U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2008–5053

In Cooperation with Price County Land Conservation Committee

Water Quality, Hydrology, and Simulated Response 

to Changes in Phosphorus Loading of Butternut Lake, 

Price and Ashland Counties, Wisconsin, with Special 

Emphasis on the Effects of Internal Phosphorus 

Loading in a Polymictic Lake

Water Quality, Hydrology, and Simulated 

Response to Changes in Phosphorus 

Loading of Butternut Lake, Price and 

Ashland Counties, Wisconsin, with 

Special Emphasis on the Effects of 

Internal Phosphorus Loading in a 

Polymictic Lake

By Dale M. Robertson and William J. Rose

In cooperation with the Price County Land Conservation Committee

Scientific Investigations Report 2008–5053

U.S. Department of the Interior

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

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2008

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

reproduce any copyrighted materials contained within this report.

Suggested citation:

Robertson, Dale M., and Rose, William J., 2008, Water quality, hydrology, and simulated response to changes 

in phosphorus loading of Butternut Lake, Price and Ashland Counties, Wisconsin, with special emphasis on the 

effects of interal phosphorus loading in a polymictic lake: U.S. Geological Survey Scientific Investigations Report 

2008–5053, 46 p.

ISBN 978-1-4113-2177-9
iii

Contents

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

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

Butternut Lake and Its Watershed............................................................................................ 5

Shallow Polymictic Lakes and Internal Phosphorus Loading .............................................. 7

Purpose and Scope ..................................................................................................................... 8

Study Methods and Sampling Sites................................................................................................... 8

Lake-Stage and Water-Quality Monitoring.............................................................................. 8

Lake Classification....................................................................................................................... 9

Lake-Sediment Analyses............................................................................................................ 9

Stream Monitoring..................................................................................................................... 10

Ground-Water Monitoring........................................................................................................ 11

Measured Lake Water Quality.......................................................................................................... 12

Inferred Lake Water Quality from Lake-Sediment Analyses ....................................................... 20

Hydrology and Water Budget ........................................................................................................... 20

Change in Storage ..................................................................................................................... 21

Precipitation................................................................................................................................ 21

Evaporation................................................................................................................................. 24

Surface-Water Inflow ............................................................................................................... 24

Surface-Water Outflow............................................................................................................. 25

Ground-Water Inflow and Outflow.......................................................................................... 25

Water-Budget Summary........................................................................................................... 26

Sources of Phosphorus...................................................................................................................... 29

Precipitation................................................................................................................................ 29

Surface-Water Inflow .............................................................................................................. 29

Butternut Creek Inlet....................................................................................................... 29

Spiller Creek....................................................................................................................... 32

Small Tributaries and Ungaged Near-Lake Area......................................................... 32

Ground Water............................................................................................................................. 32

Septic Systems........................................................................................................................... 32

Release of Phosphorus from Lake Sediments ...................................................................... 32

Surface-Water Outflow ............................................................................................................ 34

Phosphorus Budget Summary................................................................................................. 34

Simulated Changes in Water Quality in Response to Changes in Phosphorus Loading ........ 34

Modeling Approach................................................................................................................... 36

Data Requirements.................................................................................................................... 36

Algorithms and Calibration....................................................................................................... 36

Response in Water Quality to Changes in Phosphorus Loading........................................ 39

Changes in Phosphorus Concentrations ...................................................................... 39

Changes in Chlorophyll a Concentrations .................................................................... 41

Changes in Secchi Depths (Water Clarity)................................................................... 41

Changes in Trophic Status............................................................................................... 41

Changes in the Percentage of Days with Algal Blooms............................................. 41
iv

Importance of Internal Phosphorus Loading ................................................................................. 42

Summary and Conclusions................................................................................................................ 43

Literature Cited.................................................................................................................................... 44

Figures

1–2. Maps showing:

1. Watershed of Butternut Lake, Price and Ashland Counties, Wis....................... 3

2. Subbasins and land use/land cover of the near-lake drainage area 

of Butternut Lake, Wis., with locations and types of data-collection 

sites identified ............................................................................................................. 6

3–12. Graphs showing:

3. Changes in phosphorus release rates (ratio) from aerobic and 

anaerobic sediments of the Upper Mississippi River as a function 

of water temperature ............................................................................................... 11

4. Distributions of water temperature and dissolved oxygen from 

March 10, 2003, through September 21, 2004, at the Deep-hole Site in 

Butternut Lake, Wis.................................................................................................. 13

5. Near-surface total phosphorus concentrations, chlorophyll a

concentrations, and Secchi depths at various locations in 

Butternut Lake, Wis., during 2003 and 2004.......................................................... 15

6. Near-surface total phosphorus concentrations, chlorophyll a

concentrations, and Secchi depths at the Deep-hole Site in 

Butternut Lake, Wis., from 1972 to 2006 ................................................................ 17

 7. Trophic state index values based on surface concentrations of 

total phosphorus and chlorophyll a , and Secchi depths, 

in Butternut Lake, Wis.............................................................................................. 19

8. Estimated changes in summer total phosphorus concentrations based 

on changes in the diatom community in the sediment cores from 

Butternut Lake, Wis.................................................................................................. 20

9. Measured daily water levels of Butternut Lake, Wis. ........................................ 21

10. Precipitation at Butternut Lake, Wis., during November 2002 to October 2004, relative to long-term average precipitation at Park Falls, Wis. ....... 24

11. Daily-average flow and total phosphorus concentrations in Butternut 

Creek at Cutoff Road and Spiller Creek at Highway B, tributaries to 

Butternut Lake, Wis., November 1, 2002, through October 31, 2004................. 25

12. Daily-average flow and total phosphorus concentrations in Butternut 

Creek at Highway B, outlet from Butternut Lake, Wis., November 1, 

2002, through October 31, 2004............................................................................... 26

13. Map showing estimated ground-water contributing area to 

Butternut Lake, Wis.......................................................................................................... .27

14–19. Graphs showing: 

14. Water budgets for Butternut Lake, Wis., for monitoring years 2003 

and 2004...................................................................................................................... 28

15. Monthly accuracy of the water budget based on monthly total water 

inputs and outputs plus storage change for Butternut Lake, Wis.................... 29

16. Phosphorus budgets for Butternut Lake, Wis., for monitoring years 

2003 and 2004............................................................................................................. 35
v

17. Measured and simulated (prior to and after calibration with the 

BATHTUB model) average summer near-surface total phosphorus 

concentrations, chlorophyll a concentrations, and Secchi depths 

in the three basins in Butternut Lake, Wis., and the lake as a whole.............. 38

18. Simulated changes in near-surface total phosphorus concentrations, chlorophyll a concentrations, and Secchi depths at the 

Deep-hole Site in Butternut Lake, Wis., in response to various 

phosphorus-loading scenarios............................................................................... 40

19. Simulated changes in the percentage of days from May through

September with an algal bloom in response to various phosphorusloading scenarios for Butternut Lake, Wis. ......................................................... 42

Tables

1. Summary of activities affecting the loading of nutrients into Butternut Lake, 

Price and Ashland Counties, Wis...................................................................................... 4

2. Morphometric characteristics of the basins in Butternut Lake, Price and 

Ashland Counties, Wis........................................................................................................ 5

 3. Land use/land cover in the Butternut Lake, Wis., watershed from classifications defined by WISCLAND.............................................................................................. 7

4. Estimated area of aerobic sediment and anaerobic sediment in the 

three basins in Butternut Lake, Wis. .............................................................................. 12

 5. Summer average water quality throughout Butternut Lake, Wis., 

for monitoring years 2003 and 2004. ............................................................................... 14

 6. Near-surface, summer-average and August water quality and trophic 

state index values for the Deep-hole Site in Butternut Lake, Wis............................. 18

7. Water budgets for Butternut Lake, Wis., for monitoring years 2003 and 2004, 

and average for the two years. ....................................................................................... 22

8. Phosphorus budgets for Butternut Lake, Wis., for monitoring years 2003 and 

2004, and average for the two years. ............................................................................. 30

9. Summary of estimated rates of phosphorus release from the sediments of 

Butternut Lake, Wis., in August 2004.............................................................................. 33

10. Algorithms within the BATHTUB model that were used to simulate water 

quality in the basins in Butternut Lake, Wis.................................................................. 37

11. Calibration coefficients used in the BATHTUB model simulations of the 

water quality in the basins in Butternut Lake, Wis. ..................................................... 37

12. Estimated near-surface phosphorus concentrations in Butternut Lake, Wis., 

from various hydrologic and phosphorus loading models contained in the 

Wisconsin Lakes Modeling Suite and estimated total annual phosphorus load 

needed to result in a 0.044 mg/L total phosphorus concentration in the lake......... 39
vi

Conversion Factors

Multiply By To obtain

Length

micrometer (μm) 0.00003937 inch (in.)

centimeter (cm) .3937 inch (in.)

meter (m) 3.281 foot (ft) 

kilometer (km) .6214 mile (mi)

Area

square meter (m2

) 10.76 square foot (ft2) 

hectare (ha) 2.471 acre

hectare (ha) .003861 square mile (mi2

) 

square kilometer (km2

) 247.1 acre

square kilometer (km2

) .3861 square mile (mi2)

Volume

liter (L) 0.2642 gallon (gal)

cubic centimeter (cm3

) .06102 cubic inch (in3) 

cubic meter (m3

) .0008107 acre-foot (acre-ft) 

Flow rate

cubic meter per second (m3

/s) 35.31 cubic foot per second (ft3/s)

Mass

kilogram (kg) 2.205 pound avoirdupois (lb)

Application Rate

kilogram per square kilometer 

(kg/km2

)

5.7099 pound per square mile (lb/mi2

)

kilogram per square kilometer 

(kg/km2

)

.00892 pound per acre (lb/ac)

milligrams per square meter 

(mg/m2

)

.000000205 pounds per square foot (lb/ft2

)

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).
vii

Acknowledgments

Technical Reviewers

Herbert S. Garn, Assistant Center Director, U.S. Geological Survey, Middleton, Wis.

James Kreitlow, Water Resources Management Specialist, Wisconsin Department of 

Natural Resources, Rhinelander, Wis.

Chet Zenone, Hydrologist (retired), U.S. Geological Survey, Salem, Ore.

Local Project Coordinators

Robert “Butch” D. Lobermeier, County Conservationist, Price County Land and Water 

Conservation Department, Phillips, Wis.

Diane Daulton, County Conservationist, Price County Land and Water Conservation 

Department, Phillips, Wis.

Editorial and Graphics

Elizabeth A. Ciganovich, Technical Editor, U.S. Geological Survey Columbus Publishing 

Service Center, Ohio

Jennifer L. Bruce, Geographer, U.S. Geological Survey, Middleton, Wis.

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

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

Data Collection

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

Approving Official

Dorothy Tepper, Bureau Reports Approving Official, Eastern Region, U.S. Geological Survey, 

Reston, Va.

Water Quality, Hydrology, and Simulated Response 

to Changes in Phosphorus Loading of Butternut Lake, 

Price and Ashland Counties, Wisconsin, 

with Special Emphasis on the Effects of Internal 

Phosphorus Loading in a Polymictic Lake

By Dale M. Robertson and William J. Rose

Abstract

Butternut Lake is a 393-hectare, eutrophic to hypereutrophic lake in northcentral Wisconsin. After only minor 

improvements in water quality were observed following 

several actions taken to reduce the nutrient inputs to the lake, 

a detailed study was conducted from 2002 to 2007 by the U.S. 

Geological Survey to better understand how the lake functions. 

The goals of this study were to describe the water quality and 

hydrology of the lake, quantify external and internal sources 

of phosphorus, and determine the effects of past and future 

changes in phosphorus inputs on the water quality of the lake. 

Since the early 1970s, the water quality of Butternut 

Lake has changed little in response to nutrient reductions from 

the watershed. The largest changes were in near-surface total 

phosphorus concentrations: August concentrations decreased 

from about 0.09 milligrams per liter (mg/L) to about 

0.05 mg/L, but average summer concentrations decreased only 

from about 0.055–0.060 mg/L to about 0.045 mg/L. Since the 

early 1970s, only small changes were observed in chlorophyll a concentrations and water clarity (Secchi depths).

All major water and phosphorus sources, including the 

internal release of phosphorus from the sediments (internal 

loading), were measured directly, and minor sources were 

estimated to construct detailed water and phosphorus budgets 

for the lake during monitoring years (MY) 2003 and 2004. 

During these years, Butternut Creek, Spiller Creek, direct 

precipitation, small tributaries and near-lake drainage area, and 

ground water contributed about 62, 20, 8, 7, and 3 percent of 

the inflow, respectively. The average annual load of phosphorus to the lake was 2,540 kilograms (kg), of which 1,590 kg 

came from external sources (63 percent) and 945 kg came 

from the sediments in the lake (37 percent). Of the total external sources, Butternut Creek, Spiller Creek, small tributaries 

and near-lake drainage area, septic systems, precipitation, and 

ground water contributed about 63, 23, 9, 3, 1, and 1 percent, 

respectively. 

Because of the high internal phosphorus loading, the 

eutrophication models used in this study were unable to simulate the observed water-quality characteristics in the lake without incorporating this source of phosphorus. However, when 

internal loading of phosphorus was added to the BATHTUB 

model, it accurately simulated the average water-quality characteristics measured in MY 2003 and 2004. Model simulations 

demonstrated a relatively linear response between in-lake total 

phosphorus concentrations and external phosphorus loading; 

however, the changes in concentrations were smaller than the 

changes in external phosphorus loadings (about 25–40 percent 

of the change in phosphorus loading). Changes in chlorophyll a concentrations, the percentage of days with algal 

blooms, and Secchi depths were nonlinear and had a greater 

response to reductions in phosphorus loading than to increases 

in phosphorus loading. A 50-percent reduction in external 

phosphorus loading caused an 18-percent decrease in chlorophyll a concentrations, a 41-percent decrease in the percentage 

of days with algal blooms, and a 12-percent increase in Secchi 

depth. When the additional internal phosphorus loading was 

removed from model simulations, all of these constituents 

showed a much greater response to changes in external phosphorus loading. 

Because of Butternut Lake’s morphometry, it is polymictic, which means it mixes frequently and does not develop 

stable thermal stratification throughout the summer. This characteristic makes it more vulnerable than dimictic lakes, which 

mix in spring and fall and develop stable thermal stratification 

during summer, to the high internal phosphorus loading that 
2 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

has resulted from historically high, nonnatural, external 

phosphorus loading. In polymictic lakes, the phosphorus 

released from the sediments is mixed into the upper part of 

the lake throughout summer. Once Butternut Lake became 

hypereutrophic (very productive), it became very difficult 

to alter its trophic state through reductions in external 

phosphorus loading because the high internal loading 

does not respond quickly to reductions in external nutrient 

loading. For Butternut Lake to become significantly less 

productive (change to a borderline mesotrophic/eutrophic 

state) a combined approach to reduce or eliminate internal 

phosphorus loading and reduce the external phosphorus 

loading by about 50 percent is needed. 

Introduction

Butternut Lake is a relatively shallow, 393-ha lake in 

the Northern Lake and Forests ecoregion of northcentral 

Wisconsin (Omernik and others, 2000). The lake is about 5 

km northwest of Park Falls, which is between the popular 

recreational areas near Hayward and Minocqua in northern Wisconsin. The lake is an important water resource in 

southern Ashland and northern Price counties (fig. 1), and 

it is popular for fishing and swimming.

Prior to about 1860, Butternut Lake was relatively 

pristine, and its watershed was populated by only a small 

band of Chippewa Indians who lived along the lake and its 

tributaries (Scott, 2005). However, with logging activities 

that began in the area in the mid to late 1800s and with 

construction of the railway through the area in the late 

1870s, changes in many activities and land use affected 

the amount of nutrients input to the lake (table 1). In the 

1870s, agricultural activities began in the watershed, 

and the Village of Butternut was established. Along with 

increased development in the watershed came additional 

nutrients from a sewage-treatment facility, a creamery, and 

two cheese factories. It is believed that nutrient input from 

the watershed peaked in the 1960s, when there were inputs 

from extensive agricultural activities in the watershed 

(including a barnyard with cattle immediately adjacent 

to the lake), from untreated effluent from the municipalwaste system, a creamery, and two cheese factories that 

released nutrients directly into Butternut Creek, and from 

deficient or poorly functioning septic systems that released 

effluent into nearshore areas around the lake. As a result of 

the high input of nutrients, the water quality of Butternut 

Lake degraded and extensive algal blooms were common. 

