deposition Data.............................................................................9

Ground-Water Monitoring...................................................................................................................9

Estimation of Nearshore Erosion .......................................................................................................9

Measured Lake-Water Quality ..................................................................................................................11

Historical Changes in the Water Level of Silver Lake............................................................................15

Hydrology and Water Budget ....................................................................................................................16

Change in Storage ..............................................................................................................................16

Precipitation.........................................................................................................................................16

Evaporation and Net Groundwater Inflow......................................................................................18

Surface-Water Inflow ........................................................................................................................20

Groundwater Inflow and Outflow.....................................................................................................21

Water-Budget Summary....................................................................................................................23

Sources of Phosphorus...............................................................................................................................24

Precipitation.........................................................................................................................................24

Surface-Water Inflow .......................................................................................................................25

Groundwater and Septic Systems ...................................................................................................25

Nearshore Erosion..............................................................................................................................26

Phosphorus-Budget Summary .........................................................................................................28

Simulated Changes in Water Quality in Response to Changes in Phosphorus Loading..................29

Modeling Approach............................................................................................................................29

Verification and Adjustments for Model Biases............................................................................32

Response in Water Quality to Basinwide Changes in Phosphorus Loading.............................32

Model Validation and Sensitivity of Lake-Water Quality to Phosphorus Inputs 

from Erosion ...........................................................................................................................32

Response in Water Quality to Specific Natural and Anthropogenic-Change Scenarios.......33

Relative Importance of Anthropogenic Changes in the Watershed to Natural 

Hydrologic Changes.......................................................................................................................34

Summary and Conclusions.........................................................................................................................35

References Cited..........................................................................................................................................36
iv

Figures

1–3. Aerial photographs showing:

1. Silver Lake, Barron County, Wis., with its watershed and area from which 

surface water has been diverted into the Silver Lake watershed delineated ..........3 

2. Silver Lake, Barron County, Wis., with sampling locations and 

10-ft bathymetric contours identified ...............................................................................7

3. Silver Lake, Barron County, Wis., showing areas for which sediment and 

phosphorus input from erosion were observed and estimated.................................10

4–12. Graphs showing:

4. Near-surface total phosphorus concentrations, chlorophyll a

concentrations, and Secchi depths in Silver Lake, Barron County, Wis., 

1986 to 2008.........................................................................................................................12

5. Near-bottom total phosphorus concentrations in Silver Lake, 

Barron County, Wis., 1986 to 2008 ...................................................................................14

6. Trophic state index values based on surface concentrations of total 

phosphorus and chlorophyll a, plus Secchi depths, in Silver Lake, 

Barron County, Wis., 1986 to 2008 ...................................................................................14

7. Estimated and measured average annual lake stage, in Silver Lake,

Barron County, Wis., 1900 to 2008 ...................................................................................15

8. Daily water levels computed from the full water budget in comparison to 

measured water levels of Silver Lake, Barron County, Wis., from 

November 1, 2004, to October 31, 2006...........................................................................15

9. Precipitation at Silver Lake, Barron County, Wis., relative to long-term 

average precipitation at Gordon, Wis. ...........................................................................18

10. Measured and modeled (with the Dynamic Lake Model) distribution 

of water temperature ........................................................................................................19

11. Daily evaporation from the surface of Silver Lake, Barron County, Wis., 

based on output from the Dynamic Lake Model...........................................................20

12. Estimated streamflow in tributary 7 to Silver Lake, Barron County, Wis. ................20

13. Schematic showing the original and revised description of ground-water flow 

near Silver Lake, Barron County, Wis. ....................................................................................21

14–17. Graphs showing:

14. Water levels in Silver Lake, Barron County, Wis., and in nearshore 

piezometers during periods with high water and low water levels 

in the lake............................................................................................................................22

15. Water budgets for Silver Lake, Barron County, Wis., for monitoring years 

2005 and 2006......................................................................................................................23

16. Monthly total water inputs and outputs plus storage change for 

Silver Lake, Barron County, Wis., based on results from the water balance..........24

17. Total monthly phosphorus input from three main tributaries and the 

ungaged nearshore area to Silver Lake, Barron County, Wis. ..................................26 

18. Photographs showing erosion at two locations on Silver Lake, Barron County, Wis. 

A, Site 3 near the county park. B, Site 21................................................................................27
v

19–20. Graphs showing:

19. Phosphorus budgets for Silver Lake, Barron County, Wis., for monitoring 

years 2005 and 2006...........................................................................................................28

20. Measured and simulated average summer near-surface concentrations 

of A, total phosphorus, B, chlorophyll a, and C, Secchi depths in 

Silver Lake, Barron County, Wis., in response to various phosphorusloading scenarios ..............................................................................................................31

Tables

1. Morphometric characteristics of Silver Lake, Barron County, Wis., 

at three elevations........................................................................................................................2

2. History of known land-use changes near Silver Lake, Barron County, Wis., and

water diversions into the Silver Lake watershed....................................................................5

3. Average near-surface water quality and trophic state index values for 

Silver Lake, Barron County, Wis. .............................................................................................13

4. Water budget for Silver Lake, Barron County, Wis., for monitoring years 

2005 and 2006...............................................................................................................................17

5. Phosphorus budget for Silver Lake, Barron County, Wis., for monitoring years 

2005 and 2006...............................................................................................................................25 

6. Estimated water quality in Silver Lake, Barron County, Wis., in response to 

various phosphorus-loading scenarios based on the Canfield and Bachman 

natural-lake model and Carlson trophic-state-index equations.........................................30
vi

Conversion Factors and Abbreviations

Multiply By To obtain

Length

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

acre 0.004047 square kilometer (km2)

Volume

cubic foot (ft3) 0.02832 cubic meter (m3

) 

acre-foot (acre-ft) 1,233 cubic meter (m3)

Mass

pound, avoirdupois (lb) 0.4536 kilogram (kg) 

ton, short (2,000 lb) 0.9072 megagram (Mg) 

Miscellaneous rates and yields

inch per day (in/d) 25.4 millimeter per day (mm/d)

inch per year (in/yr) 25.4 millimeter per year (mm/yr)

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

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

pound per year (lb/yr) 0.4536 kilogram per year (kg/yr)

pound per cubic ft (lb/ft3) 0.01602 gram per cubic centimeter (g/cm3)

pounds per square mile per year 

(lb/mi2/yr)

0.1751 kilograms per square kilometer per 

year (kg/km2/yr)

Temperature in degrees Celsius (°C) may be converted to degrees Fahrenheit (°F) as follows:

°F=(1.8×°C)+32

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

25 °C).

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

or micrograms per liter (μg/L).

Concentrations of chemicals in soil and sediment are given in milligrams per kilogram (mg/kg).

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

(NGVD 29).
vii

Acknowledgments

Technical Reviewers

Timothy Asplund, Statewide Limnologist, Wisconsin Department of Natural Resources, 

Madison, Wis.

Paul F. Juckem, Hydrologist, U.S. Geological Survey, Middleton, Wis.

Local Project Coordinators

Dale Hanson, County Conservationist, Barron County Soil and Water Conservation Department, 

Barron, Wis.

Pamela Toshner, Water Resources Management Specialist, Wisconsin Department of Natural 

Resources, Spooner, Wis.

Editorial and Graphics

C. Michael Eberle, Technical Writer-Editor, U.S. Geological Survey Columbus Publishing Service 

Center, Columbus, Ohio

Michelle M. Greenwood, Reports Specialist, U.S. Geological Survey, Middleton, Wis.

James L. Kennedy, Geographer, U.S. Geological Survey, Middleton, Wis.

Laura L. Nelson, Science Support Assistant, U.S. Geological Survey, Middleton, Wis.

Data Collection

Tom Popowski, Hydrologic Technician (retired), U.S. Geological Survey, Rice Lake, Wis.

Josef G. Schuler, Hydrologic Technician, U.S. Geological Survey, Rice Lake, Wis.

Bernard Lenz, Hydrologist, U.S. Geological Survey, Rice Lake, Wis.

Approving Official

Kevin J. Breen, Acting Bureau Approving Official, U.S. Geological Survey, 

New Cumberland, Penn. 

Abstract

Silver Lake is typically an oligotrophic-to-mesotrophic, 

soft-water, terminal lake in northwestern Wisconsin. A terminal lake is a closed-basin lake with surface-water inflows but 

no surface-water outflows to other water bodies. After several 

years with above-normal precipitation, very high water levels 

caused flooding of several buildings near the lake and erosion 

of soil around much of the shoreline, which has been associated with a degradation in water quality (increased phosphorus 

and chlorophyll a concentrations and decreased water clarity). To gain a better understanding of what caused the very 

high water levels and degradation in water quality and collect 

information to better understand the lake and protect it from 

future degradation, the U.S. Geological Survey did a detailed 

study from 2004 to 2008. This report describes results of the 

study; specifically, lake-water quality, historical changes in 

water level, water and phosphorus budgets for the two years 

monitored in the study, results of model simulations that demonstrate how changes in phosphorus inputs affect lake-water 

quality, and the relative importance of changes in hydrology 

and changes in the watershed to the water quality of the lake.

From 1987 to about 1996, water quality in Silver Lake 

was relatively stable. Since 1996, however, summer average 

total phosphorus concentrations increased from about 0.008 

milligrams per liter (mg/L) to 0.018 mg/L in 2003, before 

decreasing to 0.011 mg/L in 2008. From 1996 to 2003, Secchi 

depths decreased from about 14 to 7.4 feet, before increasing 

to about 19 feet in 2008. Therefore, Silver Lake is typically 

classified as oligotrophic to mesotrophic; however, during 

2002–4, the lake was classified as mesotrophic to eutrophic.

Because productivity in Silver Lake is limited by phosphorus, phosphorus budgets for the lake were constructed for 

monitoring years 2005 and 2006. The average annual input 

of phosphorus was 216 pounds: 78 percent from tributary and 

nearshore runoff and 22 percent from atmospheric deposition. Because Silver Lake is hydraulically mounded above the 

local groundwater system, little or no input of phosphorus to 

the lake is from groundwater and septic systems. Silver Lake 

had previously been incorrectly described as a groundwater 

flowthrough lake. Phosphorus budgets were constructed for a 

series of dry years (low water levels) and a series of wet years 

(high water levels). About 6 times more phosphorus was input 

to the lake during wet years with high water levels than during 

the dry years. Phosphorus from erosion represented 13–20 

percent of the phosphorus input during years with very high 

water levels.

Results from the Canfield and Bachman eutrophication 

model and Carlson trophic state index equations demonstrated 

that water quality in Silver Lake directly responds to changes 

in external phosphorus input, with the percent change in chlorophyll a being about 80 percent of the percent change in total 

phosphorus input and the change in Secchi depth and total 

phosphorus concentrations being about 40 and 50 percent of 

the percent change in input, respectively. Therefore, changes 

in phosphorus input should impact water quality. Specific 

scenarios were simulated with the models to describe the 

effects of natural (climate-driven) and anthropogenic (humaninduced) changes. Results of these scenarios demonstrated that 

several years of above-normal precipitation cause sustained 

high water levels and a degradation in water quality, part of 

which is due to erosion of the shoreline. Results also demonstrated that 1) changes in tributary and nearshore runoff have 

a dramatic effect on lake-water quality, 2) diverting water into 

the lake to increase the water level is expected to degrade the 

water quality, and 3) removal of water to decrease the water 

level of the lake is expected to have little effect on water 

quality.

Fluctuations in water levels since 1967, when records 

began for the lake, are representative of what has occurred 

since 1900; fluctuations of about 4 to 10 feet occurred about 

every 15 years. During periods of sustained low water levels 

caused by a series of dry years and low runoff, the lake 

probably was oligotrophic to mesotrophic, whereas during 

sustained high water levels caused by a series of wet years 

and high runoff, water quality of the lake degraded and the 

lake probably was mesotrophic to eutrophic. Therefore, the 

recent degradation in water quality is consistent with possible 

Water Quality and Hydrology of Silver Lake, 

Barron County, Wisconsin, With Special Emphasis on 

Responses of a Terminal Lake to Changes in Phosphorus 

Loading and Water Level

By Dale M. Robertson, William J. Rose, and Faith A. Fitzpatrick
2 Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin

past occurrences associated with high water levels. During 

the 1940s and 1950s, because of high phosphorus inputs from 

agriculture in the watershed, the lake may have been typically 

classified as mesotrophic to eutrophic and possibly classified 

as moderately eutrophic during years with high water levels, 

especially around 1945 and 1954 when water levels were 

likely to have been very high. 

As of 2008, Silver Lake is typically oligotrophic to 

mesotrophic because of the relatively small contributions of 

phosphorus from its watershed, although its water quality 

changes dramatically because of natural changes in water and 

phosphorus inputs during years of high runoff. Because of the 

limited phosphorus that is presently input into the lake, small 

increases in phosphorus input could have a very large effect on 

lake-water quality. Therefore, management actions to minimize future phosphorus input to this lake are likely to have 

great effect on maintaining the quality of its water.

Introduction

Silver Lake is a deep, soft-water lake in northwestern 

Wisconsin. Several years with above-normal precipitation 

caused increased runoff and very high water levels in the lake 

during 2001–4. The high water levels, in turn, caused extensive erosion and flooding of homes and cottages near the lake. 

In addition, on the basis of data collected by the Citizen Lake 

Monitoring Network (Citizen Monitoring; Wisconsin Department of Natural Resources, 2008), the water quality of the lake 

degraded during the period with highest water levels: phosphorus and chlorophyll a (algae) concentrations were higher 

and water clarity was worse during 2002–4 than during 1988–

98. Local residents were unsure whether the cause of increased 

water level was only above-normal precipitation and whether 

the cause of degraded water quality was increased runoff and 

high water levels or some anthropogenic (human-induced) 

factor(s) in the watershed. A detailed study, described in this 

report, was done from 2004 to 2008 by the U.S. Geological Survey (USGS) to (1) aid in understanding what caused 

the high water levels in the lake and degradation of its water 

quality and (2) find evidence as to whether such changes have 

occurred in the past. This study was done in cooperation with 

the Barron County Soil and Water Conservation Department 

and was partially funded through the Lake Protection Grant 

Program of the Wisconsin Department of Natural Resources 

(WDNR) and the Cooperative Water Program of the USGS.

Silver Lake and Its Watershed

Silver Lake (fig. 1)—a natural, closed-basin, terminal 

lake in Barron County, in northwestern Wisconsin—is about 

5 mi northeast of Cumberland, Wis., and 9.5 mi northwest 

of Rice Lake, Wis. A closed-basin lake has no surface-water 

outflows, and a terminal lake is a closed-basin lake that has 

inflowing streams. Precipitation that falls within the watershed 

of a closed-basin lake does not flow out of the basin and leaves 

the lake only by evaporation and seepage into the underlying 

groundwater system. Silver Lake is typically oligotrophic to 

mesotrophic, meaning it does not contain an abundance of 

nutrients (phosphorus and nitrogen compounds); it is characterized by relatively clear, deep water and low-to-moderate 

primary productivity. Mesotrophic and oligotrophic lakes are 

extremely sensitive to increases in phosphorus input (Newton 

and Jarrell, 1999).

The area and volume of Silver Lake were given on the 

1967 Wisconsin Conservation Department lake survey map as 

336.7 acres and 12,793 acre-ft, respectively. In this study, the 

morphometry of the lake was reevaluated on the basis of an 

aerial image obtained in 2005 from the National Agricultural 

Imagery Program (U.S. Department of Agriculture, 2006). In 

2005, the lake was near full volume, similar to when the original map was constructed in 1967. The resulting surface area 

of the lake was determined to be 355 acres and the volume to 

be 12,654 acre-ft (table 1). These values are slightly different 

from the original 1967 estimates. All the calculations in this 

study are based on the recently estimated morphometry. Given 

that the water level of the lake fluctuates widely, the morphometric information for the lake was also computed for elevations 3 ft greater and 5 ft less than in 2005 (table 1).

The natural drainage area of Silver Lake is 1,800 acres 

(fig. 1). During several periods after 1934, however, part or all 

the water from the Sylvan Lake watershed (just north of the 

Silver Lake watershed in fig. 1) was diverted into Silver Lake 

(discussed in detail below). If the Sylvan Lake watershed is 

included, the total area draining to Silver Lake increases to 

4,490 acres. The land cover of the natural watershed (based 

on data from Homer and others, 2007) is primarily a mixture 

of forest (76 percent), wetlands (7 percent), and pasture/grassland/agriculture (9 percent). The Sylvan Lake watershed contains more pasture/grassland/agriculture (31 percent) than does 

the natural Silver Lake watershed. The soil in the Silver Lake 

watershed consists primarily of a hilly, moderately permeable, Milaca-Cloquet peat complex (from midlake northward); 

Table 1. Morphometric characteristics of Silver Lake, Barron County, Wis., at three elevations. 