Massive algal blooms were reported in the 1960s and early 

1970s (McKersie, and others, 1970; R. Jasinski, Wisconsin Department of Natural Resources, written commun., 

1982). 

In recent decades, area residents and authorities near 

Butternut Lake implemented several measures to improve 

the lake’s water quality, which they felt had become 

degraded because of nutrient inputs from the watershed. 

Most of the intense agricultural activities were discontinued between the 1960s and 1980s, the creamery and 

cheese factories in the watershed were closed in the 1970s, 

and in 1983 sewage effluent from the Village of Butternut 

was directed to an on-land infiltration site that drains away 

from Butternut Creek (table 1). In addition, implementation and enforcement of a zoning ordinance that regulated septic systems likely has eliminated or significantly 

reduced the amount of nutrients from these sources. As 

a result of all of these measures, by the early 1980s, the 

number and intensity of algal blooms decreased from those 

during the 1960s and early 1970s, while the amount of 

macrophyte growth increased (R. Jasinski, written commun., 1982). The water quality of the lake, however, was 

still believed to be degraded compared to natural, presettlement conditions. 

As of the early 2000s, the lake was still very productive, with occasional algal blooms and extensive 

macrophyte growth. Lake-area residents, lake users, and 

Price County officials would like to implement additional 

management or restoration efforts to return the lake to a 

more natural state. Recycling of phosphorus from bottom sediments (referred to as internal loading) rather than 

excessive inputs from external sources is now believed to 

be the cause of the continued poor water quality (R. Jasinski, written commun., 1982). Quantitative information, 

however, was not available to evaluate the significance of 

the various sources of phosphorus as a percentage of the 

total input to the lake. To aid future management decisions and development of a lake-management plan, a better 

understanding of the lakes’s hydrology, phosphorus input 

by specific source, and the importance of the internal recycling of phosphorus from the lake’s sediments is needed. 

In addition, information on the likely response of the lake 

to incremental increases or decreases in phosphorus loading would be useful for determining practices or actions to 

help restore the lake.

To provide a better understanding of the factors that 

affect the water quality of Butternut Lake, a detailed study 

of the lake and its watershed was begun in 2002 by the 

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

Price County Land Conservation Committee and the Wisconsin Department of Natural Resources (WDNR). The 

WDNR provided partial funding for this study through the 
Introduction 3

Figure 1. Watershed of Butternut Lake, Price and Ashland Counties, Wis. Land use/land cover from the WISCLAND geographic 

information system coverage (Wisconsin Department of Natural Resources, 1998).

EXPLANATION

Urban (high/moderate density)

Rural residential (low density)

Agriculture

Pasture/grassland

Forest/shrubland

Open water

Wetlands

Barren

Stream

Road

Highway

Watershed boundary

County boundary

Land use/land cover

WISCONSIN

Study area

ASHLAND CO.

PRICE CO.

90°25'

90°30'

46°5'

46°

0 2 4 MILES

0 2 4 KILOMETERS

Base map from U.S. Geological Survey

digital data, 1:24,000

B u t t e r n u t L a k e

Village of

Butternut

Spiller Creek

Butternut Creek

Schnur Lake

County Highway B

State Highway 13



B
4 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

Table 1. Summary of activities affecting the loading of nutrients into Butternut Lake, Price and Ashland Counties, Wis.

[ha, hectare; m3/d, cubic meter per day; mg/L, milligram per liter]

Year or period Activity Source

1860s Logging activity documented in the Butternut watershed. 1

1870s Farming in the Butternut watershed began. 1

1870s Village of Butternut established. 1

1878 Rail service to Butternut established. 1

1879 1.2-ha reservoir constructed on Butternut Creek for grist mill operation. 1

1895 First creamery built in Butternut and effluent discharge to Butternut Creek. 1

1893–1902 Charcoal manufacturing industry in operation. 1

1902 Village of Butternut incorporated. 1

1900–1964 Various wood-products factories dominated industries in the area. 1

1910 Population of Butternut was 717. 5

1920s Logging activity diminished. 1

1938 Waterworks and sewer system installed in Butternut. 1

1938–

early 1970s

Relatively untreated municipal waste and creamery wastes discharged directly into Butternut Creek. 2

1938–

early 1970s

Municipal-waste system consisted of a primary tank with effluent going into Butternut Creek. 3

Mid 1900s Fluid wastes from paper mill dumped on farm fields as a fertilizer and on roads to settle dust. 4

1940–1950 Population of Butternut dropped from 669 to 522. 5

Before 1960 Deficient septic systems existed along lake. 2

1960s–1980s Agricultural activity began to decline. Agriculture changed from dairying, to beef, to cropping, with some 

land going out of production.

4

1976 Dairying at farm on west shore of lake converted to beef farming. 4

1986 Beef farming at farm on west shore of lake ceased. 4

1960–1982 Deficient septic systems around the lake were improved. 2

1970s Creamery closed operation. During last few years of operation, effluent dumped into ridge-and-furrow 

system on land.

3

Early 1970s–

1983

Three-pond sewage treatment with effluent discharged (227–273 m3

/d at 2–5 mg/L) into 

Butternut Creek during open-water season. 

3

1983 Effluent from three-pond municipal system directed to on-land-infiltration site away from Butternut Creek. 3

2000 Population of Butternut was 407. 5

Sources:

1. Scott, R., 2005, The written history of Butternut, Wisconsin, based on oral history of townspeople and an essay by Ruth Gear. 

2. Jasinski, R., Wisconsin Department of Natural Resources, written commun., 1982.

3. Olson, C., Wisconsin Department of Natural Resources, oral commun., 2007.

4. Szymik, F., Butternut citizen, oral commun., 2007.

5. Wells, P., Wisconsin Department of Administration, Madison, written commun. 2007.
Introduction 5

Lake Protection Grant program. The study had the following objectives:

•	 Describe the water quality of the lake.

•	 Define the hydrology of the lake.

•	 Quantify the external sources of phosphorus to the 

lake.

•	 Quantify the release of phosphorus from the lake 

sediment, and determine its relative importance to 

the phosphorus budget of the lake.

•	 Assess how the water quality of the lake should 

respond to changes in phosphorus inputs.

Butternut Lake and Its Watershed

Butternut Lake is a natural drainage lake in the Butternut Creek watershed about 2 km south of the Village 

of Butternut and about 5 km northwest of Park Falls. 

The lake is about 5.6 km long and has a maximum width 

of about 1.5 km (table 2). Butternut Creek flows into the 

north end of the lake and flows out of the south end of 

the lake (fig. 1).

The area and volume of Butternut Lake were given on 

the 1967 Wisconsin Conservation Department lake survey 

map as 407 ha and 17,284,000 m3, respectively. The lake 

survey map listed the total shoreline length as 18.0 km 

and the maximum depth as 9.8 m. In this study, the morphometry of the lake was reevaluated on the basis of an 

aerial image obtained from the 2005 National Agricultural 

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

The resulting surface area of the lake was determined to be 

393 ha and the volume to be 15,850,000 m3

. The surface 

delineation for this study did not include channeled areas 

at the northern and southern ends of the lake, which may 

account for the difference in the two determinations of 

area and volume. The area and volume values determined 

in this study were used for all of the computations in this 

report. The lake is divided into three major basins: the 

North, Middle, and South Basins (fig. 2). The morphometry of each basin is listed in table 2.

The major tributary to the lake is Butternut Creek, 

which flows into the north side of the North Basin. The 

drainage area of Butternut Creek at the inlet to the lake is 

74.7 km2 (table 3). The second largest tributary is Spiller 

Creek, which flows into southwest side of the North Basin, 

and has a total drainage area of 23.5 km2. Six additional 

small tributaries, along with ungaged near-lake areas, have 

a combined drainage area of 20.5 km2. The total drainage area of the watershed upstream from Butternut Lake’s 

outlet, not including the lake, is 118.7 km2. Drainage areas 

contributing to each of the lake basins are also identified in 

table 3.

Land use/land cover in the Butternut Lake watershed 

is primarily a mixture of forest (46.6 percent) and wetland 

(31.3 percent), with areas of agriculture (9.9 percent), 

grassland (9.7 percent), and smaller areas of water, urban, 

nearshore residential, and barren land (table 3). Land use 

in the Butternut and Spiller Creek watersheds and the 

watersheds draining into each of the basins are given in 

table 3.

Table 2. Morphometric characteristics of the basins in Butternut Lake, Price and Ashland Counties, Wis.

[ha, hectare; km, kilometer; m, meter; m3, cubic meter; km2, square kilometer; --, not available]

Basin Area

(ha)

Length

(km)

Maximum 

depth

(m)

Mean 

depth

(m)

Volume 

(1,000,000s 

of m3

)

Osgood 

Index1

Drainage 

area

(km2

)

Residence 

time 

(days)

Phosphorusturnover ratio 

(annual loading)

North 183 3.09 7.6 4.23 7.75 1.26 107 86 --

Middle 126 1.96 9.8 4.46 5.61 2.82 3.57 60 --

South 84 1.55 5.5 2.97 2.49 4.24 8.28 26 --

Entire lake 393 5.60 9.8 4.04 15.9 .26 119 165 5.4

1

 Osgood Index: mean depth ÷ area0.5 (Osgood, 1988)
6 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

Figure 2. Subbasins and land use/land cover (Wisconsin Department of Natural Resources, 1998) of the near-lake drainage area 

of Butternut Lake, Wis., with locations and types of data-collection sites identified.

90°32'30" 90°30'

46°

45°57'30"

2

8

3

7

4

5

6

1

2

8

3

7

4

5

6

1

0 .5 1 MILE

0 .5 1 KILOMETER

EXPLANATION

Rural residential (low density)

Agriculture

Pasture/grassland

Forest/shrubland

Open water

Wetlands

Barren

Stream

Continuous stream sites

Lake stage

Piezometer and identifier

Small tributary sites

Auxiliary lake sites

Lake-monitoring sites

Watershed boundary

Lake-basin boundary

Land use/land cover

Base map from U.S. Geological Survey

digital data, 1:24,000.

B

u t t e r n

u t L a

k e

S c h n u r L a k e

Mud Lake

Butternut

Creek

(outlet)

Spiller Creek

Butternut

Creek

(inlet)

SOUTH BASIN

MIDDLE

BASIN

NORTH

BASIN

Deep-hole

Site

5
Introduction 7

Shallow Polymictic Lakes and Internal 

Phosphorus Loading

Butternut Lake and each of its basins are relatively 

shallow with respect to their surface areas. Shallow lakes, 

defined as having a maximum depth less than 6 m (Osgood 

and others, 2002), typically experience only short periods 

of stratification rather than a single extended period of 

stratification from early summer through early fall. Lakes 

that mix only during spring and fall are called dimictic, 

and lakes that mix frequently throughout the open-water 

period are called polymictic. Deeper lakes with relatively 

large surface areas may also be prone to frequent deep 

mixing. Osgood (1988) described the functional aspects 

of mixing based on the mean depth and surface area of 

lakes in terms of the Osgood Index. The Osgood Index is 

defined as the mean depth (z, in meters) of a waterbody 

divided by the square root of the surface area (A, in km2

), 

or z/A0.5. The Osgood Index is used to describe the degree 

to which a lake or reservoir is likely to mix because of the 

forces of wind. Lakes with Osgood Index values greater 

than 9 generally are dimictic, and lakes with Index values 

less than 4 tend to be polymictic. All of the basins in Butternut Lake have either a maximum depth less than 6 m or 

have Osgood Indices less than 4 (table 2); therefore, the 

entire lake should be polymictic.

When the deep water of a productive lake becomes 

anaerobic (devoid of dissolved oxygen) because of the loss 

of oxygen associated with the decomposition of organic 

materials, the rate of phosphorus release from the deep 

sediments often increases dramatically (Mortimer, 1941). 

Typically, in deeper, dimictic lakes, phosphorus released 

from the deep sediments is contained in the hypolimnion 

(deep, cold layer) of the lake and is released to the epilimnion (surface layer) primarily at fall overturn. Therefore, 

near-surface phosphorus concentrations in dimictic lakes 

usually remain stable or decrease as summer progresses 

(Welch and Cooke, 1995). In polymictic lakes, however, 

when the deeper water becomes anaerobic during the short 

periods of stratification and phosphorus is released from 

the sediments, the frequent mixing events deliver the phosphorus to the surface of the lake throughout summer. This 

frequent mixing results in near-surface concentrations of 

phosphorus increasing throughout the summer and the lake 

being very productive in late summer (Welch and Cooke, 

1995). Polymictic lakes are extremely vulnerable to high 

external phosphorus loading and difficult to rehabilitate 

because the high rate of internal loading usually does 

not quickly respond to reductions in external phosphorus 

inputs (Newton and Jarrell, 1999; Nurnberg, 1998; Welch 

and Cooke, 1995). 

Polymictic lakes typically have two alternative stable 

states—phytoplankton (algae)-dominated or macrophyte 

(plant)-dominated (Newton and Jarrell, 1999). In moderate densities, macrophytes are beneficial in these lakes. 

Macrophytes keep sediment from being resuspended by 

the wind and, therefore, help keep the water less turbid. 

Macrophytes also provide a place for attached algae to 

grow and remove phosphorus from the water column. If 

the macrophytes are removed or if external phosphorus 

Table 3. Land use/land cover in the Butternut Lake, Wis., watershed from classifications defined by WISCLAND (Wisconsin 

Department of Natural Resources, 1998).

[km2, square kilometer; %, percent]

Basin/drainage Area

(km2

)

Agriculture

(%)

Barren

(%)

Forest

(%)

Grassland

(%)

Nearshore 

residential area

(%)

Wetland

(%)

Urban

(%)

Water

(%)

Gaged drainage areas

Butternut Creek 74.7 6.2 0.5 62.1 11.0 0.0 41.0 0.5 1.3

Spiller Creek 23.5 20.9 .8 35.5 13.3 .0 32.5 .0 .2

Watersheds of individual basins

North 106.8 8.9 0.6 47.4 9.8 0.1 31.4 0.3 1.4

Middle 3.6 26.0 1.6 43.4 6.6 1.0 21.4 .0 .1

South 8.3 14.9 .4 37.9 8.7 .8 33.7 .0 3.5

Entire watershed

Entire lake 118.7 9.9 0.6 46.6 9.7 0.2 31.3 0.2 1.5
8 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

inputs increase, the lake can shift from a macrophytedominated state to an algal-dominated state. Once a lake is 

in the algal-dominated state, macrophytes have a difficult 

time re-establishing themselves because algae reduce the 

penetration of light. In the 1960s and early 1970s (and 

presumably several years before that), Butternut Lake was 

believed to be in the algal-dominated state with frequent 

massive algal blooms. After the mid 1970s, however, the 

actions taken in the watershed lake (table 1) are believed 

to have reduced the nutrient input to the lake and switched 

the lake to a macrophyte-dominated state (R. Jasinski, 

written commun., 1982). Of these two conditions, it is 

commonly believed that the present-day macrophyte-dominated state is more desirable for human and biological 

use than the previous algal-dominated state (Newton and 

Jarrell, 1999).

Purpose and Scope

This report describes the water quality of Butternut 

Lake, quantifies the water and phosphorus budgets for the 

lake based on data collected from November 2002 through 

October 2004, provides an estimate of the phosphorus 

released from the bottom sediments, and presents the 

results of model simulations that demonstrate the potential 

effects of changes in phosphorus inputs on the lake’s water 

quality.

The water-quality data and water and phosphorus 

budgets described in this report improve the understanding 

of the hydrologic system of Butternut Lake and aid in the 

understanding of how shallow lakes respond to changes 

in nutrient inputs. Results of the study should be useful 

to Price and Ashland Counties and local officials 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 stream and lake data from 

2002 to 2004 as part of this study. In addition, water-quality data for the lake were collected by the U.S. Environmental Protection Agency (USEPA), U.S. Forest Service 

(USFS), WDNR (Wisconsin Department of Natural 

Resources, 2006), and volunteers from the community as 

part of the WDNR’s Wisconsin Citizen Lake Monitoring 

Program (Wisconsin Department of Natural Resources, 

2008). Data collected by the USEPA were obtained from 

U.S. Environmental Protection Agency (1974), data collected by the USFS and the WDNR were provided by 

J. Vennie (Wisconsin Department of Natural Resources, 

written commun., 2004), 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, and Secchi depths, were 

used to characterize long-term changes in the water quality 

of the lake; however, only data collected from November 

1, 2002 to October 31, 2004 were used to describe the 

hydrology and phosphorus inputs to the lake. This latter period was divided into two monitoring years (MY): 

November 2002 through October 2003 (hereafter referred 

to as MY 2003) and November 2003 through October 

2004 (hereafter referred to as MY 2004).

Lake-Stage and Water-Quality Monitoring

A continuously recording (15-minute interval) lakestage gage was installed and operated near the public boat 

landing on the west side of the lake (fig. 2). The gage was 

operated for the 2-year monitoring period. 

Water-quality data for the lake were collected by the 

USEPA and WDNR from 1972 to 1975 as part of two 

statewide assessments (Lillie and Mason, 1983). Data also 

were collected by the WDNR from 1986 through 1997 as 

part of their long-term trend monitoring program (Wisconsin Department of Natural Resources, 2006). These data 

were collected at the deepest location (the Deep-hole Site 

between the North and Middle Basins) in the lake 

(fig. 2). Volunteers from the community (Citizen Monitoring) collected water-quality data from 1992 to 2006. The 

USGS collected data from 2002 to 2004 as part of this 

study. The USGS protocols for sampling at the Deephole Site from 2002 to 2004 were similar to those of the 

WDNR long-term trend monitoring program. Each year, 

the lake was sampled in late winter, spring, and summer 

(monthly from May through September). During each 

visit, profiles of water temperature, dissolved oxygen, 

specific conductance, and pH were collected with a multiparameter meter, and water clarity was measured with 

a standard 20-cm diameter black and white Secchi disk 

(Secchi depth). Near-surface samples, which were collected with a Van Dorn sampler by USGS and a Kemmerer 

sampler by WDNR, were analyzed for total phosphorus 

and chlorophyll a concentrations and, during midsummer, 

for various nitrogen species. Near-bottom samples were 

collected about 1 m above the sediment/water interface and 
Study Methods and Sampling Sites 9

were analyzed for total phosphorus concentration. Water 

samples collected during spring were analyzed for common ions and other characteristics such as color, turbidity, 

alkalinity, total dissolved solids, and silica.

During this study, three additional lake-monitoring 

sites also were sampled (fig. 2). Sampling protocols for 

two of these sites, the North and Middle Sites, were the 

same as those for the Deep-hole Site, except that the spring 

sample was not analyzed for common ions and other 

characteristics such as color, turbidity, alkalinity, total 

dissolved solids, and silica. At the other auxiliary site, 

the South Site, only Secchi depth and profiles of water 

temperature, dissolved oxygen, specific conductance, and 

pH were measured.

Butternut Lake was sampled 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, 2004; 2005). Quality-assurance 

samples are not collected in each of the lakes sampled; 

however, replicates were collected in Butternut Lake in 

2003. The replicates for total phosphorus and chlorophyll 

a were within 5 percent of each other, which is consistent 

with replicates collected in other lakes in Wisconsin. Concentrations of total phosphorus and chlorophyll a in the 

blanks analyzed in 2003, and in other years, were below 

the laboratories' detection limits (0.004–0.005 mg/L for 

total phosphorus and 0.03–0.1 μg/L for chlorophyll a). 

Lake-stage, water-quality, and quality-assurance data 

collected during this study were published in the USGS 

annual data report series “Water Quality and Lake-Stage 

Data for Wisconsin Lakes, Water Years 2003 and 2004 

(U.S. Geological Survey, Wisconsin District Lake Studies 

Team, 2004; 2005).

Lake Classification

One method of classifying the water quality of a lake 

is by computing trophic state index (TSI) values based 

on near-surface concentrations of total phosphorus and 

chlorophyll a, and Secchi depths, as developed by Carlson (1977). The indices were developed to place these 

three characteristics on similar scales to allow comparison 

of different 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 average summer (May through 

September) 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)] (2)

TSISD = 60.0 – 14.41[ln Secchi depth

(in meters)] (3)

Oligotrophic lakes (TSI values less than 40) have a 

limited supply of nutrients, and they typically are clear, 

have low algal populations and low phosphorus concentrations, and contain oxygen throughout the year in 

their deepest zones (Wisconsin Department of Natural 

Resources, 1992). Mesotrophic lakes (TSI values between 

40 and 50) have a moderate supply of nutrients, moderate 

clarity, and a tendency to produce moderate algal blooms; 

occasional oxygen depletions in the deepest zones of the 

lake are possible. Eutrophic lakes (TSI values greater 

than 50) are nutrient rich and have correspondingly severe 

water-quality problems, such as poor clarity and frequent 

seasonal algal blooms; oxygen depletion is common in the 

deeper zones of the lake. Eutrophic lakes with TSI values 

greater than 60 are often further classified as hypereutrophic, and they typically have even more severe water-quality problems, with frequent extensive algal blooms. 

Lake-Sediment Analyses

Internal release rates of phosphorus from the sediments during aerobic and anaerobic conditions were 

determined from analysis of sediment cores collected at six 

locations in the lake (lake-monitoring sites and auxiliary 

sites, fig. 2) using the sediment-core-incubation techniques 

described by James and Barko (1991). A Wildco sedimentcore sampler equipped with acrylic core liners was used 

to collect either two or four sediment cores from each location. At three locations, four cores were collected: two for 

aerobic analysis and two for anaerobic analysis. At three 

additional locations, only two cores were collected for 

aerobic analysis. After retrieval, the core liners, containing both sediment and overlying water, were immediately 

sealed using rubber stoppers and stored in a protective container for shipping to the Wisconsin State Laboratory of 

Hygiene. Additional lake water was collected for incubation with the collected sediment. 
10 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

At the State Laboratory of Hygiene, the sediment 

cores were carefully drained of overlying water. Then 

additional water, collected from the lake, was filtered 

and siphoned onto the sediment contained in each of the 

core liners. All of the liners containing the sediment were 

placed in the dark and incubated at a constant temperature 

(approximately 22oC) for 1 to 2 weeks. The incubation 

temperature was a constant temperature similar to that 

above the original sediment during summer. 

The aerobic/anaerobic environment of each core was 

controlled in the laboratory by gently bubbling either air 

(aerobic environment) or nitrogen (anaerobic environment) 

through an air stone placed just above the sediment surface. The limited bubbling action insured complete mixing 

of the water column but did not disrupt the sediment. 

Twelve of the cores (two from each location) were subjected to aerobic conditions and six of the cores (two from 

each of three stations) were subjected to anaerobic conditions. Therefore, all incubations were run in duplicate.

Samples for soluble reactive phosphorus analysis were collected daily from water above the sediment 

in each core and filtered through a 0.45-μm filter. The 

volume of water that was removed was replaced with an 

equivalent volume of lake water (with a measured phosphorus concentration). Rates of phosphorus release from 

the sediments (mg/m2

/d) were then calculated as a linear 

change in mass in the overlying water divided by the time 

and the cross-sectional area of the incubation core liner. 

All results were corrected for the water (and phosphorus) 

that was removed from above the core and replaced with 

lake water. Aerobic and anaerobic sediment release rates 

were then averaged for each basin. The rate of release 

of phosphorus from aerobic and anaerobic sediments is 

typically a function of the temperature of the sediments 

and overlying water, with a higher release rate at warmer 

temperatures than at lower temperatures. Release rates 

from the sediments of Butternut Lake were computed 

only at 22oC; however, release rates from the sediments of 

the Upper Mississippi River were examined as a function 

of water and sediment temperatures (James and Barko, 

2004). Therefore, the release rates were adjusted by a ratio 

computed from the release-rate equations obtained for 

the sediments of the Upper Mississippi River (fig. 3). The 

release rate at 22oC was used as a reference; therefore, the 

release-rate ratio at 22oC was set to 1.0. Daily water temperatures at the sediment/water interface in Butternut Lake 

were assumed to be similar to that estimated at 2 m for 

a nearby lake (Whitefish Lake in Douglas County, Wis.; 

unpublished results) through the use of the Dynamic Lake 

Model (Robertson and others, 2002). Daily aerobic and 

anaerobic release rates were then obtained by multiplying 

the rates measured at 22oC by the estimated daily releaserate ratios. 

For each basin, the amount of phosphorus released 

from the sediment was obtained by summing the amount 

released from the aerobic and anaerobic areas of the 

basin. The area of anaerobic sediment in each basin was 

estimated from the area at the depth at which a dissolved 

oxygen concentration of less than or equal to 0.5 mg/L was 

measured in the profiles collected in the deepest area of 

each basin, assuming that the dissolved oxygen concentrations were horizontally uniform throughout the basin. The 

area of aerobic sediment was computed by subtracting 

the area of anaerobic sediment and the area of sediment 

at depths less than 1 m from the total area of the basin. It 

was assumed that no phosphorus was released from areas 

less than 1-m deep because these areas typically have 

little accumulated organic sediment. From the 2 years of 

profile data, the areas of aerobic and anaerobic sediment 

were estimated for specific dates throughout the year. The 

daily sediment release was then computed as the product 

of the temperature-adjusted release rates and the respective 

aerobic and anaerobic areas.

A separate paleoecological study of the lake-bottom 

sediments of Butternut Lake was done by the WDNR, 

Bureau of Integrated Science Services, to age-date specific 

sediment depths and to quantify historical changes in the 

external sediment and nutrient loading to the lake, the 

sedimentation rates in the lake, and the chemistry of the 

lake (Garrison, 2006). Sediments from a deep region of the 

North Basin (fig. 2) were extracted with a piston-coring 

device in February 2005 and then analyzed to reconstruct 

the water-quality history of the lake. Analysis of diatom 

assemblages was used to assess historical changes in phosphorus concentrations in the lake.

Stream Monitoring

Three stream sites (fig. 2) were equipped with instrumentation to continuously monitor flow (15-minute intervals). At two of the sites, Spiller Creek at County Highway 

B and Butternut Creek at County Highway B (just downstream of the lake’s outlet), water level (stage) was measured to determine flow by use of standard stage-discharge 

relations (Rantz and others, 1982). The third site, Butternut 

Creek at Cutoff Road at the lake’s inlet, was not suited to 

flow determination by standard stage-discharge methods 

because of backwater conditions. This site was equipped 

with an acoustic doppler velocity meter and a water level 

sensor and was operated as a velocity-index station (Sauer, 
Study Methods and Sampling Sites 11

2002). From the 15-minute data, average daily flows for 

each site were computed. The data are stored and maintained in the USGS National Water Information System 

(NWIS) database.

Flow at six small tributaries to Butternut Lake (fig. 

2) was measured intermittently at approximately monthly 

intervals. The measured flows at each tributary were correlated with the continuously recorded flow at Spiller Creek 

to develop a regression relation between flow at each tributary and flow at Spiller Creek. The regression relations for 

each site and the daily flows at Spiller Creek were then 

used to estimate daily flows in each tributary. Temporally 

varying offsets were then applied to all estimated flow data 

to force estimated flows to equal those measured in the 

tributaries.

Water samples were collected at the stream sites and 

analyzed for concentrations of phosphorus. Water samples 

were collected by three different methods. Automated 

water samplers were used to collect samples at Butternut 

Creek (inlet) and at Spiller Creek. Additional samples 

at these two sites were collected manually by the EqualWidth-Increment (EWI) method (Edwards and Glysson, 

1999) to compare with the automated samples. Butternut 

Creek near the lake outlet was sampled approximately 

monthly by the EWI method. Sites on the additional small 

tributaries were sampled approximately monthly by either 

EWI or grab methods. 

Phosphorus loads for the continuously monitored sites 

at the Butternut Creek inlet, Spiller Creek, and the Butternut Creek outlet were computed by use of techniques 

for integrating streamflow and concentration described by 

Porterfield (1972). Phosphorus loads for the small tributaries were determined by multiplying temporally varied 

concentrations (computed on the basis of concentrations 

of intermittently collected samples) multiplied by the 

estimated flow. Loads for the near-lake ungaged area were 

determined by multiplying the average unit-area load (load 

divided by drainage area) for the six tributaries by the 

ungaged near-lake area. All concentration data and daily 

flows and loads were published in the annual USGS waterdata report series (Waschbusch and others, 2004; 2005).

Ground-Water Monitoring

Eight shallow piezometers (1.25-cm diameter observation wells) were installed around the periphery of the 

lake (fig. 2) to help define areas contributing ground water 

to the lake, to determine the phosphorus concentration 

in the ground water entering the lake, and to quantify the 

phosphorus loading from ground water. The piezometers 

Figure 3. Changes in phosphorus release rates (ratio) from aerobic and anaerobic sediments of the Upper Mississippi River 

as a function of water temperature, estimated from the equations in James and Barko (2004), using the release rate at 22oC as a 

reference value (ratio of 1.0).

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 5 10 15 20 25

Aerobic ratios

Anaerobic ratios

WATER TEMPERATURE, IN DEGREES CELSIUS

SEDIMENT PHOSPHORUS RELEASE RATE RATIO
12 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

were installed approximately 1 m below the water table, to 

depths of 1.5 to 2 m. Five piezometers were on the eastern 

shore and three were on the western shore. Ground-water 

gradients, which were determined from the differences in 

water elevation in the piezometers and elevation of the lake 

surface, and dissolved phosphorus concentrations in the 

ground water were measured twice in 2003 and twice in 

2004 for each piezometer. 

All lake, stream, and ground-water samples and 

water from above the sediment cores 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). 

Measured Lake Water Quality

Temperature profiles collected throughout the lake 

confirmed that the North, Middle, and South Basins were 

polymictic, which means that they do not develop stable 

thermal stratification during summer and thus allowed a 

great deal of vertical mixing throughout that period. This 

mixing resulted in only a few degrees Celsius of thermal stratification during most summer sampling periods. 

Changes in temperature are shown for the Deep-hole Site 

in figure 4A. The bottom temperatures at all of the sites 

warmed throughout summer. In each of the basins, the 

bottom temperatures reached a maximum temperature of 

about 20oC in August. Thermal stratification was most 

extensive when the lake was frozen. Temperatures just 

under the ice were about 4oC cooler than near the bottom 

by late winter. During the presence of weak stratification, 

the near-bottom water was often anaerobic (fig. 4B). However, due to frequent vertical mixing, the area of the lake 

that was anaerobic was never large. Thermal stratification 

in the South Basin was less extensive than in the other 

basins, because this basin is shallower and probably had 

more deep-mixing events. 

The area of anaerobic sediment in each basin was 

estimated from the depth at which a dissolved oxygen concentration of 0.5 mg/L was found in the profiles collected 

in their deepest areas. From the 2 years of data, the area of 

aerobic and anaerobic sediment were estimated for specific 

dates throughout the year (table 4); daily estimates of these 

areas were then obtained by linearly interpolating between 

these dates.

Specific conductance typically was about 80 μS/cm 

throughout the lake, but increased to about 200 μS/cm near 

the bottom when these areas were anaerobic. The pH in 

the lake typically ranged from 7 to 8 (standard units), with 

the lowest pH values measured during cooler periods and 

the highest pH values were measured during summer when 

productivity was highest. The lowest pH value (6.4) was 

measured on May 4, 2004, near the bottom in the North 

Basin, and the highest value (9.4) was measured on Aug. 

13, 2003, near the surface in the South Basin. 

Table 4. Estimated area of aerobic sediment (greater than 1 meter in depth) and anaerobic sediment in the three basins in 

Butternut Lake, Wis.

[All values given in thousands of square meters]

Date

North Basin Middle Basin South Basin

Aerobic Anaerobic Aerobic Anaerobic Aerobic Anaerobic

Jan.1 1,710 0 1,180 0 754 0

Feb. 1 1,710 0 777 400 754 0

Mar. 31 1,710 0 777 400 754 0

Apr. 1 1,710 0 1,180 0 754 0

June 1 1,710 0 1,180 0 754 0

June 15 1,330 377 1,180 2 704 50

July 15 937 552 606 571 539 215

Aug. 15 1,170 539 606 571 539 215

Sept. 1 1,710 0 1,180 0 754 0

Dec. 31 1,710 0 1,180 0 754 0
Measured Lake Water Quality 13

Figure 4. Distributions of A, water temperature and B, dissolved oxygen from March 10, 2003, through September 21, 2004, at the 

Deep-hole Site in Butternut Lake, Wis.