[Altitude of the local datum is 1165.31 feet above the National Geodetic Vertical Datum of 1929]

Elevation 

(feet above a local datum)

Area 

(acres)

Length 

(miles)

Width 

(miles)

Maximum depth

(feet)

Mean depth 

(feet)

Volume 

(acre-feet)

90.18 371 1.57 0.37 94 37.4 13,845

87.181 355 1.57 .37 91 35.6 12,654

82.18 317 1.54 .37 86 34.6 10,974

1

 Elevation of lake for morphometric map in Figure 2.
Introduction 3

Figure 1. Aerial photograph of Silver Lake, Barron County, Wis., with its watershed delineated. The area from which surface water has 

been diverted into the Silver Lake watershed also is delineated with a yellow line. 

Sylvan Lake

Wildlife Area

Grassy Lakes

Wildlife Area

Grassy Lakes

Silver

Lake

Silver

Lake

Little North Lake

0 0.25 0.5 MILES

0 0.25 0.5 KILOMETERS

Figure 1. Aerial photograph of Silver Lake, Barron County, Wis., with its watershed delineated. The area from which surface water 

has been diverted into the Silver Lake watershed also is delineated with a yellow line. 

Aerial image from U.S. Department of Agriculture, 2006

Study area

Flow to the

Yellow River

Flow to the

Yellow River

91°59' 91°54'

45°35'

45°39'

WISCONSIN

Rice Lake

Cumberland

Yellow RiverYellow River

Silver Lake original 

drainage basin

Area diverted into 

Silver Lake watershed

Streams

EXPLANATION
4 Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin

however, the extreme southern part of the watershed is a 

relatively flat, with moderate to very permeable mixture of 

Campia silt loam and Chetak sandy loam soils (from midlake 

southward; U.S. Department of Agriculture, 1958). Although 

the surficial soils are moderately permeable, well logs indicate 

a poorly permeable layer of till below these soils just north of 

the lake.

Before 1900, the land cover around Silver Lake was 

primarily pristine forests and wetlands; however, beginning in 

the early 1900s, agriculture began to spread throughout most 

of the flatter parts of the region, including the southern part 

of the Silver Lake watershed (table 2). By the early 1950s, 

agriculture in the watershed peaked, with more than half of the 

area immediately adjacent to the lake being used for farming 

(based on the 1951 aerial photograph), including at least three 

small herds of cattle (Edward Jacobson, local resident, oral 

commun., 2008). One dairy farm was on the southwest shore 

of the lake, and each day about 25 cows were moved along the 

shore to a nearby pasture. In addition, about 20 head of cattle 

were pastured on the southeast shoreline, and 20–25 head of 

cattle were pastured just north of the lake. The cattle on the 

southeast shoreline had direct access to the lake. In the early 

1960s, most of the agriculture in the watershed was discontinued. In the 1960s, weedbeds were more prevalent in the lake 

than in 2008, and the bay on the extreme southeast part of 

the lake was dredged (Edward Jacobson, local resident, oral 

commun., 2008). A Wisconsin Conservation Department lake 

survey map shows 86 cottages and permanent homes near the 

lake in 1967. The number of cottages and permanent homes 

has been relatively stable since the 1970s, increasing to just 

over 100 in 2008 (Robert Wenzel, local resident, written commun., 2008). Several residents, however, have replaced small 

seasonal structures with large, year-round structures.

Large fluctuations in water level have been documented 

in Silver Lake since the 1930s. Residents around the lake have 

tried to modify the extremes in water levels, especially the low 

water levels. Before 1934, the magnitude of fluctuations in 

water level was driven primarily by climatic variations. During the drought in the early 1930s (Dust Bowl years), water 

levels were very low, which resulted in cottages being built 

near the lake, including a small cottage on a small island in 

the northwest end of the lake. To try to increase the very low 

water levels, a ditch was dug sometime around 1934 between 

the Grassy Lakes Wildlife Area and Little North Lake and 

between Little North Lake and Little South Lake to divert 

water that normally flows from Sylvan Lake to the Yellow 

River into Silver Lake (R.R. Read, local resident, written 

commun., 1943). To increase the flow through this channel, 

a berm was built between the Grassy Lakes Wildlife Area 

and the natural flow path to the Yellow River. A history of the 

use of this diversion is summarized in table 2. The ditch has 

intermittently increased the drainage area and input of water 

(and nutrients) to Silver Lake. In the 1950s, two small dams 

with boarded openings were constructed to control the flow 

through these channels (D. Hanson, Barron County Soil and 

Water Conservation Department, written commun., 1996). The 

specific periods when this diversion was used were not able 

to be determined; however, the diversion was documented to 

have been used between the late 1930s and early 1940s, and 

between the late 1990s and September 16, 2003, when the 

ditch was permanently filled with stone and gravel (Silver 

Lake Association, 2003).

In the interest of managing the water level of Silver Lake 

and protecting its water quality, the Silver Lake Association 

was formed in the mid 1990s. The purpose of the Association 

is to promote a sense of community, to address various environmental and/or public-nature issues, to promote safety in 

lake use, and to help educate its members and nonmembers on 

lake preservation. During 2001–4, high water levels in Silver 

Lake caused flooding of many homes and cottages and erosion 

of shoreline around parts of the lake. In addition, the high 

runoff and high water levels apparently caused deterioration in 

the water quality of the lake. It was believed that water being 

diverted from Sylvan Lake was part of the reason for the high 

water and that nutrients (phosphorus) in the diverted water 

helped degrade the water quality of Silver Lake (D. Hanson, 

Barron County Soil and Water Conservation Department, written commun., 1996). The Silver Lake Association and the Barron County Soil and Water Conservation Department worked 

together to permanently fill the upstream diversion ditch (work 

completed in September 2003) and to find funds for a study to 

describe the factors affecting the water quality of Silver Lake. 

The main goals of the study were to (1) determine whether 

the wide fluctuations in water level were natural phenomena 

or caused primarily by increased input through the diversion 

ditch and (2) to determine whether the deterioration in lakewater quality during 2002–4 was caused by the high water 

levels or by changes in human activity in the watershed.

Effects of Changes in Nutrient Loading, Water 

Level, and Climate on Water Quality

Degradation in water quality (trophic conditions) of many 

lakes is caused by an increase in nutrient inputs from their 

watersheds. The effects of nutrient loading (input of nutrients 

over a specified period of time) are sufficiently understood that 

empirical eutrophication models can be used to predict in-lake 

phosphorus and chlorophyll a concentrations and water clarity 

(Secchi depth) from external phosphorus loading (Reckhow 

and Chapra, 1983; Cooke and others, 1993; Panuska and 

Kreider, 2003). Most of these models were derived from 

analyses of many lakes with widely differing loading rates 

and hydrologic conditions (for example, Vollenweider, 1975; 

Canfield and Bachmann, 1981); however, Lathrop and others (1998; 1999) also developed response models based on 

changes in nutrient loading to a specific lake––Lake Mendota, 

Wisconsin. 

Changes in nutrient inputs to lakes are usually associated with changes in anthropogenic factors in the watershed, 

such as changes in land use or inputs from point sources (for 

example, pipe discharge from a factory or wastewater-treatment plant); however, changes in nutrient inputs also occur 

naturally as a function of hydrologic changes. For example, 
Introduction 5

more nutrients are typically delivered to a lake during wet 

years than during dry years. In addition, Lathrop and others 

(1998) demonstrated that water quality in Lake Mendota, Wis., 

had a larger response following a series of wet or dry years 

than during a single unusual year. Therefore, a few years may 

pass before a lake comes into equilibrium with inputs from 

its watershed. After a series of wet years, additional sources 

of nutrients can develop, such as shoreline erosion caused by 

increased water level, increased runoff from wetlands around 

a lake, or increased nutrient release from nutrient-rich soils 

or old septic systems near the lake when groundwater levels 

increase or nearshore areas are flooded (Leira and Cantonati, 

2008). Therefore, persistent extremes in precipitation and 

runoff can result in changes in water level that can affect the 

water quality of lakes.

Changes in water levels are natural phenomena for most 

lakes; however, global climate change may have lake-level 

implications and may have already affected the extent of 

water-level fluctuations in lakes (Wantzen and others, 2008). 

Many scientists believe, based on results from General Circulation Models, that climate change will either cause systematic 

decreases or increases in the hydrologic budgets and water 

levels of lakes or cause water levels to fluctuate more widely 

than they have previously, in response to larger fluctuations 

in precipitation and runoff (Mulholland and Sale, 1998; Bates 

and others, 2008). Predicting the effects of climate change 

on a particular lake from large global and regional circulation models is difficult because a lake’s hydrological cycle 

involves many interrelated components, including precipitation patterns, water temperatures, evaporation rates, groundwater inputs and outputs, and surface-water flow rates (Wittman, 2008). Scientists believe, however, that closed-basin 

lakes, such as Silver Lake, are most vulnerable to changes in 

climate because of their sensitivity to changes in the balance 

of inflows and evaporation (Bates and others, 2008). Results 

from some circulation models indicate that seasonal precipitation patterns will change, resulting in more precipitation in 

winter and less in summer, which could cause groundwater 

levels to increase and cause a rise in the water levels of lakes 

that have large groundwater inputs. Increased air temperatures, 

however, may cause an increase in evapotranspiration and 

cause water levels to drop (Wittman, 2008).

In addition to affecting a lake’s hydrology and water 

level, climate change may also affect lake-water quality in 

other ways because of warming air temperatures (Bates and 

others, 2008). Increased air temperatures will increase water 

Table 2. History of known1 land-use changes near Silver Lake, Barron County, Wis., and water diversions into the Silver Lake 

watershed.

Year(s) Action Expected upstream flow Expected change in phosphorus 

loading

Land use and land-use changes

Prior to 1900 Natural forest. Background Background

About 1900 Agriculture begins in watershed. Slight increase Slight increase

1940s–1950s Agriculture peaks in watershed. Slight increase Large increase

Mid 1960s Agriculture mostly ending in watershed and 

homes and cottages built near lake.

Slight decrease Moderate decrease

2000s Minimal pastureland (north of lake) and 

homes and cottages surround lake.

Slight decrease Slight decrease

Water diversions into the watershed

Prior to about 

1934

Natural flow to the Yellow River as evidenced 

by many large old trees near lake.

No Sylvan Lake water Background

About 1934 – 

about 1940

Dams built stopping flow to the Yellow River 

and ditches dug to Silver Lake.

All Sylvan Lake water Large increase

1942 Some water going into the Yellow River. Most of Sylvan Lake water 

(about 75 percent)

Moderate increase

1943 Temporary ditches dammed. All natural flow 

diverted to the Yellow River.

No Sylvan Lake water Background

1950s Two small dams built in the ditches. Dam 

in wetland washed out. All natural flow 

diverted to the Yellow River.

No Sylvan Lake water Background

1997 Channels to Silver Lake opened. Most of the 

natural flow diverted to Silver Lake.

Most Sylvan Lake water Large increase

2003 Diversion completely filled with gravel in late 

summer.

No Sylvan Lake water Background

1

 Additional undocumented land-use changes and diversions may have occurred.
6 Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin

temperatures which, in turn, may stimulate algal blooms. 

Increased air temperatures will also decrease the duration of 

ice cover and increase the length of the growing season; which 

in turn, may result in a longer growth period for macrophytes 

(rooted aquatic plants). The longer growing season, however, may result in the available nutrients being depleted and 

fewer algal blooms later in the year. Only a few studies have 

examined how changes in water level affect the water quality 

of lakes (Leira and Cantonati, 2008), and these studies mainly 

examined changes in primary ions and alkalinity (for example, 

Webster and others, 1996; White and others, 2008).

The recent degradation in water quality of Silver Lake 

that occurred in conjunction with high water levels has led to 

several questions: Were the recent changes in water quality 

caused by changes in the watershed, or were they caused by 

changes in precipitation leading to more runoff and higher 

water level? Were the recent extremes in water level caused 

by global climate change or were they caused by the diversion of water from Sylvan Lake? And, are the recent changes 

in water level and water quality indicative of what may occur 

in the future? Determining whether climate change caused the 

changes in water levels of Silver Lake or exactly what type 

of climatic changes may occur in the future may be difficult; 

therefore, examining how conditions leading to lower and 

higher water levels affect the water quality of Silver Lake is 

important.

Several approaches can be used to predict how the water 

quality of a specific lake may respond to hydrologic changes 

and future climate change. One approach is to examine how 

the lake has responded to conditions leading to past changes in 

water level, if data are sufficient for such an analysis. Another 

approach is to use numerical models to simulate how the lake 

should respond to specific climate scenarios. A third approach 

is to try to determine how water quality of the lake responds 

to a range of conditions, such as those leading to low and high 

water levels.

 Purpose and Scope

The primary purpose of this report is to provide an interpretation of what may have caused the degradation in water 

quality of Silver Lake (as detected by the ongoing monitoring 

program) and, therefore, furnish information that can be used 

by managers to protect this lake in the face of increased developmental pressure and possible climatic changes. This report 

(1) describes the water quality of Silver Lake, (2) describes 

changes in its water level since 1900, (3) quantifies water and 

phosphorus budgets for the lake on the basis of data collected 

from November 2004 through October 2006 and also includes 

an estimate of erosion occurring during the high water levels 

of 2001–3, (4) presents the results of model simulations that 

demonstrate the potential effects of changes in phosphorus 

inputs on lake-water quality, and (5) examines how climatic 

changes (hydrologic changes in the watershed and changes in 

water level) and potential strategies in managing water levels 

may affect the water quality of the lake.

The water-quality data and water and phosphorus budgets described in this report improve the understanding of the 

hydrologic system of Silver Lake and aid in the understanding 

of how changes in the water levels and nutrient loading affect 

the water quality of closed-basin terminal lakes. Results of the 

study should be useful to local managers in the preparation of 

a comprehensive lake-management plan. In addition, results of 

the study add to the database of lakes for which detailed hydrologic, phosphorus-loading, and lake-water-quality information 

are available to compare with other lakes in the region.

Study Methods and Sampling Sites

USGS personnel collected lake, groundwater, and meteorological data from 2004 to 2006. In addition, water-quality 

data for the lake were collected by the WDNR from 1987 

to 1998 as part of their long-term trend-monitoring program 

(Wisconsin Department of Natural Resources, 2006) and from 

1987 to 2008 by volunteers from the community as part of the 

WDNR’s Wisconsin Citizen Lake Monitoring Network (Wisconsin Department of Natural Resources, 2008). Data collected 

by the WDNR were furnished by J. Vennie (Wisconsin Department of Natural Resources, written commun., 2006), and 

Citizen Lake Monitoring data were obtained from the WDNR’s 

Web site (Wisconsin Department of Natural Resources, 2008). 

All available data—but primarily near-surface concentrations 

of total phosphorus and chlorophyll a, plus Secchi depths—

were used to describe the lake-water quality and characterize 

long-term changes in water quality; however, only data collected from November 1, 2004, to October 31, 2006, were used 

to describe the hydrology and phosphorus inputs to the lake. 

This latter period was divided into two monitoring years (MY): 

November 2004 through October 2005 (hereafter referred 

to as MY 2005) and November 2005 through October 2006 

(hereafter referred to as MY 2006). Little input of phosphorus 

from erosion occurred during the intense monitoring period; 

therefore, to estimate the potential input of phosphorus from 

erosion during periods of high water level, a separate erosion 

study was done during May 2005.

Lake-Stage and Water-Quality Monitoring

A continuously recording (15-minute interval) lake-stage 

gage was installed just south of the public boat landing on the 

south side of the lake (fig. 2). Lake stage was monitored by 

means of a gas-purge system with a pressure transducer. The 

gage was operated for the 2-year monitoring period.

From 1987 to 1998, the WDNR sampled the lake in 

spring, summer (monthly from May through September), and 

late winter. During 2005 and 2006, the USGS sampled the lake 

in spring and summer (monthly from May through September). The USGS and WDNR protocols for sampling the lake 

were similar. During each visit, profiles of water temperature, 

dissolved oxygen, specific conductance, and pH were collected 
Study Methods and Sampling Sites 7

Figure 2. Aerial photograph of Silver Lake, Barron County, Wis., with sampling locations and 10-ft bathymetric contours identified. 

L

K

M

N

A

3

4

L

K

J

I

H

G

E

F

D

C

B

M

N

A

5

6

7

1

3

4

2

Figure 2. Aerial photograph of Silver Lake, Barron County, Wis., with sampling locations and 10-ft bathymetric contours identified.

Aerial image from U.S. Department of Agriculture, 2006

Nearshore piezometer 

with identifier

Silver Lake nearshore area

Bathymetric contour, 10-foot

interval

Lake-stage monitoring site 

Lake-sampling site

Tributary monitoring site

with identification number

Ancillary tributary monitoring site

with identification number

Domestic well

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

Silver

Lake

Silver

Lake



7

7 

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A 

45°34'

45°36'

91°56' 91°54'

EXPLANATION

0 0.25 0.5 MILES

0 0.25 0.5 KILOMETERS

10

20

30

40

50

60

70

80 90

50
8 Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin

with a multiparameter meter, and water clarity was measured 

with a standard 7.9-in.-diameter black and white Secchi disk 

(Secchi depth). Near-surface samples, which were collected 

with a Van Dorn sampler by the USGS and a Kemmerer 

sampler by the WDNR, were analyzed for total phosphorus 

and chlorophyll a concentrations. Near-bottom samples were 

collected about 3 ft above the sediment-water interface and 

were analyzed for total phosphorus concentration. Additional 

water samples were collected during spring by the USGS and 

analyzed for nutrients, common ions, and other characteristics 

such as color, turbidity, alkalinity, total dissolved solids, and 

silica. In addition, volunteers from the community (Citizen 

Monitoring) measured Secchi depths from 1987 to 2008 and 

total phosphorus and chlorophyll a concentrations from 2002 

to 2008, in accordance with protocols described by Betz and 

Howard (2005). All water-quality data were collected near the 

deepest location in the lake (fig. 2).

Sampling by the USGS was done by the Lake Studies 

Team of the USGS Wisconsin Water Science Center. This 

team implements a quality-assurance plan each year that 

involves collecting three types of samples from a subset of 

the lakes studied each year, which include blanks, replicates, 

and spikes (U.S. Geological Survey, Wisconsin District Lake 

Studies Team, 2006; 2007). During the monitoring period, the 

replicates for total phosphorus were within 0.006 mg/L over 

a wide range in concentrations (except for one replicate from 

a eutrophic lake that was within 0.02 mg/L) and replicates for 

chlorophyll a were within 18 percent of each other. Concentrations of total phosphorus and chlorophyll a in the blanks 

analyzed in 2005 and 2006 were below the laboratory’s detection limits (0.005 mg/L for total phosphorus and 0.26 μg/L for 

chlorophyll a).

All lake samples were analyzed by the Wisconsin State 

Laboratory of Hygiene in accordance with standard analytical 

procedures described in the “Manual of Analytical Methods, 

Inorganic Chemistry Unit” (Wisconsin State Laboratory of 

Hygiene, 1993). Lake-stage and water-quality data collected 

by the USGS were published in the annual data report series 

“Water Quality and Lake-Stage Data for Wisconsin Lakes,” 

water years 2005 and 2006 (U.S. Geological Survey, Wisconsin District Lake Studies Team, 2006; 2007).

Lake Classification

One method of classifying the water quality of a lake is 

by computing trophic state index (TSI) values based on nearsurface concentrations of total phosphorus and chlorophyll a, 

along with Secchi depths, as developed by Carlson (1977). 

TSI values were developed to place these three characteristics on similar scales to allow comparison among lakes. 

TSI values based on total phosphorus concentrations (TSIP), 

chlorophyll a concentrations (TSIC), and Secchi depths (TSISD) 

were computed for each sampling by use of equations 1–3. 

The individual index values were averaged monthly, and the 

monthly average values were then used to compute summer 

(May through September) average TSI values:

TSIP = 4.15 + 14.42 [ln total phosphorus 

(in micrograms per liter)], (1)

TSIC = 30.6 + 9.81[ln chlorophyll a

(in micrograms per liter)], and (2)

TSISD = 77.12 – 14.41[ln Secchi depth 

(in feet)]. (3)

Oligotrophic lakes have TSI values less than 40, a limited 

supply of nutrients, very high clarity, low algal populations, 

and low phosphorus concentrations, and they generally contain 

oxygen throughout the year in their deepest zones (Carlson, 

1977). Mesotrophic lakes have TSI values between 40 and 50, 

a moderate supply of nutrients, moderate clarity, a tendency 

to produce moderate algal blooms, and oxygen is occasionally 

depleted in the deepest zones of the lake. Eutrophic lakes have 

TSI values greater than 50, a large supply of nutrients, and 

severe water-quality problems—such as low clarity and frequent seasonal algal blooms—and oxygen is typically depleted 

in the deeper zones of the lake.

Stream Monitoring

Flows from three small tributaries to Silver Lake (tributaries 2, 3, and 7) were measured intermittently at sites 2, 3, 

and 7 (fig. 2) at approximately monthly intervals. The measured flows were statistically related to the daily average flows 

measured in the Yellow River at Barron, Wis., to develop 

regression relations between flow in the Yellow River and flow 

in each tributary. The regression relations for each site and 

the daily flows in the Yellow River were then used to estimate 

daily flows in each tributary. Temporally varying offsets were 

applied to all estimated flow data to force the estimated flows 

to equal those measured in the tributaries. Flows in four additional tributaries (tributaries 1, 4, 5, and 6) were also measured 

intermittently (fig. 2). Flow was zero or negligible at these 

sites during most of the visits except during snowmelt runoff. 

Flows at these sites did not correlate very well with flow in 

the Yellow River; therefore, runoff in these four tributaries 

were combined with runoff from the other ungaged near-lake 

areas and collectively were estimated as the amount of flow 

needed to balance the water-budget mass-balance equation 

during the snowmelt-runoff period of each monitoring year. 

Water samples at the stream sites were collected manually by 

means of the Equal-Width-Increment (EWI) method (Edwards 

and Glysson, 1999) or the grab method and were analyzed 

for concentrations of total phosphorus. In addition, four grab 

samples were collected near the outlet of Sylvan Lake during 

the spring of 2006 and analyzed for total phosphorus to determine the phosphorus concentration of water prior to entering 

the wetland system north of the lake.

Daily phosphorus loads for tributaries 2, 3, and 7 were 

determined by multiplying temporally varied concentrations 
Study Methods and Sampling Sites 9

(linearly interpolated between intermittently measured concentrations) multiplied by the estimated daily flows. Loads for 

the combined runoff from tributaries 1, 4, 5, and 6 and other 

near-lake ungaged areas were determined by multiplying the 

combined runoff by the flow-weighted average concentration 

of all samples collected in all tributaries during each monitoring year.

All stream samples were analyzed by the Wisconsin State 

Laboratory of Hygiene in accordance with standard analytical 

procedures described in the “Manual of Analytical Methods, 

Inorganic Chemistry Unit” (Wisconsin State Laboratory of 

Hygiene, 1993). All flow and concentration data were published in the annual USGS Water-Data Report series (Waschbusch and others, 2005; 2006).

Meteorology and Atmospheric Deposition Data

During the 2-year study period, precipitation was 

measured continuously (at 15-minute intervals) during most 

nonfreezing periods at the lake-stage monitoring site (fig. 2). 

During periods when continuous recorded precipitation data 

were not available, precipitation was estimated by averaging 

the daily data from the National Weather Service (NWS) stations (National Climatic Data Center, 2004–6) at Cumberland, 

Wis. (about 5 mi southwest of the lake) and Rice Lake, Wis. 

(about 9.5 mi southeast of the lake). Other meteorological data 

needed for simulating the thermal structure of the lake and 

computing daily evaporation rates were obtained from meteorological stations in the area operated by the USGS, WDNR, 

and the NWS. Daily total snowfall and average air temperature were obtained from the NWS station at Cumberland, Wis. 

Average daily wind speeds were obtained by averaging the 

data from the WDNR weather stations (James Barnier, Division of Forestry, unpublished data; http://www.dnr.state.wi.us/

forestry/fire/weather/ ) at Minong, Wis. (about 35 mi north of 

Silver Lake) and Ladysmith, Wis. (about 40 mi southeast of 

Silver Lake). Total daily solar radiation data were obtained 

from a continuously recording meteorological station installed 

on a small peninsula in Whitefish Lake (about 40 mi north of 

Silver Lake) by the USGS (Robertson and others, 2009). 

Phosphorus deposition on Silver Lake was determined 

from phosphorus concentrations measured in wetfall (rain and 

snow) and phosphorus dryfall deposition rates, both of which 

were measured at the USGS meteorological station on Whitefish Lake and operated during the entire 2-year monitoring 

period (Robertson and others, 2009). Wet samples were collected after a period with rainfall or snowfall, and dry samples 

were collected after several days (usually 7–10 days) with no 

precipitation. Phosphorus in precipitation was computed as the 

product of precipitation on the surface area of Silver Lake and 

the estimated seasonal phosphorus concentrations measured 

for snow (0.009 mg/L) and rain (0.017 mg/L). Phosphorus in 

dryfall was estimated from the surface area of Silver Lake and 

deposition rates measured at Whitefish Lake for a lake with 

few conifers in the surrounding area (26.1 lb/mi2/yr).

Groundwater Monitoring

Fourteen shallow piezometers (0.5-in.-diameter observation wells) were installed around the periphery of the lake 

(fig. 2) in November 2004 to help define areas contributing 

groundwater to the lake. These piezometers were installed 2 to 

19 ft from the edge of the lake to depths of 4 to 6 ft. At installation, the piezometers penetrated 3–4.5 ft below the water 

table except at four sites where the water table was too deep 

to be reached. To determine the direction of flow near each 

piezometer, groundwater gradients were determined from the 

differences in water elevation in the piezometers and elevation of the lake surface measured at approximately 3-month 

intervals from November 2004 to November 2006.

Estimation of Nearshore Erosion

A shoreline-erosion study was done during May 17–18, 

2005, to determine the amount of sediment and phosphorus 

delivered to Silver Lake during the high water levels from 

2001 to 2003. It was assumed that during 2001–3, the water 

had risen 2 ft higher than it had during any other recent period. 

As part of this study, the entire shoreline of the lake was 

examined for signs of erosion. Twenty-eight eroding areas 

along the shoreline (ranging from 50 to 950 ft in length and 

more than 2 mi total) were located with a global positioning 

system. Length, width, and estimated depth of retreat were 

measured for each eroding area. Field grading of texture was 

done by rubbing soil between the fingers (Milfred and others, 

1967). The estimated total volume of sediment potentially 

eroded was calculated by summing the estimated eroded sediment from each of the 28 erosion sites. The estimated total 

mass of eroded sediment was computed by multiplying the 

volume of eroded sediment by the average aerated specific 

weight of sand/gravel/clay mixture of 90 lb/ft3 (Chow, 1964; 

table 17-1-5).

Sediment cores were collected by hand from eroding 

shoreline areas and near-shore sandy depositional zones in 

the lake (fig. 3). A subset of core samples selected for laboratory analysis included eight samples from the banks and four 

samples from nearshore deposits. The sediment samples were 

analyzed for total phosphorus and phosphate (milligrams per 

kilogram of sediment) by the Wisconsin State Laboratory of 

Hygiene in accordance with standard analytical procedures 

described in the “Manual of Analytical Methods, Inorganic 

Chemistry Unit” (Wisconsin State Laboratory of Hygiene, 

1993). It was assumed that the difference in phosphorus (and 

phosphate) concentrations from the bank samples and the 

nearby lake-bottom samples was the result of phosphorus 

being released into the lake. 

To determine how the water and phosphorus inputs to 

the lake vary during different hydrologic conditions and the 

relative importance of phosphorus input from erosion during 

periods of very high water levels, water and phosphorus inputs 

were also estimated for 2002, 2003, and during a series of dry 

and wet years.
10 Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin

Figure 3. Aerial photograph of Silver Lake, Barron County, Wis., showing areas for which sediment and phosphorus input from erosion 

were observed and estimated. 

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18

10

28

1

13

19

26

25

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30

Figure 3. Areal photograph of Silver Lake, Barron County, Wis., showing areas for which sediment and phosphorus input 

from erosion were observed and estimated.

Nearshore sample

Bank sample

Eroding zone

11

Aerial image from U.S. Department of Agriculture, 2006

0 0.25 0.5 MILES

0 0.25 0.5 KILOMETERS

91°56' 91°54'

45°36'

45°34'

EXPLANATION

Silver

Lake

Silver

Lake
Measured Lake-Water Quality 11

(May–September) average phosphorus concentration was 

0.013 mg/L in MY 2005 and MY 2006 (table 3). Therefore, 

based on total phosphorus concentrations, Silver Lake would 

be classified as oligotrophic to mesotrophic.

Near-bottom total phosphorus concentrations were 

similar to those near the surface during unstratified periods; 

however, the concentrations increased slightly after the nearbottom water became anoxic in summer and winter (fig. 5). 

Maximum concentrations in late summer in MY 2005 and 

MY 2006 were about 0.08 to 0.06 mg/L, respectively.

Since 1986, near-surface total phosphorus concentrations have ranged from 0.005 to 0.021 mg/L (fig. 4). The two 

concentrations measured in 1986 were 0.02 mg/L. Average 

June–August concentrations then consistently were about 

0.007–0.008 mg/L during 1987–96. Concentrations began 

to increase in 1997 (0.009 mg/L) before reaching a maximum value in 2003 (0.018 mg/L). After 2003, concentrations 

decreased to about 0.010 in 2007 and 2008 (table 3). The 

highest total phosphorus concentrations occurred in 1986 and 

2002–4 (when water levels in the lake were high). Maximum 

annual near-bottom total phosphorus concentrations were 

relatively constant from 1986 to 1998 (fig. 5). Maximum 

concentrations then increased to almost 0.16 mg/L in 2003 and 

gradually decreased to 0.055 mg/L in 2006. The high near-bottom concentrations coincided with the high near-surface total 

phosphorus concentrations measured in the lake.

Near-surface total nitrogen concentrations (computed as 

the sum of Kjeldahl nitrogen and dissolved nitrite plus nitrate) 

were measured during spring from 1988 to 1997 and during 

2005 and 2006. Total nitrogen concentrations ranged from 

about 0.3 to 0.55 mg/L. No consistent trend in concentrations 

was observed.

The ratio of the near-surface concentrations of total nitrogen to total phosphorus (N:P ratio) is often used to determine 

the potential limiting nutrient in a lake. The specific value of 

this ratio that determines which nutrient potentially is limiting differs under different ambient conditions such as water 

temperature, light intensity, and nutrient deficiencies (Correll, 

1998); however, a ratio greater than about 16:1 by weight 

indicates that phosphorus should be the potentially limiting 

nutrient. The N:P ratios for the 1988–1997 data ranged from 

26:1 to 46:1, and ratios for the 2005–6 data ranged from 26:1 

to 35:1. This indicates that phosphorus should typically be 

the potentially limiting nutrient and should be the nutrient of 

concern when considering management efforts to improve or 

prevent degradation of the water quality in Silver Lake.

Chlorophyll a is a photosynthetic pigment found in algae 

and other green plants. Its concentration is commonly used 

as a measure of the density of the algal population in a lake. 

Average concentrations less than 2 μg/L indicate oligotrophic 

conditions, and average concentrations greater than about 

7 μg/L indicate eutrophic conditions (Carlson, 1977). During 

MY 2005 and MY 2006, concentrations ranged from less than 

1 μg/L to about 10 μg/L (fig. 4). The highest concentrations 

were measured in fall; concentrations during summer were 

Measured Lake-Water Quality

Temperature profiles collected in the lake indicated that 

strong thermal stratification develops during summer and thus 

limits the extent of vertical mixing. The maximum temperature in the upper layer of the lake (epilimnion) reached about 

26oC in early August. A thermocline developed in May and 

reached a depth of about 16–23 ft in July before descending in 

late summer and fall. During summer, near-bottom temperatures reached about 7–7.5oC.

Dissolved oxygen concentrations of about 10–11 mg/L 

were near saturation throughout the lake during nonstratified 

periods in spring and about 8 mg/L throughout the epilimnion during summer. Once stratification developed, dissolved 

oxygen concentrations in the lower layer of the lake (hypolimnion) began to decrease. Near-bottom concentrations reached 

0 mg/L by the beginning of August. The maximum extent 

of anoxic conditions (0 mg/L) occurred in September, when 

anoxia reached from the bottom to about 46–50 ft from the 

surface.