2

4

6

8

10

12

14

16

18

20

22

24

0

1

2

3

4

5

6

7

8

9

10

TEMPERATURE, IN DEGREES CELSIUS DISSOLVED OXYGEN, IN MILLIGRAMS PER LITER

0

2

4

6

8

0

2

4

6

8

DEPTH, IN METERS DEPTH, IN METERS

MAR.

APR.

MAY

JUNE

JULY

AUG.

SEPT.

APR.

MAY

OCT.

NOV.

DEC.

JAN.

FEB.

MAR.

JUNE

JULY

AUG.

SEPT.

2003 2004

MAR.

APR.

MAY

JUNE

JULY

AUG.

SEPT.

APR.

MAY

OCT.

NOV.

DEC.

JAN.

FEB.

MAR.

JUNE

JULY

AUG.

SEPT.

2003 2004

A. Water temperatures

B. Dissolved oxygen
14 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

Water chemistry in Butternut Lake is fairly typical 

of northwestern Wisconsin lakes, as described by Lillie 

and Mason (1983). Lillie and Mason collected data from 

a random set of about 660 Wisconsin lakes, 282 of which 

were in northwestern Wisconsin. The average concentrations of calcium, magnesium, chloride, and alkalinity in 

Butternut Lake were 10, 3, 3, and 32 mg/L, respectively. 

The average concentrations for these constituents for 

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. The water color in Butternut Lake averaged 

85 (platinum-cobalt units) from two measurements made 

during this study, which is more colored than the average 

value of 30 for the northwestern Wisconsin lakes.

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 (that is, accelerated aging and increased productivity) 

of lakes. Concentrations of near-surface total phosphorus 

greater than about 0.024 mg/L indicate eutrophic conditions, and concentrations greater than about 0.050 mg/L 

indicate hypereutrophic conditions. The near-surface 

phosphorus concentrations in Butternut Lake had distinct 

seasonality (fig. 5A). During MY 2003 and MY 2004, 

concentrations ranged from about 0.03 mg/L in late winter 

and early spring to more than 0.060 mg/L in late summer 

of both years. Concentrations increased throughout the 

summer, which is typical for polymictic lakes (Welch 

and Cooke, 1995). The average near-surface summer 

(May–September) phosphorus concentration during 

MY 2003–04 ranged from 0.044 mg/L at the Deep-hole 

Site to 0.048 mg/L in the North Basin (table 5). No consistent differences were found among basins. Therefore, 

based on total phosphorus concentrations, Butternut Lake 

would typically be classified as on the border between 

eutrophic and hypereutrophic.

In general, phosphorus concentrations measured 

near the bottom of the water column were similar to those 

measured near the surface; however, a few very high concentrations were measured near the bottom. The highest 

near-bottom concentrations were measured in June, July, 

and August, with the highest phosphorus concentration of 

Table 5. Summer (May through September) average water quality throughout Butternut Lake, Wis., for monitoring years 2003 

and 2004.

[mg/L, milligram per liter; μg/L, microgram per liter; c.v.; coefficient of variation; m, meter; --, no data]

Basin/site Total phosphorus Secchi depth Chlorophyll a

(mg/L) (c.v.) (m) (c.v.) (μg/L) (c.v)

2003

North Basin 0.043 -- 1.18 -- 20.88 --

Deep-hole Site .039 -- 1.24 -- 20.72 --

Middle Basin .044 -- 1.20 -- 23.92 --

South Basin .044a -- 1.25 -- 23.92a --

2004

North Basin 0.053 -- 1.10 -- 18.01 --

Deep-hole Site .049 -- 1.14 -- 18.92 --

Middle Basin .050 -- 1.16 -- 17.58 --

South Basin .050a -- 1.18 -- 17.58a --

2003–2004

North Basin 0.048 0.20 1.14 0.15 19.4 0.38

Deep-hole Site .044 .20 1.24 .15 19.8 .38

Middle Basin .047 .20 1.18 .15 20.8 .38

South Basin .047a .20a 1.22 .15 20.8a .38a

a

 Assumed to be similar to the Middle Basin. 
Measured Lake Water Quality 15

Figure 5. Near-surface A, total phosphorus concentrations, B, chlorophyll a concentrations, and C, Secchi depths at various 

locations in Butternut Lake, Wis., during 2003 and 2004.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

TOTAL PHOSPHORUS, IN MILLIGRAMS PER LITER

0

10

20

30

40

50

60

01/01/03 04/01/03 07/01/03 10/01/03 01/01/04 04/01/04 07/01/04 10/01/04 01/01/05

01/01/03 04/01/03 07/01/03 10/01/03 01/01/04

DATE

04/01/04 07/01/04 10/01/04 01/01/05

01/01/03 04/01/03 07/01/03 10/01/03 01/01/04 04/01/04 07/01/04 10/01/04 01/01/05

CHLOROPHYLL A, IN MICROGRAMS PER LITER

0.0

0.5

1.0

1.5

2.0

SECCHI DEPTH, IN METERS

North Basin

Deep-hole Site

Middle Basin

South Basin

Citizen-monitoring data 

– Deep-hole Site

North Basin

Deep-hole Site

Middle Basin

Citizen-monitoring data 

– Deep-hole Site

A.

B.

C.
16 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

0.351 mg/L measured on August 10, 2004, at the Deephole Site. The high near-bottom phosphorus concentrations 

do not persist throughout the summer in polymictic lakes, 

because the frequent deep-mixing events redistribute the 

phosphorus that is released from the bottom sediments 

throughout the water column. 

Since 1972, near-surface total phosphorus concentrations have ranged from 0.018 mg/L to greater than 

0.15 mg/L (fig. 6A). All of the concentrations greater than 

0.10 mg/L were measured during the ice-covered period. 

Although few data were available prior to 1986, it appears 

that phosphorus concentrations have declined since 1972. 

During each year, concentrations increased throughout 

summer; therefore, to demonstrate how near-surface 

concentrations have changed, the concentrations measured 

in August (the month most consistently sampled) were 

identified on figure 6A and summarized in table 6. During 

August, total phosphorus concentrations decreased from 

about 0.09 mg/L in the early 1970s, to about 0.06–0.08 in 

the 1980s, to about 0.05 mg/L in the 2000s (fig. 6A). From 

the 1980s to the 2000s, average summer concentrations 

also decreased, but only from about 0.055–0.060 mg/L to 

about 0.045 mg/L. These decreases in near-surface phosphorus concentrations are consistent with those expected 

with the discontinuation of discharge of sewage effluent 

from the Village of Butternut into Butternut Creek, the 

upgrading of near-lake septic systems, and the general 

decline in agricultural activity in the watershed (table 1).

During the summers of 2003 and 2004, near-surface 

total nitrogen concentrations (computed as the sum of 

Kjeldahl nitrogen and dissolved nitrite plus nitrate) ranged 

from 0.49 to 0.88 mg/L; Kjeldahl nitrogen represented 

more than 70 percent of the total nitrogen. These values 

are similar to those measured in the late 1980s (0.52 to 

0.72 mg/L), but less than those measured prior to 1986. 

The high nitrogen concentrations measured prior to 1986 

were primarily caused by high concentrations of Kjeldahl 

nitrogen, which often exceeded 1 mg/L. 

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 usually indicates that 

phosphorus should be the potentially limiting nutrient. The 

N:P ratios for 1970s data ranged from 15:1 to 35:1, with 

an average ratio of 23:1. This indicates that phosphorus 

should have been the potentially limiting nutrient. Incremental additions of nitrogen and phosphorus (bioassays) 

also can be used to indicate whether phosphorus or nitrogen may be the limiting nutrient. During 1972, bioassay 

experiments indicated that nitrogen was the limiting nutrient in the lake (U.S. Environmental Protection Agency, 

1974). Since 1986, the N:P ratios have ranged from 12:1 

to 21:1, with an average of 17:1. These ratios indicate 

that phosphorus typically should be the limiting nutrient. 

Based on the earlier bioassays and the few low N:P ratios, 

however, algal productivity may often be colimited by both 

nitrogen and phosphorus. 

Further reductions in phosphorus concentrations 

should not only increase the N:P ratio, but also favor 

the growth of green algae over the growth of blue-green 

algae. Blue-green algae usually are not limited by nitrogen 

because they can fix nitrogen from the atmosphere. Bluegreen algae are the least desirable type of algae because 

they commonly form extensive blooms or scums on the 

surface, are potentially toxic, and are usually the least 

preferred by grazing zooplankton. Therefore, phosphorus 

should be the nutrient of concern when considering management efforts to improve the water quality of Butternut 

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 between about 2 

and 7 μg/L indicate mesotrophic conditions, and average 

concentrations between 7 and 20 μg/L indicate eutrophic 

conditions. Concentrations greater than 20 μg/L indicate 

hypereutrophic conditions and are usually associated with 

frequent algal blooms. During MY 2003 and MY 2004, 

concentrations ranged from 1 to 2 μg/L in early spring to 

more than 30 μg/L in late summer of both years (fig. 5B). 

The average near-surface summer chlorophyll a concentration measured throughout the lake during MY 2003–04 

was about 20 μg/L (table 5). Therefore, based on chlorophyll a concentrations, Butternut Lake would typically be 

classified as on the border between eutrophic and hypereutrophic.

Since 1972, chlorophyll a concentrations ranged from 

less than 1 μg/L to more than 90 μg/L (fig. 6B). The few 

chlorophyll a data prior to 1986 indicated two different 

conditions: low concentrations in 1972 and high concentrations in 1978. From 1978 to about 1990, near-surface 

chlorophyll a concentrations have declined; however, since 

1990, no consistent long-term change was apparent. The 

overall average summer concentration from 1986 to 2005 

was 28 μg/L, and the average August concentration was 

45 μg/L. 
Measured Lake Water Quality 17

Figure 6. Near-surface A, total phosphorus concentrations, B, chlorophyll a concentrations, and C, Secchi depths at the Deephole Site in Butternut Lake, Wis., from 1972 to 2006 (EPA, U.S. Environmental Protection Agency; WDNR, Wisconsin Department of 

Natural Resources; USFS, United States Forest Service; USGS, U.S. Geological Survey).

1972 1976 1980 1984 1988 1992 1996 2000 2004

0.0

0.5

1.0

1.5

2.0

2.5

3.0

DATE

SECCHI DEPTH, IN METERS

1972 1976 1980 1984 1988 1992 1996 2000 2004

0

10

20

30

40

50

60

70

80

90

100

CHLOROPHYLL A CONCENTRATION, 

IN MICROGRAMS PER LITER

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

1972 1976 1980 1984 1988 1992 1996 2000 2004

TOTAL PHOSPHORUS, IN MILLLIGRAMS PER LITER

EPA

WDNR

USFS

Citizen monitoring

USGS

August average

Summer average

A.

B.

C.
18 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis. Table 6. Near-surface, summer-average (May–August) and August water quality and trophic state index (TSI) values for the Deep-hole Site in Butternut Lake, Wis. Data were collected by the U.S. Geological Survey, U.S. Environmental Protection Agency, U.S. Forest Service, Wisconsin Department of Natural Resources, and citizen monitoring. [mg/L, milligram per liter; μg/L, microgram per liter; m, meter; --, no data] Year May–August August Trophic state index values (August) Total phosphorus (mg/L) Chlorophyll a

(μg/L)

Secchi depth 

(m)

Total phosphorus 

(mg/L)

Chlorophyll a

(μg/L)

Secchi depth 

(m) Phosphorus Chlorophyll a Secchi depth

1972 0.079 5.5 1.05 0.093 4.1 0.8 69.5 44.3 62.5

1973 .052 -- 1.24 .057 -- 1.0 62.4 -- 59.3

1974 .076 -- 1.08 .090 -- .9 69.0 -- 62.3

1975–77 -- -- -- -- -- -- -- -- --

1978 .058 41.4 1.46 .061 51.8 1.3 63.4 69.3 56.4

1979–85 -- -- -- -- -- -- -- -- --

1986 .067 49.9 -- .068 85.1 -- 65.0 74.2 --

1987 .042 32.7 1.58 .062 65.0 .8 63.7 71.6 63.2

1988 .061 30.3 1.20 .070 40.0 1.0 65.4 66.8 60.0

1989 .057 41.5 1.37 .084 77.0 .9 68.0 73.2 61.5

1990 .047 31.3 .97 .055 50.0 .6 61.9 69.0 67.4

1991 .046 35.9 1.00 .052 46.0 1.0 61.1 68.2 60.7

1992 .049 34.0 1.34 .053 49.1 1.1 61.4 68.8 58.5

1993 .035 15.4 1.36 .034 18.0 1.2 55.0 58.9 57.4

1994 .046 35.7 1.26 .061 53.5 .8 63.3 69.6 63.2

1995 .036 11.1 1.36 .040 20.8 1.3 57.3 60.4 56.2

1996 .035 25.2 1.22 .035 30.1 1.1 55.4 64.0 58.6

1997 .054 13.9 1.55 .054 19.8 1.5 61.7 59.9 54.2

1998 -- -- -- -- -- -- -- -- --

2001 .048 25.7 1.00 .054 44.0 .7 61.7 67.7 64.7

2002 .041 19.0 1.05 .047 41.0 1.1 59.7 67.0 59.1

2003 .039 19.4 1.31 .041 34.8 1.1 57.7 65.4 59.0

2004 .049 19.5 1.17 .056 27.0 1.0 62.2 62.9 59.5

2005 .036 31.4 1.09 .043 63.5 .8 58.4 71.3 63.9

2006 -- -- 1.46 -- -- 1.4 -- -- 55.4

Average: All years .050 27.3 1.24 .058 43.2 1.01 62.1 65.9 60.1Average: 1986–2006 .046 27.8 1.25 .053 45.0 1.02 61.1 67.0 60.2Average: 2003–04 .044 19.4 1.24 .049 30.9 1.05 59.9 64.2 59.3
Measured Lake Water Quality 19

During MY 2003 and MY 2004, Secchi depths in 

Butternut Lake ranged from 0.65 m on August 13, 2003, 

in the South Basin to about 1.5 m in the fall of 2004 at 

several locations (fig. 5C). Little consistent seasonal or 

spatial variability was apparent in Secchi depths. During 

MY 2003–04, the average summer Secchi depth was about 

1.2 m (table 5). Since 1972, Secchi depths have changed 

very little (fig. 6C). Secchi depths between 2 and 4 m indicate mesotrophic conditions, from 1 to 2 m indicate eutrophic conditions, and less than 1 indicate hypereutrophic 

conditions. Therefore, based on Secchi depths, Butternut 

Lake would typically be classified as eutrophic.

All three TSIs, based on near-surface concentrations 

of total phosphorus and chlorophyll a, and on Secchi 

depths, indicate that in MY 2003 and MY 2004, Butternut 

Lake was typically eutrophic to hypereutrophic (fig. 7 and 

table 6). During late summer, when phosphorus concentrations were higher and water clarity was poorer than in 

other parts of the year, the lake was typically classified as 

hypereutrophic. In general, TSI values based on chlorophyll a concentrations were a little higher than those based 

on total phosphorus concentrations or Secchi depths. 

Figure 7. Trophic state index (TSI) values based on surface concentrations of total phosphorus (TP) and chlorophyll a (CHL), 

and Secchi depths (SD), in Butternut Lake, Wis. Data were collected by the U.S. Geological Survey, U.S. Environmental Protection 

Agency, U.S. Forest Service, Wisconsin Department of Natural Resources, and citizen monitoring.

30

40

50

60

70

80

1972 1976 1980 1984 1988 1992 1996 2000 2004

DATE

TROPHIC STATE INDEX VALUES

Phosphorus

Chlorophyll a

Secchi depth

August TP

August CHL

August SD
20 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

Inferred Lake Water Quality from 

Lake-Sediment Analyses

Results of analyses of a sediment core extracted from 

the deep area of the North Basin in February 2003 were 

used to quantify changes in sedimentation rates and reconstruct historical changes in the water quality of the lake 

(Garrison, 2006). The average annual sedimentation rate 

for Butternut Lake (0.026 g/cm2) was about average for the 

lakes that have been studied in Wisconsin. The annual sedimentation rate steadily increased from about 0.01 g/cm2

in 1840 to about 0.04–0.08 g/cm2 in 1930–40. Since 1940, 

there was no discernable trend in sedimentation rates, but 

the rates fluctuated from about 0.025 to 0.050 g/cm2. 