Silver Lake has soft water (alkalinity less than 10 mg/L 

as calcium carbonate) with a specific conductance typically 

about 25–26 μS/cm throughout the water column; however, 

when the deep areas became anoxic, the specific conductance 

increased to about 40 μS/cm near the bottom of the lake. The 

pH in the lake typically was about 7.5–8 (standard units) when 

the lake was unstratified, and about 8 in the epilimnion and 6 

in the hypolimnion when the lake was stratified.

Water chemistry in Silver Lake is different from that of 

most northwestern Wisconsin lakes, as described by Lillie and 

Mason (1983), with softer water and lower concentrations of 

most constituents. Lillie and Mason collected data from a random set of 660 Wisconsin lakes, 282 of which were in northwestern Wisconsin. The average concentrations for the northwestern Wisconsin Lakes were 7 mg/L for calcium, 3 mg/L for 

magnesium, 4 mg/L for chloride, and 27 mg/L for alkalinity, 

compared to 2.1, 0.9 or less, 1.2, and 9 mg/L, respectively, for 

Silver Lake. The water color in Silver Lake ranged from 5 to 

20 (platinum-cobalt units; based on two measurements), which 

is less colored than most other northwestern Wisconsin lakes 

(average value of 30).

Phosphorus and nitrogen are essential nutrients for plant 

growth and are the nutrients that usually limit algal growth 

in most lakes. High nutrient concentrations can cause high 

algal populations (blooms); therefore, high nutrient inputs can 

be the cause of accelerated eutrophication of lakes (that is, 

accelerated aging and increased productivity). Near-surface 

concentrations of total phosphorus less than about 0.012 mg/L 

indicate oligotrophic conditions, whereas concentrations 

greater than about 0.024 mg/L indicate eutrophic conditions; 

concentrations between these two concentrations indicate 

mesotrophic conditions (Carlson, 1977). During MY 2005 

and MY 2006, phosphorus concentrations ranged from 0.008 

to 0.018 mg/L (fig. 4). Near-surface total phosphorus concentrations had little seasonality. The near-surface summer 
12 Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin

Total phosphorus

0.000

0.005

0.010

0.015

0.020

0.025

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008

T

O

T

AL PHOSPHORUS CONCENTRATION,

 IN MILLIGRAMS PER LITER

U.S. Geological Survey

Citizen Monitoring

Wisconsin Department of Natural Resources

Average summer concentration

Chlorophyll a

0

5

10

15

20

25

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35

CHLOROPHYLL A CONCENTRATION, 

IN MICROGRAMS PER LITER

U.S. Geological Survey

Citizen Monitoring

Wisconsin Department of Natural Resources

Average summer concentration

Secchi depth

0

5

10

15

20

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30

SECCHI DEPTH, IN FEET

U.S. Geological Survey

Citizen Monitoring

Wisconsin Department of Natural Resources

Average summer depth

Figure 4. Near-surface total phosphorus concentrations, chlorophyll a concentrations, and Secchi depths in Silver Lake, 

Barron County, Wis., 1986 to 2008. 

Figure 4. Near-surface total phosphorus concentrations, chlorophyll a concentrations, and Secchi depths in Silver Lake, Barron 

County, Wis., 1986 to 2008. 
Measured Lake-Water Quality 13

During MY 2005 and MY 2006, Secchi depths in Silver 

Lake ranged from 6.4 to 15.1 ft, both extremes measured 

in July 2006 (fig. 4). No consistent seasonal variability was 

apparent. The near-surface summer (May–September) average 

Secchi depth was 10.1 ft in MY 2005 and 11.2 ft in MY 2006 

(table 3). Since 1986, Secchi depths have ranged from 3.9 ft 

(October 2003) to 24.9 ft (June 1990). Average June–August 

Secchi depths were relatively steady from 1986 to 1998, 

then gradually decreased to about 7.5 ft in 2002–4, and then 

increased to 19.4 ft in 2008. The poorest clarity was measured 

in 2003 (average depth of 7.4 ft), and the best clarity was 

measured in 2008. Secchi depths greater than 13 ft indicate 

usually 3–7 μg/L. The near-surface summer (May–September) 

average chlorophyll a concentration was 5.0 μg/L in MY 2005 

and 5.8 μg/L in MY 2006 (table 3). Therefore, on the basis of 

chlorophyll a concentrations, Silver Lake would usually be 

classified as mesotrophic.

Since 1998, near-surface chlorophyll a concentrations 

have ranged from less than 1 μg/L to greater than 30 μg/L (fig. 

4). The highest chlorophyll a concentrations were measured in 

2002 and 2003. Summer average concentrations appeared to 

gradually decrease from 1986 to 1995. Average June–August 

concentrations have fluctuated around 5 μg/L, except in 2003 

(13.3 μg/L), 2007 (9.4 μg/L), and 2008 (1.4 μg/L; table 3). 

Table 3. Average near-surface water quality and trophic state index (TSI) values for Silver Lake, Barron County, Wis., 1986 

to 2008.

[mg/L, milligrams per liter; μg/L, micrograms per liter]

------------Trophic state index values--------------

Year Total phosphorus 

(mg/L)

Chlorophyll a

(μg/L)

Secchi depth 

(feet) Phosphorus Chlorophyll a Secchi depth

June–August average

1986 0.020 5.0 17.1 47 46 36

1987 .007 5.0 16.3 31 46 37

1988 .007 5.0 14.3 33 46 39

1989 .006 3.5 17.3 30 43 36

1990 .007 3.0 17.0 31 41 37

1991 .008 3.7 11.6 35 43 42

1992 .007 3.0 14.8 32 41 39

1993 .008 2.6 13.2 33 40 40

1994 .007 1.9 13.3 32 37 40

1995 .007 1.2 15.6 32 31 38

1996 .008 2.9 13.6 34 41 40

1997 .009 2.5 14.7 35 39 39

1998 -- -- 15.6 -- -- 38

1999 -- -- 12.4 -- -- 41

2000 -- -- 10.8 -- -- 43

2002 .017 4.5 7.5 44 45 48

2003 .018 13.3 7.4 46 51 48

2004 .016 5.6 8.0 44 47 47

2005 .012 3.9 10.1 40 41 44

2006 .013 4.9 11.2 41 43 43

2007 .010 9.4 12.3 36 51 42

2008 .011 1.5 19.4 37 34 34

May–September average

2005 .013 5.0 10.2 41 44 44

2006 .013 5.8 11.1 41 46 43

Average 2005–6 .013 5.4 10.7 41 45 43
14 Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin

oligotrophic conditions and less than 6.6 ft indicate eutrophic 

conditions (Carlson, 1977). Therefore, based on Secchi depths, 

Silver Lake is usually classified as oligotrophic to mesotrophic 

except in 2002 to 2004 when the lake was mesotrophic to 

eutrophic.

All three TSIs, based on near-surface concentrations 

of total phosphorus and chlorophyll a and on Secchi depths, 

Figure 5. Near-bottom total phosphorus concentrations in Silver Lake, Barron County, Wis.,1986 to 2008.

Figure 6. Trophic state index (TSI) values based on surface concentrations of total phosphorus and chlorophyll a, plus Secchi depths, 

in Silver Lake, Barron County, Wis., 1986 to 2008.

indicate that, in MY 2005 and MY 2006, Silver Lake was 

typically oligotrophic to mesotrophic (fig. 6 and table 3). Since 

1986, Silver Lake has usually been classified as oligotrophic 

to mesotrophic; however, in 2002–4, the lake was classified as 

mesotrophic to eutrophic.

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

TOTAL PHOSPHORUS CONCENTRATION, 

IN MILLIGRAMS PER LITER

U.S. Geological Survey

Citizen Monitoring

Wisconsin Department of Natural Resources

Average summer concentration

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008

Figure 5. Near-bottom total phosphorus concentrations in Silver Lake, Barron County, Wis.,1986 to 2008. 

Eutrophic

Mesotrophic

Oligotrophic

20

30

40

50

60

70

TROPHIC STATE INDEX

Phosphorus

Chlorophyll a

Secchi depth

1986 1988 1990 1992 1994 1996 1998 2000 2002 2004 2006 2008

Figure 6. Trophic state index (TSI) values based on surface concentrations of total phosphorus and chlorophyll a, plus 

Secchi depths, in Silver Lake, Barron County, Wis., 1986 to 2008. 
Historical Changes in the Water Level of Silver Lake 15

Historical Changes in the Water Level 

of Silver Lake

Detailed historical water-level measurements are available for only a few lakes in Wisconsin. Changes in the water 

level (stage) of Silver Lake have been intermittently measured 

since 1967 and were measured continuously from November 

1, 2004, to October 31, 2006, as part of this study. Before this 

study, most water-level measurements were made during the 

period of open water; therefore, the available data were used 

to estimate average May through October water levels (fig. 7). 

Since 1967, the water level of Silver Lake has gone through 

almost three complete three cycles of rising and falling. 

During these cycles, water levels have fluctuated about 5 ft 

(1968–75), 8 ft (1975–89), and 10 ft (1989–2007). During the 

study period, the water level generally declined for the third 

time since 1967 (figs. 7 and 8); the highest stage recorded was 

87.42 ft on the first day of monitoring (Nov. 1, 2004) and the 

lowest stage recorded was 83.99 ft on the last day of monitoring (Oct. 31, 2006). There were three relatively large rises 

and many other small rises in stage in response to rainfall and 

Figure 7. Estimated and measured average annual (May–October) lake stage (water level) in Silver Lake, Barron County, Wis., 1900 to 

2008. [Altitude of the local datum is 1165.31 feet above the National Geodetic Vertical Datum of 1929.]

Figure 8. Daily water levels (stages) computed from the full water budget in comparison to measured water levels of Silver Lake, 

Barron County, Wis., from November 1, 2004, to October 31, 2006. [Altitude of the local datum is 1165.31 feet above the National Geodetic 

Vertical Datum of 1929.]

78

80

82

84

86

88

90

92

1900 1920 1940 1960 1980 2000

LAKE STAGE, IN FEET ABOVE AN ABRITRARY DATUM

Measurement

Best estimated stage

Figure 7. Estimated and measured average-annual (May–October) lake stage water level in Silver Lake, Barron County 

Wis., from 1900 to 2008. [Altitude of the local datum is 1,165.31 feet above the National Geodetic Vertical Datum of 1929.]

Figure 8. Daily water levels stages computed from the full water budget in comparison to measured water levels of Silver 

Lake, Barron County, Wis., from Nov. 1, 2004 to Oct. 31, 2006. [Altitude of the local datum is 1,165.31 feet above the National 

Geodetic Vertical Datum of 1929.]

83

84

85

86

87

88

89

11/1/2004 3/2/2005 7/1/2005 10/30/2005 2/28/2006 6/29/2006 10/28/2006

YEAR

STAGE, IN FEET ABOVE AN ARBITRARY DATUM 

Measured stage

Calculated stage
16 Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin

runoff during the study period. In late March and early April 

of both years, the stage increased about 0.7–0.8 ft over a few 

days in response to snowmelt and rainfall. In addition, rainfall 

during Oct. 4–5, 2005 (6.72 in., 0.56 ft) caused a 0.62-ft rise 

in stage.

The intermittent measurements in Silver Lake were 

insufficient for continuous annual estimates of water level 

before 2001. Therefore, to better describe how the water level 

of Silver Lake changed before 2001, two multiple-regression 

relations were developed to predict past average May–October 

water levels. The first relation used average May–October 

water levels measured in Shell Lake (9 mi north of Silver 

Lake) to estimate average May–October water levels in Silver 

Lake from 1936 to 2000. Detailed water-level measurements 

were available for Shell Lake from 1936 to 2007 (Krohelski 

and others, 1999; Shell Lake Chamber of Commerce, 2009); 

however, measurements after 2003 were not used to develop 

the relations because a diversion system was used to reduce 

the water level in Shell Lake starting in 2003. In all, 17 years 

of overlapping data were available to develop this linearregression relation. A second relation was used to extend the 

Shell Lake and Silver Lake water levels back to 1900. In this 

second relation, the water levels of Shell Lake from 1900 

to 1935 were first estimated by use of a time-series model 

that related the water level in Shell Lake to the total annual 

precipitation at Spooner, Wis. (5 mi north of Shell Lake), from 

the previous year and the average of the four previous years. 

The first relation was then applied with the estimated water 

levels in Shell Lake to estimate the average May–October 

water levels in Silver Lake from 1900 to 1935.

The final constructed water levels for Silver Lake indicate 

about seven cycles of rising and falling water levels since 

1900 (fig. 7). The fluctuation in water level of 10 ft after 1990 

was a little more extreme than what occurred between 1900 

and 1990. Large fluctuations in water level have been known 

to occur in Silver Lake and have affected the area and the 

behavior of people around the lake. After prolonged lowwater levels in the early 1930s (fig. 7), residents near the lake 

constructed a channel to divert water leaving Sylvan Lake into 

Silver Lake. This channel was also used during other periods 

of low water since the 1940s (table 2). The measured high 

water levels around 1968 and 1984 are similar to those predicted with the relations described above; therefore, it appears 

that the diversion channel was being used in a manner similar 

to that from around 2000. If the channel was not used around 

1968 and 1984, the estimated stage in the lake would have 

been expected to be higher than that measured. The estimated 

changes in water level before 1935, especially the periods with 

high water levels, may be greater than what actually occurred 

in the lake because of the linear-regression assumption that the 

relation between water levels in Shell Lake and Silver Lake 

was similar to that after 1967, when water leaving Sylvan 

Lake was occasionally diverted into Silver Lake.

Hydrology and Water Budget

Because the productivity in Silver Lake should be limited 

or potentially limited by the input of phosphorus (as indicated 

by N:P ratios), phosphorus should be the nutrient of concern 

when considering management efforts to improve or prevent degradation of the water quality of the lake. Most of the 

phosphorus entering the lake is transported by water inputs; 

therefore, to quantify phosphorus inputs, water inputs first 

need to be quantified. Water and phosphorus budgets for the 

lake were quantified for each of the two detailed monitoring 

years. This information is then used to estimate water and 

phosphorus budgets for two years with high water levels for 

which monitoring data were available (2002 and 2003) and for 

years during very dry and wet conditions.

The hydrology of a terminal lake, like Silver Lake, can 

be described in terms of components of its water budget. The 

water budget for a period of interest may be represented by:

ΔS = (P + SWIn + GWIn ) – (E + GWOut ), (4)

where ΔS is change in the volume of water stored in the lake 

and is equal to the sum of the volumes of water entering the 

lake minus the sum of the volumes leaving the lake. Water 

enters the lake as precipitation (P), surface-water inflow 

(SWIn), and groundwater inflow (GWIn). Water leaves the lake 

through evaporation (E) and groundwater outflow (GWOut). 

Daily values for each term in the water budget were measured 

or estimated.

Change in Storage

Changes in the volume of the lake were determined from 

water elevations (fig. 8) measured continuously at the lakestage gage near the south end of the lake (fig. 2). To simplify 

computations of changes in volume, an average area of the 

lake was used for each year of the study: 354.6 acres in MY 

2005 and 343.1 acres in MY 2006. The amount of water 

stored in the lake decreased by 593 acre-ft in MY 2005 and by 

749 acre-ft in MY 2006 (table 4).

Precipitation

Precipitation on the lake surface during MY 2005 was 

30.11 in. (890 acre-ft) and during MY 2006 was 22.36 in. 

(639 acre-ft; table 4). During both years, precipitation was 

below normal: 90 percent of the long-term average (1971–

2000) of 33.56 in. measured at Cumberland, Wis., during 

MY 2005 and 67 percent during MY 2006. Monthly precipitation during each monitoring year is compared to the 1971–

2000 average monthly precipitation in figure 9. In MY 2005, 

precipitation totals for all months were at or below normal 

except in June and October. In MY 2006, totals for all months 

were below normal except for December and January.
Table 4. Water budget for Silver Lake, Barron County, Wis., measured for monitoring years 2005 and 2006, and estimated for 2002, 2003, and a series [Monitoring year, November–October; MY, monitoring year; all data in acre-feet or percentage of total]

Measured Esti

Budget component MY 2005 MY 2005 (percent) MY 2006 MY 2006 (percent) Two-year average Two-year average (percent) 2002 2003 

Change in storage

Change in storage -593 -749 -671 345 -202 

Inputs to lake

Precipitation 890 68.6 639 68.9 765 68.7 1,260 1,210 Surface-water inflow (total) 407 31.4 288 31.1 348 31.3 1,210 659 

By surface-water component:Tributary 2 89 6.9 53.3 5.7 71 6.4Tributary 3 35 2.7 11.7 1.3 24 2.1Tributary 7 141 10.9 121 13.0 131 11.7Ungaged nearshore area 142 10.9 103 11.1 122 11.0

Groundwater 0 0 0 0 0 0 0 0 Total input 1,300 100 928 31.1 1,110 100 2,470 1,870 

Outputs from lake

Evaporation 690 37.7 731 42.2 711 39.9 748 743 Groundwater 1,140 62.3 1,000 57.8 1,070 60.1 1,380 1,320 Total output 1,830 100 1,730 100 1,780 100 2,120 2,070 
18 Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin

Evaporation and Net Groundwater Inflow

Because Silver Lake is deeper than many nearby lakes, 

its water temperature increases more slowly in spring and 

decreases more slowly in fall than in most other lakes; therefore, rates of evaporation from the surface of the lake may 

differ from those of other nearby lakes. In addition, evaporation varies among years depending on meteorological conditions. Therefore, evaporation rates from other nearby lakes 

or evaporation estimated from nearby evaporation-pan data 

that are typically used to estimate evaporation for small lakes 

may provide misleading information. As an alternative, daily 

evaporation was estimated for the 2-year detailed monitoring 

period by use of the one-dimensional hydrodynamic model, 

the Dynamic Lake Model (DLM; McCord and others, 2000; 

Robertson and others, 2002). In the process of simulating 

the hydrodynamics of the lake, the model computes detailed 

energy and hydrologic budgets, which includes heat transfer 

from the lake associated with evaporation. Therefore, if the 

detailed energy budget is accurate, the amount of evaporation 

should be correctly estimated.

DLM is a lake and reservoir model, which was modified 

from the DYnamic REservoir Simulation Model, DYRESM 

(Imberger and Patterson, 1981) by McCord and others (2000). 

Both DLM and DYRESM are process based and have been 

successfully used to simulate vertical changes in water temperatures and ice cover of many lakes and reservoirs around 

the world. DLM is based on parameterizations of each of the 

individual mixing processes, so site-specific model calibration 

is generally not necessary. For a more complete description 

of the DLM model and its application to estimate evaporation 

rates, see Robertson and others (2002).

Inputs to DLM include data descriptions of lake morphometry, meteorological conditions, inflow and outflow 

(outflow was assumed to be equivalent to groundwater leaving 

the lake), average light extinction in the lake, and initial water 

temperature and salinity (or specific conductance) profiles in 

the lake. Daily average air temperature, vapor pressure, wind 

speed, and inflow characteristics (temperature and specific 

conductance or salinity) are used, whereas daily total values 

for inflows, outflows, longwave radiation (or average percent 

of clear sky), shortwave radiation, rainfall, and snowfall are 

used. Meteorological data were obtained from meteorological 

stations in the area operated by the USGS, WDNR, and the 

NWS. An average Secchi depth of 10.7 ft (the average during 

the open-water period during the simulation period) was used 

to estimate a light-extinction coefficient of 0.523 ft-1. Water 

temperature and conductivity profiles measured on April 19, 

2005, were used as the initial conditions for the simulation. 

Daily evaporation rates, before the start of the simulation, 

were assumed to be equal to the average of that estimated 

in 2005 and 2006 for each calendar day. Evaporation was 

assumed not to occur when the lake was frozen.

To demonstrate that DLM accurately simulated the 

energy balance of the lake, the simulated thermal structure 

of the lake was compared with that measured (fig. 10). The 

model accurately simulated the changes in the thermal structure of the lake during the entire simulation period (onset of 

stratification, surface and deep temperatures, and the depth 

of the thermocline); therefore, DLM should have correctly 

simulated the energy and hydrologic balances of the lake. 

Results from the model can also be used to describe changes 

in the thermal structure of the lake during periods when the 

lake was not monitored, such as in late fall and winter. During 

the simulation period, the model required an additional loss 

of 1.48 ft3/s (1,070 acre-ft/year) of water to properly simulate 

the changes in water level measured in the lake. The additional 

loss of water was assumed to be caused by the net loss of 

water from the lake to the groundwater system. The net loss 

of water to the underlying aquifer was assumed to be equal to 

the total loss to the groundwater system because, as described 

below in “Groundwater Inflow and Outflow” section, there 

was no groundwater inflow to the lake.

Figure 9. Precipitation at Silver Lake, Barron County, Wis., November 2004 to October 2006, relative to long-term average precipitation 

at Gordon, Wis.

0

1

2

3

4

5

6

7

8

Nov. Dec. Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct.

Nov. 2004−Oct. 2005

Nov. 2005−Oct. 2006

1971−2000 average

PRECIPITATION, IN INCHES

Figure 9. Precipitation at Silver Lake, Barron County, Wis. during November 2004 to October 2006, relative to long-term 

average precipitation at Gordon, Wis.
Figure 10. Measured and modeled (with the Dynamic Lake Model; McCord and others, 2000) distribution of water temperature, April 19, 2005, to Dece

Missing data Missing dat

Figure 10. Measured and modeled (with the Dynamic Lake Model; McCord and others, 2000) distribution of water temperature, April 19, 2005, 

2005 2006

Nov. 

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Dec. May June July Aug. Sept. Oct.

Nov. 

Jan. Feb. Mar. Apr. May June July Aug. Sept. Oct. Nov. Ma Dec. y June July Aug. Sept. Oct.

6030502010

0

40908070

6030502010

0

40908070

DEPTH, IN FEET DEPTH, IN FEET
20 Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin

Daily evaporation, computed by DLM from Nov. 1, 2004, 

through Dec. 31, 2006, was variable but demonstrated a strong 

seasonal pattern, with highest evaporation in summer (especially July–August; fig. 11). The highest daily evaporation 

was about 0.35 in/d. The annual evaporation from the surface 

of the lake was 23.4 in. (690 acre-ft) in MY 2005 and 25.6 in 

(731 acre-ft) in MY 2006 (table 4). These estimates are a little 

less than the average total annual free-surface evaporation estimated for the area (approximately 28 in.) by Farnsworth and 

Thompson (1982). 

Surface-Water Inflow

Seven small tributaries to the lake were identified (fig. 2) 

and monitored intermittently. None of these tributaries flowed 

continuously. The most significant of these tributaries in terms 

of flow and duration of flow after storms were tributaries 7, 

2, and 3, listed in descending order of importance. Tributary 

7 drains most of the northern part of the watershed and flows 

through extensive wetlands before entering the lake. Tributary 

2 drains a small mostly forested area northeast of the lake. 

Figure 11. Daily evaporation from the surface of Silver Lake, Barron County, Wis., November 2004 through October, 2006, based on 

output from the Dynamic Lake Model.

Figure 12. Estimated streamflow in tributary 7 (fig. 2) to Silver Lake, Barron County, Wis., November 1, 2004, to October 31, 2006. 

0

0.1

0.2

0.3

0.4

11/1/04 3/1/05 7/1/05 11/1/05 3/1/06 7/1/06 11/1/06

DATE

EVAPORATION, IN INCHES PER DAY

Figure 11. Daily evaporation from the surface of Silver Lake, Barron County, Wis., November 2004 through October, 2006, 

based on output from the Dynamic Lake Model.

0

2

4

6

8

10

12

14

16

11/1/04 3/1/05 7/1/05 11/1/05 3/1/06 7/1/06 11/1/06

DATE

STREA

MFLO

W, IN CUBIC FEET PER SECOND 

Measured flow

Estimated flow

Figure 12. Estimated streamflow in tributary 7 (fig. 2) to Silver Lake, Barron County, Wis., November 1, 2004, to October 31, 

2006. 
Hydrology and Water Budget 21

Tributary 3 drains a small part of the watershed southeast of 

the lake. Approximately one-third of the total surface-water 

inflow comes from tributary 7. The estimated daily flows from 

tributary 7 are shown in figure 12. Total runoff volumes for 

tributaries 2, 3, and 7 are summarized in table 4. Runoff volumes from tributary 7 were 141 acre-ft in MY 2005 and 121 

acre-ft in MY 2006, which were more than those from all of 

the other tributaries combined except during spring snowmelt. 

Observations of flow in tributaries 1, 4, 5, and 6 were 

infrequent and flow was mostly only associated with runoff 

during snowmelt in spring; therefore, estimating flows in these 

tributaries was not possible. Hence, these tributaries were 

grouped with other ungaged near-lake areas and referred to 

as the “ungaged nearshore area.” Runoff from the ungaged 

nearshore area was estimated by determining the amount of 

runoff needed to balance the mass-balance equation during 

the spring snowmelt period. Runoff volumes for the ungaged 

nearshore area were estimated to be 0.4 ft (142 acre-ft, table 4) 

in MY 2005 (assumed to occur over the 4 days from April 1 to 

April 4, 2005) and 0.3 ft (103 acre-ft) in MY 2006 (assumed to 

occur over the 3 days from April 1 to April 3, 2006). 

Groundwater Inflow and Outflow

Before this study began, Silver Lake was described as a 

groundwater flowthrough lake (fig. 13A), with groundwater 

entering the lake from the northern one-third of its periphery 

and water leaving the lake from the southern two-thirds of 

its periphery (Young and Hindall, 1972). This interpretation 

seemed plausible without the availability of detailed groundwater data and considering the water level in Silver Lake in 

Figure 13. Groundwater flow near Silver Lake, Barron County, Wis. A, Original description of flow, with Silver Lake as a groundwater 

flowthrough lake. B, Revised description of flow, with Silver Lake hydraulically mounded above the water table.

A. Original description: Silver Lake is a groundwater flowthrough lake

B. Revised description: Silver Lake is hydraulically mounded above the water table

Yellow River 

Silver Lake 

Yellow River 

Silver Lake 

Figure 13. Groundwater flow near Silver Lake, Barron County, Wis. A, Original description of flow, with Silver Lake as a 

groundwater flowthrough lake. B, Revised description of flow, with Silver Lake hydraulically mounded above the water 

table.

Water table 

Water table 
22 Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin

relation to those of nearby streams and lakes, especially with 

the strong gradient between the water level of the lake and that 

of the nearby Yellow River. Water levels measured in 14 nearlake piezometers installed around the periphery of the lake 

(fig. 2) and those recorded during nearby domestic well installation, however, were consistently at an elevation lower than 

the lake surface, which indicates the hydraulic gradient was 

downward or away from the lake to the ground. Water elevations in the piezometers are compared with that in the lake 

during periods with high and low water levels in figure 14. In 

addition, water levels in five selected domestic wells, located 

80 to 250 ft to the north and northeast of the lake (fig. 2), were 

5–25 ft below the lake surface at the time of well construction. 

Therefore, it is clear that, rather than being a groundwater 

flowthrough lake, Silver Lake is hydraulically mounded above 

the water table (fig. 13B) and there is no groundwater inflow 

to the lake. 

Discharge of water from the lake to the ground was 

estimated from the DLM simulations and as the residual in the 

water-budget equation when all of the other variables were 

measured or estimated. Leakage of water from the lake to 

the ground over the entire 2-year period was approximately 

1.48 ft3/s, or 0.0084 ft/d. The amount of groundwater leaving the lake is expected to increase as the water level in the 

lake increases because, at higher lake levels, the water would 

likely be in contact with more permeable sandy deposits (for 

Figure 14. Water levels in Silver Lake, Barron County, Wis., and in nearshore piezometers during periods with high water (November 

11, 2004) and low water levels (November 2, 2006) in the lake. For some piezometers, the water table was below the bottom elevation of 

the piezometer. [Altitude of the local datum is 1165.31 feet above the National Geodetic Vertical Datum of 1929.]

November 11, 2004

82

83

84

85

86

87

88

A B C D E F G H I J K L M N

PIEZOMETER

ELEVATION, IN FEET ABOVE 

LOCAL DATUM 

ELEVATION, IN FEET ABOVE 

LOCAL DATUM 

November 2, 2006

82

83

84

85

86

87

88

A B C D E F G H I J K L M N

PIEZOMETER

Water-table elevation

Bottom elevation of dry piezometer

Lake stage

Figure 14. Water levels in Silver Lake, Barron County, Wis., and in nearshore piezometers during periods with high water 

(November 11, 2004) and low water levels (November 2, 2006) in the lake. For some piezometers, the water table was below 

the bottom elevation of the piezometer. 
Hydrology and Water Budget 23

example, Krohelski and others, 1999). To estimate how the 

rate of water leakage from the lake may have varied between 

MY 2005 and MY 2006, the annual rates in MY 2005 (higher 

water level) were increased and the rates in MY 2006 (lower 

water level) decreased by constant incremental rates, and the 

overall errors in the daily water budget (eq. 4 and fig. 8) were 

then compared. The optimum estimation for water leakage to 

the groundwater was 0.0088 ft/d in MY 2005 and 0.0080 ft/d 

in MY 2006. Therefore, the total water outflow from the lake 

to groundwater was 1,140 acre-ft in MY 2005 and 1,000 acreft in MY 2006 (table 4).

Water-Budget Summary

During the 2-year study period, precipitation was the 

largest source of water to the lake, supplying 68.7 percent of 

the total input (table 4; fig. 15). Surface runoff supplied 31.3 

percent of the water entering the lake. The total input of water 

in MY 2005 (1,300 acre-ft) was more than in MY 2006 (928 

acre-ft), reflecting near-normal precipitation during MY 2005 

and below-normal precipitation in MY 2006. The residence 

time, or the length of time required for water entering the lake 

to completely replace the volume of water in the lake, was 9.7 

and 13.1 years on the basis of the total inflows for MY 2005 

and MY 2006, respectively, or an average residence time of 

11.4 years. 

Figure 15. Water budgets for Silver Lake, Barron County, Wis., for monitoring years (MY) 2005 and 2006. [%, percentage]

WATER INPUTS, MY 2005 

[1,300 acre-feet]

WATER OUTPUTS, MY 2005

[1,830 acre-feet]

Tributary 2

7%

Tributary 3 

3%

Tributary 7 

11%

Precipitation

68%

Ungaged 

11%

Ungaged 

11%

Evaporation 

38%

WATER INPUTS, MY 2006

[928 acre-feet]

Tributary 7

13%

Tributary 3

1%

Tributary 2

6%

WATER OUTPUTS, MY 2006 

[1,730 acre-feet]

Figure 15. Water budgets for Silver Lake, Barron County, Wis., for monitoring years (MY) 2005 and 2006. [%, percentage of 

total input]

Groundwater 

outflow

62%

Groundwater 

outflow

58%

Precipitation

69%

Evaporation 

42%
24 Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin

The total annual outputs of water from the lake were 

greater than the total inputs, which resulted in a decrease in 

storage from the beginning to the end of each monitoring year. 

This resulted in a decrease in lake stage of 3.43 ft or 1,340 

acre-ft of storage in the lake over the 2-year period. On average, outflow to the groundwater system accounted for about 

60 percent of the total water output from the lake, and evaporation accounted for about 40 percent (table 4; fig. 15).

The quality or accuracy of the water budget was evaluated by comparing the monthly sum of all inputs with the sum of 

all outputs plus the change in storage for the lake, expressed in 

acre-feet (fig. 16). The differences between calculated inputs 

and outputs reflect the cumulative errors in the estimates of 

all of the components in the water budget for each month. The 

largest monthly differences were 50–60 acre-ft. On an annual 

basis, the percentage errors were less than 3 percent.

Sources of Phosphorus

To help define where the phosphorus in Silver Lake 

originates and how much may be controllable, a detailed daily 

phosphorus budget was computed for each monitoring year. 

The external sources of phosphorus to the lake examined 

included precipitation, surface- and groundwater inflow, and 

contributions from septic systems and erosion. In addition to 

these external sources, phosphorus can be released from the 

bottom sediments of the lake; this release is considered an 

internal source of phosphorus (internal loading). Very little 

phosphorus from internal loading is released into the epilimnion during summer because of the strong thermal stratification (fig. 10), which prevents mixing, and because of the 

relatively low phosphorus concentrations in the hypolimnion 

(fig. 5); therefore, this source was not considered. Phosphorus is removed from the lake through deposition to the lake 

sediments.

Precipitation

Phosphorus deposition on Silver Lake was determined 

from phosphorus concentrations measured in wetfall (rain and 

snow) and phosphorus deposition rates measured in dryfall at 

the weather station at Whitefish Lake (Robertson and others, 2009). Phosphorus in precipitation was estimated from 

the seasonal phosphorus concentrations measured for snow 

(0.009 mg/L; Dec.–Mar.) and rain (0.017 mg/L; Apr.–Nov.). 