Changes in the diatom assemblages in the lake sediments were used to infer changes in the nutrient concentrations in the water column of Butternut Lake. On the basis 

of changes in the diatom assemblages, the average in-lake 

phosphorus concentrations increased steadily from about 

0.015–0.020 mg/L in 1850 to about 0.040 mg/L in 1970 

(fig. 8). Since 1970, the inferred total phosphorus concentrations fluctuated from about 0.030 to 0.040 mg/L and 

appeared to have stabilized. The increases in concentrations from 1840 to 1970 are consistent with the increase 

in phosphorus inputs caused by logging and agricultural 

activities in the watershed, sewage effluent from the Village of Butternut, discharges from a creamery and cheese 

factories, and seepage from leaking septic systems. Based 

on the inferences from analysis of the sediment core, 

all of the efforts in the watershed to reduce phosphorus 

inputs from these sources have stopped the increase in 

total phosphorus concentrations. Given the fluctuations in 

the inferred total phosphorus concentrations from 1980 to 

the present, however, it is not possible to determine if the 

concentrations have decreased in recent years. 

Hydrology and Water Budget

Because the productivity in Butternut Lake is limited 

or colimited by phosphorus (based on N:P ratios) and 

because reductions in phosphorus concentrations should 

favor production of green algae over blue-green algae, 

further reductions in the input of phosphorus to the lake 

should reduce phosphorus concentrations in the lake and 

thus improve water quality. Most of the phosphorus entering the lake is transported by water inputs; therefore, to 

Figure 8. Estimated changes in summer total phosphorus concentrations based on changes in the diatom community in the 

sediment cores from Butternut Lake, Wis. (from Garrison, 2006).

1830

1850

1870

1890

1910

1930

1950

1970

1990

2010

0.000 0.010 0.020 0.030 0.040 0.050

INFERRED TOTAL PHOSPHORUS CONCENTRATION,

IN MILLIGRAMS PER LITER

YEAR
Hydrology and Water Budget 21

quantify phosphorus inputs, it is necessary to first quantify 

the water inputs. Water budgets for the lake were quantified for each of the two monitoring years.

The hydrology of Butternut Lake can be described in 

terms of components of its water budget. The water budget 

for a period of interest may be represented by:

∆S = (P + SWIn + GWIn) – (E + SWOut + GWOut), (4)

where ∆S 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), surfacewater inflow (SWIn), and ground-water inflow (GWIn). Water 

leaves the lake through evaporation (E), surface-water 

outflow (SWOut), and ground-water outflow (GWOut). Each 

term of the water budget was estimated on a daily basis.

Change in Storage

Changes in the volume of the lake were determined 

from water elevations measured continuously at the lakestage gage on the northwestern side of the lake (fig. 2). 

Lake stage fluctuated from a minimum of 1.46 m (relative 

to an arbitrary datum) to a maximum of 2.25 m in 

MY 2003, and from a minimum of 1.49 m to a maximum 

of 2.19 m in MY 2004 (fig. 9). To simplify computations, 

the area of the lake was assumed to be constant (393 ha) 

during the study. The change in storage from beginning to 

end of the period for MY 2003 was +112,000 m3

, and for 

MY 2004, it was +422,000 m3.

Precipitation

During the 2-year study period, total daily precipitation was measured at Butternut Creek at Cutoff Road 

near the northern end of the lake and at Butternut Creek 

at Highway B near the southern end of the lake during 

nonfreezing periods. During winter, precipitation was 

estimated by averaging the daily data from the National 

Weather Service stations (National Climatic Data 

Center, 2002–2004) at Butternut (about 2 km north of 

the lake) and at Park Falls (about 5 km southeast of the 

lake). Precipitation on the lake surface during MY 2003 

was 63.9 cm (2,510,000 m3

) and during MY 2004, it was 

89.9 cm (3,530,000 m3; table 7). Precipitation was 

78 percent of the long-term average (1971–2000) in 2003 

and it was 110 percent of the long-term average in 2004. 

Figure 9. Measured daily water levels of Butternut Lake, Wis.

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

11/1/02 2/1/03 5/1/03 8/1/03 11/1/03 2/1/04 5/1/04 8/1/04 11/1/04

LAKE STAGE, IN METERS

DATE
22 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

Table 7. Water budgets for Butternut Lake, Wis., for monitoring years 2003 and 2004, and average for the two years.

[MY, monitoring year (November–October); m3, cubic meter; Cty., county; Hwy., highway]

Budget component MY 2003

(thousands of m3

)

MY 2003

(percent)

MY 2004

(thousands of m3)

MY 2004

(percent)

Inputs to lake

Precipitation 2,510 7.1 3,530 8.7

North Basin 1,170 3.3 1,650 4.1

Middle Basin 803 2.3 1,130 2.8

South Basin 534 1.5 752 1.9

Tributaries 31,300 89.2 35,600 88.0

Butternut Creek inlet 22,100 63.0 24,400 60.2

Spiller Creek 6,830 19.5 8,500 21.0

Sum of small tributaries 2,390 6.8 2,740 6.8

Tributary at Cty. Hwy. B 105 .3 62 .2

Schnur Lake Outlet 665 1.9 665 1.6

Southwest Tributary #1 142 .4 291 .7

Southwest Tributary #2 173 .5 252 .6

Southeast Tributary 75 .2 72 .2

Mud Lake Outlet 549 1.6 614 1.5

Ungaged near-lake areas 681 1.9 780 1.9

Tributary input by basin 31,300 89.2 35,600 88.0

North Basin 30,100 85.8 34,100 84.3

Middle Basin 482 1.4 721 1.8

South Basin 710 2.0 799 2.0

Ground water 1,280 3.6 1,320 3.3

North Basin 640 1.8 659 1.6

Middle Basin 384 1.1 395 1.0

South Basin 256 .7 264 .7

TOTAL INPUT 35,100 100.0 40,400 100.0

Outputs from lake

Evaporation 2,650 7.6 2,520 6.2

North Basin 1,240 3.6 1,180 2.9

Middle Basin 849 2.4 809 2.0

South Basin 565 1.6 538 1.3

Outlet (Butternut Creek) 32,100 92.4 37,900 93.8

Ground water 0 .0 0 .0

TOTAL OUTPUT 34,700 100.0 40,400 100.0
Hydrology and Water Budget 23

Table 7. Water budgets for Butternut Lake, Wis., for monitoring years 2003 and 2004, and average for the two years—Continued.

[MY, monitoring year (November–October); m3, cubic meter; Cty., county; Hwy., highway]

Budget component 2-year average

(thousands of m3

)

2-year average

(percent)

Inputs to lake

Precipitation 3,020 8.0

North Basin 1,410 3.7

Middle Basin 967 2.6

South Basin 643 1.7

Tributaries 33,400 88.6

Butternut Creek inlet 23,200 61.5

Spiller Creek 7,660 20.3

Sum of small tributaries 2,560 6.8

Tributary at Cty. Hwy. B 84 .2

Schnur Lake Outlet 665 1.8

Southwest Tributary #1 216 .6

Southwest Tributary #2 212 .6

Southeast Tributary 74 .2

Mud Lake Outlet 581 1.5

Ungaged near-lake areas 731 1.9

Tributary input by basin 33,400 88.6

North Basin 32,100 85.0

Middle Basin 601 1.6

South Basin 755 2.0

Ground water 1,300 3.4

North Basin 650 1.7

Middle Basin 390 1.0

South Basin 260 .7

TOTAL INPUT 37,800 100.0

Outputs from lake

Evaporation 2,590 6.9

North Basin 1,210 3.2

Middle Basin 829 2.2

South Basin 552 1.5

Outlet (Butternut Creek) 35,000 93.1

Ground water 0 .0

TOTAL OUTPUT 37,600 100.0
24 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

Figure 10. Precipitation at Butternut Lake, Wis., during November 2002 to October 2004, relative to long-term average 

precipitation at Park Falls, Wis.

0

3

6

9

12

15

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

PRECIPITATION, IN CENTIMETERS

Nov. 2002–Oct. 2003

Nov. 2003–Oct. 2004

Long-term average

Monthly precipitation during each study year is compared 

to the 1971–2000 average monthly precipitation in figure 

10. In MY 2003, precipitation totals for December, April, 

May, September, and October were above or near the longterm average; all other monthly totals were much below 

average. In MY 2004, totals for all months except January 

and June were near or above average. 

Evaporation

Evaporation from the lake surface was estimated from 

June–September pan evaporation measured at Marshfield, 

Wis., and published long-term monthly estimates of pan 

evaporation at Green Bay, Wis. Pan evaporation at Marshfield was available only for June, July, August, and September (National Climatic Data Center, 2003; and 2004). 

Estimates of long-term monthly average pan evaporation 

for Green Bay were available for the nonsummer months 

(Farnsworth and Thompson, 1982). Measured pan data 

from Marshfield and long-term monthly pan data from 

Green Bay were adjusted for the difference in location to 

Butternut Lake. Monthly lake/pan coefficients computed 

as part of a study on Vandercook Lake, Vilas County 

(Wentz and Rose, 1991) were then used to adjust the pan 

evaporation rates to obtain total lake evaporation. These 

coefficients ranged from 0.75 in May to 1.17 in October. 

It was assumed that evaporation from the lake was zero 

during periods of ice cover, and that the lake was ice covered from December through March. Annual evaporation 

in MY 2003 and MY 2004 was estimated to be 67.5 cm 

(2,650,000 m3) and 64.3 cm (2,520,000 m3), respectively 

(table 7).

Surface-Water Inflow

Daily inflow from Butternut Creek, the main tributary to the lake, was measured at the gaging station at 

Cutoff Road (fig. 2). The drainage area above this location 

is 74.7 km2 (table 3). The annual average streamflow at 

this site was 0.70 m3/s (22,100,000 m3) in MY 2003 and 

0.77 m3/s (24,400,000 m3) in MY 2004 (table 7; fig. 11). 

For comparison, the flow measured at the long-term USGS 

gaging station on the Chippewa River at Bishops Bridge 

near Winter, Wis. (about 25 km southwest of the lake) 

was 96 percent of the 94-year average for MY 2003 and 

100 percent of the average for MY 2004 (Waschbusch and 

others, 2004; 2005). 

Inflow to the lake from Spiller Creek was monitored 

at the gaging station at County Highway B, about 0.5 km

west of the lake (fig. 2). The drainage area upstream 

from the gaging station is 22.8 km2

. The annual average 

streamflow at this site was 0.22 m3/s (6,830,000 m3) in 
Hydrology and Water Budget 25

Figure 11. Daily-average flow and total phosphorus concentrations in Butternut Creek at Cutoff Road and Spiller Creek at 

Highway B, tributaries to Butternut Lake, Wis., November 1, 2002, through October 31, 2004.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

11/1/2002 1/31/2003 5/1/2003 8/1/2003 11/1/2003

DATE

2/1/2004 5/1/2004 8/1/2004 11/1/2004

TOTAL PHOSPHORUS CONCENTRATION, 

IN MILLIGRAMS PER LITER

0

 200

400

600

800

1,000

1,200

1,400

1,600

DAILY FLOW, IN THOUSANDS OF CUBIC METERS

Butternut Creek, concentration

Spiller Creek, concentration

Butternut Creek, daily flow

Spiller Creek, daily flow

MY 2003 and 0.27 m3/s (8,500,000 m3) in MY 2004 (table 

7; fig. 11).

Of the six small tributaries that were monitored 

(fig. 2), Schnur Lake outlet and Mud Lake outlet yielded 

the most flow. The 2-year average flow volumes were 

665,000 m3 and 581,000 m3 at Schnur Lake and Mud Lake 

outlets, respectively (table 7). The average annual flow 

volume from the remaining ungaged near-lake area was 

731,000 m3

 during the 2-year period. The sum of flow 

from the six tributaries and the ungaged near-lake area 

was 2,390,000 m3 and 2,740,000 m3 in MY 2003 and 

MY 2004, respectively. 

Surface-Water Outflow

Total annual surface-water outflow from the lake to 

Butternut Creek at the southern end of the lake (figs. 1 and 

2) was 32,100,000 m3

 in MY 2003 and 37,900,000 m3 in 

MY 2004 (table 7; fig. 12). Most of the outflow occurred 

during May and June.

Ground-Water Inflow and Outflow

Ground-water inflow to the lake was calculated on 

the basis of base-flow estimates for the area contributing 

ground water to Spiller Creek and hydraulic-head data 

from the near-lake piezometers (fig. 2). The hydraulic 

gradient in the eight near-lake piezometers indicated that 

the flow of ground water was from the aquifer to the lake 

along most of the lake’s shoreline. The head differences 

relative to the lake surface ranged from near 0.0 m at 

piezometer 3 to greater than 0.5 m at piezometer 8.

Several assumptions were necessary to estimate the 

amount of ground-water inflow to the lake because the 

data needed to do a rigorous analysis were not available. 

Base flow in Spiller Creek was assumed to be mostly 

ground-water discharge. The ground-water contributing 

area for Spiller Creek was assumed to coincide with its 

surface watershed. Ground-water discharge to the lake was 

assumed to be proportional to the ground-water discharge 

to Spiller Creek by the ratio of the ground-water contributing area of Butternut Lake to the contributing area to 

Spiller Creek. The ground-water contributing area to the 

lake was coarsely determined by an analysis of topography 
26 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

and the altitudes of nearby water features. The estimated 

ground-water contributing area is shown in figure 13.

The estimated ground-water discharge to Butternut 

Lake was 1,280,000 m3 in MY 2003 and 1,320,000 m3 in 

MY 2004 (table 7). Ground-water discharge from the lake, 

or leakage, was assumed to be zero, because the near-lake 

piezometer data showed no areas where flow was coming 

from the lake. It is possible that there is some, but insignificant, leakage in a small area near the outlet at the southern 

end of the lake.

Water-Budget Summary

Butternut Creek is the largest source of water to the 

lake, supplying 61.5 percent of the total input during the 

2-year study period (table 7; fig. 14). Other sources were 

Spiller Creek (20.3 percent), precipitation (8.0 percent), 

small tributaries and the ungaged near-lake drainage (6.8 

percent), and ground water (3.4 percent). The total input 

of water in MY 2003 (35,100,000 m3

) was less than in 

MY 2004 (40,400,000 m3), because of the below-normal 

precipitation during MY 2003 and above normal precipitation in MY 2004. 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 0.45 and 

0.39 years on the basis of the total inflows for MY 2003 

and MY 2004, respectively, or 0.42 years on the basis of 

the 2 years of data averaged. 

The total annual outputs of water from the lake were 

slightly less than the total inputs and resulted in a small 

increase in storage from the beginning to the end of each 

study year. This amounted to an increase in lake stage of 

0.13 m or about 534,000 m3

 of storage in the lake during the 2-year study period. On average, 93.1 percent of 

the total water leaving the lake left through the Butternut 

Creek outlet, and evaporation accounted for the remaining 

6.9 percent (table 7; fig 14).

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 as meters on the surface of the lake 

(fig. 15). The differences between the calculated inputs 

and outputs reflect the cumulative errors in the estimates 

of all of the components in the water budget. The largest 

monthly differences were in May 2003 and April 2004, 

Figure 12. Daily-average flow and total phosphorus concentrations in Butternut Creek at Highway B, outlet from Butternut Lake, 

Wis., November 1, 2002, through October 31, 2004.

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

11/1/02 1/31/03 5/1/03 8/1/03 11/1/03

DATE

2/1/04 5/1/04 8/1/04 11/1/04

TOTAL PHOSPHORUS CONCENTRATION, 

IN MILLIGRAMS PER LITER 

0

200

400

600

800

1,000

1,200

1,400

1,600

DAILY FLOW, IN THOUSANDS OF CUBIC METERS

Outlet concentration

South Basin concentration

Daily flow
Hydrology and Water Budget 27

Figure 13. Estimated ground-water contributing area to Butternut Lake, Wis. Land use/land cover from the WISCLAND 

geographic information system coverage (Wisconsin Department of Natural Resources, 1998).