Monthly wetfall deposition was computed by multiplying the 

monthly average phosphorus concentrations by the estimated 

precipitation on the lake. Wetfall deposition was highest during summer, when phosphorus concentrations were highest 

and precipitation was greatest. A dryfall deposition rate of 

26.1 lb/mi2/yr was used, which represented deposition on a 

lake with few conifers in the surrounding area. The total phosphorus contributed by precipitation was 53.4 lb in MY 2005 

and 41.0 lb in MY 2006 (table 5); approximately 75 percent of 

the deposition was from wetfall.

Figure 16. Monthly total water inputs and outputs plus storage change for Silver Lake, Barron County, Wis., based on results from the 

water-balance model (equation 4). The difference between inputs and outputs indicates the cumulative error for all components of the 

water budget for each month.

0

50

100

150

200

250

300

350

Nov. 04

Dec. 04

Jan. 05

Feb. 05

Mar. 05

Apr. 05

May 05

June 05

July 05

Aug. 05

Sept. 05

Oct. 05

Nov. 05

Dec. 05

Jan. 06

Feb. 06

Mar. 06

Apr. 06

May 06

June 06

July 06

Aug. 06

Sept. 06

Oct. 06

VOLUME, IN ACRE-FEET

Inputs

Outputs plus storage change

Figure 16. Monthly total water inputs and outputs plus storage change for Silver Lake, Barron County, Wis., based on results 

from the water-balance model (equation 4). The difference between inputs and outputs indicates the cumulative error for all 

components of the water budget for each month.
Sources of Phosphorus 25

Table 5. Phosphorus inputs to Silver Lake, Barron County, Wis., measured for monitoring years 2005 and 2006, and estimated for 2002, 2003, and a series of dry and wet years.[Monitoring year, November–October; MY, monitoring year; all data in pounds or percentage of total]

Measured Estimated

Budget component MY 2005 MY 2005 (percent) MY 2006 MY 2006 (percent) Two-year average Two-year average (percent) 2002 2003 Series of dry years Series of wet years

Precipitation 53.4 18.3 41.0 29.3 47.2 21.9 69.0 66.7 44.5 65.1Surface-water inflow (total) 238 81.7 99.0 70.7 169 78.1 586 319 45.2 399By surface-water component:

Tributary 2 19.4 6.7 8.8 6.3 14.1 6.5Tributary 3 14.4 4.9 2.5 1.8 8.5 3.9Tributary 7 107 36.7 45.7 32.6 76.4 35.4Ungaged nearshore area 97.3 33.4 42.0 30.0 69.7 32.3

Shore erosion .0 .0 .0 93.1 93.1 0.0 93.1Groundwater .0 .0 .0 .0 .0 .0 .0 .0 .0 .0Total input 292 100 140 100 216 100 749 479 89.7 557

Surface-Water Inflow 

The total input of phosphorus from surface water in 

the watershed was estimated from the flows and total phosphorus concentrations measured at the monitoring sites on 

tributaries 2, 3, and 7 (fig. 2). Flow-weighted average total 

phosphorus concentrations in MY 2005 (wetter year) ranged 

from 0.080 mg/L in tributary 2 to 0.149 mg/L in tributary 3 to 

0.280 mg/L in tributary 7; in MY 2006 (drier year) concentrations ranged from 0.060 mg/L in tributary 2 to 0.080 mg/L in 

tributary 3 to 0.139 mg/L in tributary 7. The flow-weighted 

average concentration of all of the discrete samples was 

0.252 mg/L in MY 2005 and 0.150 mg/L in MY 2006. These 

concentrations were used to compute phosphorus input from 

the ungaged nearshore area. Because of the higher volume 

of water and higher phosphorus concentrations in tributary 

7 than in the other tributaries, most of the phosphorus in 

surface water enters the lake through this tributary. Most of 

the phosphorus in surface water entered the lake in March and 

April, especially during snowmelt (fig. 17). The total quantity 

of phosphorus delivered from tributary 7 was 107 lb in MY 

2005 and 45.7 lb in MY 2006 (table 5). The total quantities 

of phosphorus from tributaries 2 and 3 were 19.4 and 14.4 lb, 

respectively, in MY 2005 and 8.8 and 2.5 lb, respectively, in 

MY 2006. The ungaged nearshore area is estimated to have 

contributed 97.3 and 42.0 lb of phosphorus in MY 2005 and 

MY 2006, respectively. Therefore, the total quantity of phosphorus delivered from surface water in the watershed was 238 

lb in MY 2005 and 99 lb in MY 2006, almost half of which 

entered the lake during the short snowmelt period.

Phosphorus yields from the tributary 7 watershed were 

58.6 lb/mi2 in MY 2005 and 25.0 lb/mi2 in MY 2006. These 

yields are lower than those from 48 of the 50 rural watersheds 

that were monitored in Wisconsin and lower than 4 of the 

5 watersheds monitored in the Northern Lakes and Forests 

ecoregion by Corsi and others (1997). Yields from the tributary 2 watershed were a little higher than from the tributary 

7 watershed: 130 lb/mi2 in MY 2005 and 58.9 lb/mi2 in MY 

2006. These yields, however, are still lower than those estimated from 45 of the 50 rural watersheds in Wisconsin and 

lower than 2 of the 5 watersheds in the Northern Lakes and 

Forests ecoregion.

Total phosphorus concentrations were also measured 

near the outlet of Sylvan Lake during spring 2006 prior to 

the stream entering the wetland system north of the lake. The 

flow-weighted average phosphorus concentration in the four 

samples was 0.055 mg/L.

Groundwater and Septic Systems

On the basis of measured gradients between the lake and 

14 nearshore piezometers, it is evident that water leaks from 

all areas of the lakebed into the groundwater system; therefore, 

groundwater and septic systems would not supply phosphorus 

to the lake. The only condition for which a septic system may 
26 Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin

supply phosphorus to the lake would be if the system were 

totally flooded or directly discharged to the lake.

Nearshore Erosion

Because the water level of Silver Lake had dropped during MY 2005 and MY 2006 from that in 2001–3, there was 

little, if any, erosion of the shoreline of Silver Lake during the 

two detailed monitoring years. Phosphorus from nearshore 

erosion may be important in years with high water levels; 

therefore, the phosphorus input to the lake during 2001–3 

was estimated and compared with the loading of phosphorus 

estimated during two of these years. Approximately 50 percent 

of the shoreline (28 areas with a total length of approximately 

12,000 ft) showed signs of erosion. The height of the eroded 

areas was typically 1 to 2.5 ft, with a retreat of 1 to 2 ft. The 

shoreline is steeper on the east and south sides of the lake 

than on the other sides of the lake, which resulted in slumps 

or block failures being more evident in these areas. Effects 

of erosion at site 3 (near the county park) and site 21 (on the 

east side of the lake) are shown in figure 18. The total amount 

of sediment eroded from these areas was estimated to be 

34,400 ft3, or 1,550 tons (assuming an aerated specific weight 

of the sand/clay/gravel to be 90 lb/ft3; Chow, 1964).

The amount of phosphorus released from the eroded 

sediment was needed to determine how much phosphorus 

was introduced into the water column of the lake. Phosphorus 

concentrations were measured in the sediment near the lake 

(eight sites) and in the nearby lake bottom (four sites), and the 

difference in the average concentrations of these two areas was 

assumed to be the result of phosphorus being released into the 

water column. The estimated change in phosphorus concentrations was based on (1) total phosphorus concentrations, which 

may lead to a high estimate because part of this phosphorus 

may not be available to the water column, and (2) phosphate 

concentrations, which may lead to a low estimate because 

other forms of phosphorus also may dissolve into the water 

column. The average total phosphorus content in the bank 

sediment was 265 mg/kg and nearby lake sediments was 

132 mg/kg; therefore 133 mg/kg of total phosphorus should 

have been released into the water column. The average 

phosphate content (as phosphorus) in the bank sediment was 

71 mg/kg and in the lake sediments was 25 mg/kg; therefore, 

47 mg/kg of phosphate should have been released into the 

water column. The changes in concentrations of total phosphorus and phosphate in the sediment were then multiplied by the 

total mass of eroded sediment. This resulted in a total phosphorus release of 414 lb and total phosphate release of 145 lb. 

If the average of these two estimates is used to determine the 

amount of phosphorus introduced to the water column, then 

279 lb would have been delivered into the lake. If this erosion 

is assumed to have taken place over the three years from 2001 

Figure 17. Total monthly phosphorus input from three main tributaries and ungaged nearshore area to Silver Lake, Barron County, Wis., 

November 2004 to October 2006. 

0

20

40

60

80

100

120

140

160

Nov.

04

Jan.

05

Mar.

05

May

05

July

05

Sept.

05

Nov.

05

Jan.

06

Mar.

06

May

06

July

06

Sept.

06

PHOSPHORUS INPUT, IN POUNDS

Ungaged nearshore area

Tributary 3

Tributary 2

Tributary 7

Figure 17. Total monthly phosphorus input from three main tributaries and ungaged nearshore area to Silver Lake, Barron 

County, Wis., November 2004 to October 2006. 
Sources of Phosphorus 27

Figure 18. Erosion at two locations on Silver Lake, Barron County, Wis. A, Site 3 near county park, with erosion around the support 

beams of the steps down to the water. Notice that the middle support beams are hanging in the air. B, Site 21, demonstrating examples 

of erosion on the east side of the lake. Site locations shown in figure 3.

Figure 18. Erosion at two locations on Silver Lake, Barron County, Wis. A) Site 3 near county park, with erosion around the 

support beams of the steps down to the water. Notice that the middle support beams are hanging in the air. B) Site 21, 

demonstrating examples of erosion on the east side of the lake. Site locations shown in figure 3.

A

B
28 Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin

to 2003 when water levels were highest, then 93 lb/yr would 

have been introduced into the lake during these years.

Phosphorus-Budget Summary

During MY 2005 and MY 2006, the average annual input 

of phosphorus to the lake was 216 lb, of which 47 lb came 

from precipitation (21.9 percent) and 169 lb (78.1 percent) 

came from surface-water inflow (table 5). About 50 percent of 

the phosphorus in surface-water inflow came from tributary 7 

(fig. 19). The total phosphorus input to the lake ranged from 

292 lb in MY 2005 (the wetter year) to 140 lb in MY 2006 (the 

drier year). During these years, there was no phosphorus input 

from groundwater, septic systems, or erosion.

To determine how the water and phosphorus inputs to 

the lake vary when hydrologic conditions differ, the information from the detailed monitoring years was used to estimate 

water and phosphorus inputs for two years with high water 

levels for which water-quality data were available for the lake 

(2002 and 2003), and for a series of dry and wet years. The 

series of dry and wet years were the three consecutive years 

with the lowest and highest precipitation from 1960 to 2007. 

The three consecutive years with the lowest precipitation were 

from 1988 to 1990 (average precipitation of 28.2 in.), and the 

three consecutive years with the highest precipitation were 

from 2002 to 2004 (average precipitation of 38.5 in.). For 

each of these years, the surface area of the lake was estimated 

from the water levels in figure 7 and the morphometry of 

the lake (fig. 2). Phosphorus from wetfall was estimated by 

multiplying the total volume of precipitation (surface area of 

the lake multiplied by the precipitation at Cumberland) by an 

average annual phosphorus concentration in precipitation of 

0.016 mg/L (Robertson and others, 2009). Phosphorus from 

dryfall was assumed to be deposited at a constant rate of 

26.1 lb/mi2/yr (Robertson and others, 2009). The total phosphorus from precipitation was 69.0 lb for 2002, 66.7 lb for 

2003, 44.5 lb/yr for the three dry years, and 65.1 lb/yr for the 

three wet years (table 5).

The volume of surface-water inflow to the lake was computed for each year using a water-budget approach; in other 

words, solving for the surface-water-inflow (sum of all tributaries and ungaged area) term in equation 4. The changes in 

storage (table 4) were computed from changes in the estimated 

water elevations for consecutive years (fig. 7), with volumes 

computed from the morphometric map of the lake (fig. 2). The 

total water removed by evaporation was computed by using 

the surface area of the lake and assuming a constant evaporation rate of 24.5 in/yr (the average rate for MY 2005 and MY 

2006). The total water added by precipitation was computed 

by multiplying the surface area of the lake by the precipitation measured at Cumberland. The rate of water outflow to 

groundwater was assumed to be directly related to the water 

level of the lake. The leakage rates for MY 2005 (1,140 acre-ft 

for an elevation of 87.07 ft) and MY 2006 (1,000 acre-ft for 

an elevation of 85.56 ft) were used to estimate leakage at other 

elevations based on the assumption that these two rates were 

sufficient to define a linear relation between elevation and 

leakage.

Therefore on the basis of the water-budget approach, the 

surface-water inflow in 2002 was 1,210 acre-ft, in 2003 was 

659 acre-ft, the average annual inflow during the dry years 

was 93 acre-ft, and during the wet years was 824 acre-ft (table 

4). The phosphorus concentration in the inflow was assumed 

to be 0.178 mg/L, which was the volumetrically weighted 

Figure 19. Phosphorus budgets for Silver Lake, Barron County, Wis., for monitoring years (MY) 2005 and 2006. [%, percentage of total 

input]

PHOSPHORUS INPUTS, MY 2005

[292 pounds]

Ungaged areas

33%

Tributary 2

7%

Tributary 7

37%

Tributary 3

5%

Precipitation

18%

PHOSPHORUS INPUTS, MY 2006

[140 pounds]

Tributary 3

2%

Tributary 7

33%

Tributary 2

6%

Precipitation

29%

Ungaged areas

30%

Figure 19. Phosphorus budgets for Silver Lake, Barron County, Wis., for monitoring years (MY) 2005 and 2006. [%, percentage 

of total input.]
Simulated Changes in Water Quality in Response to Changes in Phosphorus Loading 29

concentration for all of the tributary input during MY 2005 

and MY 2006. Therefore, the total annual phosphorus input 

from surface inflow during 2002 was 586 lb, during 2003 was 

319 lb, during the dry years was 45.2 lb/yr, and during the wet 

years was 399 lb/yr (table 5). In addition to these sources, it 

was assumed that during 2002, 2003, and during the wet years, 

93 lb/yr of phosphorus was contributed from erosion.

In 2002, the total water input to the lake was 2,470 acre-ft 

and total phosphorus input was 749 lb (tables 4 and 5). In 

2003, the total water input was 1,870 acre-ft and total phosphorus input was 479 lb. During the dry years, the average 

annual water input was 831 acre-ft and phosphorus input was 

89.7 lb. During the wet years, the average annual water loading to the lake was 1,990 acre-ft and phosphorus input was 

557 lb. The total water input to the lake, therefore, ranged by a 

factor of 2.4 and total phosphorus input ranged by a factor of 

6.2. The residence time of water in the lake was 5.5 years in 

2002, 7.2 years in 2003, 12.9 years during the dry years, and 

6.5 years during the wet years.

Simulated Changes in Water Quality 

in Response to Changes in Phosphorus 

Loading

Empirical eutrophication models that relate phosphorus 

loading to specific water-quality characteristics can be used to 

determine how natural and anthropogenic changes in phosphorus loading could modify the water quality of Silver Lake. 

These models were developed on the basis of comparisons of 

hydrologic and phosphorus loading determined for many kinds 

of lake systems with specific measures describing lake-water 

quality, such as near-surface phosphorus and chlorophyll a 

concentrations and Secchi depth (Reckhow and Chapra, 1983; 

Cooke and others, 1993; Panuska and Kreider, 2003). Most of 

the phosphorus models were derived from analyses of many 

lakes with widely differing phosphorus-loading rates and 

hydrologic conditions (for example, Vollenweider, 1975; and 

Canfield and Bachmann, 1981). Most empirical models that 

predict phosphorus concentrations are very sensitive to the 

residence time of water in the lake, and they are not capable of 

simulating water quality in closed-basin, terminal lakes—lakes 

without continuous outlets and therefore with relatively long 

residence times. One empirical model that has been shown by 

Robertson and Schladow (2008) to be relatively insensitive to 

residence time is the Canfield and Bachman (1981) naturallake model. This model has also been shown to be one of the 

best empirical models for predicting the phosphorus concentrations of lakes in Wisconsin (Robertson and others, 2002, 

2005; Robertson and Rose, 2008). Therefore, the Canfield 

and Bachman natural-lake model (1981; eq. 5) was applied to 

Silver Lake to determine how changes in phosphorus loading 

are expected to affect phosphorus concentrations in the lake:

Total phosphorus concentration

(micrograms per liter) = L

(5) Z(1.62 x (L/Z)0.458+1/τ)

where L is the phosphorus-loading rate (in milligrams per 

square meter per year), Z is the mean depth of the lake (in 

meters), and τ is the residence time of the water in the lake 

(in years). In this application, the average of the annual 

hydrologic and phosphorus inputs measured in MY 2005 and 

MY 2006 were used as a base case for comparison with results 

from other scenarios.

The total phosphorus concentrations predicted with the 

Canfield and Bachman model were then used to predict chlorophyll a concentrations and Secchi depths through the use of 

Carlson’s (1977) TSI equations (eqs. 1–3). In other words, the 

chlorophyll a concentrations and Secchi depths were computed that yielded a similar TSI value as that computed from 

the predicted total phosphorus concentration. There are no true 

calibration factors when Carlson’s TSI equations are used to 

estimate chlorophyll a concentrations and Secchi depths; however, the output can be adjusted to account for model biases by 

adjusting the results by the percentage of bias in the results for 

a base scenario.

Modeling Approach

To estimate how the water quality of Silver Lake may 

respond to changes in phosphorus loading, 20 scenarios were 

simulated with the Canfield and Bachman model and Carlson 

TSI equations (table 6 and fig. 20). Scenario 1 simulated the 

average water-quality conditions for MY 2005 and MY 2006, 

which established a base or reference condition (concentration) for which results from the other simulations or scenarios 

can be compared. Nine scenarios (2–10) were used to determine the general response of the lake to basinwide changes 

in phosphorus loading: simulated decreases in controllable 

external phosphorus loading by 75, 50, and 25 percent and 

increases in controllable external phosphorus loading by 25, 

50, 75, 100, 200, and 300 percent. Controllable external loading excludes phosphorus input from atmospheric deposition.

Four scenarios (11–14) were used to evaluate how well 

the model simulated water quality in specific years with high 

water and evaluate the importance of erosion. These scenarios 

simulated the conditions for 2002 and 2003, with and without 

phosphorus input from nearshore erosion.

Six scenarios were then used to determine how natural 

and anthropogenic changes in water level and associated 

changes in phosphorus loading may have modified or could 

modify the water quality of the lake. Two scenarios (15–16) 

were used to simulate the effects of natural (climatic) changes: 

following a series of three dry years and a series of three wet 

years (described earlier). Four scenarios (17–20) were simulated to determine how anthropogenic changes in the hydrology may affect water quality, which included diverting water 

to the lake during periods of low water levels and pumping 

water from the lake during periods of high water levels.
30 Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin

Table 6. Estimated water quality in Silver Lake, Barron County, Wis., in response to various phosphorus-loading scenarios based on 

the Canfield and Bachman natural-lake model (1981) and Carlson (1977) trophic-state-index equations.

[mg/L, milligrams per liter; μg/L, micrograms per liter]

Simulations Scenario 

number

Annual 

phosphorus 

load 

(pounds)

Water 

elevation 

(feet)

Surface 

area 

(acres)

Mean 

depth

(feet)

Residence 

time 

(years)a

Predicted total 

phosphorus 

concentration 

(mg/L)

Predicted 

chlorophyll a 

concentration 

(μg/L)

Predicted 

Secchi 

depth 

(feet)

General response

Percent change in 

controllable load:

- 75% 2 89 86.3 349 35.4 11.1 0.008 2.3 18.8

- 50% 3 132 86.3 349 35.4 11.1 .010 3.4 14.6

- 25% 4 174 86.3 349 35.4 11.1 .012 4.4 12.2

0% - Base or referenceb 1 216 86.3 349 35.4 11.1 .014 5.4 10.7

+ 25% 5 258 86.3 349 35.4 11.1 .015 6.4 9.5

+ 50% 6 300 86.3 349 35.4 11.1 .017 7.3 8.7

+ 75% 7 342 86.3 349 35.4 11.1 .018 8.2 8.0

+ 100% 8 385 86.3 349 35.4 11.1 .020 9.1 7.4

+ 200% 9 553 86.3 349 35.4 11.1 .024 12.6 6.0

+300% 10 722 86.3 349 35.4 11.1 .029 16.0 5.1

Simulations of specific years with and without erosion

2002–High-runoff year 11 749 89.7 367 36.9 5.5 .025 12.8 5.9

2002–Without erosion 12 655 89.7 367 36.9 5.5 .023 11.3 6.5

2003–High-runoff year 13 479 89.1 364 36.7 7.2 .020 9.2 7.4

2003–Without erosion 14 386 89.1 364 36.7 7.2 .017 7.5 8.5

Natural scenarios

Series of dry years 

(3 years ending 1991)

15 90 81.4 312 34.4 12.9 .009 2.8 16.5

Series of wet years 

(3 years ending 2004)

16 557 88.2 360 36.2 6.5 .022 10.6 6.7

Anthropogenic-change scenarios

Lower water elevation by 

5 feet (compared to MY 

2005)

17 137 82.2 317 34.6 12.5 .011 4.1 12.9

Lower elevation by 5 feet 

plus 2 feet from out of 

basin (full tributary 7 

concentration)

18 530 84.2 333 35.0 7.4 .023 11.6 6.3

Lower elevation by 5 feet 

plus 2 feet from out 

of basin (Sylvan Lake 

concentration)

19 239 84.2 333 35.0 7.4 .014 5.5 10.5

Higher water elevation 

(2002), with 2 feet 

removed from the basin

20 654 87.7 358 35.9 5.2 .023 11.6 6.3

a

 Residence time is based on hydrologic conditions in monitoring year 2006, but with the specified water level.

b

 Scenario 1 established a base or reference condition for which results from other simulations or scenarios can be compared.
Figure 20. Measured and simulated average summer near-surface concentrations of 

A, total phosphorus, 

B, chlorophyll a, and C, Secchi depths in S

County, Wis., in response to various phosphorus-loading scenarios. Phosphorus concentrations were simulated with the Canfield and Bachman naturchlorophyll a concentrations and Secchi depths were simulated with Carlson (1977) trophic state index equations. See table 6 for a description of eac

Total phosphorus

0.0050.0100.0150.0200.0250.0300.035

-100 -50 0 50 100 150 200 250 300

PERCENT CHANGE IN CONTROLLABLE PHOSPHORUS LOADING

TOTAL PHOSPHORUS CONCENTRATION, 

IN MILLIGRAMS PER LITER

-65-33

0

336598

130

PERCENT CHANGE

2002 2003 Scenarios 

Chlorophyll a 

02468

1012141618

-100 -50 0 50 100 150 200 250 300

PERCENT CHANGE IN CONTROLLABLE PHOSPHO

CHLOROPHYLL A CONCENTRATION, 

IN MICROGRAMS PER LITER

Secchi depth

0

5101520

-100 -50 0 50 100 150 200 250 300

PERCENT CHANGE IN CONTROLLABLE PHOSPHORUS LOADING

SECCHI DEPTH, IN FEET

-100

-75-50-25

0

255075

PERCENT CHANGE

Measured (2005–06)

General response Natural scenarios

Specific years Anthropogenic-change 

Unadjusted model resultsGeneral responseMeasured Modeled with erosion Modeled without erosion 

Simulated from measured total phosphorus

Series of dry years

Series of wet yearsBase or referenceBase or referenceLower water elevation (5 feet lower than 200Lower elevation plus 2 (full tributary concentLower elevation plus 2 (Sylvan outflow conceHigher water level (20

2002 2003 Scenarios

Figure 20. Measured and simulated average summer near-surface concentrations of A, total phosphorus, B, chlorophyll a, and C, Secchi depths in SCounty, Wis., in response to various phosphorus loading scenarios. Phosphorus concentrations were simulated with the Canfield and Bachman natuand chlorophyll a concentrations and Secchi depths were simulated with Carlson (1977) trophic state index equations. See table 6 for a description o

EXPLANATION

A

B

C
32 Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin

Four types of data are required as input into the Canfield 

and Bachman model (eq. 5): water-quality data in table 3, and 

morphometric data (mean depth), hydrologic data (residence 

time), and nutrient-loading data in table 6. Although loading data are summarized for the entire year, this model and 

the Carlson TSI equations simulate water quality only for 

the growing season (May through September); therefore, the 

water-quality data in table 3 were used for comparison with 

model results.

Verification and Adjustments for Model Biases

The capability of the Canfield and Bachman (1981) 

model at simulating phosphorus concentrations in this 

closed-basin terminal lake was evaluated by inputting the 

morphometry of the lake and the average hydrologic and 

phosphorus inputs for MY 2005 and MY 2006 into the model 

(eq. 5) and simulating the near-surface total phosphorus 

concentration. The simulated total phosphorus concentration 

(0.014 mg/L; fig. 20A; and scenario 1 in table 6) is similar to 

the average of that measured in the lake during these years 

(0.013 mg/L; table 3). This similarity confirms that the model 

is expected to accurately simulate changes in Silver Lake in 

response to changes in phosphorus loading.

Determining how well the Carlson (1977) TSI equations 

simulate chlorophyll a concentrations and Secchi depths in 

Silver Lake was accomplished by using the TSI value based 

on the simulated total phosphorus concentration to compute 

the chlorophyll a concentration and Secchi depth in the lake 

with equations 2 and 3. Given a TSI value of 41.9 (from eq. 1 

with the simulated phosphorus concentration of 0.014 mg/L), 

the unadjusted modeled chlorophyll a concentration was 

3.15 μg/L and Secchi depth was 11.5 ft (fig. 20B and 20C). 

The unadjusted modeled chlorophyll a concentration was 

41 percent lower than that measured (5.4 μg/L). The unadjusted modeled Secchi depth was 8 percent higher than that 

measured (10.7 ft). These discrepancies indicate that the 

measured chlorophyll a concentrations and Secchi depths in 

Silver Lake are slightly worse than would be expected given 

the phosphorus concentration measured in the lake. Because 

of the discrepancies in measured and simulated chlorophyll a

concentrations and Secchi depths, all of the simulated chlorophyll a concentrations from equation 2 were increased by 

41 percent, and Secchi-depth values from equation 3 were 

decreased by 8 percent.

Response in Water Quality to Basinwide 

Changes in Phosphorus Loading

On the basis of model simulations for basinwide changes 

in controllable phosphorus loading (scenarios 1–10), phosphorus concentrations in the lake should have a curvilinear 

response to a linear change in loading, with a larger response 

to reductions in phosphorus loading than to increases in 

phosphorus loading (fig. 20A; table 6). Changes in in-lake 

phosphorus concentrations are about 40–50 percent of the 

changes in phosphorus loading. For example, a 50-percent 

increase in controllable external phosphorus loading causes a 

23-percent increase in in-lake phosphorus concentrations.

Simulated summer average chlorophyll a concentrations responded linearly to changes in controllable external 

phosphorus loading (fig. 20B). The changes in chlorophyll 

a concentrations, on a percentage basis, are smaller than 

the changes in external phosphorus loadings. For example, 

a 50-percent change in controllable external phosphorus 

loading causes about a 35-percent change in chlorophyll a

concentrations.

Simulated summer average Secchi depths also showed a 

curvilinear response to changes in controllable external phosphorus loading and responded slightly more strongly to reductions in loading than to increases in loading (fig. 20C). The 

changes in Secchi depths, on a percentage basis, were smaller 

than the changes in external phosphorus loadings. For example, a 50-percent increase in controllable external phosphorus 

loading causes about a 20-percent reduction in Secchi depths.

The relatively small response in each of the TSI variables to changes in controllable phosphorus loading is partly 

because some of the phosphorus that is presently input into 

Silver Lake is from uncontrollable sources, not that Silver 

Lake is unresponsive to external loading. In fact, a 100-percent increase in controllable phosphorus loading increases the 

total phosphorus load by 78 percent (from 216 lb for the base 

case to 385 lb) and increases the total phosphorus concentrations in the lake by 43 percent, increases chlorophyll a concentrations by 69 percent, and decreases Secchi depths by 30 

percent. Therefore, changes in phosphorus loading may have a 

large impact on the water quality of Silver Lake.

Model Validation and Sensitivity of Lake-Water 

Quality to Phosphorus Inputs from Erosion

The eutrophication models were used to simulate the 

conditions during 2002 and 2003 to determine how well these 

models predict changes during different hydrologic conditions 

(scenarios 11 and 13). In 2002, the water level of the lake 

had just reached its maximum (fig. 7), and nutrient input was 

expected to be near its highest level. In 2003, water levels of 

the lake were just beginning to drop, and nutrient input had 

been high for a few years. Shoreline erosion was expected to 

occur in both years. During both years, only a few chlorophyll 

a samples were collected early in the year, when concentrations are typically lower than in late summer; therefore, the 

average of the measured chlorophyll a concentrations may 

result in a summer average that is biased high.

The simulated total phosphorus concentration for 2002 

(scenario 11, 0.025 mg/L; fig. 20A and table 6) was higher 

than that measured in the lake (0.017 mg/L; table 3). This 

discrepancy may have been caused by the lake not being in 

equilibrium with the inputs from the watershed. Researchers 

have found that higher phosphorus concentrations in a lake 
Simulated Changes in Water Quality in Response to Changes in Phosphorus Loading 33

occur after several years of high inputs from the watershed, 

rather than after a single year of high inputs (Lathrop and 

others, 1998). The simulated and measured total phosphorus 

concentrations for 2002 were then used to predict the average 

chlorophyll a concentration and Secchi depth. On the basis 

of the TSI values computed from the simulated (scenario 

11) and measured phosphorus concentrations, the predicted 

chlorophyll a concentrations in the lake from equation 2 were 

12.8 μg/L and 7.4 μg/L, respectively, whereas the measured 

concentration in the lake was 11.8 μg/L. Although the simulated phosphorus concentration appears to have more acccurately predicted the chlorophyll a concentrations in the lake 

than the measured phosphorus concentration, it is believed that 

the computed summer average chlorophyll a concentration is 

biased high and the actual summer average concentration was 

probably closer to that predicted from the measured phosphorus concentration. On the basis of the simulated and measured phosphorus concentrations, the summer average Secchi 

depths in the lake computed from equation 3 were 5.9 ft and 

8.6 ft, respectively, whereas the measured value in the lake 

was 7.5 ft. Therefore, the Secchi depth in 2002 was predicted 

slightly better with the actual measured phosphorus concentration than with the predicted phosphorus concentration.

The simulated total phosphorus concentration for 2003 

(scenario 13, 0.020 mg/L; fig. 20A and table 6) was similar to 

that measured in the lake (0.019 mg/L; table 3). This similarity may indicate that by 2003, after a few years with high 

phosphorus inputs, the lake was now in equilibrium with the 

inputs from the watershed. The simulated and measured total 

phosphorus concentrations for 2003 were then used to predict 

average chlorophyll a concentration and Secchi depth in the 

lake. On the basis of both concentrations, the chlorophyll a 

concentration in the lake (predicted to be 9.2 and 7.4 μg/L, 

respectively) should have been lower than the summer average 

based on measurements in the lake (11.8 μg/L). Once again, 

the summer average chlorophyll a concentration based on 

measurements was believed to be biased high and the actual 

summer average concentration in the lake may have been 

closer to that estimated by the model (9.2 μg/L). On the basis 

of the simulated and measured phosphorus concentrations, the 

predicted summer average Secchi depth in the lake was 7.4 ft, 

similar to that measured in the lake. Therefore, the models 

seem to do well at predicting phosphorus, chlorophyll a, and 

Secchi depth after a series of years of higher loading and 

higher water levels.

The models were then used to determine the importance 

of the additional phosphorus from shoreline erosion on the 

water quality of the lake (scenarios 11–14, table 6). This was 

done by reducing the nutrient loading in 2002 and 2003 by 

the amount estimated to have been contributed by erosion 

(93 lb). In both years, removing the phosphorus input from 

erosion resulted in predicted summer average total phosphorus concentrations being reduced by about 0.002–0.003 

mg/L, chlorophyll a concentrations being reduced by about 

1.5–1.7 μg/L, and Secchi depth increasing by about 0.6–1.1 

ft. Therefore, phosphorus input from erosion has a measurable 

affect on water quality.

Response in Water Quality to Specific Natural 

and Anthropogenic-Change Scenarios

The Canfield and Bachman model (eq. 5) was then used 

to predict how total phosphorus concentrations in Silver Lake 

should respond to several natural and anthropogenic changes 

that would affect the water level of the lake. This was done by 

modifying the annual phosphorus loadings, morphometry, and 

residence time of water in the lake (scenarios 15–20; table 6).