90°32'30 90°30'

46°

45°57'30"

0 .5 1 MILE

0 .5 1 KILOMETER

EXPLANATION

Rural residential (low density)

Agriculture

Pasture/grassland

Forest/shrubland

Open water

Wetlands

Barren

Piezometer and identifier

Ground-water boundary

Land use/land cover

B

u t t e r n

u t L a

k e

Base map from U.S. Geological Survey

digital data, 1:24,000.

S c h n u r L a k e

2

8

3

7

4

1

6

5

2

8

3

7

4

1

6

5

5
28 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

Figure 14. Water budgets for Butternut Lake, Wis., for monitoring years 2003 and 2004. [%, percent]

Inputs

Ground water

3.6%

Precipitation

7.1%

Other small 

tributaries

6.8%

Spiller Creek

19.5%

Total inputs = 35,100,000 cubic meters Total outputs = 34,700,000 cubic meters

Outputs

Evaporation

7.6%

Inputs

Precipitation

8.7%

Ground water

3.3%

Spiller Creek

21.0%

Other small 

tributaries

6.8%

Total inputs = 40,400,000 cubic meters Total outputs = 40,400,000 cubic meters

Outputs

Evaporation

6%

Monitoring year 2003

Monitoring year 2004

Butternut

Creek

Outlet

94%

Butternut

Creek Inlet

60.2%

Butternut

Creek Inlet

63.0%

Butternut

Creek

Outlet

92.4%
Sources of Phosphorus 29

which when expressed as percentages were only about 10 

and 8 percent, respectively. The largest errors occurred 

during spring when overland flow from the ungaged area 

was highest. On an annual basis, the percentage error was 

about 1 percent. 

Sources of Phosphorus

To help define where the phosphorus in Butternut 

Lake originates and how much may be controllable, a 

detailed phosphorus budget was computed for each monitoring year. External sources of phosphorus to the lake 

include precipitation, surface- and ground-water inflow, 

and contributions from septic systems. In addition to these 

external sources, phosphorus can be released from the bottom sediments of the lake, which is considered an internal 

source of phosphorus. Phosphorus is removed from the 

lake through surface-water outflow and deposition to the 

lake sediments. 

Precipitation

Phosphorus input to the lake from direct precipitation was estimated by multiplying the daily precipitation 

volumes by a constant concentration of 0.007 mg/L, a 

value suggested by Rose (1993) for northern Wisconsin. 

Figure 15. Monthly accuracy of the water budget based on monthly total water inputs and outputs plus storage change for 

Butternut Lake, Wis.

0

1

2

3

4

5

METERS ON LAKE

Inputs

Outputs plus change in storage

Nov. 02

Dec. 02

Jan. 03

Feb. 03

Mar. 03

Apr. 03

May 03

June 03

July 03

Aug.03

Sept. 03

Oct. 03

Nov. 03

Dec. 03

Jan. 04

Feb. 04

Mar. 04

Apr. 04

May 04

June 04

July 04

Aug.04

Sept. 04

Oct. 04

Phosphorus inputs to the lake from precipitation were 

18 kg in MY 2003 and 25 kg in MY 2004 (table 8). 

Surface-Water Inflow 

Phosphorus loads were estimated for the continuously monitored sites at the Butternut Creek inlet to the 

lake, Spiller Creek, and the Butternut Creek outlet, as well 

as for the six small tributaries to the lake and the ungaged 

near-lake area. 

Butternut Creek Inlet

Phosphorus in Butternut Creek inlet at Cutoff Road 

(fig. 2) originates from the upper watershed, including 

the Village of Butternut. Total phosphorus concentrations 

for 114 samples collected during the 2-year study ranged 

from 0.020 to 0.090 mg/L (fig. 11). The median concentration and flow-weighted-average concentrations were 

0.044 and 0.043 mg/L, respectively. On average, about 

61 percent of the phosphorus was in the dissolved form. 

The total quantity of phosphorus delivered from Butternut 

Creek was 921 kg in MY 2003 and 1,080 kg in MY 2004 

(table 8). Yields from the Butternut Creek watershed were 

12.3 kg/km2

 in MY 2003 and 14.4 kg/km2 in MY 2004. 

These yields are lower than 49 of the 52 rural watersheds 

that were monitored in Wisconsin and among the lowest 
30 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

Table 8. Phosphorus budgets for Butternut Lake, Wis., for monitoring years 2003 and 2004, and average for the two years.

[MY, monitoring year (November–October); kg, kilogram; Cty., county; Hwy., highway]

Budget component MY 2003

(kg)

MY 2003

(percent)

MY 2004

(kg)

MY 2004

(percent)

Inputs to lake

Precipitation 18 1.2 25 1.4

North Basin 8 0.6 12 0.7

Middle Basin 6 .4 8 .5

South Basin 4 .3 5 .3

Tributaries 1,370 94.5 1,650 94.9

Butternut Creek inlet 921 63.6 1,080 62.1

Spiller Creek 330 22.8 405 23.4

Sum of small tributaries 117 8.1 164 9.5

Tributary at Cty. Hwy. B 4 0.3 2 0.1

Schnur Lake Outlet 15 1.0 13 .7

Southwest Tributary #1 16 1.1 42 2.5

Southwest Tributary #2 18 1.2 25 1.5

Southeast Tributary 4 .3 4 .2

Mud Lake Outlet 27 1.9 30 1.7

Ungaged near-lake areas 33 2.3 47 2.7

Tributary input by basin 1,370 94.5 1,650 94.9

North Basin 1,290 89.1 1,530 88.0

Middle Basin 42 2.9 78 4.5

South Basin 35 2.4 41 2.4

Ground water 22 1.5 22 1.3

North Basin 11 .8 11 .6

Middle Basin 7 .5 7 .4

South Basin 4 .3 4 .3

Septic systems 41 2.8 41 2.3

North Basin 17 1.2 17 1.0

Middle Basin 11 .8 11 .7

South Basin 13 .9 13 .7

Total external input 1,450 100.0 1,730 100.0

Sediment release

North Basin 467 49.4 467 49.4

Middle Basin 306 32.4 306 32.4

South Basin 172 18.2 172 18.2

Total internal input 945 100.0 945 100.0

TOTAL INPUT 2,390 2,680

Outputs from lake

Evaporation 0 .0 0 .0

Outlet (Butternut Creek) 1,320 100.0 1,670 100.0

Ground water 0 .0 0 .0

TOTAL OUTPUT 1,320 100.0 1,670 100.0

Stored in lake

STORED IN LAKE 1,070 1,010
Sources of Phosphorus 31

Table 8. Phosphorus budgets for Butternut Lake, Wis., for monitoring years 2003 and 2004, and average for the two years—

Continued.

[MY, monitoring year (November–October); kg, kilogram; Cty., county; Hwy., highway]

Budget component 2-year average

(kg)

2-year average

(percent)

Inputs to lake

Precipitation 21 1.3

North Basin 10 0.6

Middle Basin 7 .4

South Basin 5 .3

Tributaries 1,510 94.7

Butternut Creek inlet 999 62.8

Spiller Creek 368 23.1

Sum of small tributaries 140 8.8

Tributary at Cty. Hwy. B 3 0.2

Schnur Lake Outlet 14 .9

Southwest Tributary #1 29 1.8

Southwest Tributary #2 22 1.4

Southeast Tributary 4 .3

Mud Lake Outlet 29 1.8

Ungaged near-lake areas 40 2.5

Tributary input by basin 1,510 94.7

North Basin 1,410 88.5

Middle Basin 60 3.8

South Basin 38 2.4

Ground water 22 1.4

North Basin 11 .7

Middle Basin 7 .4

South Basin 4 .3

Septic systems 41 2.6

North Basin 17 1.1

Middle Basin 11 .7

South Basin 13 .8

Total external input 1,590 100.0

Sediment release 945 100.0

North Basin 467 49.4

Middle Basin 306 32.4

South Basin 172 18.2

Total internal input 945 100.0

TOTAL INPUT 2,540

Outputs from lake

Evaporation 0 .0

Outlet (Butternut Creek) 1,490 100.0

Ground water 0 .0

TOTAL OUTPUT 1,490 100.0

Stored in lake

STORED IN LAKE 1,050
32 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

for the Northern Lakes and Forests ecoregion (Corsi and 

others, 1997). 

Spiller Creek

Total phosphorus concentrations for 132 samples 

collected at Spiller Creek during the 2-year study ranged 

from 0.018 to 0.249 mg/L (fig. 11). The median and flowweighted-average concentrations were 0.046 and 

0.048 mg/L, respectively. On average, about 67 percent of 

the phosphorus was in the dissolved form. The total quantity of phosphorus delivered to the lake by Spiller Creek 

was 330 kg in MY 2003 and 405 kg in MY 2004 (table 8). 

Yields from the Spiller Creek watershed were 14.5 kg/km2 

in MY 2003 and 17.8 kg/km2 in MY 2004. These yields 

are slightly higher than the yields from the Butternut Creek 

watershed, but they are much lower than yields for most 

of the monitored rural watersheds in Wisconsin (Corsi and 

others, 1997).

Small Tributaries and Ungaged Near-Lake 

Area

In all, 109 runoff samples were collected from the six 

small tributaries to the lake. Total phosphorus concentrations ranged from 0.015 to 0.665 mg/L. The median and 

flow-weighted-average concentrations were 0.053 and 

0.055 mg/L, respectively. The combined total quantity of 

phosphorus delivered to the lake by these tributaries and 

the other ungaged near-lake area was 117 kg in MY 2003 

and 164 kg in MY 2004 (table 8). Yields from the combined tributary and ungaged area were 5.7 kg/km2

 in 

MY 2003 and 8.0 kg/km2 in MY 2004, which are even 

lower than the yields from the Butternut Creek and Spiller 

Creek watersheds. The Mud and Schnur Lake watersheds 

represent 51.1 percent of the total area of the six small 

tributaries and ungaged near-lake area. The relatively low 

yields, in part, may be attributed to the lakes trapping some 

of the phosphorus contributed by their watersheds.

Ground Water

Dissolved phosphorus concentrations in water collected from the eight near-lake piezometers (fig. 2) were 

used to estimate the phosphorus concentration in the 

ground water entering the lake. Average concentrations 

ranged from 0.009 mg/L in piezometer 1 to 0.348 mg/L in 

piezometer 3, and the median concentration of all of the 

samples was 0.017 mg/L. The phosphorus concentration in 

piezometer 3 was about 14 times greater than the average 

concentration from the other seven piezometers. Hence, it 

was assumed that the concentration in piezometer 3 was 

not typical of ground water entering the lake, and it may 

have been influenced by a local factor such as a septic 

system. In order to estimate the phosphorus input to the 

lake by ground water, it was assumed that the concentration of water entering the lake was equal to the median 

concentration measured in the piezometers (0.017 mg/L). 

Thus, ground water delivered about 22 kg of phosphorus to 

the lake annually (table 8).

Septic Systems

The input of phosphorus from septic systems (M) 

was estimated by use of equation 5 (Reckhow and others, 

1980):

M = Es * (number of capita years) * (1-S

R), (5)

where M is a function of a phosphorus export coefficient, 

Es, a soil retention coefficient, SR, and the number of 

people using the septic systems annually (capita years). In 

applying equation 5, it was assumed that the most likely 

value for Es was 0.68 kg of phosphorus per capita per 

year. Typical export coefficients range from 0.5 kg per 

capita per year (Reckhow and others, 1980; Panuska and 

Kreider, 2002) to 0.82 kg per capita per year (Garn and 

others, 1996). The number of capita years was estimated 

to be 200, based on 150 year-round residents and 198 

3-month residents. The number of residents was estimated 

from the number of parcels of land around the lake with 

houses, assuming that the parcels with nonlocal ownership were occupied only 3 months of the year. All houses 

occupied year round were assumed to have two residents, 

and houses occupied for 3 months were assumed to have 

three residents. A value of 0.7 (70 percent retention by the 

soil) was used for SR. Based on the above assumptions, the 

annual input of phosphorus from septic systems was 41 kg 

(table 8). Because inputs from septic systems were not 

directly measured, low and high estimates for septic inputs 

were obtained by applying high and low estimates for SR

(0.9 and 0.5) in equation 5. The low and high estimates for 

phosphorus inputs from septic systems were 14 and 68 kg, 

respectively.

Release of Phosphorus from Lake Sediments

Rates of phosphorus release from the aerobic and 

anaerobic sediments in Butternut Lake were estimated 

from 18 sediment cores collected from the lake (fig. 2) and 
Sources of Phosphorus 33

analyzed in the laboratory. Average aerobic-release rates 

at 22oC ranged from 0.66 mg/m2/d in the Middle Basin 

to 0.83 mg/m2/d in the North Basin (table 9). Average 

anaerobic-release rates at 22oC ranged from 5.56 mg/m2/d 

in the North Basin to 5.91 mg/m2

/d in the Middle Basin. 

No sediment cores from the South Basin were analyzed 

under anaerobic conditions; therefore, it was assumed that 

its anaerobic-release rate was similar to that of the Middle 

Basin. 

For each basin, the amount of phosphorus released 

from the sediment was computed on a daily basis by 

summing the amount of phosphorus released from the 

aerobic and anaerobic areas. The daily aerobic and anaerobic areas were obtained by linear interpolating between 

the dates for which these areas were estimated (table 4); 

the sediment release was assumed to be similar for both 

years. The daily sediment release was computed as the 

product of the temperature-adjusted release rates (rates 

in table 9 multiplied by the values from fig. 3 correspondTable 9. Summary of estimated rates of phosphorus release from the sediments of Butternut Lake, Wis., in August 2004.

[ID, identification number; mg/m2/d, milligram per square meter per day; r, correlation coefficient; --, not applicable]

Sample description/

core ID

Aerobic or 

anaerobic

Release rate

(mg/m2

/d)

Regression fit from 

laboratory results (r)

Average release at site 

(mg/m2/d)

Lake water blank Aerobic -0.08 NA --

North Basin

1A Aerobic 0.30 0.83 0.34

1B Aerobic .39 .90 --

2A Aerobic 1.24 .92 1.53

2B Aerobic 1.82 .98 --

2C Anaerobic 5.23 .97 5.56

2D Anaerobic 5.88 .98

3A Aerobic .67 .93 .63

3B Aerobic .59 .97 --

Average Aerobic .83 -- --

Average Anaerobic 5.56 -- --

Middle Basin

4A Aerobic 1.02 0.88 0.77

4B Aerobic .52 .92 --

4C Anaerobic 7.51 .98 6.32

4D Anaerobic 5.13 .97 --

5A Aerobic .71 .97 .55

5B Aerobic .39 .93 --

5C Anaerobic 4.78 .96 5.49

5D Anaerobic 6.21 .97

Average Aerobic .66 -- --

Average Anaerobic 5.91 -- --

South Basin

6A Aerobic 1.02 0.98 0.78

6B Aerobic .53 .97 --

Average Aerobic .78 -- --

Average Anaerobic 5.91a -- --

a

 Value not computed; therefore, the release rates were obtained from the Middle Basin. 
34 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

ing to the estimated daily water temperature for that 

day) and the respective aerobic and anaerobic areas. The 

estimated phosphorus released from the sediments of the 

North Basin was 467 kg (table 8; 216 kg from aerobic 

sediments and 251 kg from anaerobic sediments), from 

the Middle Basin was 306 kg (117 kg from aerobic sediments and 189 kg from anaerobic sediments), and from 

the South Basin was 172 kg (94 kg from aerobic sediments 

and 77 kg from anaerobic sediments). Therefore, on an 

annual basis, the sediments released an estimated total of 

945 kg (427 kg from aerobic sediments and 518 kg from 

anaerobic sediments). Approximately 90 percent of the 

phosphorus was released during May through September. 

Surface-Water Outflow 

Phosphorus is discharged from the lake into Butternut 

Creek through its outlet. Total phosphorus concentrations in the 29 samples collected near the outlet during 

the 2-year study period ranged from 0.026 to 0.065 mg/L 

(fig. 12), and the flow-weighted-average concentration was 

0.043 mg/L. The total phosphorus output from the lake to 

Butternut Creek was 1,320 kg in MY 2003 and 1,670 kg in 

MY 2004 (table 8).

Phosphorus Budget Summary

The average annual load of phosphorus to the lake 

was 2,540 kg, of which 1,590 kg came from external 

sources (63 percent) and 945 kg came from the sediments 

in the lake (37 percent). Internal loading of phosphorus 

ranged from 38.5 percent of the total phosphorus load to 

the lake in MY 2003 to 35.3 percent in MY 2004 (fig. 16). 

During wet years, this internal release represents a smaller 

percentage of the total phosphorus delivered to the lake 

and during dry years, it represents a higher percentage. 

The total external input of phosphorus to Butternut 

Lake was 1,450 kg in MY 2003 and 1,730 kg in MY 2004, 

for an average annual input of 1,590 kg (table 8). The 

largest external source of phosphorus entering the lake is 

from Butternut Creek, which delivered about 63 percent of 

the external phosphorus entering the lake (table 8; about 

39 percent of the total phosphorus load to the lake, fig. 16) 

compared with about 61 percent of the water input (table 

7; fig. 14). The next largest external contribution was from 

Spiller Creek, which delivered about 23 percent of the 

external phosphorus entering the lake (about 14 percent 

of the total load to the lake). The six small tributaries and 

ungaged near-lake area contributed about 9 percent of the 

total external load to the lake (about 6 percent of the total 

load to the lake). Minor contributions were from precipitation, ground water, and septic systems, which accounted 

for 1.3, 1.4, and 2.2 percent of the external load, respectively (about 0.8, 0.9, and 1.6 percent, respectively, of the 

total load). If the high estimates for phosphorus contributions from septic systems (68 kg) were used in the budget, septic systems would increase to about 4 percent of 

the total external phosphorus load (about 3 percent of the 

total load to the lake). External phosphorus loading in 

MY 2004 was about 1.2 times that in MY 2003 because 

of the greater precipitation and accompanying runoff during MY 2004.

The average annual surface-water discharge of phosphorus into Butternut Creek was 1,490 kg; 1,320 kg of 

phosphorus in MY 2003 and 1,670 kg in MY 2004. Therefore, on average, about 94 percent of the external inputs or 

59 percent of the total load to the lake is removed from the 

lake. An even higher percentage of the phosphorus input to 

the lake would have been exported if the volume of water 

leaving the lake would have been equal to that entering 

the lake during the study period. About 6 percent of the 

new phosphorus entering the lake is retained in the lake 

sediments and contribute to the continued release from the 

sediments. 

The total load of phosphorus to the lake in MY 2003 

and MY 2004 is expected to be much smaller than it was 

prior to 1980 when sewage, creamery, and cheese-factory 

effluents were discharged into Butternut Creek and more 

intensive agriculture (including dairy or beef farming) and 

deficient septic systems in the watershed exported more 

phosphorus to the lake. The USEPA estimated that the 

total external load of phosphorus during 1972 was about 

2,600 kg, with 895 kg contributed by sewage effluent from 

the Village of Butternut and 73 kg from septic systems 

(U.S. Environmental Protection Agency, 1974), which is 

approximately 62 percent greater than in MY 2003–04.

Simulated Changes in Water 

Quality in Response to Changes in 

Phosphorus Loading 

Empirical models that relate phosphorus loading 

to measured water-quality characteristics can be used to 

determine how further reductions in phosphorus loading 

could improve the present-day water quality of the lake 

and how increases in phosphorus loading could degrade 

water quality. These models were developed on the basis 

of comparisons of hydrologic and phosphorus loading 
Simulated Changes in Water Quality in Response to Changes in Phosphorus Loading 35

Figure 16. Phosphorus budgets for Butternut Lake, Wis., for monitoring years 2003 and 2004. [%, percent]

Inputs

Inputs

Monitoring year 2003

Monitoring year 2004

Spiller Creek

13.8% 

Butternut Creek Inlet

38.5%

Internal sediment release

38.5% Precipitation

0.7%

Other small

tributaries

4.9% 

Ground water

0.9%

Septic systems

1.7% 

Total inputs = 2,390 kg Total outputs and storage = 2,390 kg

Total outputs and storage = 2,680 kg

Outputs and storage

Butternut 

Creek 

Outlet

55%

Retained in 

sediment

45%

Total inputs = 2,680 kg

Outputs and storage

Retained in 

sediment

38%

Butternut 

Creek 

Outlet

62%

Spiller Creek

15.1% 

Butternut Creek Inlet

40.2%

Internal sediment release

35.3%

Precipitation

0.9%

Other small

tributaries

6.1% 

Ground water

0.8%

Septic systems

1.5% 

estimates determined for many different lake systems, with 

specific measures for describing lake water quality, such 

as near-surface phosphorus and chlorophyll a concentrations, and Secchi depth. Some of these empirical models 

are contained within the BATHTUB model (Walker, 1996) 

and the Wisconsin Lake Modeling Suite (WiLMS; Panuska 

and Kreider, 2002). The BATHTUB model has hydrologic 

transport algorithms and is, therefore, capable of simulating changes in water quality in complex lakes (multibasin 

lakes or lakes connected by short channels), whereas 

WiLMS is more suited for simulating changes in singlebasin lakes or lakes with relatively uniform (horizontally 

uniform) water quality. To predict changes in the water 

quality of Butternut Lake that should occur with changes 

in phosphorus loading, the BATHTUB model was applied 

to the three basins of Butternut Lake using the most 
36 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

applicable algorithm in the model for each water-quality 

constituent. Because the water quality was relatively 

uniform throughout the different basins in Butternut Lake, 

several of the models within WiLMS also were applied to 

the entire lake to determine if other water-quality models 

demonstrated similar relations to the single phosphorus 

algorithm that was applied with BATHTUB. 

Modeling Approach

To estimate the expected changes in water quality in 

Butternut Lake in response to changes in phosphorus loading, nine scenarios were simulated with the BATHTUB 

model. The first scenario simulated the average conditions 

for MY 2003–04 and established a base case to which the 

other eight simulations were compared. Eight basin-wide 

strategies simulated decreases in controllable external 

phosphorus loading by 50 and 25 percent and increases 

in controllable external phosphorus loading by 25, 50, 75, 

100, 200, and 400 percent. Controllable external loading 

includes phosphorus from septic systems and all of the 

tributaries and nearshore areas of the lake. In addition, the 

base case, the 50-percent decrease, and the 400-percent 

increase in controllable external loading were simulated 

with no additional internal phosphorus loading added in 

the model to determine how the water quality of the lake 

could change if internal phosphorus loading from the 

sediments could be eliminated. Nine of the models within 

WiLMS were then used to simulate the average conditions 

in MY 2003–04. 

Data Requirements

Four types of data are required as input into these 

models: morphometric data (table 2), water-quality data 

(table 5), hydrologic data (table 7), and nutrient-loading 

data (table 8). For the BATHTUB model, all of this information is needed for each basin, whereas for the models 

in WiLMS, this information is needed only for the lake 

as a whole. For the BATHTUB model, in addition to total 

phosphorus concentrations, dissolved ortho-phosphorus 

concentrations are needed. Dissolved ortho-phosphorus 

concentrations were obtained by multiplying the flowweighted-average total phosphorus concentration for 

each stream by the fraction of phosphorus that was in the 

dissolved form in samples collected in that stream. The 

time period for the hydrologic and nutrient loading used 

in the BATHTUB model is dependent on the phosphorusturnover ratio (number of times the phosphorus mass in 

the lake is replaced in a specific time period). The model 

should be run for a period that results in a phosphorusturnover ratio greater than 2. Annual simulations resulted 

in a phosphorus turnover ratio of 5.4 for the lake as a 

whole; therefore, the average annual loadings in tables 7 

and 8 were used in the model. Even though loading data 

are summarized for the entire year, the model simulates 

water quality only for the growing season (May through 

September). All of the models within WiLMS use annual 

hydrologic and phosphorus loadings, but they simulate 

the water quality for different discrete seasons (described 

later). Phosphorus from internal loading (sediment release) 

is not typically included as a phosphorus source for BATHTUB and WiLMS, because most empirical models already 

incorporate this source; therefore, this source should be 

added only when a lake/reservoir has abnormally high 

internal loading (Walker, 1996). It was believed that Butternut Lake, being polymictic, has abnormally high internal loading; therefore, an average internal loading of 

1.0 mg/m2

/d was applied in BATHTUB simulations; a 

value of 1.0 mg/m2/d equates to about 1,400 kg per year. 

This value appears reasonable given the release rates 

obtained from the sediment cores incubated in the laboratory (table 9). The models within WiLMS also were used 

to estimate the amount of internal phosphorus loading by 

determining how much additional phosphorus would be 

required to accurately simulate the water quality measured 

in MY 2003–04. 

Algorithms and Calibration

When applying BATHTUB, the specific algorithms 

used to simulate each water-quality characteristic must be 

defined. The algorithms chosen to simulate total phosphorus and chlorophyll a concentrations are listed in table 

10; all are the default algorithms and have been shown to 

usually be the best models for most lakes and reservoirs. 

Nonalgal turbidity factors (or the reduction in clarity 

caused by factors other than algae) were computed within 

BATHTUB. Calibration coefficients for each water-quality 

constituent may be applied for each lake/basin. The calibration coefficients applied in the simulations for Butternut 

Lake are given in table 11. Only small adjustments were 

required for estimating chlorophyll a concentrations in 

the North and Middle Basins. No other calibrations were 

required. 

With the average annual loading data from WY 2003–

04, BATHTUB was used to simulate the summer-average 

water quality (May through September) in each basin and 

the entire lake. The simulated and measured values for 
Simulated Changes in Water Quality in Response to Changes in Phosphorus Loading 37

Table 10. Algorithms within the BATHTUB model (Walker, 1996) that were used to simulate water quality in the basins in 

Butternut Lake, Wis.

Process Model number Algorithm description

Phosphorus balance 1 Second order, available phosphorus

Nitrogen balance 0 Not computed

Chlorophyll a concentration 2 Phosphorus, light, and temperature

Secchi depth 1 Chlorophyll a and turbidity

Dispersion 1 Fisher numeric

Phosphorus calibration 1 Decay rates

Nitrogen calibration 0 None

Table 11. Calibration coefficients used in the BATHTUB model (Walker, 1996) simulations of the water quality in the basins in 

Butternut Lake, Wis.

Basin Total phosphorus Chlorophyll a Secchi depth

North 1.00 1.15 1.00

Middle 1.00 1.25 1.00

South 1.00 1.00 1.00

MY 2003–04 (table 5) are compared in figure 17. For each 

characteristic, the simulated values are given for the precalibrated and calibrated (simulated) models. The coefficient 

of variation for each measured value was computed on the 

basis of all of the summer-average data from 1986 to 2005 

from the Deep-hole Site and used to calculate an estimate 

of the certainty of the measured data (plus and minus one 

standard error around the average summer value). After 

model calibration, BATHTUB accurately simulated total 

phosphorus to within ± 0.001 mg/L, chlorophyll a to within ± 2 μg/L, and Secchi depths to within ± 0.01 m in all of 

the basins and the lake as a whole. 

Models within WiLMS also were used to simulate 

the average conditions in MY 2003–04. Of the 13 empirical models contained in WiLMS, 9 of the models were 

applicable to the hydrologic system of Butternut Lake. To 

determine if these nine models were capable of simulating phosphorus concentrations in this polymictic lake, the 

morphometry of the lake and the average hydrologic and 

phosphorus loadings for MY 2003–04 were input into 

these models and near-surface total phosphorus concentration was simulated. All of the models within WiLMS 

use annual hydrologic and phosphorus loadings, but they 

simulate water quality for discrete seasons; however, each 

season had a measured total phosphorus concentration of 

0.044 mg/L. 

The average simulated total phosphorus concentration for MY 2003–04 from the nine models in WiLMS was 

0.024 mg/L (table 12). This value is about one-half of the 

concentration measured in the lake (0.044 mg/L). All nine 

models simulated a total phosphorus concentration that 

was much lower than that measured in the lake, indicating 

that this polymictic lake behaves much differently than a 

typical dimictic lake. 

The models in WiLMS also can be used to determine 

how much the phosphorus load would need to be increased 

for Butternut Lake to respond as a typical lake. The annual 

phosphorus loads required for each of these models to simulate an in-lake phosphorus concentration of 0.044 mg/L 

are given in table 12. To properly simulate the measured 

conditions in Butternut Lake, the annual phosphorus load 

should be about 3,260 kg. Therefore, results from these 

models suggest that there should be an additional phosphorus load of 1,660 kg (or 51 percent more than the measured 

average-annual external phosphorus load to the lake). It 

was estimated from the core studies that the annual inter-
38 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

Figure 17. Measured and simulated (prior to and after calibration with the BATHTUB model) average summer (May through 

September) near-surface A, total phosphorus concentrations, B, chlorophyll a concentrations, and C, Secchi depths in the three 

basins in Butternut Lake, Wis., and the lake as a whole. 

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

NORTH

BASIN

MIDDLE

BASIN

SOUTH

BASIN

NORTH

BASIN

MIDDLE

BASIN

SOUTH

BASIN

NORTH

BASIN

MIDDLE

BASIN

SOUTH

BASIN

ENTIRE LAKE

TOTAL PHOSPHORUS, 

IN MILLIGRAMS PER LITER

Measured

Simulated

Precalibration

0

6

12

18

24

30

ENTIRE LAKE

CHLOROPHYLL 

A, 

IN MICROGRAMS PER LITER

Measured

Simulated

Precalibration

0.0

0.5

1.0

1.5

2.0

ENTIRE LAKE

SECCHI DEPTH,IN METERS

Measured

Simulated

Precalibration

A.

B.

C.
Simulated Changes in Water Quality in Response to Changes in Phosphorus Loading 39

Table 12. Estimated near-surface phosphorus concentrations in Butternut Lake, Wis., from various hydrologic and phosphorus 

loading models contained in the Wisconsin Lakes Modeling Suite (Panuska and Kreider, 2002) and estimated total annual 

phosphorus load needed to result in a 0.044 mg/L total phosphorus concentration in the lake.

[mg/L, milligram per liter; kg, kilogram]

Lake phosphorus model

(description)

Measured Modeled

Prediction

season

Seasonal

concentration

(mg/L)

Base

scenario

(mg/L)

Total annual phosphorus load 

required to produce 0.044 mg/L

(kg)

Canfield and Bachman, 1981 (natural lakes) Growing season 0.044 0.029 2,640

Canfield and Bachman, 1981 (artificial lakes) Growing season .044 .026 3,290

Reckhow, 1979 (general lakes) Growing season .044 .018 3,840

Reckhow, 1977 (anoxic lakes) Growing season .044 .038 1,840

Reckhow, 1977 (water load less than 50 m/year) Growing season .044 .026 1,680

Kirchner and Dillon, 1975 (general lakes) Spring .044 .015 4,570

Walker, 1977 (general lakes) Spring .044 .026 2,740

Vollenweider, 1982 (general lakes) Annual .044 .023 3,450

Vollenweider, 1982 (shallow lakes) Annual .044 .019 4,250

Average of the models .044 .024 3,260

nal phosphorus load was approximately 945 kg (table 8) 

and approximately 1,400 kg of internal phosphorus loading 

was required to accurately simulate the in-lake phosphorus 

concentration with the BATHTUB model.

Response in Water Quality to Changes in 

Phosphorus Loading

To predict the expected response in water quality 

in Butternut Lake to watershed-wide changes in external 

phosphorus loading, eight scenarios were simulated with 

the BATHTUB model. The volume-weighted-average 

total and dissolved ortho-phosphorus concentrations (total 

nutrient load divided by total water load) for each of the 

sources were decreased by 50 and 25 percent and increased 

by 25, 50, 75, 100, 200, and 400 percent. Nitrogen concentrations were not altered in the various phosphorus-loading 

scenarios. Because the lakes/basins were typically phosphorus limited, altering nitrogen concentrations was shown 

to have little effect on the simulated results. 

Changes in Phosphorus Concentrations

On the basis of BATHTUB model simulations, phosphorus concentrations in each of the basins and the lake as 

a whole should have a relatively linear response to a linear 

change in controllable external phosphorus loading (only 

the changes in the concentrations of the lake as a whole 

are shown in fig. 18A). The changes in in-lake phosphorus 

concentrations, on a percentage basis, are smaller than 

the changes in external phosphorus loadings. Changes in 

in-lake phosphorus concentrations are only about 25–42 

percent of the changes in phosphorus loading. In other 

words, a 50-percent increase in controllable external 

phosphorus loading causes a 19-percent increase in in-lake 

phosphorus concentrations and a 50-percent decrease in 

external loading causes a 21-percent decrease in concentrations. When external loading is increased by 62 percent, 

which is similar to the loading estimated by the USEPA 

to have occurred in the early 1970s (U.S. Environmental 

Protection Agency, 1974), the summer average concentration is estimated to be about 0.057 mg/L. This estimated 

concentration is less than what was measured for that time 

period (0.069 mg/L). This difference in the estimated and 

measured concentrations suggests that the relatively crude 

load estimate for the early 1970s may be low.