In simulating the conditions during 2002 and 2003, the 

models were shown to accurately simulate the water quality in Silver Lake after a few years of sustained high water 

levels and high inputs, when the lake has come into equilibrium with its inputs from the watershed. Scenarios 15 and 16 

were used to determine how a wide range in natural changes 

(changes in lake level resulting from a series of three years 

of below- or above-normal precipitation and inflow) should 

affect the water quality of the lake (fig. 20; table 6). Sustained 

low water levels (scenario 15, with a water level 5.8 ft lower 

than in fig. 1) and low phosphorus inputs, caused by a series 

of dry years with below-normal precipitation, should improve 

the water quality of the lake. The reduction in phosphorus 

loading resulted in phosphorus concentrations decreasing 

to 0.009 mg/L, chlorophyll a concentrations decreasing to 

2.8 μg/L, and Secchi depths increasing to 16.5 ft. Sustained 

high water levels (scenario 16, with a water level 1.0 ft higher 

than in fig. 1 and similar to that in 2004) and increased inflow 

and phosphorus inputs, caused by a series of wet years with 

above-normal precipitation, increased the phosphorus concentrations to 0.022 mg/L, increased chlorophyll a concentrations 

to 10.6 μg/L, and decreased Secchi depths to 6.7 ft. Therefore, 

natural changes in precipitation and inflow can have a large 

affect on the water quality of Silver Lake.

Four scenarios were then performed to simulate the 

effects of adding water to the lake during relatively dry years 

and removing water from the lake during relatively wet years 

(scenarios 17–20). Scenarios 17–19 were used to determine 

the effects of diverting water into the lake during relatively 

dry years when the water level had been lowered by reduced 

precipitation and inflow. To do this, first the water quality of 

the lake was simulated with a water level being 5 ft less than 

the full level of the lake (fig. 1; about 5 ft less than in 2005). 

The hydrology and tributary input were assumed to be similar 

to that in 2006 (a relatively dry year); however, the atmospheric input was reduced from 2006 because of the smaller 

surface area of the lake. The results of the simulation indicate 

that the water quality in the lake should improve during this 

low water-level condition compared to the base or reference 

condition (the average of that measured in MY 2005 and MY 

2006): average total phosphorus concentration of 0.011 mg/L, 

chlorophyll a concentration of 4.1 μg/L, and Secchi depth 

of 12.9 ft (scenario 17, table 6 and fig. 20). If 2 ft of water 

(672 acre-ft) were then added to the lake from outside the 

natural Silver Lake watershed at a total phosphorus concentration of 0.215 mg/L (the average concentration in tributary 7 

during MY 2005 and MY 2006), the water quality of the lake 
34 Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin

should degrade: the summer average total phosphorus concentration should increase to 0.023 mg/L, chlorophyll a concentration should increase to 11.6 μg/L, and Secchi depth should 

decrease to 6.3 ft. If, however, the additional 2 ft of water 

(672 acre-ft) could be delivered to the lake at an average concentration similar to that leaving Sylvan Lake (0.055 mg/L; 

scenario 19), the water quality in the lake should be similar to 

the average of the conditions in MY 2005 and MY 2006: average summer total phosphorus concentration of 0.014 mg/L, 

chlorophyll a concentration of 5.5 μg/L, and Secchi depth of 

10.5 ft.

A comparison among three scenarios was used to 

evaluate the effects of removing water from the lake during 

relatively wet years when the water levels are high because of 

increased precipitation and runoff. To do this, the results from 

the previous simulation of 2002 (scenarios 11 and 12, a very 

wet year with and without erosion) are compared with those 

from when the water level of the lake in 2002 was reduced 

2 ft (scenario 20). In scenario 20, the hydrology and tributary 

input were assumed to be similar to that in 2002; however, 

2 ft of water (726 acre-ft) were assumed to be pumped from 

the surface of the lake. Because 2 ft of water were removed 

from the lake, the surface area was reduced to that for an 

elevation of 87.7 ft and, therefore, atmospheric inputs were 

reduced because of the smaller surface area of the lake. Water 

quality in the lake during this lowered-water-level condition was slightly better than that predicted for 2002 when the 

input of phosphorus from erosion was included, but similar to 

that estimated for 2002 when erosion was not included in the 

simulation. Therefore, the primary benefit to water quality of 

lowering the water level of the lake is to remove the phosphorus input from shoreline erosion.

TSI values, based on near-surface concentrations of total 

phosphorus and chlorophyll a and on Secchi depths, indicate 

that Silver Lake is typically oligotrophic to mesotrophic; however, increases in phosphorus loading during periods of high 

precipitation, high inflow, and high water levels can degrade 

water quality (fig. 6). Results of model simulations indicate 

that increasing the input of water from the watershed (such 

as from tributary 7) can also have detrimental affects on the 

water quality of the lake unless the phosphorus concentrations 

in this water can be maintained at a relatively low concentration. During periods of high natural water inputs or diversion 

of water through the wetland system north of Silver Lake (if 

this were done), the increased input of phosphorus may result 

in eutrophic conditions in Silver Lake.

Relative Importance of Anthropogenic 

Changes in the Watershed to Natural 

Hydrologic Changes

One purpose of this study was to evaluate how natural 

changes in hydrology, water level, and phosphorus inputs 

affect the water quality of Silver Lake in comparison with 

water-quality effects caused by anthropogenic changes in the 

watershed. Model results indicate that most of the measured 

deterioration in water quality between 2002 and 2004 was 

caused by the large increase in phosphorus input to the lake 

that occurred during the sustained high water levels. After an 

extended period of high inflow and increased water levels, 

measured phosphorus concentrations increased by at least 

0.010 mg/L, water clarity decreased by about 8 ft, and chlorophyll a concentrations increased. Because of the limited monitoring program during 2002–4, quantifying the increase in 

chlorophyll a concentrations is difficult. The decreased water 

quality measured in 2003 was similar to that predicted with 

the eutrophication models; therefore, the models appear to 

accurately estimate changes in water quality after several years 

of high or low phosphorus inputs. The increased input of water 

and phosphorus from the diversion of water leaving Sylvan 

Lake into Silver Lake and the increased input of phosphorus 

from shoreline erosion that accounted for about 13–20 percent 

of the total phosphorus input collectively contributed to the 

poor water quality during the very high water levels.

The improvements in water quality since water levels 

began to drop in 2003 (fig. 4) also indicate that most of the 

deterioration in the water quality of Silver Lake during 2002–4 

was caused by the increase in water and phosphorus input into 

the lake from the watershed and by shoreline erosion caused 

by the higher water levels. Although the degradation in water 

quality appears to be associated primarily with increased 

inflow and high water levels, the lake is still susceptible to 

degradation associated with changes in its watershed. The 

estimated annual yields of phosphorus from the watershed are 

quite low (25.0–130 lb/mi2); however, future land development that does not consider mitigation of nutrients in runoff 

could increase these yields.

Before the 1960s, the watershed around Silver Lake was 

different than it is now in the 2000s. Much of the area immediately adjacent to the lake in 1940s and 1950s was agricultural. 

About 25 dairy cows were pastured immediately adjacent 

to the lake, and about 40–50 beef cows were pastured close 

to the lake (Edward Jacobson, local resident, oral commun., 

2008). If one dairy cow produces about 45 to 48 lb of phosphorus annually (Hollman and others, 2008; Hermanson and 

Kalita, 1994) and one beef cow produces 26 lb (Hermanson 

and Kalita, 1994), then an additional 2,300 lb of phosphorus 

may have been input to the watershed annually during that 

time (equivalent to about 1,500 people living near the lake). If 

only 10 percent of this phosphorus reached the lake, then the 

total amount of phosphorus input to the lake (446 lb) would be 

about twice that estimated in MY 2005 and MY 2006 (216 lb). 

From model results in table 6 and fig. 20 (this input would 

be similar to an increase in controllable phosphorus of about 

150 percent), the average phosphorus concentration in the 

lake would likely have been about 0.022 mg/L, and the water 

clarity would likely have been about 7 ft. Therefore, during the 

1940s and 1950s, the lake may have been typically classified 

as borderline mesotrophic to eutrophic and possibly classified 
Summary and Conclusions 35

After about 1996, summer average total phosphorus 

concentrations increased from about 0.008 mg/L to about 

0.018 mg/L in 2003, before decreasing to about 0.010 mg/L 

in 2007–8. From 1996 to 2003, Secchi depths decreased 

from about 14 ft to about 7.5 ft before increasing to about 

12–19 ft in 2007–8. Therefore, Silver Lake would typically 

be classified as mesotrophic to oligotrophic; however, during 

2002–4, the lake approached being classified as mesotrophic 

to eutrophic.

Reconstructed water levels of Silver Lake indicated that 

the measured changes in water level since 1967 are representative of fluctuations that have occurred since 1900; however, 

the most extreme fluctuation occurred between about 1989 

and 2002. Fluctuations in water levels of about 4–10 ft have 

occurred about every 15 years.

Because the productivity in Silver Lake should be limited 

by phosphorus, it should be the nutrient of concern when 

management efforts to improve or prevent degradation in the 

lake-water quality are considered. Most phosphorus enters the 

lake with water inputs; therefore, both water and phosphorus 

budgets were constructed as part of the study. Precipitation 

and surface-water inflow were the predominant sources of 

water; precipitation and surface-water inflow contributed 

about 70 and 30 percent, respectively. Before this study, 

groundwater was believed also to be a major source of water 

and phosphorus to the lake; however, results of this study 

indicate that Silver Lake is hydraulically mounded above 

the water table and that groundwater does not enter the lake. 

The average annual load of phosphorus to the lake during the 

two monitoring years was 216 lb, of which 169 lb came from 

tributary and nearshore areas (78 percent) and 47 lb (22 percent) came from atmospheric deposition. Because Silver Lake 

is hydraulically mounded above the water table, there is no 

input of phosphorus from groundwater and septic systems. To 

determine how the hydrologic and phosphorus loading to the 

lake has varied in association with fluctuations in water level, 

water and phosphorus budgets were constructed for a series of 

dry years (low water levels) and during a series of wet years 

(high water levels). The total water input to the lake ranged 

by a factor of about 2, and total phosphorus input to the lake 

ranged by a factor of about 6.

Results from the Canfield and Bachman eutrophication 

model and Carlson TSI equations demonstrated that changes 

in controllable phosphorus loading have curvilinear relations 

with phosphorus concentrations and Secchi depths in the lake. 

A larger change in phosphorus concentrations and Secchi 

depths was simulated with decreases in phosphorus loading 

than with increases in loading. The relation between changes 

in phosphorus loading and changes in chlorophyll a concentrations was linear. The changes in water quality were less 

than the changes in phosphorus inputs, however, on a percentage basis. For example, a 50-percent increase in controllable 

external phosphorus loading should cause about a 23-percent 

increase in total phosphorus concentrations, a 35-percent 

increase in chlorophyll a concentrations, and a 20-percent 

reduction in Secchi depths. Part of the reason for the relatively 

as moderately eutrophic during wet years with high water 

levels, such as around 1945 and 1954 when water levels were 

estimated to be quite high (fig. 7).

Given the results from General Circulation Models, many 

scientists believe that climate change will cause systematic 

decreases or increases in the hydrologic budgets and water 

levels of lakes or cause water levels to fluctuate more widely 

than they have previously, in response to larger fluctuations 

in precipitation and runoff (Mulholland and Sale, 1998; Bates 

and others, 2008). This study has shown that previous natural 

changes in the water and phosphorus input to this terminal 

lake from a series of dry years to a series of wet years has 

ranged by factors of 2.5 and 6, respectively. These changes in 

hydrology and phosphorus loading, alone, were sufficient to 

cause the lake to change from being classified as oligotrophic 

to mesotrophic during very dry conditions to borderline 

mesotrophic to eutrophic during very wet conditions. In many 

lakes, changes in nutrient inputs of this magnitude may be 

expected only from anthropogenic changes to the watershed; 

however, because of the unique hydrology and land use in 

Silver Lake’s watershed, changes in phosphorus loading 

associated with natural variability in precipitation are very 

large. The changes in phosphorus input from a series of dry 

years to a series of wet years may be of similar magnitude to 

the additional loading from agriculture in the watershed in the 

1940s and 1950s. The natural variability in loading, however, 

is currently larger than the phosphorus input from controllable 

sources in the watershed. Therefore, variability in precipitation patterns has affected the trophic state of Silver Lake in 

the past, and climatic change may have a large influence on its 

trophic state in the future.

Summary and Conclusions

Silver Lake is typically a mesotrophic-to-oligotrophic, 

soft-water, terminal lake in northwestern Wisconsin. Data 

collected as part of the ongoing monitoring program by the 

local community demonstrated that the water quality of the 

lake had degraded during 2002–4 (increased phosphorus and 

chlorophyll a concentrations). The decrease in water quality 

coincided with very high water levels in the lake. To gain a 

better understanding of what may have caused the apparent 

degradation in water quality and, therefore, provide information for management of the lake should development increase 

or the climate change, the USGS did a detailed study during 

2004–8. The goals of this study were to describe past and present lake-water quality, describe changes in the water level in 

the lake since 1900, construct water and phosphorus budgets 

for the lake, simulate the potential effects of changes in water 

and phosphorus inputs on lake-water quality, and compare the 

relative importance of natural changes in phosphorus inputs 

and water level and anthropogenic changes in the watershed to 

lake-water quality.
36 Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin

small response was caused by part of the phosphorus input 

coming from uncontrollable sources (atmospheric deposition), not because the lake is unresponsive to external loading. 

For example, a 78-percent increase in total phosphorus input 

should cause phosphorus concentrations in the lake to increase 

by 43 percent, chlorophyll a concentrations to increase by 

69 percent, and Secchi depths to decrease by 30 percent. 

Therefore, changes in phosphorus loading may have a large 

impact on the water quality of Silver Lake.

Specific scenarios were used to simulate the effects of 

natural climatic and anthropogenic changes on lake-water 

quality. Sustained low water levels caused by a series of dry 

years with low precipitation and low inflow improved the 

water quality of the lake, whereas sustained high water levels 

caused by a series of wet years with more precipitation and 

increased inflow dramatically degraded the water quality of 

the lake. Therefore, natural changes in the input of phosphorus 

from precipitation and inflows to the lake can have a large 

effect on lake-water quality. Additional scenarios showed 

that the degraded water quality during periods with very high 

water level was partly caused by the phosphorus input from 

shoreline erosion. Diverting water into the lake during periods 

with low water levels could measurably degrade the water 

quality unless a strategy can be found to import water with 

low phosphorus concentrations, whereas withdrawing water 

during periods of high water levels should slightly improve 

the lake-water quality because of the reduction in phosphorus 

input from shoreline erosion. During periods of high natural 

water inputs, possibly accentuated by water diverted through 

the wetland system north of Silver Lake, high inputs of phosphorus can result in eutrophic conditions in Silver Lake.

Water levels have fluctuated by as much as 10 ft during 

several wet/dry cycles since 1900. During periods of high 

phosphorus input associated with very high water levels, 

results from the eutrophication models indicated that lakewater quality should degrade (to mesotrophic-to-eutrophic 

conditions); during periods with low phosphorus input and low 

water levels, however, lake-water quality should improve (to 

oligotrophic-to-mesotrophic conditions). During the 1940s and 

1950s, because of likely agricultural inputs from the watershed, the lake may have been typically classified as borderline 

mesotrophic to eutrophic and possibly classified as moderately 

eutrophic during wet years with high runoff, especially around 

1945 and 1954 when water levels were likely to have been 

very high.

Silver Lake is typically classified as oligotrophic to 

mesotrophic because of the small input of phosphorus from its 

watershed. Natural changes in the water and phosphorus input 

to this terminal lake, however, were sufficient to cause the lake 

to change from being classified as oligotrophic to mesotrophic 

during very dry conditions to borderline mesotrophic to 

eutrophic during very wet conditions. In many lakes, changes 

in nutrient inputs of this magnitude are expected only from 

anthropogenic changes to the watershed; however, because of 

the unique hydrology and land use in Silver Lake’s watershed, 

the natural variability in loading is currently larger than the 

phosphorus input from controllable sources in the watershed. 

Therefore, variability in precipitation patterns has affected the 

trophic state of Silver Lake in the past, and climatic change 

may have a large influence on its trophic state in the future. 

Although the degradation in lake-water quality appears to be 

caused primarily by high inflow and high water levels, the 

lake is still susceptible to degradation associated with small 

changes in its watershed. Because of the limited phosphorus 

that is presently input into the lake, increases in phosphorus 

loading could have a large effect on the lake-water quality. 

Therefore, management actions to minimize future phosphorus 

input to this lake are likely to greatly benefit water quality.

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Robertson, Rose, and Fitzpatrick—Water Quality and Hydrology of Silver Lake, Barron County, Wisconsin—Scientific Investigations Report 2009–5077

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