The estimated changes in in-lake phosphorus concentrations, being smaller than the reductions in controllable 

external phosphorus loadings, are primarily the result of 

not simulating reductions in internal loading and reductions in the loads from ground water and precipitation; the 

loadings from these sources represent about 40 percent 

of the total input of phosphorus to the lake. Short-term 

changes in external phosphorus loading are not expected 
40 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

Figure 18. Simulated changes in near-surface A, total phosphorus concentrations, B, chlorophyll a concentrations, and C, 

Secchi depths at the Deep-hole Site in Butternut Lake, Wis., in response to various phosphorus-loading scenarios. Simulated 

results for changes in these constituents without additional phosphorus from internal loading are also identified.

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

-50 0 50 100 150 200 250 300 350 400

CHANGE IN CONTROLLABLE PHOSPHORUS LOADING, IN PERCENT

CHANGE IN CONTROLLABLE PHOSPHORUS LOADING, IN PERCENT

CHANGE IN CONTROLLABLE PHOSPHORUS LOADING, IN PERCENT

TOTAL PHOSPHORUS CONCENTRATION, 

IN MILLIGRAMS PER LITER 

PERCENT CHANGE PERCENT CHANGE PERCENT CHANGE

-100

-50

0

50

100

Simulated with internal loading

Simulated without internal loading

10

15

20

25

30

35

-50 0 50 100 150 200 250 300 350 400

TOTAL CHLOROPHYLL 

A, 

IN MICROGRAMS PER LITER

-50

-100

-75

-50

-25

0

25

50

-25

0

25

50

75

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

-50 0 50 100 150 200 250 300 350 400

SECCHI DEPTH, IN METERS

A.

B.

C.
Simulated Changes in Water Quality in Response to Changes in Phosphorus Loading 41

to affect the rate of internal loading immediately. When 

internal phosphorus loading is removed from the model, 

the simulated average summer phosphorus concentration is 

0.035 mg/L (a reduction of 24 percent from the base case). 

When internal phosphorus loading is removed from the 

50-percent-decrease scenario, the simulated in-lake phosphorus concentration is 0.022 mg/L (a 52-percent decrease 

from the base case and a 37-percent decrease from the base 

case with no internal loading), and when it is removed 

from the 400-percent-increase scenario, the simulated inlake phosphorus concentration is 0.091 mg/L (a 98-percent 

increase from the base case and a 168-percent increase 

from the base case with no internal loading). Therefore, 

the high internal phosphorus loading in Butternut Lake 

greatly reduces the effects of (response to) changes in 

external phosphorus loading. 

Changes in Chlorophyll a Concentrations

Simulated average-summer chlorophyll a concentrations have a nonlinear response to changes in controllable 

external phosphorus loading. The response of chlorophyll 

a concentrations is larger (on a percentage basis) for 

decreases in loading than for similar increases in loading 

(fig. 18B). A 50-percent reduction in controllable external 

phosphorus loading results in an 18-percent reduction in 

chlorophyll a concentrations, while a 50-percent increase 

in loading results in an increase by only 13 percent, and 

a 400-percent increase in loading results in an increase 

by only 57 percent. When internal phosphorus loading 

is removed from the model, the changes associated with 

reductions in external phosphorus loading are much greater 

than with increases in loading. When internal loading was 

removed, a 50-percent decrease in external phosphorus 

loading resulted in a 50-percent decrease in chlorophyll a

concentrations (a 36-percent decrease from the base case 

with no internal loading); however, with a 400-percent 

increase in loading, chlorophyll a concentrations increased 

by only 52 percent (a 93-percent increase from the base 

case with no internal loading). 

Changes in Secchi Depths (Water Clarity)

Simulated Secchi depths are more responsive to 

decreases in controllable external phosphorus loading than 

to increases in loading (fig. 18C). When external phosphorus loading is decreased by 50 percent, Secchi depths 

increase by 0.14 m (12 percent); however, when loading is 

increased by 50 percent, Secchi depths decrease by only 

about 0.09 m (7 percent). Very little change in Secchi 

depth is estimated with increases in external loading above 

100 percent. When internal phosphorus loading is removed 

from the model, the changes associated with reductions in 

phosphorus loading are much greater than with increases 

in phosphorus loading. When internal loading is removed, 

a 50-percent reduction in external phosphorus loading 

results in Secchi depth increases of about 0.35 m (42-percent increase and a 24-percent increase from the base case 

with no internal loading).

Changes in Trophic Status

The TSI values indicate that Butternut Lake is currently borderline between eutrophic and hypereutrophic 

(fig. 7). On the basis of the simulations with the BATHTUB model, even when controllable external phosphorus 

loading is reduced by 50 percent from that measured in 

MY 2003–04, the lake would remain moderately eutrophic 

(TSI values 56–58) with respect to phosphorus concentration, chlorophyll a concentration, and Secchi depth. This 

minimal response in water quality to reductions in external 

phosphorus loading is due primarily to the high internal 

phosphorus loading. However, if the internal phosphorus 

loading could be eliminated and the external phosphorus 

loading could be reduced by 50 percent, the trophic state 

of the lake should become borderline mesotrophic/eutrophic, with TSI values ranging from 49 (for phosphorus) to 

53 (for chlorophyll a and Secchi depth).

Changes in the Percentage of Days with Algal 

Blooms

All of the previously described model simulations 

were based on changes in the average water quality during 

the growing season (May through September). However, 

often what are perceived as the biggest problems in lakes 

are the visible extremes in water quality; for example, algal 

blooms. The definition of what constitutes the occurrence 

of an algal bloom can be site-specific and subjective. In 

what typically is a clear lake, a slight green color in the 

water is considered an algal bloom, whereas for a typically 

productive lake, only a very green color or an algal scum 

is considered an algal bloom. A chlorophyll a concentration of 30 μg/L represents what many would consider a 

moderate algal bloom. Results from BATHTUB model 

simulations are used to demonstrate how the percentage 

of days from May through September with a chlorophyll a

concentration exceeding a certain value (30 μg/L) changes 

in response to changes in controllable external phosphorus loadings (fig. 19). Changes in the frequency of algal 
42 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

blooms are larger with decreases in phosphorus loading 

than with similar increases in loading. When controllable 

external phosphorus loading is decreased by 50 percent, 

the number of days with algal blooms decreases by 41 

percent, while an increase in loading of 50 percent results 

in an increase in the days with algal blooms by 33 percent. 

When internal phosphorus loading is removed from the 

model, the changes caused by reductions in external phosphorus loading are much larger than those with increases 

in phosphorus loading. When internal loading is removed, 

a 50-percent decrease in phosphorus loading results in 

an 89-percent decrease in the number of days with algal 

blooms (a 79-percent decrease from the base case with no 

internal loading). 

Importance of Internal Phosphorus 

Loading

When the deep water of a productive lake, like Butternut Lake, becomes anaerobic, the rate of phosphorus 

release from the deep sediments is often greatly accelerated. Typically, in deep dimictic lakes, this phosphorus 

from internal loading is trapped in the hypolimnion during 

summer and released into the shallow water primarily at 

fall overturn. In polymictic lakes, however, the phosphorus 

released from the sediments is not trapped in the bottom of 

the lake but is intermittently released to the shallow water 

throughout the summer. These mixing events resulted in 

increases in the near-surface phosphorus concentrations in 

Butternut Lake as summer progressed, and a higher overall 

near-surface, summer-average phosphorus concentration 

than that of a dimictic lake with a similar internal phosphorus load. This is the primary reason why the additional 

internal phosphorus load had to be added to the BATHTUB model for accurate simulations and why all of the 

models in WiLMS underestimated the near-surface phosphorus concentration in Butternut Lake. It was estimated 

that internal loading added about 37 to 51 percent of the 

annual phosphorus loading to the lake.

Although the phosphorus load to Butternut Lake 

has decreased as a result of many efforts in the watershed 

(table 1), the internal phosphorus load has and probably 

will continue to limit the response of the lake to reductions in external phosphorus loading. This conclusion is 

in agreement with the small changes in measured water 

quality (fig. 6) and the small changes inferred from the 

paleoecological study (fig. 8) conducted by Garrison 

(2006). This conclusion also is in agreement with the 

Figure 19. Simulated changes in the percentage of days from May through September with an algal bloom (chlorophyll a

concentration greater than 30 μg/L) in response to various phosphorus-loading scenarios for Butternut Lake, Wis. Simulated 

results for changes in these constituents without additional phosphorus from internal loading are also identified.

0

5

10

15

20

25

30

35

40

45

-50 0 50 100 150 200 250 300 350 400

CHANGE IN CONTROLLABLE PHOSPHORUS LOADING, IN PERCENT

PERCENTAGE OF DAYS WITH ALGAL BLOOMS 

PERCENT CHANGE

Simulated with internal loading

Simulated without internal loading

-100

-50

0

50

100

150
Summary and Conclusions 43

belief that once a polymictic lake becomes hypereutrophic, 

it is difficult to alter its trophic state because the high internal phosphorus loading usually does not quickly respond 

to reductions in external phosphorus loading (Newton and 

Jarrell, 1999; Nurnberg, 1998; Welch and Cooke, 1995). 

If external phosphorus loading to Butternut Lake is 

further reduced in the future, the results from the BATHTUB model (with internal loading included) should 

accurately predict the changes in water quality that would 

occur in the lake. However, if the reduction in external 

load were to persist for a long period of time, the internal 

phosphorus release rate should gradually decrease and 

come to equilibrium with the new external loading. This 

should ultimately result in a slightly greater improvement 

in water quality than predicted in figures 18 and 19 (when 

internal loading was included). If, in addition to reductions 

in external loading, internal phosphorus loading were able 

to be reduced, such as with an alum treatment (Robertson 

and others, 2000), then the predicted in-lake water quality 

should be similar to the estimates in figures 18 and 19, 

simulations with internal phosphorus loading removed. 

Even if internal phosphorus loading were eliminated, 

a 50-percent reduction in external phosphorus loading 

would be needed for Butternut Lake to become borderline 

mesotrophic/eutrophic. When alum is used to reduce or 

eliminate internal phosphorus loading, short-term changes 

in water quality are often more dramatic than indicated in 

figures 18 and 19 because alum also immediately removes 

most of the phosphorus from the water column. The longterm changes in water quality associated with an alum 

treatment, however, should be similar to those indicated 

with no internal loading in figures 18 and 19. 

Summary and Conclusions

Butternut Lake is a eutrophic to hypereutrophic, 

polymictic lake in northcentral Wisconsin. Because water 

quality improved only slightly after many actions were 

taken to reduce nutrient loading from the watershed, a 

study was conducted by the USGS from 2002 to 2007 to 

better understand how the lake functions. The goals of 

the study were to describe the water quality and hydrology of the lake, quantify external and internal sources of 

phosphorus, and evaluate the effects of past and future 

changes in phosphorus loading on the water quality of 

the lake. To achieve these goals, water-quality data were 

collected in the lake during 2002–04 and compared with 

historical data. Water and phosphorus budgets were 

quantified to gain a better understanding of the various 

phosphorus sources. Lake water-quality models were then 

used to determine why the water quality in the lake had 

not dramatically changed in response to the reductions in 

nutrient loading. Results from model simulations will aid 

in decision-making for future lake-management actions by 

predicting the changes that may be expected with changes 

in external phosphorus inputs to the lake. 

Seasonal changes in the water quality of polymictic 

Butternut Lake were different from those in most dimictic 

lakes: bottom temperatures increased more dramatically 

throughout the summer than in other lakes, and bottom 

dissolved oxygen concentrations alternated between being 

aerobic and anaerobic as a result of frequent mixing during 

summer. Near-surface phosphorus concentrations in the 

lake increased as summer progressed as a result of the episodic release of phosphorus from an occasionally anaerobic hypolimnion. On the basis of nitrogen to phosphorus 

(N:P) ratios, phosphorus typically should be the nutrient 

limiting algal growth in Butternut Lake and should be the 

nutrient of concern when considering management efforts 

to improve the lake’s water quality.

Since the early 1970s, the water quality of Butternut Lake has not changed dramatically in response to 

the nutrient reductions from the watershed. The largest 

changes were in near-surface total phosphorus concentrations: concentrations during August decreased from about 

0.090 mg/L in the early 1970s to about 0.050 mg/L after 

2000, whereas average-summer concentrations decreased 

only from about 0.055–0.060 mg/L to about 0.045 mg/L. 

Since the early 1970s, only small changes were measured 

in chlorophyll a concentrations and Secchi depths. 

Butternut Creek was the largest source of water to 

Butternut Lake, supplying about 62 percent of its water. 

Other sources were Spiller Creek (20 percent), precipitation (8 percent), small tributaries and the ungaged nearlake area (7 percent), and ground water (3 percent). Total 

inputs of water in MY 2003 were less than those in 

MY 2004 because of the above normal precipitation in 

MY 2004. The average residence time of water in the lake 

ranged from 0.39 to 0.45 years. Butternut Creek outlet 

accounted for 93 percent of the total outflow from the 

lake and evaporation accounted for 7 percent.

The average annual load of phosphorus to the lake 

was 2,540 kg, of which 1,590 kg came from external 

sources (63 percent) and 945 kg came from the sediments 

in the lake (37 percent). The largest source of external 

phosphorus was Butternut Creek, which delivered 63 percent of the external phosphorus compared with 61 percent 

of the water input. The next largest contribution was from 

Spiller Creek, which delivered 23 percent of the external 
44 Water Quality, Hydrology, and Simulated Response to Changes in Phosphorus Loading, Butternut Lake, Wis.

phosphorus entering the lake. The six small tributaries and 

ungaged near-lake area collectively contributed 9 percent 

of the total external phosphorus load. The surface-water 

outflow into Butternut Creek removed 94 percent of the 

external phosphorus coming into to the lake, and the 

remaining 6 percent was stored in the lake sediment. 

The BATHTUB model and nine of the water-quality 

models contained in WiLMS were used to determine if the 

response in the water quality of Butternut Lake to phosphorus loading was similar to that of most other lakes or 

if it responded differently because it is a polymictic lake 

with unusually high internal phosphorus loading. Unless 

additional phosphorus from internal loading was included 

in the simulations, the BATHTUB model was unable to 

simulate the water quality in the lake, and all of the models 

within WiLMS underestimated the in-lake phosphorus 

concentration by about 50 percent. After internal loading 

of phosphorus was added to the BATHTUB model, it accurately simulated the water quality measured in MY 2003–

04. With this model, a relatively linear response was found 

between in-lake total phosphorus concentrations and external phosphorus loading; however, the changes in in-lake 

concentrations were smaller than the changes in external 

phosphorus loadings. Changes in in-lake phosphorus 

concentrations were about 25–42 percent of the changes 

in phosphorus loading. Changes in chlorophyll a concentrations, the percentage of days with algal blooms, and 

Secchi depths (water clarity) were nonlinear, with a larger 

response to reductions in external phosphorus loading than 

to increases in loading. When simulated external phosphorus loading was reduced by 50 percent, chlorophyll a concentrations decreased by about 18 percent, the percentage 

of days with algal blooms decreased by about 41 percent, 

and Secchi depth increased by about 12 percent. When the 

additional internal phosphorus loading was removed from 

the model, there was a much larger response in all of these 

constituents. 

Butternut Lake, being polymictic, was vulnerable 

to the historically high, non-natural, external phosphorus 

loading that resulted in high internal phosphorus loading. 

Once Butternut Lake became hypereutrophic, it became 

very difficult to alter its trophic state with reductions in 

external phosphorus loading. The high internal loading rate 

helps maintain the current state of the lake and does not 

respond quickly to reductions in external nutrient loading. In order to improve Butternut Lake to a mesotrophic/

eutrophic state, a combination of practices will be needed 

to reduce/eliminate internal phosphorus loading and also 

reduce the external phosphorus loading by about 50 percent. 

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